Population Dynamics of the Spruce Budworm Choristoneura … · 2011-03-26 · budworm population dynamics by simulations that use a simple time-series model. In the last section,

Population Dynamics of the Spruce Budworm Choristoneura FumiferanaAuthor(s): T. RoyamaSource: Ecological Monographs, Vol. 54, No. 4 (Dec., 1984), pp. 429-462Published by: Ecological Society of AmericaStable URL: http://www.jstor.org/stable/1942595 .Accessed: 26/03/2011 12:59

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Ecological Monographs, 54(4), 1984, pp. 429-462 ? 1984 by the Ecological Society of America

POPULATION DYNAMICS OF THE SPRUCE BUDWORM CHORISTONEURA FUMIFERANA'

T. ROYAMA Maritimes Forest Research Centre, Canadian Forestry Service, Department of the Environment, P.O. Box 4000, Fredericton,

New Brunswick E3B 5P7, Canada

Abstract. Using the latest observations, experiments, and theoretical studies, I have reanalyzed spruce budworm data from the Green River Project, and now propose a new interpretation of the population dynamics of the species.

Spruce budworm populations in the Province of New Brunswick have been oscillating more or less periodically for the last two centuries, the average period being z35 yr. Local populations over the province tend to oscillate in unison, though their amplitudes and mean levels are not always the same.

The local population process in the spruce budworm is composed of two major parts, a basic oscillation, and secondary fluctuations about this basic oscillation. The basic oscillation is largely determined by the combined action of several intrinsic (density-dependent) mortality factors during the third to sixth larval instars. These factors include parasitoids and, probably, diseases (e.g., microsporidian infection), and, most important, an intriguing complex of unknown causes, which I term "the fifth agent" (a large number of larvae with no clear symptoms died during the population decline in the late 1950s).

Other mortality factors, including predation, food shortage, weather, and losses during the spring and fall dispersal of young larvae, are not causes of the basic, universally occurring oscillation.

Because of immigration and emigration of egg-carrying moths, the ratio of all eggs laid to the number of locally emerged moths (the E/M ratio, or the apparent oviposition rate) fluctuates widely from year to year but independently of the basic oscillation of density in the local populations that were studied. The fluctuation in this ratio is the main source of the secondary fluctuation in density about the basic oscillation, and is highly correlated with the meteorological conditions that govern the immigration and emigration of moths. The E/M ratio is the major density-independent component of budworm population dynamics.

Contrary to common belief, there is no evidence to indicate that invasions of egg-carrying moths from other areas upset the assumed endemic equilibrium state of a local population and trigger outbreaks. Moth invasions can only accelerate an increase in a local population to an outbreak level, but this happens only when the population is already in an upswing phase of an oscillation caused by high survival of the feeding larvae. In other words, the "seed" of an outbreak lies in the survival of feeding larvae in the locality, and moth invasions can act only as "fertilizers."

The weight of evidence is against the idea that an outbreak occurs in an "epicenter" and spreads to the surrounding areas through moth dispersal. Rather, the egg-mass survey data in New Brunswick since 1952 favor an alternative explanation. If the trough of a population oscillation in a certain area stays comparatively high, as in central New Brunswick in the 1 960s, or if the area is more heavily invaded by egg-carrying moths when the populations in that area are in an upswing phase, these populations might reach an outbreak level slightly ahead of the surrounding populations, all of which are oscillating in unison.

If a local population oscillates because of the action of density-dependent factors intrinsic to the local budworm system, it may appear to be difficult to explain why many local populations over a wide area oscillate in unison. However, Moran's (1953) theory shows that density-independent factors (such as weather) that are correlated among localities will bring independently oscillating local populations into synchrony, even if weather itself has no oscillatory trend. I illustrate this with a simple time-series model. The same model also illustrates a principle behind the fact that outbreaks occurred fairly regularly in New Brunswick and Quebec during the past two centuries but rather sporadically in other regions of eastern Canada.

Finally, I review the commonly accepted theory of outbreaks based on the dichotomy of endemic and epidemic equilibrium states and argue that the theory does not apply to the spruce budworm system.

Key words: Choristoneura fumiferana (Clem.); Green River Project; insect life-table analysis; insect outbreaks; moth dispersal; population dynamics; spruce budworm.

INTRODUCTION

Almost 20 yr have passed since publication of the monograph (Morris 1 963a) based on the classic spruce

I Manuscript received 23 December 1982; revised and accepted 15 August 1983; final version received 28 November 1983.

budworm population study of the Green River Project. During those 20 yr, spruce budworm populations in the Province of New Brunswick declined once and subsequently have risen to the current outbreak level. Now, again, we are in the midst of controversy about whether

430 T. ROYAMA Ecological Monographs Vol. 54, No. 4

"to spray or not to spray" insecticides to protect the forests. A few years ago, a task force was formed to evaluate budworm control alternatives for better forest resource management of the province (Baskerville 1976). This task force relied heavily on a forest ecosystem model that was based primarily on the Morris (1 963a) monograph. However, this pioneering work is 20 yr old and, in many respects, inadequate from a current point of view. Besides the lack of adequate data, the major problems of the early work were its inap- propriate treatment of time-series data and its inadequate understanding of the concept of density dependence (Royama 1977, 198 la, b). Unfortunately, certain of its interpretations have continued to be accepted virtually unchanged even in the most recent Royal Commission report on the spruce budworm outbreak in Newfoundland (Hudak and Raske 1981).

The present paper reinterprets the original life tables from the Green River Project, incorporating recent information from field observations, laboratory experiments, and theoretical studies. The task is somewhat like restoring a prehistoric animal from fragments of fossilized bones. Morris's life tables provide a basic skeletal structure but are insufficient for full restora- tion; missing pieces have had to come from inference or supposition. Whenever I need to deduce indirectly, I argue only qualitatively, steering between the risk of making a false inference and that of hesitating to adopt a potentially correct hypothesis.

This paper consists of four major sections. First, I briefly describe the life cycle of the spruce budworm and the cyclic pattern of its population fluctuation, restored from recent quantitative information and supplemented by more qualitative records of outbreaks. These records include the results of the analysis of radial growth rings of some host trees that survived budworm attacks in the past two centuries.':

In the second section, the analysis of the life-table data, I identify two major components that govern yearly changes in spruce budworm populations, namely, survival of larvae during their feeding stage and apparent oviposition rate (i.e., the ratio of all eggs laid to the number of locally emerged moths; E/M ratio for short). The larval survival rate determines the basic oscillatory pattern in population fluctuations, a trend that is subject to perturbation by the E/M ratio. Im- migration and emigration of egg-carrying moths cause the E/M ratio to fluctuate widely from year to year, but without any noticeable trend. I raise all conceivable factors that could influence the two components and, by elimination, I narrow the possibilities to the few most plausible ones.

In the third section, I attempt to synthesize spruce budworm population dynamics by simulations that use a simple time-series model. In the last section, I show how my view of the population dynamics of the spruce budworm differs from other theories, which have been elaborated in models such as the one incorporated in

the Baskerville (1976) task-force report. In particular, I critically examine the notion of a dichotomy of endemic and epidemic states and the alleged role of climate and moth dispersal in the initiation and spread of outbreaks.

Life cycle

The spruce budworm (Choristoneura fumiferana [Clem.], Lepidoptera: Tortricidae) is univoltine in eastern Canada. Moths emerge from mid-July to early Au- gust in the Green River area of northwestern New Brunswick. Females lay eggs over several days. Egg masses are laid on the foliage of conifers, mainly balsam fir, Abies balsamea (L.), and several spruce (Picea) species. Each egg mass contains an average of about 20 eggs. Females raised in normal feeding conditions lay from 100 to 300 eggs, with an average of :200, but heavy defoliation caused by a high density of larvae can reduce fecundity to one-half. The eggs hatch in

10 d. Soon after hatching, the first-instar larvae disperse within tree or stand, or even beyond by wind. Surviving larvae spin hibernacula within which they molt to the second instar. No feeding occurs until spring.

Second-instar larvae overwinter in hibernacula until early May. Soon after emergence, they disperse again and settle at feeding sites on host trees. They mine in 1-2 yr old needles, or in seed and pollen cones when available. During the third to sixth instars, from about early June to early July, larvae feed on the current-year shoots. If current-year shoots become depleted, the larvae will feed on older foliage, but this often results in reduced size and fecundity of adults. Pupation normally takes place on the foliage in early July. Moths eclose in :8-12 d, completing the cycle.

Recent radar studies of moth dispersal (Greenbank et al. 1980) have revealed that both female and male spruce budworm moths are strong fliers. Dispersal takes place in the evening. Female moths usually emigrate after laying part of their egg complement at the place of emergence. Moths in exodus flight climb decisively to > 100 m in altitude and then fly to new sites, which are normally 50-100 km downwind, but which can be as far as 450 km (the distance between the east coast of New Brunswick and the west coast of Newfound- land). Female moths usually deposit at least some of their eggs where they first land, but they may leave there and deposit eggs at other sites over several eve- nings.

Dispersal flight is governed by meteorological conditions, particularly temperature; no exodus occurs at < 14'C, and if the moths encounter such a low temperature in flight, they descend with wings folded. No flight was observed at temperatures > 300.

Pattern of population fluctuation Local budworm populations fluctuate between ex-

treme levels. At high densities, budworm larvae cause extensive damage to fir and spruce stands, and even

December 1984 SPRUCE BUDWORM 431

150 _-s

0.05

194 195 195 16195 17 95 18

Fores Resarch ent4).-

I S4

E . 04 -

0.14-

0.05-

1945 1950 1955 1960 1965 1970 1975 1980

Generation year FIG. 1. Yearly changes in spruce budworm. density (number/rn2 of foliage, logarithmic scale) in northwestern New Bruns-

wick between 1945 and 1980. 0 third- to fourth-instar larvae in plot G4 near the Green River field station; 0 egg-mass densities sampled in wider, unsprayed areas, including the Green River area (data provided by E. G. Kettela, Maritimes Forest Research Centre).

kill trees. In contrast, when larvae are scarce, even intensive sampling over a wide area may find only a few larvae (Greenbank 1963a).

Commencing in 1945, densities of third- to fourth- instar larvae in a few selected study plots in northwestern New Brunswick were determined annually by intensive sampling (Fig. 1, 0), as part of the Green River Project (see Introduction: Source of Data). Al- though the Green River Project was terminated in 1972, a less intensive egg-mass sampling in many sample plots over all of New Brunswick has been carried out to date for monitoring budworm density in relation to the province's program of aerial spraying of insecticide. The graph with solid circles in Fig. 1 shows the annual changes in the average density of egg masses in some ofthose sample plots that were free from aerial spraying in the northwestern corner of the province, including the Green River area. An egg mass contains, on average, :20 eggs, and : 15% of the eggs will survive to third- to fourth-instar larvae. Therefore, the egg-mass graph in Fig. 1, if shifted upward by about one step on- the vertical (logarithmic) scale, can be used to approximate annual changes in larval density from 1968 on. It looks as though budworm populations oscillate.

This pattern of population change is not an isolated local case, but occurs widely over New Brunswick, as revealed in egg-mass surveys since 1952. I divided the province into 30 blocks and, in each block, calculated the average egg-mass density (Fig. 2). We see some regional differences in the pattern of population change. In particular, the trough tends to be much shallower in central regions than in both northern and southern parts of the province. Also, the populations in the southeastern corner appear to have started increasing slightly ahead of the rest of the province. Nevertheless, despite fuzzy year-to-year fluctuations, the trough in each graph is clearly concurrent among all populations. In other words, the budworm populations in New

Brunswick have been changing in unison for at least the past 30 yr.

An earlier widespread budworm outbreak in New Brunswick began about 1912 and subsided about 1920 (Tothill 1922, Swain and Craighead 1924). From then until the mid- 1940s, budworm populations throughout the province remained extremely low (Greenbank 1 963a). One other outbreak that occurred around 1878 is well documented in the local literature (Swain and Craighead 1924), which noted that the budworm became scarce after several years of extremely high density. We have now begun to see a pattern of oscillation in budworm population change, which has completed three full cycles in the past 100 yr.

Even older outbreaks of the budworm can be traced by examining radial growth patterns of some food trees that survived severe defoliation caused by the budworm (Swain and Craighead 1924, Blais 1962). These outbreaks, marked by the first sign of growth-ring retardation, began about 1770, 1806, 1878, 1912, and 1949 (Blais 1958, 1968, Greenbank 1963a); the last three coincide with the direct experience already mentioned. The present outbreak is probably at its peak. Similarly, Blais (1965) found evidence of outbreaks in the Laurentide Park region of Quebec, north of Quebec City, beginning about 1710, 1755, 1812, 1838, 1914, 1953, and the current outbreak concurrent with the one in New Brunswick.

Synthesizing the above facts, I restored the pattern of budworm population dynamics in Fig. 3. The graph prior to 1945 is a schematic representation of the historical documents and the tree-ring analyses already quoted; after 1945, the graph is based on actual sampling, as in Fig. 1. The intervals between periods of heavy defoliation registered in the tree rings are remarkably regular, particularly in New Brunswick (solid arrows), with the exception of a wide gap between 1806 and 1878; this gap is about twice as long as the average


F Quebec A Year

0) 0) 0) 0)

400 U 0

M0 E

50 VI

MaineIl A -~~~~~ - 41J ~~~~~~ Nova Scotia

1 2 3 4 5 6 7 FIG. 2. Yearly variations in average egg-mass density (number/M2 of foliage, logarithmic scale) across New Brunswick

(outlined by broken lines) since 1952, calculated from the Aerial Spray Program data provided by E. G. Kettela (Maritimes Forest Research Centre). In each block, egg-mass density is plotted on the vertical axis (logarithmic scale) and calendar years on the horizontal axis as shown in block E6.

interval between other successive outbreaks. A similar gap occurred in Quebec between the 1838 and 1914 outbreaks (dotted arrows). This led Blais (1968) to remark that "data on past outbreaks indicate that epi- demics of this insect do not recur at regular intervals."

However, there were comparatively light defoliation marks in trees from Quebec around 1838, when there was little sign in the specimens from New Brunswick; conversely, there were clear marks in trees from New Brunswick around 1878, when there were few in the Quebec specimens. Is it not likely then that the populations in both provinces peaked more or less at the same time, as in other outbreaks, but that the populations in one province did not reach a level high enough to affect the tree rings? The supporting facts for such a hidden peak are that (1) other outbreaks in the two provinces tended to occur fairly closely together in time, (2) the populations in New Brunswick in recent years have oscillated in unison (Fig. 2), and (3) peak densities of some local populations in the Green River area during the 1949 outbreak did not reach a level high enough to cause heavy defoliation. Nevertheless, these populations did oscillate in parallel with other populations that reached an extremely high density. The population

from plot G4 in Green River ( Fig. 1) is one such low- density case. Thus, placing a small peak at about 1840 in Fig. 2 restores the regularity of oscillations. I know of no tree-ring data from New Brunswick for the period around 1710, when the Quebec specimens showed defoliation marks.

Including the possible hidden peaks, the average cycle length was 35 yr in New Brunswick (7 peaks over 210 yr), and 38.5 yr in Quebec (8 peaks over 270 yr). The longer average for Quebec is due to two long intervals between 17 10 and 18 12. This degree of difference would not be unusual between two series of stochastic population processes that share a common endogenous density-dependent structure and, hence, the same expected (mean) periodicity.

