Interactions in a tritrophic acarine predator-preymetapopulation system IV: effects of host plantcondition on Tetranychus urticae (Acari:Tetranychidae)

GÖSTA NACHMAN1,* and ROSTISLAV ZEMEK2

1Department of Population Ecology, Zoological Institute, University of Copenhagen, Universitetsparken15, DK-2100, Copenhagen Ø, Denmark; 2Institute of Entomology, Branišovská 31, CZ-370 05, C{eskéBudejovice, Czech Republic; *Author for correspondence (e-mail: gnachman@zi.ku.dk; phone: +45 3532 12 60; fax: + 45 35 32 12 50)

Received 23 January 2001; accepted in revised form 11 July 2001

Key words: Beans, Density-dependence, Dispersal, Plant condition, Population growth, Tetranychusurticae, Two-spotted spider mites

Abstract. Feeding by spider mites can cause severe injury to a host plant and lead to a decreasing percapita growth rate and an increasing per capita emigration rate. Such density-dependent responses tolocal conditions are important in a metapopulation context because they allow the herbivores to colo-nize new host plants and thereby prolong the time until regional (metapopulation) extinction. In order toinclude density-dependent responses of the two-spotted spider mite (Tetranychus urticae) in a realisticmetapopulation model, a series of greenhouse experiments was conducted with the purpose to quantifyhow the condition of bean plants (Phaseolus vulgaris) influences the demographic parameters of T. ur-ticae. Plant age per se reduced the growth rate of the spider mites only slightly, whereas the growth ratedeclined significantly as the plants were injured by the mites. The relationships between plant condition(expressed by the plant injury index D) and the birth and loss (death + emigration) rates of the miteswere quantified so as to predict population growth as a function of D. Maximum per capita growth rate(r) was estimated to be c. 0.21 day−1. The growth rate is expected to be negative when D exceeds 0.8.When mites were allowed to emigrate to neighbouring plants via bridges, the per capita emigration rateincreased almost exponentially with D. The proportion of eggs in the population decreased with D whilethe numerical ratio between immatures to adults and the sex ratio did not change with D. Overall, im-matures and adults constituted 74% and 26%, respectively, of the active mites and c. 46% of the adultswere males. The bridges that connected a donor plant with the surrounding recipient plants were re-sponsible for the majority of the emigrations from donor plants. Most mites stopped after having crosseda single bridge, but a few crossed two bridges while none crossed three bridges within 24 h. The sig-nificance of the results for biological control is discussed.

Introduction

Spider mites are among the most serious crop pests in the world (Tomczyk andKropczynska 1985; Helle and Sabelis 1985). They inflict injury to plants by meansof their needle-shaped mouthparts that are injected into leaf tissue and used to suckout cell fluids (Liesering 1960; Tomczyk and Kropczynska 1985). In large num-

Experimental and Applied Acarology 26: 43–70, 2002.© 2002 Kluwer Academic Publishers. Printed in the Netherlands.

bers, spider mites are able to cause substantial leaf necrosis, which may affect thegrowth and yield of the infested plants (Tulisalo 1970; Tomczyk and Kropczynska1985; English-Loeb 1990; Skovgård et al. 1993a; Wilson 1993). However, as aplant deteriorates, its quality as food for the spider mites also declines, which maycounteract their population growth (Wrensch and Young 1974; Krainacker andCarey 1990; Skovgård et al. 1993b; Wilson 1994). If the negative feed-back be-tween plant condition and the growth of a spider mite population is strong enoughit may prevent the pest from overexploiting and killing the host plants. This seemsto be the case for the cassava green mite (Mononychellus tanajoa (Bondar)) attack-ing cassava (Skovgård et al. 1993b), but not for the two-spotted spider mite (Tet-ranchus urticae Koch) attacking e.g. cucumbers and beans (Hussey and Parr 1963a;Pallini et al. 1997). If a host plant is very vulnerable to spider mites (or other pestspecies), it shortens the time in which control of the pest can take place. Especiallyin case of biological control, the timing between a herbivore pest and its naturalenemies can be decisive for whether the pest surmounts the plant or not and for theextent to which the pest reduces the crop yield. For instance, at 25 °C T. urticae hasan intrinsic rate of natural increase (rm) of about 0.25 per day (Sabelis 1985), whichmeans that a single individual has the potential to produce about 40 million off-spring in less than 10 weeks. Even though this number will not be reached in prac-tice, it is far above what is needed to overexploit and kill the host plant. Therefore,an effective natural enemy should be able not only to reproduce at a high rate, butalso to localize and destroy local populations of prey before they manage to causesevere injury to the host plant. Experiments have shown that the phytoseiid preda-tor Phytoseiulus persimilis (Athias-Henriot) possesses this capacity (Nachman1981) provided the predators can move easily among the plants (Nachman 1999).However, if the predators become too efficient they may risk to overexploit theirprey at both the local and the regional scale (e.g in a greenhouse) unless prey in-dividuals can escape adverse local conditions (low food quality and/or high preda-tor density) by moving to better host plants. A prerequisite for long-term coexist-ence of prey and predators is that colonization rates on average balance extinctionrates of both species. This type of non-equilibrium dynamics (called “hide-and-seek”) has been modelled by means of a spatially explicit stochastic simulationmodel (Nachman (1987a, 1987b); Walde and Nachman 1999). In order to param-eterise this model for T. urticae and P. persimilis inhabiting a multi-plant bean sys-tem, empirical data on local and regional dynamics are needed.

This article concentrates on investigating how host plant condition affects localpopulation growth and emigration of T. urticae in the absence of predators. Theeffect of spider mites on host plants (Phaseolus vulgaris L.) was studied in Nach-man and Zemek (2001), while the dispersal of P. persimilis in response to densityof spider mites was described in Zemek and Nachman (1998, 1999). The combinedeffect of plant condition and P. persimilis on the density of T. urticae will be thetopic of a following paper (Nachman and Zemek, in prep).

