Functional Responses in Habitat Use: Availability Influences Relative Use in Trade-Off Situations

Functional Responses in Habitat Use: Availability Influences Relative Use in Trade-OffSituationsAuthor(s): Atle Mysterud and Rolf Anker ImsSource: Ecology, Vol. 79, No. 4 (Jun., 1998), pp. 1435-1441Published by: Ecological Society of AmericaStable URL: http://www.jstor.org/stable/176754 .

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Ecology, 79(4), 1998, pp. 1435-1441 C) 1998 by the Ecological Society of America

FUNCTIONAL RESPONSES IN HABITAT USE: AVAILABILITY INFLUENCES RELATIVE USE IN TRADE-OFF SITUATIONS

ATLE MYSTERUD AND ROLF ANKER IMS

Department of Biology, Division of Biology, P.O. Box 1050 Blindern, University of Oslo, N-0316 Oslo, Norway

Abstract. Current methods for evaluating habitat selection from animal space-use observations ignore possible interactions between time allocation patterns relative to different resources, their relative abundance, and their spatial arrangements. Habitat selection may occur in situations in which animals experience a trade-off, e.g., between time used foraging in areas with abundant forage but poor protective cover, and time used for resting in areas with good protective cover but low forage abundance. We show how functional responses in habitat use (i.e., change in preference with availability of one of two main habitat types) may be tested. Given radio-telemetry data for a sample of individuals, binomial logit models can be used to regress proportionate use of a habitat type P(u) against the proportion of that habitat available, P(a). Given an appropriate fit to the data by a linear predictor on a logit scale, functional response will be indicated by a estimated slope parameter ? 1, while a slope = 0 will indicate a consistent use as availability changes. Habitat preference is inferred from the logit regression parameters when the fitted value of the proportion of use at a specified proportion of availability, is significantly greater than the proportional availability.

Key words: dichotomous habitat mixes; functional response; habitat availability; habitat preference; habitat selection; logistic regression; Phasianus colchicus; radiotelemetry data; Sciurus caro- linensis; time budget; trade-offs.

INTRODUCTION

Habitat selection is an important feature of behavior and population dynamics, and it has therefore received much attention (e.g., Fretwell and Lucas 1970, Rosen- zweig 1981, Bell et al. 1994). Levins (1968) made the distinction between coarse-grained and fine-grained species based on proportionate use of different habitat patches. In the case of coarse-grained species, habitat preference may be inferred through the disproportional use of some habitats over others (e.g., Neu et al. 1974, Johnson 1980, Aebischer et al. 1993).

Habitat selection may take place at several spatial scales (Johnson 1980, Morris 1987, Orians and Wit- tenberger 1991). We restrict our consideration to habitat selection at the home range scale, i.e., how individuals allocate their time with respect to the habitat types available within the home range. Measuring habitat preference often has been done simply by relating use of a habitat to its availability (Neu et al. 1974, Alldredge and Ratti 1986, 1992, Thomas and Taylor 1990, Manly et al. 1993). Other methods rank habitats relative to each other (Johnson 1980, Aebischer et al. 1993). These incorporate the fact that when one habitat is used less, others must be more used (Johnson 1980, Aebischer et al. 1993). Although compositional analyses establish habitat rankings, the focus for this method also is an overall test of use relative to availability (Aebischer et al. 1993). A problem with these methods

Manuscript received 1 May 1996; revised 5 February 1997; accepted 17 May 1997.

for evaluating habitat selection from animal space-use observations (e.g., radio fixes) is that it is implicitly assumed that use of a habitat is directly proportional to the availability of that habitat. In the present paper we discuss situations in which this assumption may not hold true; i.e., that preference may be conditional on availability.