Even during the low-density periods between major outbreaks in this century, a few scattered patches of comparatively high density always remained on the budworm infestation maps of eastern Canada (Brown 1970, Kettela 1983). These are probably the areas where the troughs of population oscillations stayed comparatively high, as in central regions of New Brunswick in the 1960s (Fig. 2). I discuss the stochastic nature of these population oscillations in Synthesis.


.0

75 CL

0 I

CL

0

1700 1750 1800 1850 1900 1950

Year

FIG. 3. Spruce budworm population cycles (logarithmic scale) in the past two centuries, restored from sampling data since 1945 (- **; after Fig. 1), from historical records since 1878 ( ), and from radial growth-ring analysis of some surviving trees (-- -). Arrows indicate the years of first sign of ring retardation. Solid and dotted arrows are for New Brunswick and Quebec, respectively. For a small peak around 1840, see text.

Source of data Life-table studies of the Green River Project were

carried out in locations free from aerial spraying of DDT and were based mainly on sampling fir and spruce foliage at three phases in the life cycle of the spruce budworm; namely, (1) soon after all eggs had hatched, (2) when the majority of larvae were in the third and fourth instars, and (3) at the time of 60-80% moth eclosion. The length of a foliated sample branch was multiplied by its midpoint width to calculate the "branch (or foliage) surface area." Budworm density was then expressed as number per square metre (orig- inally number per 10 ft2) of the foliage surface.

The above sampling schedule determined (1) egg density, (2) initial density of first-instar larvae (i.e., those eggs successfully hatched), (3) density of "feeding larvae," the majority being in third to fourth instars, (4) density of pupae, including empty pupal cases still remaining attached to the sample foliage, and (5) total number of moths that emerged.

Although sampling was carried out at some 20 scattered plots, the period during which most plots were sampled extended over only a few years and is not long enough for analysis of temporal changes in budworm density. Only one plot, G4, a mature fir stand that was >50 yr old in 1945, yielded 12 yr of uninterrupted sampling data between 1947 and 1958, a period covering a major part of the outbreak in the province in the early 1950s. Since it covered the longest period, the set of data from this plot is the main source of information used in the present analysis.

However, in plot G4 the budworm density never reached a level high enough to cause heavy defoliation and tree mortality. The investigators considered the plot to be atypical since it was isolated from other parts of the forest by earlier clear-cutting operations. None- theless, the rise and fall of population density in this plot followed much the same pattern as in the other areas where density climbed to extreme levels. Thus, from the point of view of budworm population dynamics, I do not see that the population in plot G4 is atypical.

The second longest set of life-table data, the 9 yr between 1949 and 1957, comes from plot G5, 5 km north of plot G4. This was an "immature" fir stand (<40 yr old in 1945). Again, it was an isolated, "atypical" stand, where budworm density stayed even lower than that in plot G4. Nevertheless, the pattern of population change during the study period was again much the same as in other areas.

Additional life-table data used in the present analysis are from plots K1 (mature in 1945, as in G4) and K2 (immature, as in G5), both 15 km northeast of G4. These two plots are part of an extensive fir forest, typical of northwestern New Brunswick, where a high density of budworms caused successive years of heavy defoliation and much tree mortality. Unfortunately, the data from these plots covered no more than 7 yr (1952-1958) of the declining phase of the outbreak. Plot G2, 5 km south of G4 and with similar stand characteristics, yielded an even shorter set of life-table data, which will be used in the present analysis as sup- plementary information only.

After 1959, budworm density in the Green River area fell so low that it became extremely difficult to find larvae late in the season. Consequently, it became technically impossible to carry on a full life-table study. Only third- to fourth-instar larvae continued to be sampled at plots G4 and K1. Unfortunately, egg sampling was also discontinued after 1959. Although the population began to increase after 1968, leading to the current outbreak, the project, regrettably, was terminated after the 1972 season.

Long-range moth dispersal has been studied by aircraft and radar in recent years (Greenbank et al. 1980). Some results from this study will be used in the present analysis.

Notation and terminology

In this paper, density of the insect is denoted by the lowercase letter n, and the rate of change in n between two points in the life cycle by h; this is the survival rate in the interval defined, with the exception of the adult-to-egg rate of change. The natural logarithms of


TABLE 1. Life-table notation and life-history stages.

a. Summary of life-table notation. n, = Density at the beginning of stage s in generation t (s = 1 to 5) N, = log n,, hi! = ns+I /nst (s = 1 to 4): survival rate in stage s h5t = n,,t +/n5t: apparent oviposition rate (or E/M ratio) H3t = log h3t hg, = intrageneration survival rate H,, = HI + H2 + H3 + H4: log (intra)generation survival rate Rst = N3t+1 - Nt: log rate of change in density from stage s in generation t to the same stage in generation t + 1 R.! = H4v + H5t: log rate of change in egg density R3t = H3t + H4t + H5t + HI I,' + H2t+3,: log rate of change in third- to fourth-instar (L3) density

b. Parameter notation and stage designations in life-table data. Stage

Gen- Initial sur- Stage era- den- vival

Stage Code (s)t Period tion sity Remark rate Remark Eggs E 1 Late summer t n, All eggs laid

of year t - 1 he Egg (E) survival

Young LI 2 Fall of year t n2t All eggs hatched* larvae t - 1

h2, Survival of young (L1) larvaet

Old lar- L3 3 Early summer t n3t Majority in 3rd and 4th instars* vae of year t

h3t Survival of old (L3) larvae?

Pupae P 4 Mid-summer t n4t All pupae and pupal cases at time of year t of 60-80% moth emergence

h4, Pupal (P) survivall Moths M 5 Late summer t n5t All pupal cases at time of

of year t 60-80% moth emergence, and moths reared from remaining pupae*

h5t E/M ratio (apparent oviposition rate)JI

Eggs E 1 Late summer t + 1 nl,+ of year t

t s numbers as in Table 1a. * Time sampled; see Introduction: Source of Data. t Referred to as "small larvae" in Morris (1963a). ? Referred to as "large larvae" in Morris (1963a). 11 Mainly later part of pupal stage; see Introduction: Source of Data. ? Eggs per moth on foliage.

n and h are denoted by the corresponding uppercase letters N and H (the same notations were used in Roy- ama 198 la, b). Throughout this paper, natural logarithms are identified with the abbreviation "log."

Life-cycle stages and generations are indicated by two subscripts. For example, n,, and NS, are density and log density at the beginning of stage s of generation t. The survival rate from the beginning of stage s to that of stage s + 1 within generation t is then:

hat= ns+llnst (la)

or, taking the logarithms,

H= Ns -N (l b)

As mentioned in Introduction: Life Cycle, one generation in the budworm life cycle spans from the late summer of one year to that of the following year. Thus, the eggs, the first instar, and part of the second instar

in the calendar year t - 1 belong to generation year t, and the subscript t in Nt, Ht, etc. indicates the generation year. In graphs, these parameters are normally plotted against generation year t; only in a few graphs are they plotted against calendar years.

The parameter and stage symbols used throughout this paper are summarized in Table 1; details of the timing of the five stages listed in the table have been given in Introduction: Source of Data. As already noted, hs for s = 1 to 4 is a stage survival rate. In many published works, the survival rates h3 and h4 are often referred to as "large larval survival" and "pupal survival" after the Green River Project terminology. However, h3 includes the effect of mortality in part of the pupal stage, and, conversely, h4 excludes the early part of pupal mortality. Unlike other h's, h5t defined as n 1t+l/n5t is not a survival rate, but is an apparent oviposition rate per moth (male and female moths


combined), as it includes the effects of gain and loss of eggs through moth migration. I shall call this rate the "E/M ratio."

In the present data, H5 is always positive (or h5 > 1) despite the physical possibility of a negative value resulting from an extremely high rate of emigration. As opposed to this, the H's in all other stages are negative; i.e., a net loss, though net gain of larvae has actually been observed in a few plots at the time of second-instar dispersal (Miller 1958).

Some successive H values may be lumped. For instance, lumping the first two stages, Hit + H2,, gives the log survival rate from egg to third to fourth instar in generation t. Lumping from Hit to H4,, and desig- nating the sum as H,,, gives the log intrageneration survival rate, though this term assumes zero mortality in egg-laying moths; the effect of the moth mortality is in fact included in H5t, the log E/M ratio. We may lump all log stage survival rates to H5t, giving the log intergeneration rate of change in egg density from generations t to t + 1. This will be denoted by RI,; i.e.,

Rlt= -NNt+-Nit = Hit + H2t + ..*+ Hot = Hg1 + H5t. (2)

In general, we may define R1t (s = 1, 2, . . .) such that

Rst = Nst+ -Nst

= Hst + Hs+1 t + + Hs- It+l- (3)

For example, R3t is the t to t + 1 intergeneration (log) rate of change in the third- to fourth-instar density and is the sum H3t + H4t + . . . + H2,t + 1

The log intergeneration rate of change in density of a given stage (R in Eq. 3) has often been referred to in the literature as the "index of population trend," since Balch and Bird (1944) coined the term (Morris 1957). This is an unfortunate terminology, because the year- to-year rate of change cannot indicate population trend in the usual statistical sense; i.e., a fairly consistent tendency over a comparatively long period of time. To reveal a trend, observations must extend many more than 2 yr.

A tendency for a population to increase or decrease over a comparatively short period of time (for example, not much more than 10 yr) may be called a short-term trend, though it could have been merely an increasing or decreasing phase of an oscillation of many more years in length. Further observations might reveal that the system is merely oscillating about a horizontal level, in which case the system would be said to have no long-term trend or, alternatively, to exhibit a short- term trend that changes its direction periodically, de- pending on which aspect is emphasized. In this paper, I use the term "trend" in the above sense rather than in the Balch-Bird sense.

Note also that a "trend" in a series of no more than five or six points can occur by chance, as would be observed not infrequently in a purely random series.

To imply that this "trend" is a section of a trend in a longer series requires additional knowledge.

Reliability of data

Spruce budworm sampling in the Green River Proj- ect was very intensive to ensure a high level of reliability (Morris 1954, 1955). Nonetheless, the data suf- fer various types of errors or loss of information. In the first few years of the project, egg and pupal densities were not adequately determined, and the corresponding survival rates were indirectly estimated. Although a large sample was taken each time to ensure an accurate estimate of density, no sample was taken in the interval between third- to fourth-instar (L3) and pupal (P) stages (Table lb), so that little was known about changes in density during that important interval.

The pupal density (n4) tends to underestimate the actual number of larvae that pupated, because predators, for example, could have removed some pupae without trace before the scheduled sampling. Also, the value n5 in Table lb tends to overestimate the total number of moths that actually emerged in the field, and this, in turn, underestimates the E/M ratio (h5). This is because n5 is the sum of all pupal exuviae on the sample foliage plus the number of remaining pupae reared to adults in the laboratory, the latter being protected from predation or loss in the field. These are probably minor errors, however. The variation in the timing of L3 sampling from year to year influenced the estimations of h2 and h3, the survival of young and old larvae. I discuss this in detail in Analysis: Analysis by Stage Survival Rates.

Graphed life tables

Graphs of life-table data from plots G4, G5, K1, and K2 are shown in Figs. 4 to 7. As mentioned in Intro- duction: reliability of data, densities at some stages in the first few years are indirect estimates, as are the subsequently calculated survival rates. These indirect estimates are indicated by open circles in the figures.

ANALYSIS OF LIFE-TABLE DATA

Two major components of population fluctuations

Fig. 8 is equivalent to Fig. 1, but plots log year-to- year rate of change in density (i.e., Rt = N,,, - Nt, rather than Nt in Fig. 1) against generation year t. The log rate R exhibits frequent secondary fluctuations about its principal oscillation. (Note that the oscillation in log density [Fig. 1] and the oscillation in the log rate of change in density [Fig. 8] lag in phase; a peak or a trough in Fig. 1 corresponds to a zero in Fig. 8.] I shall now show that the log generation survival rate Hg mainly determines the basic oscillation (smooth curve in Fig. 8), and the log E/M ratio H5 is largely responsible for the secondary fluctuations.

Recall that the log rate of change in egg density (R1t)


H2-21 b y+@ -2 I -6

-1 b -3 H2 -2 -4 h

-3 + -5- ' -6 V

H 72 Ra3

CI H3 -2 4 -

-4 -4

7-e H 195 50 2 60

3 -0 I

-2

6 -f 2 k

FIG 4. Grpe lif tale in pltG erth re ie

4 -N3 R3 0 3 -1

N 2 -2 I L2? se

rto 0 o R4d -2 - -3 /- -42 -3

1945 50 55 60 1945 50 55 60

Generation year

FIG. 4. Graphed life tables in plot G4 near the Green River field station. Log survival rates in (a) eggs (H,), (b) young larvae (H2), (c) old larvae (H3), (d) pupae (H4); (e) log E/M ratio (H.); (f) log densities of eggs (N,), old larvae (N3), and pupae (N4); (g) log survival rate from beginning of egg stage to end of young larval stage (H, + H2); (h) log survival rate to end of old larval stage (H, + H2 + H3); (i) log intrageneration survival rate (Hg = H, + H2 + H3 + H4); () log intergeneration rate of change in egg density (R. = Hg + H.); log rates of change in densities of (k) old larvae and (1) pupae (R3 and R4, respectively). o- -o indirect estimates.

from generation t to t + 1 is partitioned into the log generation survival (H.1) and the log E/M ratio (H,,); i.e., R1, = Hgt + H., (Table la). In Fig. 9, I duplicate the relevant graphs from Fig. 4 (life-table data from plot G4) for ease of comparison. It is obvious that a declining trend and a secondary fluctuation about the trend in R1 (Fig. 9a) are determined, respectively, by Hg (Fig. 9b) and H. (Fig. 9c).

We do not have data on the rate of change in egg density (R1) after 1959. However, R1 is highly correlated with R3 (log rate of change in L3 density, Fig. 9a, 0). No doubt, the correlation must have held after 1959; as I show later, survival from eggs to third- or fourth-instar larvae is largely density independent, so the above correlation is unlikely to be affected. There- fore, we can substitute R3 in Fig. 8 for R1 and can conclude, by extrapolation, that the log generation survival rate Hg determines the basic population oscil-

lation, and that the log E/M ratio (H5) is largely responsible for secondary fluctuation about the trend.