Several studies have shown that plant condition affects both the growth rate andthe dispersal rate of spider mites (Wrensch and Young 1974; Bernstein 1984; Smit-ley and Kennedy 1985; Krainacker and Carey 1990; Li and Margolies 1993), but

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none of these studies provide quantitative relationships between the degree of plantinjury and these demographic parameters.

Materials and methods

General description of the experiments

In all experiments beans, Phaseolus vulgaris L. Bon-Bon from L. Dæhnfeldt Ltd,were used as host plant for the two-spotted spider mite, Tetranychus urticae Koch.The plants were grown in greenhouses under the same conditions as described inNachman and Zemek (2001). Most statistical analyses were done by means ofSAS™ for Windows version 6.12 (SAS Inst. 1994). However, circular data wereanalysed by means of a randomisation programme developed by Zemek and Nach-man (1999).

Effect of plant age on spider mite population growth rate

The purpose of this experiment was to test whether plant age has an effect on thepopulation growth rate of T. urticae. Five groups of five pots with bean plants wereused for the experiments. The groups differed with respect to plant age, since theplants were sown with intervals of two weeks. On the same day, when the plantswere 3, 5, 7, 9 and 11 weeks old, respectively, they were inoculated with 10 adultfemale spider mites per pot. Two weeks later all leaves were detached and the spi-der mites (eggs, immatures, adults) occurring on the underside of the leaves werecounted under a dissecting microscope. The area and leaf damage index (LDI) ofeach individual leaf were also recorded (see (Nachman and Zemek 2001)). The av-erage per capita growth rate of the spider mites, r, measured from the day of in-oculation (t = 0) to day t, when the experiment stopped, was estimated as (see e.g.Odum (1971))

r �1

tln�Xt

X0� (1)

where Xt denotes the number of mites on the plant at day t and X0 is the initialnumber (10 individuals). Note that since r also includes losses due to emigration, itmay underestimate the growth rate compared with a completely isolated popula-tion.

Effect of host plant condition on population growth of spider mites

Data from the previous experiment were used to estimate the rate at which a spidermite individual extracts chlorophyll from leaves of the host plant. The rate (ex-pressed as the amount of chlorophyll extracted per mite and time unit) is denoted

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�. It is estimated from the relationship (Appendix 1)

Lt � �Mt (2)

where Lt is the amount of chlorophyll the plant has lost after having been exposedto Mt mite-days. Mite-days is defined as the cumulated number of mites occupyinga given spatial unit (which in the present case is a plant) from day 0 to day t (cf.Hoyt et al. (1979)).

The empirical value of � was found from Equation (2) as the slope of the straightline passing through the origin when fitted by linear regression to empirical valuesof Lt and Mt. For a given plant, Lt was estimated as

Lt � cmax �i � 1

n

Ai � �i � 1

n

ciA (3)

where Ai is the leaf area of the i’th leaf, ci its chlorophyll concentration (�g/cm2),and cmax the maximum chlorophyll concentration, that is, if no feeding had takenplace. ci was not measured directly but estimated from the leaf damage index (LDI)as

c � cmaxe � a�LDI�bˆ

(4)

where cmax � 22.945�g/cm2, a � 0.059 and b � 1.453 (see Nachman and Zemek(2001)). Mite-days (Mt) for the same plant were calculated as (Appendix 1)

Mt �Xt � X0

r�

�Xt � X0�t

ln�Xt/X0�(5)

Equation (5) applies only as long as the spider mite population increases expo-nentially, but not when the per capita growth rate begins to decrease due to theinjury inflicted to the host plant. To incorporate the feedback between plant condi-tion and spider mites, a more sophisticated model was developed (Appendix 2). Itis based on the assumption that the per capita birth rate decreases while the percapita loss rate increases with an increase in the plant injury index D defined as

D �cmax � c

cmax � cmin

(6)

where

c � �i � 1

n

ciAi/ �i � 1

n

Ai

and cmin is the value of c if all leaves have LDI = 5 (Nachman and Zemek 2001).

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The model fitted to data predicts the density of spider mites (x) on a plant withinjury index D as

x �1

s0�b

��1 � �1 � D��� �

�

��1 � �1 � D� � ��� �x � 0� (7)

where b and � denote the per capita birth and loss rates, respectively, when D = 0and � and � are positive constants expressing the density dependent effects of D onthe growth rate. s0 is the maximum amount of leaf area a spider mite destroys perday. It is estimated as

s0 ��

cmax � cmin

(Appendix 2). The remaining parameters of Equation (7) were estimated by fittingit to data using PROC NLIN in SAS. Data consisted of the associated values of xand D obtained from the 45 donor plants used in the dispersal experiments (seebelow). Since none of these plants had very high levels of injury, six heavily in-fested plants were later added to the data to obtain more values of x for D > 0.8 inorder to show experimentally that the relationship between D and x is not monoto-nously increasing.

Dynamics of spider mites on exploited host plants

The purpose of this experiment was to follow the population growth of spider mitesas the host plants gradually deteriorated due to exploitation. In total, 50 plants wereused for this experiment. Each plant was inoculated with five adult female T. urti-cae. At two-week intervals, ten plants were sampled and all the leaves were de-tached, their leaf damage index (LDI) was assessed, mite eggs, immatures, adultmales and females were counted and the leaf area measured. Consequently, dataconsist of five groups of ten plants that had been infested with mites for 2, 4, 6, 8and 10 weeks.