Many organisms face the problem that many habitats do not have favorable combinations of essential patches (Orians and Wittenberger 1991). A suitable habitat must contain a mixture of patches that provide oppor- tunities for all essential activities required for suc- cessful reproduction. A number of studies on different taxonomic groups describe situations in which animals experience trade-off situations affecting habitat selection, when areas for different activities, e.g., foraging and escape from predators, are spatially segregated (Lima and Dill 1990, Brown 1992, Moody et al. 1996). These include studies of fish (Milinski and Heller 1978, Gilliam and Fraser 1987), insects (Sih 1980, 1982, Sih et al. 1990), salamanders (Holomuzki 1986), birds (Grubb and Greenwald 1982, Lima 1985), and small mammals (Holmes 1984, Brown 1988, Kotler and Blaustein 1995 and references therein). Similarly, there may be trade-offs between foraging and thermal ex- posure (Belovsky 1981, Schmitz 1991), between foraging outside the territory and mate-guarding within the territory (Westneat 1994), or between foraging with the goal of energy maximization in terrestrial habitat and sodium intake in water habitat (Belovsky 1986). For example, in winter, small cervids like white-tailed

1435



1436 ATLE MYSTERUD AND ROLF ANKER IMS Ecology, Vol. 79, No. 4

deer (Odocoileus virginianus) and roe deer (Capreolus capreolus) forage mainly in open habitat with abundant forage but little cover. Resting bouts often take place under conifer cover where there is little forage (Huot 1974, Armstrong et al. 1983, Schmitz 1991, Mysterud and 0stbye 1995). Using the conventional habitat preference approach in this case (see references above) would have indicated preference for feeding habitat if it was rare, but avoidance if it was common. The con- cept of preference defined as greater use of a habitat than expected from its availability (see Thomas and Taylor 1990 for a discussion of definitions of habitat selection and preference) in this case does not have any clear biological meaning. Indeed, the conventional approach for testing for habitat preferences may some- times obscure or distract attention from the processes underlying animal space-use patterns, for example, the allocation of time for foraging and resting. A few authors (Armstrong et al. 1983, white-tailed deer; Luch- erini et al. 1995, red fox [Vulpes vulpes]) have implicitly acknowledged this point and approached the problem indirectly by splitting their analysis according to different activity types or periods (see also Palo- mares and Delibes 1992). Two authors have, however, noted that use was not directly proportional to availability, but without formal testing and without relating their findings to time budgets (Kenward 1982a, Thir- good 1995).

We propose an approach to test for what we define as functional responses in habitat use, i.e., a change in relative use with changing availability of two habitat types. The approach is primarily applicable to animals with well-defined home ranges encompassing two essential habitat elements (e.g., containing protective cover and food resources, respectively). We illustrate the utility of the approach with two case studies.

METHODS

Statistical approach

We used logistic regression to test for a functional response in habitat use in a habitat mix consisting of two habitat types (A and B) appearing coarse-grained to the study animal. The following conditions must be fulfilled in applying the approach:

A two-level sampling regime has produced an ade- quate sample of N individuals from a target population of animals with well-defined home ranges (level 1) and a sample of (ni, i = 1, 2, . . ., N) spatial observations (e.g., radio-fixes) have been obtained from each individual (level 2). At both levels it must be assumed that the sampling scheme has produced a random sample of independent observations. As most methods of home range analysis are based on the assumption of independent observations, this aspect has been thoroughly explored in the literature on home range analysis, both with respect to devising optimal data sampling schemes (White and Garrot 1990, Andreassen et al. 1993) and

post hoc tests for autocorrelation in space-use data (Schoener 1981, Swihart and Slade 1985, Hansteen et al. 1997). For statistical methods correcting for serially autocorrelated observations (at the within home range level) when testing habitat selection, see Arthur et al. (1996).

Under the assumption of independence of ni, the number of observations in habitat type A(n(A)i) can be assumed to have a binomial distribution Bin(ni, P(,)), where P(u)i is the probability for an individual i of being located in habitat A (which can be estimated as P(u) =

n(A)ilni) and ni = n(A)i + n(B)i. Our approach is to inves- tigate whether P(u)i is conditional on the proportional availability of that habitat (p(a)i) in the home range of each individual. For this purpose we propose to use logistic regression to regress the expectation of proportional use P(U) against proportional availability (P(A)) for the target population. The regression approach requires that the predictor variable p(a) actually vary among the N individuals in the sample (see Discussion). Furthermore, we assume that p(a) can be mapped and quantified within a delineated home range based on the ni radio-fix points without error (for a discussion see Thomas and Taylor 1990 and Manly et al. 1993).

To make the expectation linear on the logit scale we logit-transform the predictor variable yielding the regression equation

logit P(U) = log(p(U)/I I -P(J)

= (X + 13 log(p()[l - P(a)])

where o( (regression intercept; logit p(a) = 0 for p(a) = 0.5) and P (regression slope = [change in logit use]/ [change in logit availability]) are parameters to be estimated from the data by maximum likelihood.