The log generation survival rate Hg, however, does not always show a smooth oscillation, but shows some sporadic dips, as in the 1953 generation in plot G4 (Fig. 9b) and in 1947 and 1951 in plot G5 (Fig. Si); a very low Hg in 1952 in plot K1 (Fig. 6i) is probably one such dip, though the data series is too short. In- terestingly, all these dips in the generation survival rate are caused by dips in survival rates among feeding larvae (H3); compare graph c with graph i in Figs. 4, 5, and 6. These dips in Hg that are caused by H3 may in turn cause dips in the log rate of change in egg density (R1); for example, the one in the 1951 generation in plot G5 (Fig. Si and j). Therefore, Hg, like H5, can be a cause of secondary fluctuations in the log rate of change in density (Fig. 8). However, a dip in H3 may be countered by a high log E/M ratio (H5), as in the 1953 generation in plot G4; consequently, the dip in H3 would not show in the log rate of change R, (Fig. 4e, i, and j). On the whole, the variation in the log E/M ratio H5 is a far more important cause of the secondary fluctuation in the log rate of population change than are sporadic dips in the log generation survival rate Hg, though the latter is an important subject from the

H1 0a0 Ia a HI ~J +_ -2 g

-I -3 -

-2 - Hg -4 - -3 z -5 0

H3~ f -6 0 -6 - -3 -41 Hg -5 0

H4 5 d -6 -

7-

H5 6 - 2 j 4 -

1 1 0-01R1 c

3 RI

-

6 - -2 -

5 --3 4-f N 2- k

2 - ~~R3 0 2~~~~~~~~

62 --R N 3 N -2

-4 ~ ~ 4 -2- -5

O'-3 -6 6 1945 50 55 60 1945 50 55 60

Generation year FIG. 5. Same as Fig. 4 but in plot G5.


biological control point of view. What causes the dips is currently unknown.

E/M ratio Fig. 10 compares the graphs of H5 (log E/M ratio)

taken from Figs. 4-7. The dashed line in each graph indicates one-half of the mean potential fecundity (full egg complement) of a local female moth; I call this the mean fecundity per moth (including males) and refer to it by the symbol fi. I use this measure to compare with the E/M ratio because the denominator of the ratio includes all locally emerged moths, whose sex ratio is usually 1:1 (McKnight 1968, T. Royama, personal observation). If neither moth dispersal nor mortality has occurred in the locality concerned, the E/M ratio should coincide with the dashed line.

Note three features in the graphs of Fig. 10: (1) the log E/M ratios (H5) often deviate widely from the mean potential fecundity per moth (logsf, ---); (2) the H5's often fluctuate in unison between plots, but at distinctly lower levels (as compared with ---) in the K than in the G plots; (3) no trend is apparent in the H5's in the G plots (the series in the K plots are too short).

To aid in explaining these features, I use a model composed of the following six parameters.

HI 0- a I ~ -209-

X _ Ha -2 it+ -2 - IF -3

0 b

H2 -3 - i | H

H2-2 - +-4 h -3 -56

-61:

H3 -2 C -3

-4 ~~~~~~~~4

55 H4 5 d 55 -6

7- 6 - e 2-

H 5 - I

FIG 6. Sam RI Fi.4btinpo

3-

7 N1 -2 6 f 23 5 -32 k

3 ~~~~R3_I 2 N- -2

N I 2 0 -1 R4 0 -2 - I /% -3 -- -4 -2- -5b- 1945 50 55 60 1945 50 55 60

Generation year

FIG. 6. Same as Fig. 4 but in plot Ki.

. a W

HI 0L a X I -2 9 \~ + 92 g IE -3

I? b '-3 12 2- t -4 h

-3 I -5 -

-I6 -3 -2 - C-3 -

Hg5- H d d., .-6 7-

H 6 e 2i j 5 a- | l l l l lRl 3 -gj 7 - N-2 6 fN 5 - 0N3 2 k 5

FIG N4 R3S 0 2 -2-

N i--2 -I

n 0: number2of moths that emerge-2 -4~~~~~~~~~~

-5 -31 1945 50 55 60 1945 50 55 60

Generation year

FIG. 7. Same as Fig. 4 but in plot K2.

n,: number of moths that emerged locally A: mean potential fecundity of a local moth, including

males p1: proportion of f laid locally before emigration m: number of immigrants f2: mean number of eggs carried per immigrant, in-

cluding males P2: proportion of f2 laid at the landing site before re-

emigration

Note that Pi takes into account the effects of the rate of emigration, the preemigration rate of oviposition, and the preemigration mortality among the emigrants; P2 takes into account the same effects applied to the immigrants that reemigrate.

The total number of eggs laid locally is the sum ftpln5 + f2p2m, and dividing the sum by n, gives the E/M ratio h5; i.e.,

h5 =f1p1 +f2p2m/n5. (4)

This equation applies, without notational change, to a more general situation, as in Appendix 1.

Deviation of E/M ratiofromfecundity. -The potential fecundity of a female moth (2f1) is linearly related to its pupal size, is usually <250 eggs, and is rarely >300 eggs (Miller 1963a: Fig. 13.3). The dashed lines


3 C e02

0

.s 0 -

*~-3

0 1945 1950 1955 1960 1965 1970 1975 1980 0

Generation year, t

FIG. 8. Equivalent to Fig. 1, but shows yearly fluctuation in log rate of change in L3 density (R31, 0) from generation t to t + 1, plotted against t, and the log rate of change in egg-mass density (Rlt, 0). The smooth trend curve is drawn by eye. Arrows indicate years of moth invasions from outside; see Analysis: Frequency of Moth Invasions.

o

I I

It R Qo d I

-2 0 '1,0 a -3

-3_

-4 _-H Hg -5 b

-6 b ae -7 -

H55F_______ 7

6

N14

3

3i 4

2

1945 1950 1955 1960

Generation year

FIG. 9. The log rate of change in egg density in plot G4 (R., 0, graph a) is partitioned into log generation survival (Hg, graph b) and log E/M ratio (H5, graph c). The log rate of change in L3 density (R3, graph a, 0) is highly correlated with R1. All graphs here are taken from Fig. 4.

in Fig. 10 are the average f's estimated from the pupal size sampled in each plot (Miller 1957, 1963a). Low fecundity in the K plots is associated with heavy defoliation of the current-year shoots (Table 2).

An E/M ratio well above the dashed line indicates immigration of egg-carrying moths. Because of mortality among laying moths, only 60-80% of the full complement of eggs may be laid locally (Thomas et al. 1980, and Appendix 2), even if local female moths do not emigrate. Therefore, an E/M ratio falling between the potential fecundity f and 0.6f1 does not necessarily indicate emigration. However, many points in Fig. 10 are well below log 0.6f1, indicating net emigration.

Note that although the lowest average fecundity in the heavily defoliated K plots was as low as one-half of that in the G plots, such a difference had little effect on variation in the E/M ratio. Thus, variation in fecundity is a trivial factor in budworm population dynamics relative to moth dispersal.

Climatic influence on E/M ratio. -Fig. 11 compares the average net moth dispersal over the Green River area with three meteorological factors during the adult period for the years 1950-1958. The three factors are (1) number of cold fronts passing over the area, (2) number of thunderstorms, and (3) mean daily minimum relative humidity (data taken from the first nine rows in Greenbank's [1963b] Table 14.3). Note that Greenbank's net moth dispersal (fifth column in his table) is proportional to my E/M ratio. The inverted mean daily minimum relative humidity (graph c) seems to be the best predictor of the log E/M ratio H5.

A good correlation between inverted mean daily minimum relative humidity and E/M ratio seems to hold over a much longer period. As shown in Fig. 9, we have a direct measurement of the E/M ratio in a few plots, but only between 1946 and 1958. During this period, the fluctuation in the log E/M ratio H5 in plot G4 was nearly identical with that in the log rate of change in L3 density (R3), except for a declining trend in R3 and a lack of it in H5. Thus, allowing for this

December 1984 SPRUCE BUDWORM

r G4

3 i ~ ~~ ~~~~~~I I I

I2 4 -

2

6 _ ,,

5 _ K

2 _A

1945 1950 1955 1960

Generation year FIG. 10. Patterns of fluctuations in the log eggs/moth (E/M)

ratio (H5) in plots G4, G5, K1, and K2. Dashed line in each graph is the log mean potential fecundity per locally emerged moth (logs,); details are in the present section.

difference, we could use R3 in Fig. 8 (plot G4) as an indicator of fluctuation in H5 after 1959. We also have daily readings of minimum relative humidity at the Green River field station, 2.5 km south of G4, from 1946 to 1972. However, I have to estimate the dates of the adult period in each year indirectly in the following way.

First, accumulated heat units (in degree-days) above a threshold temperature of 5.60C can adequately pre- dict the development of the spruce budworm (Miller et al. 1971). We have the dates on which moth eclosion peaked each year at the Green River station between 1949 and 1957 (Fig. 12, 0), from which I calculated the average accumulated heat units to be 607.2 degree- days. The date on which this number of degree-days was accumulated in each year was in turn read from the meteorological record at the station; I take this as the day of peak moth eclosion for each year (Fig. 12, 0). Over an interval of 20 d, with the estimated peak- day in the middle, as an effective adult period, I calculated the mean daily minimum relative humidity

TABLE 2. Average potential fecundity* of local female moths in relation to defoliation of current-year shoots on balsam fir, Abies balsamea, in Green River area.

G plotst K plotst Defolia- Defolia-

tion Fecundity tion Fecundity Year (%) (eggs/9) (%) (eggs/9) 1947 5 normal? _ 1 1948 17 normal 1949 7 normal 1950 24 186 - - 1951 11 178 73 159 1952 9 178 96 139 1953 11 176 99 93 1954 26 normal 99 121 1955 10 normal 58 136 1956 13 normal 68 150 1957 17 normal 51 170 * Estimated from pupal size; see text. t Average of G2, G4, and G5. t Average of KI and K2. ? Normal (unstarved) pupal size, indicating the average fe-

cundity was ;200 eggs. II Dash indicates no data.

from the meteorological record in each year (Fig. 13, 0). The series of these estimated degree-days is well correlated with the series of log E/M ratios (H5; Fig. 13, 0) from 1946 to 1958 and is still quite well correlated with the series of R3 (log rate of change in L3

0 8 - a FW - C 6k-

7o 2 - .0

0 e

Z~ ~ ~ : I I I I I IX

1905 52 -35 65 75

0 0 ,

I 1 0-

.0 3--]0 4) &_. I E

0c -a

) 0 I

-2 I ~~~~~~E

195051 52 53 54 555657 58

Year

FIG. 11. Effect of climate on the eggs/moth (E/M) ratio, after Greenbank (1 963b: Table 14.3). a. Number of cold fronts passing over the Green River area during the moth flight period. b. Number of thunderstorms. c. Mean daily minimum relative humidity (%, *, inverted scale on the right), and the logarithms of Greenbank's index of net moth dispersal (proportional to my E/M ratio) averaged over the Green River area (0, scaled on the left).


o 10

0 > 5 5

a 20 o tO~~~~~~~~l e=L <>20t ; 0

0 10 _

a 1946 48 50 52 54 56 58 60 62 64 66 68 70 72

Year

FIG. 12. Estimation of dates of peak moth eclosion in the Green River area from 1946 to 1972. 0 recorded peak eclosion dates on which heat units had accumulated to, on average, 607.2 degree-days above 5.60C. 0 dates on which heat units had just accumulated to 607.2 degree-days.

density, x ), a substitute for the H. series between 1959 and 1971. Note that both R3 and inverted mean daily minimum relative humidity exhibited an upward trend after 1963, which was probably coincidental (see Anal- ysis: influence of weather).

The minimum relative humidity of a day normally occurs in the early afternoon, and moth dispersal takes place in the evening. Then, why is there an inverse correlation between E/M ratio and mean daily minimum relative humidity? Probably, meterological conditions that affect moth dispersal activity in the evening are correlated with the minimum relative humidity. Greenbank et al. (1980) observed that the evening exodus flight of a moth usually occurred between 1930 (Atlantic Daylight Saving Time) and midnight (the peak was at about 2130), and mostly at temperatures at canopy level of between 180 and 230C; no exodus was observed below 14.5?, above 29.50, in heavy rain, or in still air. Their observations by radar and aircraft revealed that moths on the wing, immigrating from elsewhere, were forced to land with their wings folded when encountering a cold air mass (presumably < 140C); if temperatures remain high enough, however, the moths might continue to fly even after midnight. Light inten-

sity is another controlling factor. Moths do not take off much before 1900 regardless of temperature (an exception was the unusually earlier flights during a 95% sun eclipse in New Brunswick at 1735 on 10 July 1972).

Greenbank et al. (1980) have shown that peak hours of exodus tend to be earlier on cold nights than on warm nights. However, a cold night is likely to reduce the overall chance for exodus. A cold night may also force immigrants to land if they happen to be flying over the area. Therefore, in a year when cold nights prevail, more eggs tend to be deposited locally, resulting in a high E/M ratio in the area, and vice versa. Since a low minimum relative humidity tends to indicate a cool night (and vice versa), we get the observed inverse relation between E/M ratio and the mean daily minimum relative humidity.

The warmth of a night may be indicated by average temperatures between 1930 and midnight. However, as shown in Fig. 14, a night with a high initial temperature and a steep decline (curve a) could be just as "warm" as one with a lower initial temperature and a less-steep decline (curve b). Chances for exodus flight probably are less on a "cold" night, as in curve d rather

. 3 8 _ _ 20

a, Lo0 15 96 95 17

la 2 7 - . -30 V) 1~~~~~ : I /

- 0~~~~~~ 0

3 I I~~t , 1950 195 196 4965 197

Year FIG. 13. Comparison between fluctuations in mean daily minimum relative humidity (%, 0; inverted scale) during the

estimated effective adult period, and the log eggs/moth (E/M) ratio (He, 0), supplemented by log rate of change in L3 density (R3, x) after 1959. Data from plot G4. For the estimation of effective adult period, see Analysis: Climatic Influence on E/M Ratio.


25

0Q

b

20 E

0)

14

2000 2100 2200 2300 0000

Hour (A.D.T.)

FIG. 14. A schematic representation of "warm night" conditions ( a and b) and "cold night" conditions ( --- c and d) in relation to moth dispersal activities. Hour is Atlantic Daylight Saving Time. For details, see Analysis: Climatic Influence on E/M Ratio.

than curve c, even if the average temperature is the same. As far as I am aware, Greenbank et al. (1980) did not discuss the effect of these differences.

Synchronous fluctuations between plots, and spatial density-dependence in E/M ratio. -Fig. 10 reveals that the log E/M ratio H5 often fluctuated in unison between plots. But H5 in the G plots varied about the log potential fecundity per moth (logf; - - -), whereas in the K plots, H5 was nearly always below log f1; compare, in particular, plots G5 and K1. These differences must be related to differences in local population density. To test this idea, I regressed the log E/M ratio H5 against the log density of locally emerged moths N5 for all plots where data were available in each of the calendar years 1954, 1955, and 1956 (Fig. 15). Since my present interest is the differences between plots, data from each of the 3 yr are shown separately; there were insufficient plots in other years for such an analysis. The 1955 and 1956 data show similar inverse relationships between H5 and N5, whereas the relationship is somewhat different in 1954.

Variations in fecundity and moth mortality could be density dependent, but the effects of these variations are unlikely to be a maj or cause of the inverse relationship in Fig. 15. This is because the variation in oviposition rate without dispersal would be confined mostly within narrow limits, with the upper one being the average potential fecundity (Jj in Eq. 4) and the lower one due to moth mortality (;0.6f, for the reason given in Appendix 2). Many points in Fig. 15 are outside these limits, suggesting that the relationship in Fig. 15 must be due to density dependence in moth dispersal.

Greenbank (1 963b) remarked that if moth invasion

occurred evenly over an area containing several plots, the E/M ratio should be high in a plot where the density of local females is low, and vice versa. This idea, however, does not adequately explain the observed relationship in Fig. 15, because net emigration evidently occurred toward the higher end of the density spectrum.