Effect of host plant condition on dispersal of spider mites

The purpose of this experiment was to investigate the influence of host plant con-dition on the tendency of T. urticae to move from one plant to another. The experi-mental set-up corresponded to the way plants were connected with each other inthe multi-plant experiments described in Nachman (1999). The pots with beanplants were placed on a table as shown in Figure 1. The distance between two potsin the main cardinal directions (measured from centre to centre) was 25 cm. Onlythe central (donor) plant was infested by spider mites. The donor plant was con-nected to either eight (variant A, Figure 1) or four recipient plants (variant C, Fig-ure 1). One variant consisted of eight recipient plants of which half were connected

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(variant B, Figure 1). Connections were established by means of metal/plastic“bridges” (see Zemek and Nachman (1998) for details). Bridges were either 13 cmor 24 cm long. The latter type was used to connect plants in the diagonal. Since thetable was covered by a water-saturated blanket, mites could not easily move fromone pot to another unless they used a bridge. At the end of an experiment, the miteson the donor plant and the recipient plants were counted. The leaf area and the LDIof all the leaves on the donor plant were also recorded. Immatures, adult males andfemales were counted separately in 19 experiments, whereas the two sexes werepooled in the remaining 26 experiments to make counting faster. By a mistake, im-matures on the recipient plants were not recorded in six of the experiments witheight bridges. Since the initial number of mites present on the donor plant has to beestimated at the end of an experiment (see later), it is an advantage to make theduration of an experiment as short as possible. Otherwise, natural mortality andegg hatching (which occurs c. three days after an egg is laid) could bias the esti-mates. On the other hand, if the duration of an experiment is too short, no or veryfew dispersal episodes will be recorded, especially when the donor plant is lightlyinfested. To balance these two considerations, experiments lasted two or three dayswhen lightly infested donor plants were used, but only one day if the plant washeavily infested.

A total of 45 dispersal experiments was conducted. 30 were of variant A, 6 ofvariant B, and 9 of variant C. The unconnected pots in variant B served as a checkof the assumption that the bridges were the main mediator of mite dispersal be-tween plants. The 30 experiments of variant A served also as a check of whetherthere was any effect of bridge length on the dispersal rate. Within each experiment,the numbers of dispersing mites (immatures and adults) found on the four recipientplants connected by short bridges (N, W, E, S) and on the four plants connected bylong bridges (NW, NE, SW, SE) were summed and the difference between the twosums calculated. To test for a possible effect of bridge length, matched pairs tests

Figure 1. Experimental set-up used for estimating emigration rates, with the donor plant (filled circle)in the centre connected by bridges (lines) to the eight recipient plants (open circles) in the periphery. A:Variant with 8 recipient plants and 8 bridges; B: Variant with 8 recipient plants and 4 bridges; C: Variantwith 4 recipient plants and 4 bridges.

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were applied (sign test and Wilcoxon signed ranks test (Siegel and Castellan 1988)).Both tests control for the between-experiment variation and do not require normallydistributed data. Besides, the tests are not sensitive to the fact that the bridges maydiffer with respect to how accessible they are for the mites (i.e. dispersal events arenot independent) as long as this property is randomly distributed among short orlong bridges, which seems to be a reasonable assumption. The sign test comparesthe number of times where more mites had crossed the short bridges than the longbridges with the number of times the opposite occurred, whereas Wilcoxon’s testuses the ranks of the numerical differences between the numbers of mites found onthe two groups of recipient plants. The latter test has the highest power.

Data from the experiments with eight bridges were also used for testing whetherdispersing mites had a preferred direction of movement. The statistical analysis wasperformed by means of randomisation of the numbers of individuals recovered fromthe eight directions (see Zemek and Nachman (1999) for details). Dispersal pro-pensities of immatures and adults, and of adult males and females were comparedusing matched pairs tests (sign test and Wilcoxon signed ranks test (Siegel andCastellan 1988)).

The rate of dispersal was estimated from the data by means of a model based onthe following assumptions:

1. Individuals emigrate independently of each other.2. During an experiment, the mite population inhabiting the donor plant grows with

a constant per capita rate r.3. All dispersal takes place via bridges.4. The instantaneous rate of emigration is proportional with the number of bridges

(B)5. Immigrants on the recipient plants do not die or leave again during an experi-

ment.As shown in Appendix 3, the model implies that the per capita rate of dispersal perbridge (�) of the individuals present on the donor plant can be estimated as

� �rRt

BXt�1 � e � rt��r � 0� (8)

� �Rt

BXtt�r � 0� (9)

where Rt is the number of individuals of a given stage and sex present on the Brecipient plants at the end of an experiment lasting t time units and Xt is the totalnumber of individuals on the donor plant at time t. r estimated as

r � b�1 � D�� ��

�1 � D��

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(see Equation (18)), where the parameters have been found from Equation (7).The parameters �0 and �1, which are used to model the propensity of individu-

als to emigrate (Equation 28), were estimated from data by fitting the expression(see Appendix 3)

E�Rt� ��

r�1 � D���1 � �1 � e�0 � �1D� � B�Xt�1 � e � rt� (10)

to observed values of Rt. Finally, the expected per capita rate of emigration perbridge is found from

E��� ��

B�1 � D���1 � �1 � e �0 � �1D� � B� (11)

which can be compared with the values of � estimated directly by means of Equa-tion (8).

Effect of host plant condition on the stage distribution and sex ratio

The data from the dispersal experiments were also used to analyse whether plantcondition affects the stage composition and sex ratio of T. urticae. Three differentstages were considered: eggs, immatures and adults. The proportions of each stagerelative to all individuals are denoted pE, pJ and pA, respectively. The proportion ofeggs on the donor plant (pE) was found by dividing the number of eggs with thetotal number of individuals on the donor plant plus all the motiles(immatures + adults) on the surrounding recipient plants, since these individualsoriginated from the donor plant. The relationship between D and pE was analysedby means of logistic regression (PROC GENMOD in SAS). If data showed over-dispersion, the tests were adjusted by means of a scaling parameter (see McCullaghand Nelder (1989)). The model fitted to data was

pE �e�0 � �1D � �1D2

1 � e�0 � �1D � �1D2 (12)

where �0, �1 and �2 are parameters. The model was reduced until all included pa-rameters were significant at the 5% level.

The next step was to analyse whether the proportion of immatures (or adults) ofthe total number of motile mites on the donor and recipient plants changed with D,using the same approach as with the eggs. Since the proportions of immatures andadults can be considered as conditional probabilities, i.e. provided an individual isknown to be a motile, it is an immature with probability pJ� and an adult withprobability pA� so that pJ�+pA� = 1. The unconditional probabilities are finally ob-tained as pJ = pJ� (1-pE) and pA = pA� (1-pE). The relationship between the propor-

50

tion of males (pM = males/(males + females)) and D was also analysed by means oflogistic regression.