Different statistical hypotheses may be framed in terms of the regression parameters, especially when the two habitat types have been defined with respect to different activity types. Random use of habitat implies x = 0 and P = 1. We expect 3 = 0 when all individuals spend consistent proportions of time in each habitat, regardless of availability (e.g., always foraging in habitat A and resting in habitat B), which is translated into a fixed proportion of radiolocations in habitat A for the entire range of P(a)i so that the expected (or fitted) proportion used is P(u) = exp(oL)/[ I + exp(oL)]. The situation ox > 0 and 3 ? 1 implies that habitat A is always selected (disproportionately more used than available). For P > 1 and oL > 0 the strength of habitat selection increases with p(a), indicating one kind of functional response. For other combinations of the regression parameters (and functional responses), whether habitat selection occurs or not may be conditional on p(a). Spe- cifically, habitat selection may be inferred when the lower limit of the 95% confidence interval for the fitted value of proportion of habitat used, for a given habitat availability, exceeds proportional availability of that



June 1998 FUNCTIONAL RESPONSES TO HABITAT 1437

habitat, i.e., P(u) I P(a) > p(a). Thus certain combinations of (x and a may indicate habitat selection in some part of the empirical range of p(a) and not in others (cf. gray squirrel case study below).

Standard diagnostics for logistic regression may be used to check for sources of lack of fit, e.g., identifying outlying individuals (Hosmer and Lemeshow 1989). Appropriately, nonlinear functional responses (on the logit scale) may be probed by including higher order predictor terms and subsequently tested by likelihood ratio tests (Hosmer and Lemeshow 1989, Collett 1991). More flexible tools for testing nonlinear responses (e.g., for detecting thresholds) are logistic additive models (Venables and Ripley 1994). Nonrandom variation in habitat preferences between individual animals due to identifiable biological factors such as sex and age may be tested for by adding sex or age terms to the linear predictor (see Heisey 1985 for an equivalent approach to log-linear modeling of habitat selectivity). For example, a significant effect of sex might require separate sex-specific estimates of ofj (i = 1, 2) (additive sex effect on a logit scale) and by (significant interaction between logit p(a) and sex). Furthermore, unjustified lumping of biologically different habitat types in order to achieve the dichotomous classification required in our approach will lead to significant heterogeneity in the observed proportions 1(u)i I P(a) In our approach such unaccounted heterogeneity (overdispersion) is assessed by the statistical significance of the residual deviance (i.e., the goodness of fit statistic) of the fitted model. There may also be several nonbiological sources of lack of fit. In particular, one should be cautious with regard to the possibility that measurement errors (due to im- precise radio-fix recordings; Springer 1979) may lead to biases when certain habitat types become increas- ingly rare and/or fragmented. Specifically, increasing fragmentation will lead to an increase in the number of incorrectly assigned fixes and possibly also a mis- match between the animals' perception of habitat availability within the home range and the measured availability based on the estimated home range. Also rare habitats may not be measured very accurately using mapping methods (Thomas and Taylor 1990). For this reason, we recommend that the availability of the rarest habitat must exceed some minimum limit before a home range is included in the regression analysis. For discussion about sample size requirements and power of logistic regression analyses on grouped data see Agresti (1990).

Two case studies: gray squirrels and pheasants

We applied this approach to data from Aebischer et al. (1993) concerning gray squirrels (Sciurus caroli- nensis) and Ring-necked Pheasants (Phasianus colchicus). For an individual to be included in the analysis, we used the criterion that >5% of the rarest habitat must be available within the home range.