Immigrants are probably unable accurately to assess local population density (n5) before they land, so their number, m in Eq. 4, would be essentially independent of n5 in each plot. However, as long as climate permits, the immigrants could reemigrate if the local population was high enough to have caused substantial defoliation. In other words, it must be emigration, reemigration, and preemigration oviposition rates that become inversely dependent on local density, at least above a certain density level; that is, a major part of the preemigration oviposition rates P1 and P2 in Eq. 4 must be inversely dependent on n5 at higher values. (I shall discuss a low-density situation shortly.)

In 1954, log E/M ratios (H5) in those plots in Fig. 15 where N5 < 2 were much lower than those in 1955 and 1956 for the same range of log moth density N5, though differences were less toward the higher end of the density spectrum. This implies either that no plots received immigrants in 1954, or that, under the favorable weather conditions indicated by the high mean daily minimum relative humidity in 1954 (Fig. 11), emigration and reemigration outweighed immigration by a substantially greater margin than in 1955 and 1956.

Thus, the proportion of eggs the immigrants lay at the place they land is dependent on the level of defoliation and the duration of the immigrants' stay at that place, which in turn depends on climatic conditions. Because the immigrants stay at least until the following evening, some proportion of eggs would be deposited there, even if defoliation was heavy; it is very unlikely

"' 6

6 5 - X

:E X- X0 'x N 3 _ (O LU x \

a) 2 x 0 X

-3 -2 -I 0 2 3 4 5

log moth density, N5

FIG. 15. The dependence of the log eggs/moth (E/M) ratio (H5) on log moth density (N5) of the various plots in years 1954 (x), 1955 (0), and 1956 (0). The curve is drawn byL eye through the 1955 and 1956 data. Upper - -- log potential fecundity (log fl); lower --- log l.6fl


that the immigrants lay no eggs during their stay. It makes sense, then, that the log E/M ratios should fluctuate in unison between the plots (Fig. 10), but at a much lower level in the K than in the G plots.

Data on moth dispersal and oviposition rate relative to local population density that might support the above deduction are mostly circumstantial. Greenbank et al. (1980: Table 8) summarized a set of observations, made between 1971 and 1976, on the rate of emigration (direct count of moths taking off) relative to pupal density at five localities scattered widely over New Brunswick, and another set made in 1976 at four localities in On- tario. The data show that the rate of emigration tended to be much lower in low-density than in high-density localities. However, no clear relation was detected among the seven high-density localities (10-50 moths/ m2 of foliage) in New Brunswick. Indeed, in two plots the rate of emigration was negligible despite moder- ately high moth densities of 23 and 50 moths/M2 of foliage. Differences in climate between years and between distant localities probably masked the relationship.

Blais (1953) observed that female moths in a severely defoliated stand "were able to fly in an upward direction [this must have been an exodus flight] soon after emergence." In 1982, in a severely defoliated fir stand near Fredericton, New Brunswick, we (E. Eveleigh and T. Royama, personal observations) confirmed that many moths caught in their exodus flights had laid very little of their complement of eggs. Because of the favorable weather in the 1982 season, the rate of emigration was high. No immigration occurred in the sample area, and consequently the E/M ratio h5 was < 15 (i.e., H5 < 2.6).

I will now discuss the rate of emigration in a low- density situation. If high density and consequent defoliation necessarily induce a high rate of emigration, one might conversely expect a low rate of emigration from a plot of low density and little defoliation. How- ever, this does not seem to be the case in the Green River data. The rate of emigration appears to have been unexpectedly high in the two lowest density plots in 1955 and 1956 (Fig. 15); my explanation for this is as follows.

Suppose emigration was negligible in a low-density plot (the null hypothesis) and local moths laid on average 60-90% of their eggs in the plot due to moth mortality (Appendix 2). Because of little defoliation, the mean fecundity of local moths (Jj) is ; 100 eggs. Then, the value of fpt in Eq. 4 is 60 to 90. If the density of local moths (n5) and the E/M ratio (h5) in the plot are known, then, under the above assumptions, we can calculate an expected number of eggs (per unit foliage area) laid by immigrants (f2p2m) by using Eq. 4; i.e., f2p2m = n5(H5 - fiPl).

There is a set of six plots in 1955 and 1956 in which the E/M ratio was well above the potential fecundity of local moths (Fig. 15), which suggests that these plots received immigrants. In the two lowest-density plots,

the observed n, and h5 were on average 0.065 (N5 = -2.8) and 700 (H5 = 6.55), respectively. The calcu- latedf2p2m in these two plots is, by the above equation, in the order of 40 eggs/M2 of foliage. In the other four plots, where the observed n5 and h5 were on average 0.75 (N5 = -0.29) and 415 (H5 = 6.0), the calculated f2p2m is in the order of 250 eggs, which is more than six times larger than the calculated value for the two lowest density plots. Certainly, in the two lowest density plots, immigration could have been, by chance, as low as calculated. However, I think that in these plots the rate of emigration or reemigration was high, rather than that the rate of immigration was low. Presumably, at the height of widespread outbreaks, a very low density means a poor habitat for the budworm, which might have provoked emigration and/or reemigration.

Finally, the spatial density-dependence of the E/M ratio has an important implication in the synchronized population oscillation between plots. Notice in Figs. 4-7 that the log generation survival rate (Hg, graph i) over the same generations was on average much higher in the K than in the G plots. This tendency was associated with lower log E/M ratios (H5) in the K than in the G plots because H5 is spatially density-dependent. Thus, Hg and H5 cancelled each other's effects on the intergeneration rate of change in egg density (R1), which is the sum Hg + H5 (Eq. 2). As a result, populations in these plots peaked (or R1 zeroed) at more or less the same year (about 1953). If this had not been the case (i.e., if the H5's were not density- dependent in space) the population oscillation in these two groups of plots would have been off phase.

Lack of temporal density-dependence in E/M ratio. -The within-plot relationship between H5t (log E/M ratio) and N5t (log moth density), which is analogous to the between-plot relationship in Fig. 15, is the regression of Ht on N5t in a given plot (Fig. 16). Only in Fig. 16a (G plots) is H5t inversely correlated with N5t, and even that relationship is not as clear as the between- plot relationship in Fig. 15. As a general rule, the spatial density-dependence of a population parameter does not imply that its temporal series is necessarily density- dependent (Royama 1981 a). Unlike Fig. 15, however, the regressions in Fig. 16 do not provide insight into the relationships, because a correlation in trend between the time series is indistinguishable from a correlation in fluctuation after trends are removed.

We have the required time-series information in Fig. 9. It shows that the series of H5t (graph c) has no trend that is correlated with the increasing trend followed by the decreasing trend in the series of N1t (log egg density, graph d), and one might suppose that the E/M ratio (H5t) is temporally density-independent. Curiously, however, H5t does show a clear inverse correlation with N1t during the period between 1950 and 1957, when N1t fluctuated at a plateau without trend. This correlation between H5t and N1t is the cause of the inverse correlation in Fig. 16a because N5t (log moth density


7 - a *.

00 6 - .

5 _

4 0 0 *

3LO 2_

II I _

0 b 3 * 0

2 0 .0 0

-5 -4 -3 -2 -I 0 1 2 3 4 5

log moth density, N5t

FIG. 16. Observed relationships between log eggs/moth (E/M) ratio (H5t) and log moth density (N5,) at four separate plots over several years. a. Plots G4 (t = 1945 to 1958; 0) and G5 (t = 1946 to 1957; *). b. Plots K1 (t = 1951 to 1958; 0) and K2 (t = 1951 to 1957; 0).

at the end of generation t) is correlated with N1, (log egg density at the beginning of the generation).

However, Fig. 16a includes data when N1, (hence, N5,) was either increasing or decreasing. Such a trend in density considerably weakens the inverse correlation with the log E/M ratio because the latter has no trend. The correlation is even worse in Fig. 1 6b than in Fig. 1 6a because moth density was steeply declining in the K plots during the period observed (cf. Figs. 6f and 7f).

But, why is log E/M ratio (H5,) correlated with log egg density (N,,) only when N1, has no trend? This is, in fact, an interesting property of a stochastic process, in which the inverse correlation, unlike the one in Fig. 15, does not imply density dependence. I have shown (Royama 198 la) that, even if H5, is a series of completely independent random numbers, hence, without trend and independent of N1t, H5, would still show an inverse correlation with N1, only in an interval in which N,, has no trend (Appendix 3). Thus, the observed relationship (Fig. 9c and d) makes sense if we assume that the E/M ratio in a given plot is density independent. I now need only to explain why the time series of E/M ratios behaves as though it is density independent.

The origin of the majority of immigrating moths is within 100 km of landing sites (Greenbank et al. 1980), and Fig. 2 suggests that local budworm populations within such distances must be oscillating in unison.

Then, the populations in which the immigrants originate and the populations that receive them are likely to be in phase. It follows that, in a given year t, the number of immigrants mt and the number of local moths n5t are likely to be positively correlated, and, by Eq. 4, this correlation tends to nullify the dependence, in trend, of H5t on N5,

The life-table data from the Green River Project did not encompass even one full cycle of population oscillation, and we do not know if E/M ratios increased in the K plots after the recovery of the forest from the 1950 budworm outbreak, as it might have if healthy foliage induced net immigration. A series of E/M ratios might show a trend if the relative level of density grad- ually changes between the local population and one in which immigrants originate. Temporal changes in the E/M ratio would also be dependent on the degree of synchrony in population oscillations between localities within the reach of moth dispersal. In my view, the density dependence of the E/M ratio will not show clearly in time series for the above reasons; hence, for most practical purposes, I treat the series of H5t as density independent.

Generation survival rate In this section, I analyze generation survival in two

ways (first, by stage survival rates and, second, by mortality factors) to find stage survival and mortality factors that cause population oscillation. Stage divisions are eggs, young larvae (L1 to L2), old larvae (L3 to L6), and pupae. Mortality factors to be examined are dispersal losses in young larvae, parasitism, predation, food shortage, weather influence, and a complex of disease and undetermined mortality (which I call the "fifth agent") in old larvae.

I find that survival of old larvae is the main driving force of population oscillation. Survival of young larvae, though a significant contributor to generation survival, does not cause the basic oscillation. Both egg and pupal survival rates have a minor influence on generation survival. I find the evaluation of mortality factors more difficult than the evaluation of stage survival rates, because of insufficient data on mortality. However, by elimination I deduce that a combination of parasitism and the "fifth agent" is the most likely cause of population oscillation.

Analysis by stage survival rates In Figs. 4 to 7, generation survival (Hg, graph i) is

partitioned into H1 (egg survival, graph a), H2 (young larval survival, graph b), H3 (old larval survival + early part of pupal survival; graph c), and H4 (latter part of pupal survival, graph d). The pattern of fluctuations in H1 and H4 is almost identical among plots. In every plot, H4 contributed slightly to the declining trend in Hg, while H1 did not. Both H1 and H4, however, were such minor contributors to Hg that I will not discuss them further in this paper.


-3 NG4

I 3 G5 -4 _ h - -5 '

%O -6

- X 5

? -6-

f3 K K2 -4_ _5_

-6 I,&[ . II,, 94648 50 52 54 56 58

Generation year

FIG. 17. Yearly fluctuations in the log total survival rate of larvae (H2 + H3) in plots G4, G5, Kl, and K2. 0-- 0 indirect estimates; see Introduction: Graphed Life Tables.

Survival of both young larvae (H2) and old larvae (H3) contributed the most to the yearly variation in generation survival (Hg). However, a declining trend in H3 was the cause of the same trend in Hg, whereas H2 did not show such a trend, as is clear in plots G4 and G5 (Figs. 4 and 5). As already discussed, the declining trend in Hg in the 1950s is the decreasing part of its oscillation. Therefore, I conclude that H3 is the driving force of population oscillation. Only in plot K2 did H2 show an apparently decreasing trend (Fig. 7b), but I do not take this short-term trend to be the decreasing section of an oscillation.

Now notice a tendency for H3 to fluctuate about its downward trend but in the opposite direction to H2, as typically exemplified in the G4 data; compare graphs b (H2) and c (H3) in Fig. 4. As a result, fluctuations in H3 about its trend tended to cancel those in H2, so that the sum H2 + H3 revealed an almost smooth downward trend (Fig. 17), except for the occasional dips in H3 mentioned above.

The survival of old larvae (H3) in the G plots not only compensates for fluctuations in survival of young larvae (H2), but also tends to counteract the mean level of H2. Thus, H2 tended to be higher in plot G5 (Fig. 5b) than in plot G4 (Fig. 4b), while the reverse was true for H3 (Figs. 4c and 5c). Consequently, the sums, (H2 + H3)'s, are similar in the two plots (Fig. 17). This

situation does not apply to the K plots, where the H3's are much higher than in the G plots but the H2's are more or less the same as H2 in G4. I will return to this point.

The curious compensations between survival of young (H2) and old (H3) larvae result from the variation in the timing of sample collections. Usually, in a life table, the end of one stage constitutes the beginning of the next stage, so the calculated survival rate in one stage is not independent of that in the other stage; generally, they are inversely correlated with each other. I call this "stage-framing bias" in a life table.

As shown in Table lb, the survivals of young and old larvae were determined by sampling (1) the number of first-instar larvae successfully hatched, (2) the number of larvae sampled when most larvae were in the third to fourth instars, and (3) all pupae and pupal cases found at the time of 60-80% moth emergence. The timing of sample collection does not much influence the estimation of (1) and (3), because egg and pupal cases remain attached to foliage for a while. However, the midpoint samples (2) were collected just when a comparatively heavy mortality began to deplete

40 - 1951

30

20 -

? - L4 L.

>, ~~~~~~~P C 3 .> 30 - ~- + 1952

Eo 20 - <

X0 lo L3 3: 2- L3L m .

L 6 2 ~~~4L5 L

50 - -__+ 1954 40 -

30 _

20 -

10 -- L3 0 o L3 L -

4L5

May June July Aug.

FIG. 18. Decrease in population density (number/M2 of foliage) from second-instar (L2) to pupal (P) stages on selected trees in plot G4 in three years. The arrows indicate the dates of L3-sampling in the plot in each year. Adapted from Miller (1955: Fig. 2) and his unpublished data (Maritimes Forest Research Centre).


G2 q 2 -10 -10

IE I I ,I I ,

. G0 4 -0> -br~~~~~~~-

-1 t1 '?'m

01~~~~~~0

10r t 2

l l l l l l -3 94 500 52 s4 q5

%_ KI I

Im ~ ~ ~ ~ C ~ ~ ~ ~ I -30

KI0 >

I I I - 948 505254565

Generation year

FIG. 19. Comparison between log survival rate in young larvae (H2,@*, scaled on the right) and the timing of L3-sampling relative to the mid-date between peaks of third- and fourth-instars (0). Relative timing is measured as deviation in days (scaled on the left); a negative deviation indicates a relatively earlier sampling, and vice versa. Zero deviation of a sampling date was arbitrarily matched, on the vertical scale, with H2 = -1 and differences in the level of matching differ from plot to plot. For details, see Analysis by Stage Survival Rates.

the larval population every day (Fig. 18). Therefore, a comparatively early midpoint sampling would tend to overestimate the survival of young larvae (H2) and underestimate the survival of old larvae (H3), and vice versa.