Dispersal distances of spider mites

The purpose of this series was to find the distance moved by spider mites afterleaving an infested plant. 18 pots with bean plants without spider mites were placedon the water-saturated blanket in a set-up as shown in Figure 2. The distances be-tween plants corresponded to those in the previous dispersal experiments. A beanplant, heavily infested with spider mites, was placed in the centre. Half of the sur-rounding pots (the recipient plants) were connected with the central (donor) plantthrough five short (13 cm) and four long (24 cm) bridges. The unconnected plantsserved the same purpose as before. An experiment lasted 24 h, whereupon all mitesoccurring on the plants were counted under a dissecting microscope. The area andLDI of the donor plant’s leaves were also recorded. Four experiments were con-ducted. They differed with respect to the position of the connected plants in orderto account for a possible effect of light/shadow on the direction of movement.

Figure 2. Experimental set-up used for estimating dispersal distances. The donor plant (filled circle) issurrounded by eighteen recipient plants (open circles) of which half are connected by bridges (lines).The numbers assigned to the recipient plants denote the minimum number of bridges required to estab-lish connection to the donor plant.

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Results

Effect of plant age on spider mite population growth rate

Figure 3 shows the per capita net growth rate (r) against the pivotal age (mid pointof an age interval) of the plants during the experiment. On one of the five 8-weeksold plants no spider mites were found at all. Since the most likely explanation forthis is that the plant by a mistake was never inoculated, it was omitted from theanalysis.

The scatter of r within each plant group was considerable, which blurred theslight decreasing trend in r with plant age. Hence, a straight line fitted to the indi-vidual observations of r was far from being significant (r2 = 0.065; t = 1.237; df = 22;P = 0.229). Overall, the 24 values of r ranged from 0.053 day−1 to 0.259 day−1 (av-erage r = 0.184 day−1; SD = 0.058 day−1; SE = 0.012 day−1).

There was no clear trend between treatments with respect to the stage distribu-tion of the spider mites when the mites were counted at the end of an experiment(Figure 4). Overall, eggs constituted 56.1%, immatures 17.8%, and adults 26.1% ofall individuals.

Figure 5 shows the loss of chlorophyll as a function of mite-days. The straightline represents the fit of Equation (2) to the untransformed data. The model ex-

Figure 3. Per capita growth rate (r) of T. urticae as a function of plant age defined as the mid-point oftwo-week intervals. The growth rate shows no time trend (r2 = 0.065; t22 = 1.237; P = 0.23).

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plained 83.9% of the variation in the observed values of Lt (t23 = 11.24; P < 0.0001).� was estimated to be 0.1453 (SE = 0.0129) �g chlorophyll mite−1 day−1.

Effect of host plant condition on the growth rate of spider mites

The maximum leaf area destroyed per spider mite individual per day (s0) was es-timated to be

s0 �0.1453

22.945 � 12.449� 0.0138cm2day � 1

Figure 6 shows the fit of Equation (7) to data from 51 plants. The parameters wereestimated as b � 0.3157 (SE = 0.1360) day−1, � � 0.1010 (SE = 0.0310) day−1,� � 0.1016 (SE = 0.0464), and � � 0.6001 (SE = 0.0012). All parameters were sig-nificantly different from 0. The maximum per capita growth rate (r) is found asr � b � � � 0.215 day−1. Figure 6 also includes data from 250 plants used in dis-persal experiments with P. persimilis (Zemek and Nachman (1998, 1999)), but inorder to avoid a confounding effect of predators these plants were not used for es-timation of the parameters of Equation (7). The fact that the model also fits theplants hosting both prey and predators indicates that the number of predators and/orthe time they had been allowed to interact with the spider mites (one day) was not

Figure 4. Relative distributions of eggs, immatures and adults of T. urticae on plants of different age.Mites were sampled fourteen days after a plant had been inoculated with ten adult females.

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sufficient to clearly separate these plants from those without predators. Figure 7shows that the model predicts a slightly decreasing birth rate and a steeply increas-ing loss rate as D increases. The two rates balance (r = 0) when D is approximately0.8.

Dynamics of spider mites on exploited host plants

Figure 8 shows the observed densities of mites (all stages combined) overlaid bythe predicted dynamics obtained by solving Equations (17) and (18) numericallyusing a time step (�t) of 0.1 day. Since plant area at the time of inoculation wasnot measured, it was assumed that plants on average had a leaf area of 125 cm2

corresponding to an initial density of 0.04 mites/cm2. The model predicts the maxi-mum density to be reached after about 35 days, but unfortunately the intervals be-tween two successive samplings were too long to provide convincing data on thismaximum. Besides, the model overestimates the mite density at day 28, whereasagreement between the predicted and the observed plant injury is acceptable takingthe large scatter in the data into consideration. The model correctly predicts thatthe mites overexploit the plants within 50 to 70 days. It also predicts that D willapproach an upper limit of about 0.95, but in reality all plants died after havingbeen so severely damaged, implying that D eventually reached one.

Figure 5. The relationship between the number of mite-days (Mt) (cumulative number of mites occu-pying a plant from day 0 to day t) and the amount of chlorophyll lost per plant (Lt). The straight linerepresents the fit of Equation (2) to data with � � 0.1453 (SE = 0.0129) �g chlorophyll mite−1 day−1.

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Effect of host plant condition on dispersal rates of spider mites

In the six experiments where only half of the recipient plants were connected to thedonor plant, 369 immatures and 2155 adults were found on the connected plants,whereas only one immature and 24 adults were found on the unconnected plants.Thus, mites recovered from the unconnected plants constituted only 0.27%(SE = 0.53%) and 1.1% (SE = 0.22%) of the dispersing immatures and adults, re-spectively.