Aebischer et al. (1993) considered initially five veg-

etation types in their gray squirrel study, but their compositional analysis revealed that only two broader classes were significantly different. Gray squirrels are considered typically woodland animals, but Aebischer et al. (1993) found that squirrels foraged in a wheat field adjacent to the woods (see also Kenward 1982b). Gray squirrels thus experienced a situation with two resources in distinct habitats; they foraged predomi- nantly in open habitat and sought protective cover in the forest habitat (see also Lima et al. 1985). Although food also was present in the forest, the open habitat provided substantially more forage per unit area. Hence, in this case study eventual changes in the strength of habitat selection with availability may be interpreted biologically in terms of change or stasis in the time budget with respect to habitat. Data from 11 gray squirrels each with >5% of open habitat available to them were included in the regression analysis. Squir- rels were tracked in July 1979 on Elton Estate, Nor- thamptonshire, United Kingdom (Aebischer et al. 1993). Thirty radio locations were obtained per individual, comprising three locations per day over a 10- d period. Home ranges were estimated using the minimum convex polygon method (Mohr 1947). We used the proportion of fixes in the open habitat as the response variable. The proportion of open habitat available in the home ranges ranged from 5 to 41%.

Data from 12 radio-tagged Ring-necked Pheasants with >5% availability of broadleafed forest habitat also were obtained from Aebischer et al. (1993) (see also Robertson 1986). The pheasants were tracked in March 1985 on Lyons Estate, County Kildare, Ireland. Home ranges were estimated using the minimum convex polygon method (Mohr 1947). Thirty radio locations per bird were collected, comprising three radio locations per day over a 10-d period (Aebischer et al. 1993). Also in this case only two broad habitat classes from five initial vegetation classes could be distinguished based on Aebischer et al.'s ranking method. In contrast to the case of the gray squirrel there were no a priori reasons to relate different habitat types to biologically distinct activity types. Therefore, we somewhat arbitrarily distinguished broadleafed forest habitat from nonforest habitats (pooled), because broad-leafed forest was present in all the pheasants' home ranges (5.73- 53.16% availability).

RESULTS

Gray squirrels

The regression model based on all individuals provided an appropriate fit to the data (Table 1, Fig. 1). Thus our dichotomous classification of squirrel habitats seemed justified. The estimated value of the slope parameter (j) was negative (Table 1) and there was a significant decrease in the use of the open habitat as the availability of the open habitat increased (Fig. 1), i.e., gray squirrels spent less time in open habitat as




TABLE 1. Test for goodness-of-fit and parameter estimates (point estimates and 95% confidence limits) for the logistic regression equation logit(proportion used) = (x + a logit(proportion available) for data from gray squirrels and pheasants reported by Aebischer et al. (1993).

Resid- Resid- Intercept Slope ual ual

Species G P G/df (X 95% CL a 95% CL

Gray squirrel N = 11 11.97 0.22 1.33 -2.56 [-3.43, -1.79] -0.47 [-0.92, -0.04]

Pheasants N= 12 56.90 <0.001 5.69 0.79 [0.46, 1.16] 0.99 [0.74, 1.28] N = 11 34.74t <0.001 3.86 1.06 [0.68, 1.46] 1.07 [0.81, 1.36] N= 10 14.56t 0.07 1.82 0.80 [0.43, 1.20] 1.02 [0.75, 1.29] N = 9 6.611 0.48 0.93 1.25 [0.76, 1.78] 1.32 [0.98, 1.70]

Notes: N = number of individuals of that species. Goodness-of-fit statistics are residual deviance (G) and P value for the model (small P values indicate that the models fit the data poorly), as well as residual deviance divided by error df. The model based on the complete sample showed lack of fit for pheasants. An appropriate fit was obtained by removing three individuals. The expected value of the slope parameter ( = 1, and the expected intercept x = 0 (proportion available = 0.5) under the null hypothesis of no habitat selection (random use of the two habitats).

t One misfitting observation removed from the model. :D Two misfitting observations removed from the model.

Three misfitting observations removed from the model.

availability increased. The regression curve and its confidence envelope indicated that selection for open habitat (p(u) I P(a) > P(a)) occurred only for p(a) < 0.1

(Fig. 1).

Ring-necked Pheasants

The regression model based on all individuals provided a poor fit to the data (Table 1). Adding higher order terms to the model (thus testing for a nonlinear response) did not improve the fit. Inspection of the residuals from the linear model suggested that the lack of fit was due to strongly deviating habitat use by three individuals with an intermediate proportion of broadleafed forest habitat in their home ranges (Fig. 1, Table 1). To obtain an appropriate fit these three outlying individuals had to be removed from the analysis. Al- though the slope of the regression did not differ significantly from 1 (no change in selection) for any of the models (Table 1), the estimates of the intercept were less stable and invalidated any reliable inference about habitat selection for ring-necked pheasant in this study area. Unfortunately, no additional information about the pheasant individuals (e.g., sex) was available so that the eventual improvement of the fit could not be evaluated by including additional terms in the model.