To demonstrate this, in each year between 1948 and 1958 I took the mid-date between the peaks of the third and fourth instars observed near the Green River field station where the G plots clustered (see Point 2 in Area 1 in Fig. 1.1 of Morris 1 963a). The deviations of the actual dates sampled in each plot from these mid-dates are shown in Fig. 19 (0). A negative deviation indicates earlier sampling, and vice versa. Devia- tions are compared with the H2's (0) taken from graph b of Figs. 4-7. For convenience of comparison, zero- deviation of a sampling date was arbitrarily matched

to the level at which H2 = -1 (or 37% survival). Be- cause annual larval development was recorded in only one plot, and not even in the same plot each year, the true mid-date between the two peak dates in a given plot could be in error by a few days. Despite this, we see a good match in the patterns of fluctuation between H2 and the relative timing of sampling in most plots, revealing a clear influence of stage framing.

Partitioning into young and old larval stages is de- sirable in budworm life-table studies because the types of mortality change distinctly between the two stages. However, without a technique to estimate reliably the number of larvae that successfully molt into the third instar, bias in framing the consecutive stages is practically unavoidable.

Nevertheless, from the relations in Fig. 19 we could reduce the stage-framing bias and adjust survival of young larvae to the developmentally standard time, the mid-date between peaks of third and fourth instars.

0 -

G2 -2 _

0

II- -I L

? -I -

0 -2 _

so 0r

I KKI 4) -I -

E 0 -

K2

-2 -

1948 50 52 54 56 58

Generation year

FIG. 20. Estimated log young larval survival (H2). Ob- served H2 was adjusted to the mid-date between the peaks of third and fourth instars. For the method of adjustment, see Appendix 4.


Fig. 20 shows a result of one such adjustment (details in Appendix 4), though lack of exact phenological information in individual plots makes it difficult to adjust the mean level of H2.

The adjusted log survival rates in young larvae (H2's) do not show a declining trend in most plots, and even where they do (e.g., G4), the trend is too weak to account for the decreasing trend in H2 + H3 in Fig. 17. Thus, although the method of adjustment is quantitatively crude, it is adequate to demonstrate that the survival rate of young larvae is unlikely to be a major source of population oscillation. It follows that the main cause of the oscillation must lie in the mortality of old larvae.

Analysis by mortality factors Mortality of young larvae. -Miller (1958) showed

that most of the mortality in young larvae occurs during dispersal in the fall and the spring. Other mortality (e.g., mortality within hibernacula, or mortality due to failure to spin hibernacula, to loss of hibernacula, or to diapause-free development) was either minor or did not vary much from year to year or from stand to stand.

Many larvae drop on silk threads, and some are carried away by air currents during fall dispersal (when they are searching for overwintering sites) and during spring migration from the hibernacula to feeding sites. Dropping on silk might be triggered by contact with other larvae or by other tactile stimuli, but mostly it seems to be a reaction to light (Wellington and Henson 1947, Henson 1950). Then, dispersal in young larvae must be largely independent of population density. This is consistent with the lack of trend in H2 that was discussed in the preceding section, but disagrees with Mott's (1963) earlier analysis, in which average survival rates of young larvae exhibited an apparently hyperbolic inverse relationship with density (Mott 1963: Fig. 9.2). However, in Mott's more detailed Fig. 9.5, in which individual data points are plotted, the inverse relationship in the averages can be seen to be heavily dependent on one single outlier at the lowest end of the density spectrum. In addition, Mott's data points in his Fig. 9.5 were scattered widely and were influenced by the framing bias already noted. Thus, there is no firm evidence of density-dependent survival of young larvae.

Mott (1963) and Morris and Mott (1963) concluded that the survival of young larvae was dependent on some physical characteristics of the stand, such as stand density, foliage thickness, stand continuity, and level of defoliation, that influence the larvae's chances of landing on suitable feeding sites. For instance, dispersal loss could be less in denser stands, and vice versa (see Figs. 9.1 and 29.1 and Table 29.1 in Morris 1963a). Unfortunately, data on this were not explicit, so there is no way to reassess their conclusion. Rather, existing data (Fig. 20) reveal no clear heterogeneity in the level of H2 among plots G2, G4, Ki, and K2, despite sub-

stantial differences in the physical structure of these stands (see Table 4.1 in Morris 1963a). The distinctly higher H2's in plot G5 were probably due to the earlier average sampling dates, as already discussed.

Loss of young larvae during dispersal was consis- tently high in all years (Miller 1958); though not a cause of population oscillation, this could be a major factor determining the level about which the population oscillates. However, as far as I am aware, no reliable data exist on whether the rate of larval dispersal loss differs among different forest types.

Mortality of old larvae. - 1. Parasitism. -Several hymenopterous and dipter-

ous parasitoids attack spruce budworm larvae at different stages (Miller 1955, Miller and Renault 1976). The two most common wasps, Apantelesfumiferanae (Braconidae) and Glypta fumiferanae (Ichneumoni- dae), attack the first- and second-instar budworm larvae in the late summer, and the second-generation wasps emerge and kill their hosts in the following summer, when the host larvae are at their fourth or later instars, though these parasitized larvae develop much more slowly than unparasitized ones. The rate of parasitism by these species can be determined accurately by rearing larvae that have been collected from hibernacula before spring emergence.

Other parasitic wasps (e.g., Meteorus trachynotus [Braconidae] and several tachinid flies) attack the third- to fifth-instar larvae, and adult parasitoids emerge from the sixth-instar larvae or pupae. M. trachynotus often leaves hosts that stay alive for a while, but never pupate (E. Eveleigh and T. Royama, personal observations). Therefore, accurate estimations of parasitism by these species would require frequent sampling. Sampling at intervals of -7-10 d, supplemented by graphical in- terpolation (Miller 1955: Figs. 2, 3), probably underestimates parasitism. Keeping this in mind, I have shown Miller's results on annual parasitism (by all parasitoids) in Table 3, part of which has been published (Miller 1963b: Table 34.1). Also, letting 100p be the percentage parasitism in Table 3, I plotted 100(1 - P)% in log scale over generation'year in Fig. 21.

The number 1 - p is the proportion of old larvae that escaped parasitism, of which, let us say, 1 - q proportion survived from all other mortality factors. The overall survival rate of old larvae (H3) is then approximately

H3 = log(l - p) + log(l - q) (5)

(Miller 1 963b, Royama 1981 b). Therefore, the graphs in Fig. 21 are the contributions of parasitism to log survival of old larvae (H3) in the four sample plots. Comparing the graphs in Fig. 21 with the corresponding graphs of total larval survival (H2 + H3) in Fig. 17, we see that the declining trend in log(l - p) is not large enough to account for the same but steeper trend in


TABLE 3. Percent parasitism (all parasitoids) in old larvae.*

Year

Plot 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958

G4 13 10 18 6 19 12 41 47 36 52 33 38 25 48 G5 8 16 6 21 17 19 39 37 52 36 41 K . 8 20 18 25 19 16 35 K2 16 29 19 26 18 34 * Data from Miller (1 963b: Table 34.1) and his unpublished data (on file at the Maritimes Forest Research Centre, Fred-

ericton, New Brunswick, Canada).

H2 + H3. In other words, parasitism alone cannot be a major source of the declining trend in generation survival rate and, hence, cannot be by itself a main cause of the observed population oscillation.

2. Predation.-Major predators are small insectiv- orous birds, such as warblers of the family Parulidae, and a complex of invertebrates, predominantly spiders (Morris 1963c). The rate of predation was not adequately quantified in the Green River Project (nor, for that matter, in any published works on the spruce budworm, as far as I am aware); nevertheless, I deduce that predation is unlikely to be a primary cause of the budworm population oscillations.

Mitchell (1952) analyzed gizzard contents of some song birds over 2 yr (1949 and 1950) of high budworm density in a Maine spruce-fir forest. His results showed that several species of birds consumed budworm larvae and pupae in varying degrees (Mitchell 1952: Table 1), of which about a dozen species (Mitchell 1952: Table 2) contained the budworm in substantial proportions (in volume) of their stomach contents. On the other hand, a series of experiments by Miller and Renault (1981) over 5 yr (1959-1963) of low budworm density in the Green River area, in which caged and uncaged larvae were used, has shown little sign of bird predation on the insect.

In the experiments by Miller and Renault, second- instar larvae were collected and individually "replant- ed" in three groups on practically budworm-free balsam fir branches. The larvae of one group were completely protected from predation and parasitism in cages covered with very fine nylon mesh, though some small predators were occasionally caged with the larvae and some larvae were already parasitized. A second group of larvae, placed in a cage with coarse wire mesh, was protected only from birds and large invertebrate predators. In a third group, each larva was placed on a marked but completely exposed branch. Each planted larva in all groups was frequently inspected and its fate recorded until it disappeared, was found dead on the foliage, or survived to the moth stage (or left the empty pupal case on the branch in the exposed and semiexposed groups). I have summarized the results in Fig. 22.

Needless to say, bird predation should show as a difference in the "disappeared" category (graph a) between the exposed (@) and semiexposed (0) groups.

There is no obvious difference, and we cannot attribute the loss in the exposed group to bird predation.

From the above observations, I deduce that birds took a substantial number of budworm larvae and pupae when insect density was high, and ignored this source of food when the insect was scarce. This is in accord with the theory of predation by profitability: birds tend to pay more attention to a more profitable (usually more abundant) source of food but tend to reject an unprofitable (usually scarce) source (Royama 1970, 1971). Predation under this mechanism is probably a first-order density-dependent process (i.e., dependent on prey density in the current generation only) that does not generate an oscillation in a predator-prey interaction system (Royama 1981 a). For bird predation to be a primary cause of a population oscillation, it must be at least a second-order density-dependent process; that is, the rate of predation must be dependent on the initial prey density, both of the current generation and of the previous generation. For birds this is unlikely, because they do not multiply effectively

G4 600

o100 G5 X 60 -

. 0 0 35 -

x I KI 60

100 I- K2 60 - 35 -

I I l l l I 194648 50 52 54 56 58

Generation year

FIG. 21. Yearly variations in the proportion of larvae unparasitized, 100(1 - P)%, plotted on a log scale, p being total proportion of old larvae parasitized; lOOp% is given in Ta- ble 3.


X 50 a @ 40 * : 30 o a. 0. 20 - (0 x

X a o 0X X X

? o 20 x 501b

l 40 - x 44 O

l 30l

C~~~~~~~~~~'