The total numbers of dispersing mites (immatures + adults) found on the recipi-ent plants connected by short and long bridges were 4287 (47.1%) and 4817(52.9%), respectively. In four of the experiments, no mites were found on any ofthe recipient plants, while in the remaining 26 experiments, most mites were foundon the plants connected by short bridges in 12 cases. This distribution is close theexpected assuming that bridge length does not influence dispersal (sign test:P = 0.845; Wilcoxon test: T = 170, P > 0.05; n = 26).

The observed mean direction of movement of the 9104 mites(immatures + adults) was 293°, which corresponds to a westerly-north westerly di-rection (North = 0°). However, the intensity of the mean vector was only 0.065,which is not significantly different from 0 (Randomisation test based on 10,000

Figure 6. The relationship between the plant injury index (D) of a host plant and the concomitant den-sity of spider mites (x). Filled circles: Data obtained from 51 experiments with only spider mites; Opencircles: Data obtained from 250 plants inhabited by both spider mites and predatory mites (Zemek andNachman (1998, 1999)). The line shows the fit of Equation (7) to the data set without predators(R2 = 0.433; n = 51). The parameter values are: s0 = 0.0138 cm2 day−1, b � 0.3157 day−1, � � 0.1010day−1, � � 0.1016, and � � 0.6001.

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permutations: P = 0.556, SE(P) = 0.005). Thus, the result indicates that movementof T. urticae is undirected.

The total numbers of dispersing mites found on the donor and recipient plants atthe end of the experiments are presented in Table 1 together with the percentagepresent on the recipient plants. In order to compare immatures and adults, the sixexperiments in which immatures on the recipient plants had not been counted wereomitted from the data set. In the remaining 39 experiments, 9.8% of the immaturesand ca. 54.3% of the adults were found on the recipient plants, indicating that adultsare about five times more likely to disperse than immatures. In 36 of the experi-ments, the proportion of adults found on the recipient plants was higher than theproportion of immatures, while in three cases the proportions were the same (andequal to 0). Both a sign test and a Wilcoxon signed ranks test showed that the dif-ference between immatures and adults is highly significant (P < 0.0001).

In the 19 experiments where adults were sexed, 70.8% of the males and 58.8%of the females were found on the recipient plants. In eight of the experiments, ahigher proportion of males than females occurred on the recipient plants, while ineight other experiments the opposite applied. In the three remaining experiments,the proportions were the same.

When Equation (10) was fitted to data, the model explained 48.3% of the vari-ation in the observed values of Rt (number of mites on the recipient plants at theend of an experiment), but since the variance of Rt tends to increase proportionallywith Xt

2, we compared the predicted and observed values of log (R + 1) instead.

Figure 7. The predicted effects of plant injury (D) on the per capita birth rate (dotted line), loss rate(dashed line) and growth rate (full line) of T. urticae. The relationships are found from Equation (18)using the parameter values given in Figure 6.

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The model explained 70.6% of the observed variation in log(R + 1). The parameters�0 and �1 of Equation (10) were both significantly different from 0 (�0 � � 4.210(SE = 1.191) and �1 � 3.469 (SE = 1.694)). This result shows that the propensity toemigrate (ps) increases with D (from ps = 0.0146 when D = 0 to ps = 0.323 whenD = 1).

Figure 9 shows that the per capita emigration rate per bridge (�) increases by afactor 100 as D of the donor plant increases from 0 to 1. The differences betweenexperimental set-ups with four (variant B + C) and eight (variant A) bridges withrespect to the predicted emigration rate are relatively small and cannot be demon-strated statistically. The model (Equation 11) explained 57.4% of the variation in

Figure 8. The observed (dots) and predicted (full line) dynamics of spider mites and the observed(squares) and predicted (broken line) development in plant injury index (D) of host plants initially in-oculated with five adult female spider mites. Vertical lines indicate 95% confidence limits about themean (n = 10). The predicted curves are described by Equations (17) and (18) with parameter valuesgiven in Figure 6 and assuming an initial density (x0) of 0.04 mites cm−2 leaf area.

Table 1. Numbers of motile mites on donor and recipient plants and numbers of experiments in eachcategory. Omitting six experiments in which the immatures were not counted gives the values in paren-theses

Immatures Adults Males Females

Mites on donor plant 48370 11077 (8438) 1296 2169

Mites on recipient plants 5265 12309 (10031) 3146 3099

Total 53635 23386 (18469) 4442 5268

% of mites on recipient plants 9.8 52.6 (54.3) 70.8 58.8

Number of experiments 39 45 (39) 19 19

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log � obtained from experiments with four bridges (n = 13) and 37.7% from ex-periments with eight bridges (n = 22).

Effect of host plant condition on stage and sex distribution

When Equation (12) was fitted by means of logistic regression to the observed val-ues of pE, the only explanatory variable that remained in the model was D2. Theparameters of the reduced model are �0 � 0.285 (SE = 0.272) and �2 � � 2.669(SE = 0.718). �2 was highly significant even after adjustment for overdispersion(1

2 = 13.803; P = 0.0002). The result shows that the proportion of eggs declines withincreasing damage to the host plant.

It was not possible to find any significant change in the relative composition ofmotile mites. Overall, immatures constituted c. 74% (95% C.L: 68.0% −79.9%) ofthe motile mites. Consequently, the proportions of immatures and adults in the totalpopulation are both expected to increase with an increase in D (Figure 10).

No effect of plant condition on sex ratio was found when using data from the19dispersal experiments where the adults were sexed, although there was a trend to-wards relatively fewer males as D increased. Omitting D and D2 from the model

Figure 9. The predicted relationship between the plant injury index (D) of donor plants and the percapita emigration rate per bridge (�) to the recipient plants. Broken line and open circles: Predicted andobserved values of � when the donor plant is connected to four recipient plants. Full line and filledcircles: Predicted and observed values of � when the donor plant is connected to eight recipient plants.The lines are based on Equation (11). Four experiments with eight bridges in which D ranged between0.035 and 0.245 (D = 0.128; SD = 0.093) are not shown because no individuals were found on the re-cipient plants so that � = 0.