DISCUSSION

We have provided a means for detecting whether animals' relative use of two different habitat types changes when the relative availability of these types changes between individual home ranges. Although our regression approach may be used for purely exploratory purposes, we have emphasized its potential utility for testing hypotheses about the behavioral mechanisms (e.g., involving time-budgets) as they relate to habitat

use, which can be formulated in terms of regression parameter values.

The approach is valid when observations within home ranges are independent (e.g., have a binomial error). Most radio-telemetry studies strive towards this goal (McNay et al. 1994), although it is perhaps rarely accomplished. Fortunately, in our approach severe vi- olation of the assumption of independence will be iden- tified as lack of fit of the data to the model (i.e., an overdispersed error term). Other sources of lack of fit might be due to random or unaccounted differences between individuals included in the sample. Further- more, a dichotomous classification of the habitat as we have done may be too simplistic in a truly polycho- tomous case (see below). It is likely that the poor fit of the model in the pheasant case study may have been due to this as the two habitats could not be attributed to two different resources or to different behaviors.

The issue raised in this paper hinges on variable habitat composition among individual home ranges in a population. There may be several reasons for such variation. Most mammals, at least females, adjust their home range size to resource levels (e.g., food; Ims 1987). Consider two habitat types each containing one resource, e.g., food or cover (Fig. 2). When food is the limiting factor, the animal will adjust home range size to include a certain minimum amount of food (and vice versa when cover is limiting). For example, if satiation is reached for the feeding habitat at 50 ha and for the cover habitat at 5 ha, and if the availability of feeding habitat is ?10%, then the animal will establish the home range so as to include at least 50 ha of feeding habitat. Within this home range, the amount of cover habitat will vary, but often will exceed 5 ha if habitats are sufficiently mixed. Assuming all home ranges in-




0.4 Grey squirrel

x 0.3-

0. 0

0.0 ~ ~~ ~ ~~~~~~~~ -. -------------- - - - -........ - - - - -

0.2 00

0 0-- o 0. 1 0~

0.0 0.1 0.2 0.3 0.4

Ring-necked Pheasant 0.8 0

. 0.

o 0.4-

o 0.2 - 7 0.

0.0 --

0 .0 0.1 0 2 0.3 0.4 0.5 0.6 Proportion available

FIG. 1. Logistic regression of proportional use against proportion of that habitat available within an individual's home range for gray squirrel and Ring-necked Pheasants, with 95% confidence envelopes. Note that the regression for the Ring-necked Pheasant includes three misfitting observations (solid circles); thus the confidence envelopes may be under- estimated.

dude the same amount of feeding habitat, then with increasing home range size, the ratio of food to cover in the home range decreases (Fig. 2). Thus, availabil- ities of the different habitats will vary even though the amount of feeding habitat in all home ranges is constant. If time budgets remain stable as availability changes, then the strength of selection or the correla- tion between habitat and activity must change. The same pattern may emerge with increasing distance between suitable habitat patches surrounded by habitats

without resources (e.g., Rosenzweig 1981, Carey et al. 1992, Ims et al. 1993). This latter situation is different from the spatially segregated resource distribution, because one habitat will not be used except for move- ments between suitable habitats (i.e., transition habitat sensu Hansson [1977] or traveling habitat sensu Ro- senzweig [1981]). Since the transition or traveling habitat will likely contain few observations, a varying proportion of transition habitat among home ranges is not likely to influence the measured habitat ranking, although the strength of selection may change. Also, the availability of habitats may not vary among individuals because of a homogenous study area or because the animals establish home ranges in areas with certain amounts or arrangements of habitats at the landscape scale. Thus, although functional responses in habitat selection, as defined in this paper, bear some resem- blance to the well-known functional responses in prey selection (e.g., both satiation and switching may be involved in habitat selection), aspects regarding spatial scales become more critical for space use in mosaic habitats. Indeed, a complete understanding of habitat selection and, eventually, the type of functional response shown requires evaluation at different spatial scales; e.g., as choice of a home range within a landscape (first-order habitat selection), and then as use within a home range (second-order habitat selection; Johnson 1980). Given sufficient replicates at the landscape level (i.e., several landscapes with varying habitat composition), our approach also could be used at this scale by regressing landscape composition against the corresponding composition in the home ranges.