v 20 - i * X 10 - x ? ? Q ? I ~~~~~~~~I X X

0

* ~~~C

, 200 * 0.N

20- .0~~~

. E 100 0 , ? 'C '

0 ~ ~ I I 1

1959 60 61 62 63

Year

FIG. 22. Results of the cage experiments by Miller and Renault (1981). Proportions of larvae that a. disappeared; b. were found dead; and c. had been parasitized, percentage of the initial numbers of third-instar larvae in graph d. x fine- mesh cages, 0 coarse-mesh cages, and * open branches.

in numbers from one year to the next, as the budworm does.

Some bird species were reported to be more abundant during budworm outbreaks than at other times (Kendeigh 1947, Morris et al. 1958, Gage and Miller 1978). But many other species, though feeding on the budworm when it was abundant (Mitchell 1952), either did not noticeably change in abundance, or became even less abundant at high budworm density. On the whole, there were only twice as many birds of all in- sectivorous species during outbreaks in some Green River study plots in the 1950s as there were during a period in the 1960s after outbreaks there (Gage and Miller 1978). A change in the bird population of this magnitude would have had little effect on the budworm population, which changed much more drastically. Moreover, a correlation in abundance between the budworm and some birds could be coincidental. In- consistent responses to changes in budworm density by many bird species (Morris et al. 1958, Gage and Miller 1978) that fed on budworms at high density (Mitchell 1952) support this idea. Some of the correlation could have been due to the fact that birds re- distributed themselves in response to local differences in budworm density. However, such spatial density-

dependence of a predator population need not necessarily imply a second-order density-dependent process, as would be necessary to induce the budworm oscillation.

It is unlikely that breeding populations of birds increase through high reproductive success in the previous year in response to high budworm density. Mook (1963) found that birds did not take the small budworm larvae before the sixth instar. Only 10% (presumably, in numbers) of the larvae found in the gizzards were fifth or younger instars. This implies that the birds fed on budworms effectively for only a few weeks, at most, each season. It is hardly conceivable that year-to-year changes in breeding bird populations could be determined primarily by the abundance of a particular type of food that could be utilized effectively for only a few weeks each year. A high budworm density might assure a high nesting success in some bird species, but is unlikely to assure high fledgling survival, for by the time the young become independent, they can no longer utilize this once-abundant source of food.

A similar argument applies to omnivorous invertebrate predators that utilize a narrow range of prey size. Budworms rapidly develop in size during the season, and the length of the period during which a predator species can utilize budworms is undoubtedly limited. Perhaps, few predator species depend entirely on budworms throughout their life cycle, and so few, if any, respond reproductively to budworm abundance. In fact, Renault and Miller (1972) have shown that some spiders (e.g., of genus Dictyna) could consume many young (mainly second-instar) budworm larvae, but the species composition and density of spiders stayed remarkably constant during their 8-yr study, confirming the earlier conclusion of Loughton et al. (1963) that spiders showed little change in density during the 1950s.

Predation, though unlikely to be a primary cause of budworm population oscillations, may nonetheless influence the mean level of those oscillations. Little quantitative information on this subject is available, however.

3. Food shortage. -If budworms kill a large proportion of trees in a stand, the budworm population per unit area of the stand must decrease as well. How- ever, tree mortality did not necessarily imply a decline in survival of old larvae (H3) in the Green River study, because survival was measured by the reduction in the number of larvae per unit foliage surface area on living trees.

In his laboratory studies, Miller (1977) found that nearly 90% of the total food consumption by a larva occurred after it became sixth instar. Thus, even the total consumption of current-year shoots at very high budworm density, and the subsequent feeding on older foliage, would occur only toward the end of the larval stage. Food shortage often retards larval development or produces small female moths with reduced fecundity, but does not necessarily produce weak larvae or


cause mortality among larvae, unless reinforced by other factors, such as diseases (discussed later).

When high densities of second- or third-instar larvae are mining into buds, current-year shoots can be totally destroyed well before the larvae reach their final stage of feeding (Blais 1979). However, each larva in these early stages eats so little that very heavy defoliation of the current-year shoots and subsequent serious food shortages occur infrequently and only at extremely high larval densities. Moreover, even in this extreme cir- cumstance, the larvae can still survive at the expense of body size and fecundity, as was observed on Cape Breton Island, Nova Scotia, in 1977 and 1978 (Piene et al. 1981). A. W. Thomas (personal communication) observed that moths that were produced from starved larvae could be as small as one-fifth of the normal weight but still not show any noticeable weakness and seem as vigorous as those produced from well-fed larvae. Probably, budworms maintain their physiological vigor at the expense of body size to cope with a high- density situation lasting as long as 10 yr and occurring as frequently as once every 30-40 yr.

During the late 1 950s, the survival of old larvae (H3) was still much higher in the heavily damaged K plots than in the little damaged G plots (Figs. 4-7). Never- theless, the populations in all plots declined in parallel. Evidently, food shortage was neither a primary nor a universal cause of population decline. This is not an isolated observation. All populations in New Bruns- wick declined in the late 1950s and early 1960s (Fig. 2) regardless of defoliation and tree mortality at the stand level. Thus, budworm outbreak cycles cannot be adequately explained by habitat destruction-regeneration cycles, as postulated in the task-force report (Bas- kerville 1976).

4. Influence of weather.-Some earlier analyses (Wellington et al. 1950, Greenbank 1956, 1963a, Mor- ris 1963b) yielded a climatic-control hypothesis: a dry, warm summer favors the development of the feeding larvae, and so a series of favorable years allows populations to increase. (A wet, cool summer produces the opposite result.) Greenbank (1956 [Fig. 2], 1963a [Fig. 3.2]) took 4- or 5-yr moving averages of the average precipitation and the average daily range of temperature in June and July (the interval covering a major part of the larval feeding period in the northern part of New Brunswick) and showed an on-average dry, warm period between 1945 and 1949, an intermediate condition between 1950 and 1955, and an on-average wet, cool period between 1956 and 1960. The pattern appeared to coincide with the rise and fall of budworm populations in the province over the same period. There were also several on-average dry, warm years around 1910, which coincided with the well-known outbreak of the same period (see Fig. 3). However, another such favorable period around 1925 was associated with low populations in the province. After careful examination, I have found no evidence that weather has much of an

I10 4 15-V

*20- ao 25 -

30

O323 - 0

22 - a. E 21-

20 -A

o 19 -

18 -

17- 301-

* 40- c 50_-

E 60_ L, , I ,, .I , ..I ...

1945 50 55 60 65 70

Year

FIG. 23. Yearly fluctuations in precipitation (inverted scale), mean daily maximum temperature, and mean daily minimum relative humidity (inverted scale) between 1 June and 15 July at the Green River field station. Horizontal line in each graph indicates average.

influence on the survival of feeding larvae, as was pre- viously thought.

As already shown, fluctuations in the survival of old larvae (H3) about the downward trend of the 1950s were influenced by the timing of the sample collection at the beginning of the stage concerned. Eliminating framing bias by combining H3 with H2 results in a smoother declining trend, particularly in plot G4 (Fig. 17). If the survival of larvae was much influenced by weather, the compensation of H2 and H3 is incompre- hensible. Although temperature and precipitation exhibit a pattern of oscillation if smoothed by taking moving averages, the larvae in the Green River area could not possibly respond to the smoothed (by moving average) pattern of the average weather over the province and ignore the detailed, much more irregular yearly fluctation at the Green River station (Fig. 23), where there was no consistent dry, warm period between 1945 and 1949.

In fact, fluctuations in log larval survival rates (H2 + H3; Fig. 17) are not well correlated with weather records in Fig. 23. Although survival in plot G5 between 1951 and 1957 is vaguely correlated with mean daily maximum temperature, this is probably coincidental. First, the distinctly low survival rate in G5 in 1951, which coincided with a low mean temperature for that year, was likely a local phenomenon rather than an effect of the prevailing wet, cool weather of that year, because


23 -

,22 - - 30_

E 21 -0-4 4W 0 o1

19 ~~~~~0 (U 18 70~

1946 48 50 52 54 56 58 60 62 64 66 68 70

Year

FIG. 24. Comparison between the yearly fluctuation in mean daily maximum temperature (0) during the larval feeding period, 1 June to 15 July and the fluctuation in mean daily minimum relative humidity (0, inverted scale) during the estimated moth period (cf. Fig. 12) in late July to early August, recorded at the Green River field station.

it did not influence the survival in plot G4. Conversely, the even worse weather in 1950 did not have any ad- verse effect on survival in any plot, including G2. Fur- thermore, an intensive study by daily sampling in 1977 at a fir stand near Fredericton (data on file at Maritimes Forest Research Centre) revealed an extremely high larval survival rate, despite the unusually wet, cool summer of that year.

To compare survival rate and weather over a much longer period, we can use the yearly fluctuation in the log rate of change in larval density (R3) shown in Fig. 8. Simple correlation shows some degree of association between the temperature fluctuation in Fig. 23 and the secondary fluctuations in R3 about its basic oscillation. This association, however, does not imply a causal relationship. As already shown, the secondary fluctuation in R3 is due largely to a fluctuation in the log E/ M ratio (H5), which is determined in the moth stage in late July and early August, and which shows a good correlation with mean daily minimum relative humidity during that period. There happened simply to be a very good correlation between the mean daily maximum temperature during the feeding period in June to the early part of July and the mean daily minimum relative humidity during the moth period in late July to early August (Fig. 24).

Another example of spurious relation is a coincidence in trend between mean daily minimum relative humidity (Fig. 23; inverted for ease of comparison) and R3 (Fig. 8) between 1953 and 1970. However, the two series do not agree at all in the previous outbreak period between 1946 and 1952.

Fig. 25 shows the annual fluctuation in mean daily maximum temperature during the approximate period of larval feeding in various parts of New Brunswick from as many stations as had records for the 1870s onward. The larval feeding period differs among the areas where the weather stations are located (see Fig. 26). Usually, budworms develop in the province ear- liest around Fredericton, where most larvae feed usu-

ally between 15 May and 30 June. In the Green River study area, the development is 2 wk behind many other parts of the province. Therefore, the period over which the average temperature was calculated in Fig. 25 is adjusted accordingly. One of the bases for the adjustment is the phenology of spring budbreak in balsam fir, shown as a contour map in Fig. 26.

Over the period covered by the temperature records in Fig. 25, there were four known province-wide outbreak periods at about the times indicated by the arrows (cf. Fig. 3). As we see, there is no particular pattern, such as a succession of warmer summers, associated with the initiation of these outbreaks. Fur- ther, to compare with the argument of the earlier work- ers already cited, I took as an example the 5-yr moving averages in the Chatham weather data of Fig. 25, which by themselves cannot be distinguished from a pure random series by a simple run test. The resultant moving-average series (Fig. 27) tends to oscillate because of positive autocorrelations that do not exist in the original series (details in Appendix 5). Again, there is no particular association of the four outbreaks with the "smoothed" weather changes, except for a vague tendency for some years of on-average cooler weather following an outbreak that might have been associated with the decline ofthe budworm population. This point will be discussed in the section on the "fifth agent." (Oscillations could be created artificially by taking moving averages of a pure random series of numbers; it could be misleading to compare such an artificial oscillation with a population oscillation [see Appendix 5].)

In his key-factor analysis, Morris (1 963b) found that there has been a consistent upward trend since the mid- 1 920s in mean daily maximum temperature (recorded in the City of Edmundston, 50 km south of the Green River station) during the main part of the larval feeding period, which in the Green River area usually falls between 1 June and 15 July (Morris 1963b: Fig. 18.2). I find the association to be spurious, however. The


20 . / VAX:V\FJr MVJ':" J '."V\\ 25-

20 25-

20- 25 25

.20 25-

20[ I

1880 1900 1920 940 1960 1980 Year

FIG. 25. Yearly fluctuations in the mean daily maximum temperature during the approximate period of larval feeding, since the late 1 800s in various locations in New Brunswick. From top: Fredericton (15 May to 30 June), Sussex (15 May to 30 June), Chatham (15 May to 30 June), Chatham (25 May to 1 0 July), Bathurst (Dalhousie, -----;20 May to 5 July), Grand Falls (15 May to 30 June), Edmundston (1 June to 15 July), Saint John (1 June to 15 July). Data are taken from the Monthly Record, meteorological observations in eastern Canada, Canada Department of the Environment. The arrows in the top graph indicate the occurrence of four province-wide outbreaks of the spruce budworm taken from Fig. 3.

upward trend in temperatures during the feeding period, used in Morris's analysis, was due to an upward trend in July temperatures. In many parts of the province, the budworm larvae should have completed their feeding by the end of June, and there is no such trend in the temperatures of May and June, except in the

Sussex region; in Bathurst, there was even a slightly declining trend (Fig. 25). Nevertheless, the population trend was much the same everywhere (Fig. 2).

I have argued that weather is unlikely to be a direct cause of budworm population oscillations and, hence, of outbreaks. However, my arguments do not exclude possible weather influences on larval survival. For instance, late frost, which is not infrequent in New Bruns- wick, might kill buds and thus cause high mortality among young larvae, though I have seen no concrete evidence. Near the northern limit of the budworm, such as at higher elevation on the Gasp6 Peninsula in Quebec, accumulated heat units may be insufficient in some years for complete larval development (Blais 1958). Conspicuous dips in the survival rate of old larvae (Fig. 17) might indicate some localized weather hazards, because the dips were sporadic, did not coincide in years among plots, and left no effect on survival in the following generation. Weather might also act through the efficacy of diseases. I shall discuss this in the following section.

5. Thefifth agent. -The last of the mortality factors to be discussed is a complex of viral and protozoan diseases and "death from unknown causes."

Neilson (1963) found microsporidioses and granu- losis to be the most prevalent protozoan and viral diseases, respectively, in the Green River area. Other viral diseases, such as nuclear and cytoplasmic polyhedro- ses, and bacterial and fungal diseases were infrequent.

Between 1954 and 1958, Neilson (1963) collected weekly samples of budworm larvae in plot K2, beginning from the third instar and lasting until 80% pupation, reared each collection of larvae in the laboratory for 1 wk, and examined dead larvae for diseases. He found no apparent symptoms of disease in a large proportion of larvae that died in the laboratory. More- over, because all pathogens that were identified by Neilson were of low virulence, it is not certain if those

Green _-i\Dalhousie River. 11 14

15-18 *e r 0 >Bathurst Edmundston 15-18 11-14

Grand Falls Chatham

7-10

36 Frederi on J12

516 7-0 Saint John

FIG. 26. Phenocontours of New Brunswick, numerals rep- resenting differences in timing of spring budbreak of balsam fir, Abies balsamea, in days later than that in Fredericton. Unpublished map by Forest Insect and Disease Survey (Mar- itimes Forest Research Centre).


0)1

? 202{

E 19 _ 9 I I I I I I I I I I I

1888 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980

Year

FIG. 27. Five-year moving averages of the series of mean daily maximum temperatures from 15 May to 30 June in Chatham, New Brunswick (Fig. 25), showing an oscillation caused by positive autocorrelations in the moving-average series, not existing in the original series. Arrows indicate four province-wide spruce budworm outbreaks taken from Fig. 3.

pathogens actually killed the larvae bearing them. Therefore, I treat this inadequately understood complex of mortality from diseases and unknown causes as one category, the "fifth agent, or Neilson's syn- drome."

For several reasons, it is unlikely that the fifth agent occurred only during laboratory rearing. First, spruce budworm larvae are well known among entomologists as easy to rear in the laboratory, and, of course, Neilson took the ulmost caution in rearing his larvae. Second, Neilson took weekly samples, reared the larvae individually for 1 wk, and obtained consistent results. The third and most interesting reason is a similarity in frequency between total field mortality and the combination of field parasitism and fifth-agent mortality in Neilson's study. This suggests that the fifth agent was also operating in the field.

In Tables 4 and 5, I list gross field mortality (l00q. of the life tables) and parasitism as well as fifth-agent mortality, as determined by Neilson in samples taken from plot K2; Table 4 is for old larvae, and Table 5 is for pupae. The gross mortality, 1 00q, in Table 4 is related to the survival of old larvae, H3 in Fig. 7c, by q_ = 1 - exp(H3). In the last column of each table, I have combined parasitism and the fifth agent by the

TABLE 4. Total stage mortality (1 00q_), parasitism, and mortality due to the fifth agent, in old larvae from plot K2 in Green River area.

Union of parasitism? and fifth

Year IOOq* Parasitismt Fifth agentt agent Percentage

1954 69 19 54 63 1955 31 26 14 36 1956 57 18 76 80 1957 87 1611 49 57 1958 84 34 66 78 * log(l -q_) = H3 in Fig. 7. t Same as in Table 3 (bottom row). : Sum of "total diseased" and "unknown" determined by

laboratory rearing in Neilson (1963: Table 38.5). ? Union = p + q - pq, where p = proportion parasitized

and q = proportion succumbing to the fifth agent. 11 Substituted for by the KI data.