58

yielded �0 � 0.171 (SE = 0.114), which corresponds to an overall sex ratio of 45.8%males (95% C.L: 40.3% −51.3%).

Dispersal distances of spider mites

As shown in Table 2, five adults were found on unconnected plants, but since theseplants constituted half of the recipient plants, the number of adults that managed tomove from the donor plant to an adjacent plant without crossing a bridge is as-sumed to be twice that number. Thus, of the 135 adult mites found on the recipientplants, approximately 10 (7.4%) did so without using a bridge. Apparently no im-matures managed to cross without using a bridge.

Two immatures and 29 adults managed to cross two bridges. Assuming that theseindividuals have already crossed one bridge, the conditional probability that an in-dividual will cross an additional bridge is estimated as 11.8% (SE = 8.1%) and22.3% (SE = 2.2%) for immatures and adults, respectively. The two groups werenot significantly different (1

2 = 0.471; P = 0.493).No mites were found on the two most distant plants separated from the donor

plant by three bridges. Assuming bridge crossing to be a Markovian process, theexpected numbers of mites on these two plants can be calculated as 0.06 immaturesand 1.68 adults.

Figure 10. The predicted effect of plant injury (D) on the stage distribution of T. urticae. The propor-tion of eggs (pE) is predicted from Equation (12) with parameters �0 � 0.285, �1 = 0 and �2 � � 2.669.The proportion of immatures (pJ) is predicted from pJ = pJ� (1-pE) and the proportion of adults (pA)from pA = pA� (1-pE), where pj = 0.744 and pA� = 0.256.

59

Discussion

The purpose of the present study was to quantify the effects of spider mites on theirhost plant and the simultaneous responses of the mites to degradation of their foodresource. In order to make the experiments more realistic and comparable withgreenhouse data, we used entire host plants instead of excised leaves as substratefor the mites (see e.g. Yaninek et al. (1989) and Wilson (1994)). However, the useof entire plants grown under greenhouse conditions also imposes some disadvan-tages: (1) Temperature, humidity and light conditions in a greenhouse cannot becontrolled so precisely as in a phytotron; (2) Plants are difficult to standardise com-pared to single leaves; and (3) Population censuses cannot be made without dis-turbing the mites and were therefore done at the end of an experiment. The firsttwo points increase the experimental noise, but this can to some extent be handledstatistically. The third point requires more sophisticated solutions because we haveto rely on the adequacy of the mathematical models used to describe the underly-ing dynamics. If these models are inadequate, the results obtained will be biasedtoo. The validity of the models cannot be tested independently of the data, so theonly criteria to judge the models are whether their underlying assumptions seemreasonable and to what extent their predictions agree with the terminal observa-tions. Therefore, we encourage the readers to consider the models critically andregard them merely as our currently best suggestions as how to interpret the data ina consistent way.

Effect of plant age on spider mite population growth rate

The intrinsic rate of natural increase (rm) for T. urticae at 25 °C has previously beenreported to range from 0.218 to 0.290 day−1 (Sabelis 1985), whereas we found aper capita net growth rate (r) of merely 0.184 day−1 when we counted the numberof mites on plants that had been inoculated with ten adult female spider mites twoweeks earlier. The discrepancy between these estimates of per capita growth ratescan be attributed to the fact that we did not base our calculations on controlled

Table 2. Distance moved by migrant T. urticae from the donor plant to the recipient plants. Distance ismeasured as the minimum number of bridges required to establish contact between a donor and a re-cipient plant, although bridges may not have been present. No distinction is made between short andlong bridges.

Stage Distance between donor plant and recipient plants

Bridges present Bridges absent

1 2 3 1 2 3

Immatures 15 2 0 0 0 0

Adults 101 29 0 5 0 0

Total 116 31 0 5 0 0

60

life-table studies but obtained r from greenhouse experiments where the tempera-ture on average was below 25 °C. Besides, the populations never reached a stableage distribution, individuals could emigrate from the host plants, and the plantswere probably suboptimal for the mites after having been exposed to feeding in 14days. We did not find any effect of plant age on r, but the experimental noise mighthave obscured such an effect. Thus, Wilson (1994) found that T. urticae developedfastest on young cotton leaves and slowest on cotyledons and old leaves, whereasKarban and Thaler (1999) found the highest growth rate on the cotyledons, but littledifference between young and mature leaves. Watson (1964) showed that the fe-cundity (and to some extent also longevity) of T. urticae feeding on Lima beanswas inversely related to both leaf and plant age. Similarly, Yaninek et al. (1989)found that the growth rate of the cassava green mite (Mononychellus tanajoa(Bondar)) was highest on young leaves on young cassava plants. On the other hand,Kielkiewicz and Van de Vrie (1990) found that young leaves of chrysanthmum wererelatively better protected against two-spotted spider mites compared with olderleaves. Karban and Thaler (1999) further suggest that the growth rate of T. urticaeis positively correlated with the rate of photosynthesis, which may vary with leafage.

Effect of host plant condition on population growth and stage distributions

When we used the relationship between the plant injury index (D) and mite density(Equations 18 and 7) to model how a population of spider mites will develop whenexposed to declining plant condition (increasing D), we estimated rm to be c. 0.21day−1, which is in the lower end compared with the values given by Sabelis (1985).The model explicitly separates the effect of D on the per capita birth and loss ratesinstead of lumping these two rates into one (the per capita growth rate r) as in themodel of Pels and Sabelis (1999). There are two reasons for our approach: (1) ifthe system is going to be modelled by means of a simulation model that explicitlyincorporates demographic stochasticity (see e.g. Walde and Nachman (1999)), it isnecessary to separate the birth rate and the loss rate since their sum determines thevariance of the predicted population changes (see e.g. Pielou (1969)); and (2) itallows us to identify which of the two life-history parameters that is most sensitiveto plant condition. Figure 7 indicates that it is mainly the per capita loss rate thatincreases as the host plant starts to deteriorate, whereas the per capita birth rate israther unaffected. This result is in conflict with the conclusions by Watson (1964)and Tulisalo (1970), Mitchell (1973), Wrensch and Young (1974), Carey (1983),Wilson (1994) who found that fecundity is the most responsive parameter to over-crowding and nutritional stress as compared with mortality. However, it seemslikely that the oviposition rate would have declined more steeply if the mites hadbeen confined to a small arena from which they were unable to escape, becausethis would had intensified the intraspecific competition compared with an open sys-tem. In fact, the data indicate that a considerable part of the losses was due to emi-grations and not to mortality. The proportion of diapausing females was not re-corded separately, but was negligible. As long as light and temperature conditions

61

are favourable, food quality has a minor influence on diapause induction (Veerman1985).