The functional response we observed for gray squirrels was surprising, because the use of open habitat (time spent in open habitat) decreased with increasing availability. Interpreting such functional responses requires more information than simply the composition of habitats. In particular, we believe that variables such as patch size distribution and interpatch distances (e.g., Fig. 2), which are likely to be correlated with habitat composition (Wiens 1976, Hanski 1985), might be important determinants of habitat selection. Such spatial variables rarely are measured and incorporated in stud-

D Habitat A (food)

Habitat B (cover)

FIG. 2. Change in proportion of home range occupied by habitat A (50, 25, and 10o, respectively), when an animal scales its home range size to include a constant amount of habitat type A. Home range is shown as the minimum convex polygon that included all location records for that animal.




ies of habitat selection (it was not in the study on gray squirrels, but see Carey et al. 1992). Further clues about mechanisms underlying functional responses also may be obtained by applying more elaborate methods of space use analysis to radio-telemetry data; e.g., by es- timating aspects of the utilization distributions and movement patterns (Andreassen et al. 1993).

Our approach for testing for functional responses in habitat selection considered only two habitat catego- ries. Such a dichotomous classification may be valid if habitat patches easily can be distinguished based on two different, spatially segregated resources (e.g., cover and food). This seemed to be valid for the gray squirrel, but not for the Ringed-necked Pheasant. Re- cent studies addressing questions related to habitat fragmentation (e.g., Andren 1994) commonly use such dichotomous classifications as fragment vs. matrix habitat, source vs. sink habitat, and edge vs. interior habitat.

In this paper we have focused on situations for which a priori classification of habitat can rely on information on how animals allocate their time in relation to two identifiable and spatially segregated resources (e.g., food and cover). Then our approach may provide tests of specific biological hypotheses on changes in time- budget trade-offs conditional on spatial constraints. We believe that empirical studies of habitat use in animals would benefit from a braver exposition of such biological hypothesis (e.g., regarding time budgets). Of course, this implies more restrictive assumptions sim- ilar to those made in theoretical models of habitat selection (i.e., Levins 1968, Rosenzweig 1981). Indeed, judicious simplification to achieve analytical tractabil- ity and a mechanistic understanding of ecological phe- nomena is generally considered to be a goal for both theoretical mathematical modeling (Maynard Smith 1974) and empirical statistical modeling (Burnham and Anderson 1992). However, checking the validity of (restrictive) assumptions should be standard practice in all types of modeling. In our case, primary assumptions were a correct dichotomous classification of habitat types and distributional properties of the data (i.e., binomial residual error). In many cases, however, very little information will be available for posing distinct biological hypotheses or finding good biological jus- tifications for classification of habitat. In such cases our method still may be used as an exploratory tool for finding availability related changes in patterns of use of arbitrarily defined habitat classes (e.g., vegetation types). For such exploratory purposes, various dichotomous classifications of the habitat may be tried in the statistical setting we have suggested (with em- phasis on goodness-of-fit testing). However, in other cases it may be necessary to consider more than two habitats in order to model habitat selection properly. Testing for functional response in a multiple choice situation is clearly more complex. Future studies should explore whether our binary logistic regression

approach can be generalized to situations with more than two habitat types, for example, by applying poly- chotomous response functions (McCullagh and Nelder 1989, Lunneborg 1994).

ACKNOWLEDGMENTS

We thank Ivar Mysterud, Dana L. Thomas, Jerry Thomas Warren, and one anonymous referee for many valuable com- ments on an earlier draft of this paper.

LITERATURE CITED

Aebischer, N. J., P. A. Robertson, and R. E. Kenward. 1993. Compositional analysis of habitat use from animal radio- tracking data. Ecology 74:1313-1325.

Agresti, A. 1990. Categorical data analysis. John Wiley and Sons, New York, New York, USA.

Alldredge, J. R., and J. T. Ratti. 1986. Comparison of some statistical techniques for analysis of resource selection. Journal of Wildlife Management 50:157-165.

Alldredge, J. R., and J. T. Ratti. 1992. Further comparison of some statistical techniques for analysis of resource selection. Journal of Wildlife Management 56:1-9.