right-hand side of Eq. 5 in which q now represents the fifth-agent mortality. Note that the combined effect is the union p + q - pq rather than the simple sum p + q, because the pq proportion of larvae could have been parasitized as well as "diseased" (for details, see Roy- ama 198 lb).

Clearly, the gross field mortality (l00qj) and the combined (union) parasitism and fifth agent are not only in the same magnitude for the stages concerned; their yearly fluctuations are also similar. In other words, the gross field mortality in K2 in those years was mostly attributable to parasitism and the fifth agent. (The calculated union of these two factors sometimes exceeded the 1 00q. values, because the factors were estimated independently.) Since I have raised all conceivable mortality factors and have eliminated unlikely causes, the fifth agent combined with parasitism would seem to be the only possible driving force of oscillations in the budworm population.

Currently, E. Eveleigh and I are conducting very intensive field studies in a fir stand heavily infested by budworm near Fredericton. So far, we have found that mortality in feeding larvae has been almost totally attributable to the 50-60% parasitism, which has been increasing only slowly in the last 3 yr. This rate of parasitism, though higher than those observed in the Green River area during the 1950s (Table 3), is not high enough to reduce the budworm populations. The operation of another agent is essential for the populations to decline from the current outbreak level.

Some diseases, like typical insect parasitoids, can build up over several generations as the host population increases, to induce a host-disease oscillation (An- derson and May 1979), though the role of diseases in the budworm system is not as certain as the Anderson- May model. Potentially important microbials in the spruce budworm are summarized in Dimond (1974) and Burke (1980), but the roles of microbials in ending a budworm outbreak have not been documented. Some species of Microsporidia, though of low virulence, are common protozoan parasites of budworm that have the properties of a second-order density-dependent mortality factor because they spread by oral transmission among feeding larvae within a season, and then


TABLE 5. Same as Table 4 but for the pupal stage.

Union of parasitism and fifth

Year l 00q* Parasitismt Fifth agent agent

1954 42 18 20 34 1955 26 5 17 22 1956 42 9 30 37 1957 54 4 35 51 * log(l - qx) = H4 in Fig. 7. t C. A. Miller (Maritimes Forest Research Centre, personal

communication).

are transmitted transovarially to the next generation (Thomson 1958). Thomson (1960) and Wilson (1973, 1977) observed steady increases in the rate of infection by Microsporidia over several generations during the 1950s and 1970s in Uxbridge, Ontario. The host populations, however, were not monitored quantitatively in either study.

In his experiment, Neilson (1963) found that both diseased and "undiseased" deaths were inversely correlated with rearing temperature, and that the effect of temperature was greater on starved larvae than on well- fed ones. These results are not necessarily inconsistent with the apparent lack of relationship between the field survival of larvae and the weather pattern, which has already been discussed. If population oscillation is due to second-order density-dependent factors, the influence of density-independent agents that are not a cause of population oscillation might not show clearly in simple correlation (Royama 1981 a).

Another possibility for "unknown causes" that Neil- son (1963) considered was intrinsic physiological vigor, which decreases with increasing population density (Franz 1949, Chitty 1960, Wellington 1960) through endocrinological, behavioral, or genetic changes (Christian and Davis 1964, Pimentel 1968, Krebs 1971). No positive evidence for these mechanisms has been reported for budworm population dynamics as far as I am aware, though the possibility cannot be excluded.

Frequency of moth invasions

Some ecosystem models (e.g., Peterman et al. 1979) have assumed that if food (foliage) is plentiful, spruce budworm outbreaks can be "triggered" by mass invasions of egg-carrying moths from outside, because the invaders upset the assumed endemic equilibrium state of local populations. However, this assumption is not substantiated by the Green River data.

In plot G4, extra eggs gained from immigrants (indicated by E/M ratios much greater than the mean potential fecundity) occurred in 1946, 1947, 1949, 1953, 1955, and 1956 (Fig. 10, top graph). The high value of R3 (the log rate of change in larval density) in Fig. 8 for the years 1956-1972 indirectly indicates the gain of extra eggs, because the secondary fluctuation in R3 about its principal oscillation (smooth curve) is highly

correlated with the fluctuation in H5 (see Analysis of life-table data: climatic influence on E/M ratio). Thus, the R3's distinctly above the smoothed trend line in Fig. 8 (marked with arrows) indicate moth invasions in those years. Clearly, invasions were frequent, and they seem to be as frequent during the decreasing phase of the population oscillation as during the increasing phase. (The graph after 1972 in Fig. 8 is not a reliable indicator of invasions, because it is based on the average egg-mass density determined from small samples taken from sample points scattered over a wide area; the averages probably do not give resolution as high as did intensive sampling at a particular plot.)

It is particularly important to note that during the declining phase in plot G4 the population increased each spring following a moth invasion the previous fall, as in 1954, 1957, and 1961 (Fig. 1), but that the invasions did not reverse the overall declining population trend, even when the local food supply was still plentiful (for further discussion, see Synthesis: amplitude of oscillations and outbreak frequency). In view of the facts that the population trend was the same over wide areas (Fig. 2) and that gains of extra eggs in a local population (as in G4, Fig. 8) were far more frequent than occurrences of outbreaks, the idea that moth invasions initiate outbreaks is not as attractive as I once thought (Royama 1977, 1978).

SYNTHESIS OF BUDWORM POPULATION DYNAMICS

Translating the results of the foregoing analyses into a simple time-series model allows me to explain the following features of spruce budworm population dynamics: synchrony of oscillations between local populations, frequency and spread of outbreaks, regularity and irregularity of population cycles, and maintenance of local density-dependent population oscillations under perturbation from moth dispersal.

I consider an idealized situation in which basic prob- abilistic properties of population processes do not change in time, so that even a very simple model, necessitated from our limited knowledge, can provide insight. We can make the above idealized situation compatible with actual population processes by care- fully selecting the spatial units in which we define populations.

If we were to consider the population process in a very small forest stand, we would find that a severe outbreak might destroy the stand, and the budworm population would then become extinct. Subsequent regeneration and growth of a new forest stand would not ensure the stationarity of the local population process. Moreover, we have little knowledge of the influence of forest regeneration processes on the growth of a budworm population. If, on the other hand, we considered too large a geographical area, then environmental heterogeneity, such as differences in weather patterns, would probably be too high for simple models to de-


scribe the population processes without undesirable complications.

Thus, I consider populations in areas large enough that changes in some local stands within each area in one way over time are compensated for by changes in the other way in other stands within the same area. Therefore, the average characteristics of the area as a whole do not change drastically in time. An area as large as one block on the map in Fig. 2 is probably a convenient size for my argument (though a few large- scale outbreaks, such as the recent one on Cape Breton Island, Nova Scotia, may destroy forests over a much larger area). I also consider that budworm density is measured on the foliage of living trees, so as to avoid complications arising from the effect of tree mortality.

A simple model Let us approximate the dynamics of budworm pop-

ulations by a second-order density-dependent process of the general form

Rt =J(N, N, 1) + zt, (6)

where Nt is the log population density of the tth generation (it need not specify the stage), and zt is the net effect of all density-independent factors involved during the tth generation. Rt = Nt+ - Nt, as in Eq. 3. I now equate the function f in Eq. 6 to the density- dependent component of the log generation survival rate (Hg) in Eq. 2, and equate the log E/M ratio (H5), combined with the temperature-dependent efficacy of the fifth agent, to major elements of the density-independent term z.

Because the function f in Eq. 6, which is probably nonlinear, is difficult to determine from our limited knowledge, I further take a linear approximation of the function for simulation purposes; that is, I use the linear second-order autoregressive model

Rt= aONt + aIN,1 + zt, (7)

in which ao and a, are constant. Note that the log survival rate (Hg) is nonpositive, but the above linear approximation might violate this constraint. There- fore, I restrict most of my arguments to a qualitative level, so as to remain within the realm of this approximation.

Synchronized population oscillations and the role of climate

Moran (1953), in his statistical analysis of the Can- ada lynx (Lynx canadensis) cycles, proposed the idea that density-independent climatic influences, if correlated between localities, could synchronize local populations that are oscillating independently because of factors intrinsic to each population. This important idea, however, did not attract much attention from ecologists. As reviewed in Royama (1977, 1981 a), the autoregressive model of Eq. 7 can generate oscillations of various lengths, if the values for ao and a, are suit-

ably chosen. Simulations that use this model demonstrate Moran's idea.

In Fig. 28, I generated three sample series by Eq. 7 with the same ao and a, values that are conveniently chosen for simulations. The density-independent z's in each series are uncorrelated (zero autocorrelations) random numbers, uniformly distributed in the interval (-0.5, 0.5). The series a and b are started with an identical initial state (N1, N2), but the z's are independently generated and so are uncorrelated between the two series. These series simulate a situation in which two local populations that have a common density- dependent (endogenous) structure are under mutually independent climatic (exogenous) influences. We see a strong resemblance in their cyclic patterns due to their common endogenous structure, but the populations do not oscillate in unison, because of the independent exogenous influences. They come into synchrony occasionally, but only by coincidence.

Series c in Fig. 28 has the same endogenous structure (identical a-parameter values) as the other two series. The distribution of the density-independent z, term is also the same as in the other two series, except that zt in series c is correlated with zt in series b; the correlation coefficient is t0.7. Although series b and c were started completely out of phase, they came into phase quickly, and remained in phase thereafter. This suggests that local budworm populations that oscillate independently (due to density-dependent generation survival) can be synchronized under the influence of nonoscil- lating but correlated weather (among localities) that governs the E/M ratio and, probably, the efficacy of the fifth agent. Well-correlated weather patterns over New Brunswick are exemplified by the annual fluctuations in temperature shown in Fig. 25. Nonetheless, a degree of asynchrony always exists between series b and c. This is analogous to an increase in budworm populations in the southeastern corner that was slightly earlier than in northern areas of New Brunswick (Fig. 2).

Amplitude of oscillations and outbreak frequency

The simulated populations in Fig. 28 cycle fairly regularly, because their second-order density dependence yields periodic autocorrelations. However, the amplitude of an oscillation varies considerably from cycle to cycle under the influence of the density-independent z term. An oscillation that happens to ex- ceed the dotted line in each graph of Fig. 28 represents a hypothetical outbreak. We see then that the occurrence of outbreaks greatly depends on the random nature of the E/M ratio as a major element of the z term.

The periodicity of the autocorrelation functions (cor- relogram) of a stationary autoregressive time series is known to be uninfluenced by temporally uncorrelated exogenous perturbations (zt in Eq. 7). This implies that the average length of a local budworm population cycle


is determined by the density-dependent larval survival, not by the E/M ratio fluctuating at random from year to year. Frequent, high E/M ratios can enhance the amplitude of an oscillation to an outbreak level, but only when the population is in an upswing phase of a cycle due to high larval survival. High E/M ratios would not, however, readily reverse the population trend, once larval survival has started decreasing; high E/M ratios were observed in 1954, 1957, and 1961 on plot G4, but the population decreased, nevertheless (Fig. 1). Thus, the seed of an outbreak lies in the intrinsic density-dependent structure, most likely in the survival of old (feeding) larvae, while moth invasions (high E/M ratios) act only as fertilizers, so to speak.

Notice that not all peaks in the series b and c in Fig. 28 exceeded an outbreak level simultaneously, and that outbreaks happened to occur more often in series b than in series c. In other words, even if the phases of population oscillations are well synchronized among localities, the amplitudes need not be correlated as well. Further, outbreaks happened to occur more regularly in the latter half of series b than in the earlier half. These results in the simulation may explain differences in the outbreak frequency across eastern Canada from Ontario to Newfoundland, such as the fairly regular occurrences of outbreaks in the past few centuries in New Brunswick and Quebec (Fig. 3) and the rather sporadic ones in other regions (Blais 1965).

A particularly instructive lesson of the simulations is that an alternation between intervals of regular and sporadic outbreaks does not necessarily imply some fundamental changes in the environmental conditions or in the structure of the population processes. Simply, the random variation in the E/M ratio alone can cause such alternations in population cycles. There is a possibility, though not highly credible, that the nonlinear process of the actual budworm population dynamics may exhibit stable oscillations, such as limit cycles. If so, a rather more regular occurrence of outbreaks could be expected than from the present simulations, because the simple linear model employed here is unable to generate limit cycles.

Initiation and spread of outbreaks Spruce budworm infestation maps in eastern Canada

(Brown 1970, Kettela 1983) might appear to support a widespread notion that outbreaks begin at a few scattered points, or 'epicenters,' then spread outwards, in- festing surrounding areas through moth dispersal. However, Stehr (1968) considered, in addition to the above notion, a second possibility that an epicenter might be "merely the spot at which a general and already widespread population surfaces first," but he ad- mitted that "we actually do not know today which of these radically different structures applies to the epicenters of the spruce budworm."

Close inspection of the egg-mass survey map (Fig. 2) supports the second interpretation. Budworm pop-

a

b z

C

0

C

0 50 100 150 200 250 300

Generation, t

FIG. 28. Simulated second-order density-dependent population oscillations. In each series, 300 points (N1, N2, . . . N300) are generated by Eq. 7 (R, = a0Nt + a1N11 + z1) with ao = 0.80 and a, = -0.89. Initial conditions are (N1 = 1, N2 = 2) in both series a and b, and (N1 = -1, N2= -2) in series c. The z's in each series are temporally uncorrelated random numbers distributed uniformly in the interval (-0.5, 0.5). z, in series b is uncorrelated with z, in series a, but is correlated with z, in series c. Dotted line in each graph represents a hypothetical outbreak level. For detailed explanations, see Synthesis: Synchronized Population Oscillations and the Role of Climate.

ulations were in their troughs by the early 1960s, and started increasing again thereafter just about everywhere in New Brunswick. However, in the central region (i.e., blocks B3, B4, C3, C4, and C5 in Fig. 2) the trough populations were somehow maintained at much higher levels than in any other areas of the province. Consequently, when all populations in the province increased again in the early 1970s, an outbreak level was reached in the central region sooner than in surrounding regions. The troughs of the southeastern populations (blocks A4, A5, B5, and B6 in Fig. 2) were just as low as those of the populations in the northwestern corner, but the southeastern populations somehow increased slightly earlier and reached an outbreak level sooner. On infestation maps, these areas might look like "epicenters."

To summarize, although moth immigrations might accelerate the increase in local populations and create outbreaks earlier or more frequently, moth dispersal


is unlikely to act like a vector carrying an infectious disease. Rather, dispersal acts like a fertilizer to stim- ulate the seed of an outbreak (survival of local larvae) that has already started growing in every locality.

Maintenance of density-dependent population oscillations under perturbations

from moth dispersal A comparison between the simulated populations

(Fig. 28) and egg-mass fluctuations (Fig. 2) reveals a subtle but important difference, namely that the secondary fluctuations about the principal oscillation in the actual populations look like sawteeth as compared with the smoother appearance of the simulated populations. Errors from small samples in the egg-mass survey may contribute to the sawtooth-like secondary fluctuations, but these fluctuations may primarily be a result of strong perturbations from moth dispersal.

Using the autoregressive model (Eq. 7), we can simulate strong perturbations from moth dispersal by a large variance of z. Changes in the variance, however, influence the amplitudes of oscillations but do not produce sawtooth-like fluctuations (Royama 1979). Eq. 7 can produce rapid fluctuations in density if the a-parameter values are changed, but this tends to obscure the oscillatory pattern of population cycles. The N's in Eq. 7 are local population densities, so the density dependence of the model is maintained only by local factors such as the parasitoid complex, which is unlikely to migrate with dispersing budworm moths. Un- der this assumption, the model would not produce the desired effect.

If, however, the density-dependent oscillations in budworm populations are caused largely by the fifth agent, the situation can be quite different. The fifth agent, be it of disease or of physiological origin, would travel with its carriers, the dispersing moths. If local populations oscillate in unison, under the mechanism discussed in Synthesis: synchronized population oscillations and the role of climate, the incidence of the fifth agent should coincide among these populations. Then, the exchange of moths, carrying the agent, among local populations can cause sawtooth-like secondary fluctuations without much influencing the basic oscillation caused by the density-dependent process of the populations as a whole.

COMMENTS ON SOME OTHER ANALYSES AND

THEORIES