The observed changes in stage distribution towards relatively fewer eggs in thepopulation as D increases (Figure 10) are in accordance with the changes in birthand death rates (Carey 1983). When D = 0, we found that a population is expectedto consist of 58% eggs, 32% immatures and 10% adults. This stage composition isfairly close to the stable age distribution given by Carey (1983) as 65% eggs, 25%immatures and 10% adults. Our analysis shows that birth and loss rates balancewhen D is approximately 0.8, which sets an upper limit of about 15 spider mites(all stages) per cm2 to the average mite density a bean plant can sustain (Figure 8).However, local density (e.g. on individual leaves) may sometimes exceed 100 in-dividuals per cm2 (Nachman, pers. obs). The model provided a reasonable fit to theempirical data when it was validated against an independent data set based on plantsthat have been infested with spider mites for different periods of time (Figure 8).Unfortunately, the time intervals between samplings (14 days) were too long to re-veal the underlying dynamics clearly. In a following paper, focusing on the dynam-ics of spider mites on plants with and without predators (Nachman and Zemek, inprep.), the model is validated against another data set sampled at 7-days intervals(but with only two replicates per sampling). We estimated the amount of chloro-phyll removed by spider mites to be 0.1453 �g mite−1 day−1. This value corre-sponds to 1.38 mm2 leaf area destroyed per mite and day. In comparison, Candolfiet al. (1991) estimated the area to about 13 mm2 mite−1 day−1. However, their valuewas based on an unspecified mixture of nymphs and adults, while ours is a popu-lation value, including stages with no (eggs and moulting nymphs) and low (larvaeand protonymphs) feeding activity. Since these stages constitute a major part of anincreasing population (Carey 1983), it may explain why our estimate is only aboutone tenth of the value given by Candolfi et al. (1991).

Effect of host plant condition on dispersal rates of spider mites

We found an accelerating propensity of the mites to leave a host plant as it dete-riorated due to overexploitation. Several other studies have demonstrated that highdensities of mites and resource degradation lead to increased dispersal tendency(Hussey and Parr 1963b; Suski and Naegele 1963; McEnroe 1969; Bernstein 1984;Smitley and Kennedy 1985; Li and Margolies 1993), but none of these studies hasquantified the relationship between host plant condition and dispersal rate. Themodel shows that the per capita emigration rate increases exponentially with D upto an upper limit of 0.03 day−1 bridge−1. In an experimental set-up with eightbridges, this means that c. 25% of all mites (c. 30% of the active stages) present ona plant will emigrate within one day. In comparison, about 50% of adult femalePhytoseiulus persimilis are expected to leave a host plant devoid of prey withinfive h (Zemek and Nachman 1998). We also found that adults disperse with a higherrate than immatures, which agrees with Brandenburg and Kennedy’s (1982) obser-vation that 86% of airborne mites were adults. We were not able to demonstrate adifference between adult males and females with respect to dispersal tendency, al-

62

though Smitley and Kennedy (1985) found that adult females are the dominant winddispersers, but their tendency to disperse declines with age (Li and Margolies 1993).

In order to identify the mechanisms used by T. urticae to assess the density ofconspecifics, Dicke (1986) conducted a series of experiments in which he exposedfemale spider mites to odours from leaves that were either clean or infested withspider mites, and to clean leaves that had been artificially damaged. He found thatthe mites respond both to a volatile pheromone that elicits dispersal and to a plantkairomone that elicits attraction. The ratio between the two substances determineswhether a spider mite will emigrate or stay. However, since all female mites inDicke’s experiments were well-fed, it is not possible to compare the relative effectof volatile substances on dispersal behaviour with that exerted directly through theamount and/or quality of food when mites feed on injured plants. Pallini et al.(1997) found that adult female T. urticae placed in an olfactometer had a slightpreference for cucumber plants already inhabited by conspecifics compared to cleanplants, whereas the mites clearly avoided plants with thrips.

Dispersal distances of spider mites

The dispersal experiments show that most dispersal events were short-distance,taking place when a mite moved to a nearest neighbour plant. At relatively fewoccasions individuals crossed two bridges within one day, whereas three crossingswere never observed. It is important to note that the recipient plants were of goodcondition (D � 0), which probably reduced the dispersal distance. It should alsobe noted that the number of crossings per dispersal event may be underestimatedbecause a mite that crosses the same bridge twice will not be recorded correctly.

Implications for biological control

The experiments have shown that the dynamics of T. urticae is highly influencedby the condition of their host plant, but also that the host plant is severely influ-enced by the presence of mites (Nachman and Zemek 2001). As the plant deterio-rates, the mites suffer from a decreased birth rate and an increased loss(death + emigration) rate, which gradually slows down population growth and ulti-mately puts an upper limit to the mite density. Unfortunately, at least from a eco-nomic point of view, this negative feed-back mechanism is unable to prevent thespider mites from overexploiting their host plant within a few weeks after it hadbeen colonized. That is why biological control by means of predatory mites is sorewarding, but also the reason for why it is necessary to find natural enemies thatcan cope adequately with these extreme growth rates. The fact that the phytoseiidpredator P. persimilis is able to control T. urticae in a multiplant system (Nachman(1981, 1999); Gough 1991) makes this predator-prey system an ideal model for un-derstanding the role played by interactions in time and space between organisms atthree trophic levels and for assessing various pest management strategies. One wayto gain further insight is to incorporate the results of the present study into a real-istic simulation model of the system (Nachman, in prep.).