There are two major problems with analyses by earlier authors: their treatment of density-dependent population parameters as first order, and of autoregressive-type density-dependent population processes as regressions of independent parameters. These can seriously mislead if the processes analyzed are, in fact, second or higher order (Royama 1977, 1981a); the concept of high-order density dependence was not known 20 yr ago.

In this section, I discuss (1) Morris's key-factor model, (2) Watt's (1963) analysis of old (large) larvae, and (3) the concept of dichotomous endemic and epidemic budworm populations, or the double-equilibrium theory of outbreak processes. I use my notations throughout.

Morris's key-factor model

The key-factor model of Morris (1 963b) is a linear, first-order autoregression, a special case of Eq. 7 in which a, = 0. Morris used the log initial density of old larvae (N3 in Table 1), regressed N3,+I on N3t, and estimated the coefficient of N3, (ao in Eq. 7) by least squares to obtain do = -0.24. He then found that the residuals, as estimates of the z's, were highly correlated with the mean daily maximum temperature, T (in 0F) between 1 June and 13 July, when much larval feeding occurs in the Green River area. Based on this regression, Morris formulated his key-factor model:

R3t =-0.24N3t + 0.18Tt - 10.99. (8)

Using the temperature records from the City of Ed- mundston since 1925, Morris's backward simulation with Eq. 8 yielded an oscillation that peaked around the late 1940s and more or less coincided with the observed outbreak of that period (Fig. 18.2 in Morris 1963b).

The apparent influence of Tt on R3t in Eq. 8 is spurious, however, for two reasons. First, as discussed in Analysis: influence of weather, the rise and fall in temperatures recorded in Edmundston during the above period did not occur everywhere in the province, except in Sussex, over the two centuries (Fig. 25) and cannot explain the province-wide budworm oscillations (Figs. 2 and 3). Second, as discussed in Analysis: influence of weather, R3 was only indirectly correlated with T, because: (1) T was correlated with the mean daily minimum relative humidity during the moth season (Fig. 24), (2) the mean daily minimum relative humidity influenced the log E/M ratio H5 (Fig. 11), and (3) H5 was correlated with R3 (Figs. 9 and 13).

Morris himself was not satisfied with the simulated pattern of oscillation in his Fig. 18.2 (Morris 1963b), and so proposed an alternative double-equilibrium theory. To discuss this theory, however, I must first review Watt's (1963) analysis of survival of old (his large) larvae, because his result served as support for Morris's theory.

Watt's analysis

Watt (1963: Fig. 10.4) regressed the log survival rate H3 (log of his SL) on log density N3 (log of his NL). Data taken from many study plots in the Green River area were pooled in his analysis. He then divided the density spectrum into six intervals, calculated the average survival rate in each interval, and fitted a regression curve through these averages (Fig. 10.5 in Watt 1963). Watt found "a tendency for SL to increase with


00 OLe

>0

0)

Cy$O 0:

log density FIG. 29. A schematic illustration of the relationship be-

tween the survival of "large larvae" and their initial densities in Watt's (1963) Fig. 10.5. For explanations, see Synthesis: Watt's analysis.

NL up to about NL = 120, after which SL falls again." This curious density-dependent relationship resulted from fitting a first-order model to a second-order process and pooling time-series data taken from many different plots.

As I have deduced, budworm populations oscillate because the survival rate of old larvae oscillates. Need- less to say, the survival rate tends to be highest at medium densities when the population is fast increasing, and lowest when it is collapsing. Survival is intermediate both when the population is around its peak and when it is around its trough. Thus, with an oscillating second-order population process, H3, plotted against N3, in time-series data from a given plot tends to yield an oblong circular pattern, though somewhat irregular because of random factors. Since Watt pooled all data taken from many study plots, his Fig. 10.4

comprised fractions of many such oval trajectories because in no one plot did observations cover one whole population cycle.

In many plots, observations were made roughly between peak and trough densities. As a result, the data from these plots formed the lower right quarter of an oval trajectory. These included plots K1 and K2, which had extremely high peak densities. These data points comprise an upper section of the density spectrum in Watt's Fig. 10.4. In other plots, observations were made several years after peak density, when low survival rates were accompanied by medium to low densities, so that their data points formed a bottom section of the oval trajectories. These comprise the medium to lower sections of the density spectrum in Watt's figure. Only in two plots, G4 and G5, did observations include the increasing phase of oscillations, so that their data points formed all but the lower left quarter of the oval trajectories. Thus, average survival rates in these plots were comparatively high. Their data points comprise a middle to upper part of the density spectrum in the figure.

I have idealized the above situation in Fig. 29. It would be misleading to draw a single regression curve through the data points pooled without regard to the cyclic survival of larvae. Populations in different plots did not oscillate with similar amplitudes. In the K plots, for example, peak densities were very high because the larval survival was somehow very high during the population increase. In the G plots, on the other hand, the larval survival rates were not as high, and peak densities stayed comparatively low. Thus, higher survival rates produce higher peak densities, and then

1OO

Co 0=

E0

"E50

31. ~~~~~ . l

0

1945 1950 1955 1960 1965 1970 1975 1980

Generation year

FIG. 30. The same as Fig. 1, but density (number/M2 of foliage) is plotted on a linear scale.


some second-order density-dependent mortality factors eventually reduce the survival rate. Thus, the cause- and-effect relation is reversed between Watt's interpretation and mine.

Dichotomy of endemic and epidemic populations: the double-equilibrium theory

A first-order density-dependent process, i.e., a, = 0 in Eq. 7, will not cause the population to oscillate unless the density-independent factors involved, z in Eq. 7, oscillate (Royama 1981a). Thus, fitting a first-order model to an oscillatory data series will necessarily yield an oscillatory series of residuals and would lead one to look for some oscillatory density-independent factors.

Morris (1963b) noted that his key-factor model with oscillating temperature did not adequately simulate an endemic state of budworm populations during the 1 930s. Therefore, while still maintaining his model's first-order properties, Morris nonlinearized it in such a way that a curvilinear regression of N,+1 on N, (known as Ricker's [1954] reproduction curve) crosses the 450 line (on which N,+1 = N,) at two points from above (Fig 18.3 in Morris 1963b), forming two locally stable equilibrium points. In between these two points the reproduction curve crosses the 450 line from below. This is an unstable equilibrium point, or a "release" point, above which the population increases to the upper equilibrium point. If the population overshoots, an epidemic or an outbreak may result. However, after years of defoliation and subsequent destruction of the forest, the population recedes to a lower level, where it is again within the endemic equilibrium region. Mor- ris considered that the endemic equilibrium could be maintained by predators (e.g., birds and spiders) and parasitoids. However, he thought that even the combined effect of these natural enemies would not stem a rapid increase of budworm populations under a series of favorable weather conditions, and, hence, that "population release" would occur sooner or later. I once supported this theory and even generalized it to the second-order level (Royama 1977, 1978), but after careful examination, I have abandoned the idea for the following three reasons.

First, the apparent existence of an endemic state between the two recent outbreaks in the Green River area is mainly due to poor data resolution at low densities when these are plotted on a linear scale (Fig. 30). The same data, when plotted on a logarithmic scale (Fig. 1), give higher resolution and show no clear sign of an endemic equilibrium; the population simply decreased and then increased without any sign of negative feed- back. There is no reason to believe that this Green River situation was exceptional among the low-density situations between outbreaks over the past two centuries (reconstructed in Fig. 3).

Second, Morris's model assumes that a transition

from endemic to epidemic states occurs when weather favors larval survival during the feeding stage. Con- versely, a transition from epidemic to endemic states in the model is dependent on heavy defoliation and resultant food shortage. However, as I have argued in detail, the survival of feeding larvae does not seem to respond sensitively to weather changes (unless, possibly, the larvae are "diseased"), and food shortage is not a universal cause of population decline.

Third, Morris considered that his reproduction curve along the 450 line was of the same form as the survival- density curve of Watt's Fig. 10.5; both curves rise first and then fall as density increases. Morris argued that Watt's curve did not rise toward the lower end of the density spectrum only because the data did not include sufficiently low density situations. However, as already discussed, Watt's curve does not imply a causal effect of density on survival and, therefore, is irrelevant to the question of shape in Morris's reproduction curve.

Thus, there is no reason to assume the dichotomy of endemic and epidemic equilibrium states nor to build a model on that assumption. My hypothesis of a second-order density-dependent process with only one equilibrium point is consistent with the evidence and more parsimonious for describing the dynamics of spruce budworm populations.

ACKNOWLEDGMENTS

Many people from the Canadian Forestry Service contributed, directly and indirectly, to the completion of this paper. All original members of the Green River Project provided the life-table data. In particular, Charles A. Miller and David 0. Greenbank, both now retired, freely shared their first-hand knowledge and experience. Anthony W. Thomas spent his time in frequent and involved discussions with me during the last few years and also provided some of his unpublished data. Discussions with Jacques Regniere resulted in the dis- covery of the framing bias in estimating survival rates in young and old larvae. Harold Piene and David A. MacLean provided information on the impact of budworm defoliation on the host trees. Edward G. Kettela provided his egg-mass data. Graham Page, Eldon Eveleigh, David MacLean, and Tony Thomas read the manuscript. I owe Michael L. Rosen- zweig, University of Arizona, Stuart L. Pimm, University of Tennessee, and an anonymous referee thanks for their comments. Finally, I thank Donald Strong for his most useful advice on improving the manuscript.

LITERATURE CITED

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Balch, R. E., and F. T. Bird. 1944. A disease of the European spruce sawfly, Gilpinia hercyniae (Htg.), and its place in natural control. Science in Agriculture 25:65-80.

Baskerville, G. 1976. Report of the task-force for evaluation of budworm control alternatives, prepared for the Cabinet Committee on Economic Development, Province of New Brunswick. Department of Natural Resources, Fredericton, New Brunswick, Canada.

Blais, J. R. 1953. Effects of the destruction of the current year's foliage of balsam fir on the fecundity and habits of flight of the spruce budworm. Canadian Entomologist 85: 446-448.

1958. Effects of defoliation by spruce budworm on


radial growth at breast height of balsam fir and white spruce. Forestry Chronicle 34:39-47.

* 1962. Collection and analysis of radial growth data from trees for evidence of past spruce budworm outbreaks. Forestry Chronicle 38:474-484.

. 1965. Spruce budworm outbreaks in the past three centuries in the Laurentide Park, Quebec. Forest Science 11:130-138.

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APPENDIX 1 GENERALIZATION OF EQ. 4

Migration and mortality of moths occur over the entire adult period, say, k days. Also, the average number of eggs carried by a moth in any one day tends to decrease toward the end of the period, either because the average fecundity of a moth tends to decrease as its date of emergence gets later in the season, or because a moth lays its eggs in batches over


several days, during which batch size decreases. The product fip, is then taken to be the scalar product of the two k-element vectors fi and Pi, in which the Pth elements off and Pi are, respectively, the mean number of eggs still carried by the moths in the plot on day i and the mean proportion of that number laid in the plot. The product yields the weighted average of the effective preemigration oviposition over the

k

period of k days, i.e., zf tip1i. The productf2p2m can likewise ill

be taken to be a matrix representation of the weighted average k

A f2p2m. Thus, this general situation can be represented by ill

Eq. 4 without changes in its form.

APPENDIX 2 MORTALITY OF MOTHS AND AVERAGE

OVIPOSITION RATE A female moth normally lays its eggs over several days and,

if she dies young, has more unlaid eggs. Thomas et al. (1980) collected dead and dying moths on drop trays and examined the number of eggs still retained by them. Collection was made daily during the moth period in 2 yr at three study plots. Since the full complement of eggs of a female is highly correlated with her wing length, it is possible to estimate the proportion of eggs already laid by the dead females. Females that died early in the season had laid only a fraction of their full complement, and the average proportion of eggs laid increased steadily for the 1 st 10 d or so in each season. Only after 2 wk or more into the moth season had most of the dead females laid most of their full complement of eggs. In the three plots, the average oviposition rates were 70, 80, and 90% of the potential fecundity. The calculation did not consider moths, if any, that were preyed upon by birds, et cetera. The actual oviposition rate could therefore be even lower. Moreover, the females that died early were more likely to have emerged locally, and the females that died later probably included immigrants. Therefore, even if no emigration took place, and in conjunction with bird predation, the effective oviposition rate of the local females could be lowered to the range of 60- 80%. However, the rate would not be much lower, because females lay ;50% of their eggs usually within 2 d after mating (Outram 1973), which occurs mainly within a day of eclosion (Outram 1971). Heavy mortality within these first few days of adult life would be unusual.

APPENDIX 3 "CORRELATION" BETWEEN E/M RATIO AND DENSITY

Consider a pair of consecutive points in the series of N1, (log egg density, Fig. 9d), e.g., N, and N,+1 (stage subscript one is dropped until needed). Take the difference N,?1 - N, and write this ANt, and further take the difference of differences AN, - AN,, and write this A2Nt, i.e.,

A2Nt = ANt- Nt_=Nt-2N, + N-1. (A 1)

Now connect, by a line, N, 1 to N, and N, to N,+1 and observe if the line NN?+ 1 'swings' clockwise or anticlockwise in relation to N, 1N,. A clockwise swing means that AN, is less than AN,-,, or A2N, is negative; a positive A2N, indicates an anticlockwise swing. Next, observe that as NN,+1 in Fig. 9d swings clockwise or anticlockwise, the corresponding seg- ment HtH+?1 in Fig. 9c tends to swing otherwise; a better example is given in a simulation in Royama (198 la: Fig. 6). In other words, A2N, and A2H, tend to have opposite signs, or the covariance between them is negative. I show how this happens on the assumption that H5, (log E/M ratio) is a series of uncorrelated random numbers generated independently of N1, (log egg density) and of N5, (log moth density).

By the definition h5, = nlt+l/n5t given in Table la, H5t = Nl t+ - N5. Then, H5t should be positively correlated with Nlt+l, because H5t is independent of N5t by the above assumption. Also, in Eq. A1, A2Nt contains Nt+1 - 2N, and A2Ht likewise contains -2Ht + Ht-1. It follows that the covariance between A2Nt and A2Ht would be negative, unless the covariance between Nt+1 and Ht-1 is very large, which is unlikely. This explains why H5tH5,t+l and N1tN1,t+l tend to swing opposite ways. But, if this happens all the time, it is obvious that H5t is inversely correlated with Nlt when both series fluctuate without trend, even though H5t was generated completely independent of N1t.

APPENDIX 4 ESTIMATION OF BIAS IN H2

Let "2 be an estimate of H2 adjusted to the zero deviation of the date sampled, and let Z(D) be the adjustment term, such that

H2 = H2 + Z(D), (A2) in which D is the deviation in days, shown as 0 in Fig. 19; Z(O) = 0 by definition. We wish to estimate Z(D). One way

02 - E 0

(U (U 0 00~~~ 0 0

. -2 OA

M 0 A~~~~~~~~~~~~

0~~~~~~~~~~~~ -4

-3 N

-15 -10 -5 0 5 10 15 20

D, relative timing of L3 sampling (days)

FIG. Al. A graphical method of calculating corrected survival rate of young larvae (H2) in Fig. 20. D is the relative timing of L3 sampling in days (Fig. 19), and Z(D) is the adjustment term defined in Eq. A2 in Appendix 4. For explanations, see Analysis by stage survival rates.


to do this is to regress H2 on D; that is, to regress a 0 in Fig. 19 against the corresponding 0 in each plot. A regression curve was drawn by eye in Fig. Al. The regression is curvilinear, presumably because the later the date in relation to the reference point (i.e., the mid-date between the peak L3 and L4 stages), the steeper the slope of population decline (cf. Fig. 18), and vice versa. This regression curve is taken to be the function Z(D), so that the projection of the point for D = 0 on a vertical axis gives Z(O) = 0. Thus, Z(D) for any given D can be read on the right-hand axis in Fig. Al. H2 for that D is then given by Eq. A2.

APPENDIX 5 A NOTE ON MOVING-AVERAGE SERIES

A trend in a time series, if any, can be made more apparent by taking the moving averages of an appropriate length, a method known as smoothing or filtering. The method is effective in bringing out a true trend. Caution is needed, however, in employing this method, because an artificial trend can be created. A series of h-point moving averages taken

from a completely uncorrelated random series (hence, no trend) tends to exhibit a pattern of oscillation, known as the Slutzky effect. This is because in an h-point moving-average series, two points that are k points apart from each other are positively correlated with each other for k < h, since they share h - k points in the original series in common. This tends to result in a tendency for the derived moving-average series to stay on one side of the mean level (set by the original uncorrelated series) for some time before crossing over to the other side of the mean level. This tendency gives the impression of an oscillatory pattern. However, the oscillations have no fixed periodicity.

The budworm oscillations, on the other hand, are more like a "stochastically periodic" or "pseudoperiodic" density-dependent process whose autocorrelation coefficients have a fixed periodicity when plotted against time lags; i.e., the distance between two time points to be correlated. The pattern of oscillation generated by this mechanism (Fig. 28) gives a much more "regular" appearance than the moving-average series of weather records (Fig. 27).

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