63

Acknowledgements

The authors wish to thank Jette Andersen, Trine Søberg Nielsen, Viktor Kiel, andHenning Bang Madsen (Zoological Inst., University of Copenhagen) for their tech-nical assistance during the experiments. Professor David C. Margolies, Kansas StateUniversity, and Professor Koos Boomsma, University of Copenhagen, are thankedfor their useful comments to the manuscript. The project was supported by grantno. 11-1096-1 from the Danish Natural Science Research Council.

Appendix 1

Estimation of the feeding rate (�)

The rate at which chlorophyll is removed by spider mites is assumed to be propor-tional to the number of spider mites present at time t (Xt), i.e.,

dL

dt� �Xt (13)

where � is the extraction rate of chlorophyll per individual spider mite.Let X0 denote the number of mites released on the plant at time 0, and let it be

assumed that growth is exponential with a per capita growth rate r during a timeperiod t. If t is not so long that food becomes limiting it is reasonable to considerboth � and r as constants, which means that Equation (13) can be solved by inte-gration as

Lt � � � 0

� t

�Xd � � � � o

� t

X0erd ��

r�X0ert � X0� �

�

r�Xt � X0� (14)

� � 0

� t

Xd

is called mite-days (cf. Hoyt et al. (1979)) and expresses the cumulated number ofmites occupying a spatial unit (in this case an entire plant) from time 0 to t. Mite-days (M) can be computed directly from the initial and terminal number of mites as

Mt � � � 0

� t

Xd ��Xt � X0�t

ln�Xt/X0�(15)

because r in Equation (14) can be substituted by ln(Xt/X0)/t (cf. Equation (1)).

64

Appendix 2

Estimation of density-dependent birth and death rates

According to Equations (3) and (6) D can be written as

D �

cmax �i � 1

n

Ai � �i � 1

n

ciAi

�cmax � cmin� �i � 1

n

Ai

�L

�cmax � cmin�A

where

A � �i � 1

n

Ai

Equation (13) can therefore be replaced by

dD

dt�

1

�cmax � cmin�A

dL

dt�

�

�cmax � cmin�

X

A� sx (16)

where x = X/A is the density of spider mites and s the per capita rate at which spi-der mites inflict damage. However, since D cannot exceed 1, it is assumed that sdecreases as D approaches unity and becomes 0, when D = 1. This assumption leadsto the model

dD

dt� s0�1 � D�x (17)

where s0 is the value of

�

cmax � cmin

when � is maximal, i.e. when D is close to 0.The growth rate of the spider mites (r) is also assumed to decrease as D in-

creases. To model this, it is assumed that the per capita birth rate (b) decreases andthe per capita loss rate (�) increases with D. The loss rate combines loss of indi-viduals due to deaths and emigrations. The model chosen to describe the instanta-neous growth rate of the spider mite population has the form

dx

dt� rx � �b�1 � D�� �

�

�1 � D���x (18)

65

where b-� is the maximum per capita growth rate (rm) when D = 0. � and � areconstants.

Equations (17) and (18) cannot be solved explicitly with respect to t, but insert-ing Equation (17) in Equation (18)yields

dx

dD�

1

s0

�b�1 � D�� � 1 � ��1 � D� � � � 1� (19)

Integration of Equation (19) yields

x �1

s0�b

��1 � �1 � D��� �

�

��1 � �1 � D� � ��� (20)

provided that both � and � are positive. x is set equal to 0, if Equation (20) predictsnegative values of x (as D → 1).

Appendix 3

Estimation of dispersal rate

As a first step, it is assumed that the rate at which individuals move from the donorplant to the bridge-connected recipient plants is assumed to be proportional to thenumber of individuals on the donor plant (X), the number of bridges (B), and theper capita dispersal rate per bridge (�) i.e.

dR

dt� �BX (21)

The rate of change in the number of individuals on the donor plant is describedby Equation (18) as

dx

dt� �b�1 � D�� �

�

�1 � D���x � rx (22)

where

�

�1 � D��

is the per capita loss rate, which includes emigration. If r is considered to be con-stant during an experiment, Equation (22) can, upon integration, be inserted into

66

Equation (21) to yield

dR

dt� �BX0ert (23)

where R is the number of mites on the recipient plants and X0 is the number ofindividuals on the donor plant at the start of an experiment. When the experimentends at time t, the expected number of individuals on the recipient plants is foundas

E�Rt� � �BX0 � � 0

� t

erd ��B

rX0�e

rt � 1� ��BXt�1 � e � rt�

r(24)

where Xt is the number of mites counted on the donor plant at the end of an ex-periment. It means that � can be estimated as

� �rRt

BXt�1 � e � rt��r � 0� (25)

� �Rt

BXtt�r � 0� (26)

r is estimated as r � b�1 � Dt�� � ��1 � Dt�

� � where Dt is the plant injury indexof the donor plant at time t.

The fraction of individuals that are lost from the donor plant because of emi-gration to one of the recipient plants is denoted �, which means that � can be writ-ten as � = ��(1 − D)−�/B. � depends on the probability that a mite, “motivated” toemigrate, can find a bridge to cross. If there is a single bridge, the probability is� = ps. With B bridges, the likelihood that none of the bridges will be crossed is(1-ps)

B, implying that � = 1-(1-ps)B. The per capita emigration rate per bridge there-

fore becomes

� ��

B�1 � D���1 � �1 � ps�

B� (27)

A logistic relationship is suggested to model the influence of donor plant con-dition (D) on the emigration propensity (ps), i.e.

ps �e�0 � �1D

1 � e�0 � �1D(28)

where �0 and �1 are parameters. Substitution of Equations (27) and (28) in Equa-

67

tion (24) yields

E�Rt� ��

r�1 � D���1 � �1 � e�0 � �1D� � B�Xt�1 � e � rt�. (29)

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