Andreassen, H. P., R. A. Ims, N. C. Stenseth, and N. G. Yoccoz. 1993. Investigation of space use by means of radiotelemetry: a methodological guide. Pages 589-618 in N. C. Stenseth and R. A. Ims, editors. The biology of lem- mings. Academic Press, London, UK.

Andrdn, H. 1994. Effects of habitat fragmentation on birds and mammals in landscapes with different proportions of suitable habitat: a review. Oikos 71:355-366.

Armstrong, E., D. Euler, and G. Racey. 1983. White-tailed deer habitat and cottage development in central Ontario. Journal of Wildlife Management 47:605-612.

Arthur, S. M., B. E J. Manly, L. L. McDonald, and G. W. Garner. 1996. Assessing habitat selection when availability changes. Ecology 77:215-227.

Bell, S. S., E. D. McCoy, and H. R. Mushinski 1994. Habitat structure. Chapman and Hall, London, UK.

Belovsky, G. E. 1981. Optimal activity times and habitat choice of moose. Oecologia 48:22-30.

. 1986. Generalist herbivore foraging and its role in competitive interactions. American Zoologist 124:51-69.

Burnham, K. P., and D. R. Anderson 1992. Data-based selection of appropriate biological model: the key to modern data analysis. Pages 16-30 in D. R. McCullough and R. H. Barrett, editors. Wildlife 2001: populations. Elsevier Ap- plied Science, New York, New York, USA.

Brown, J. S. 1988. Patch use as an indicator of habitat preference, predation risk, and competition. Behavioral Ecol- ogy and Sociobiology 22:37-47.

. 1992. Patch use under predation risk: I. Models and predictions. Annales Zoologica Fennici 29:301-309.

Carey, A. B., S. P. Horton, and B. L. Biswell. 1992. The northern spotted owl: influence of prey base and landscape characters. Ecological Monographs 62:223-250.

Collett, D. 1991. Modeling binary data. Chapman and Hall, London, UK.

Fretwell, S. D., and H. L. Lucas. 1970. On territorial behaviour and other factors influencing habitat distribution in birds. Acta Biotheoretica 19:16-36.

Gilliam, J. F, and D. F Fraser. 1987. Habitat selection under predation hazard: test of a model with foraging minnows. Ecology 68:1856-1862.

Grubb, T. C., and L. Greenwald. 1982. Sparrows and a brush- pile: foraging responses to different combinations of predation risk and energy cost. Animal Behaviour 30:637-640.

Hanski, I. 1985. Single-species spatial dynamics may con- tribute to long-term rarity and commonness. Ecology 66: 335-343.

Hansson, L. 1977. Spatial dynamics of the field vole Mi-




crotus agrestis in heterogeneous landscapes. Oikos 29: 539-544.

Hansteen, T., H. P. Andreassen, and R. A. Ims. 1997. Effects of spatiotemporal scale and autocorrelation on home range estimators. Journal of Wildlife Management 61:280-290.

Heisey, D. M. 1985. Analyzing selection experiments with log-linear models. Ecology 66:1744-1748.

Holmes, W. G. 1984. Predation risk and foraging behavior of the hoary marmot in Alaska. Behavioral Ecology and Sociobiology 15:293-301.

Holomuzki, J. R. 1986. Predator avoidance and diel patterns of microhabitat use by larval tiger salamanders. Ecology 67:737-748.

Hosmer, D. W., and S. Lemeshow. 1989. Applied logistic regression. John Wiley and Sons, New York, New York, USA.

Huot, J. 1974. Winter habitat of white-tailed deer at Thirty- one Mile lake, Quebec. Canadian Field-Naturalist 88:293- 301.

Ims, R. A. 1987. Responses in the spatial organization and behaviour to manipulations of the food resource in the vole Clethrionomys rufocanus. Journal of Animal Ecology 56: 585-596.

Ims, R. A., J. Rolstad, and P. Wegge. 1993. Predicting space use responses to habitat fragmentation: can root vole Mi- crotus oeconomus serve as an experimental model system (EMS) for capercaillie grouse Tetrao urogallus in boreal forest? Biological Conservation 63:261-268.

Johnson, D. H. 1980. The comparison of usage and availability measurements for evaluating resource preference. Ecology 61:65-71.

Kenward, R. E. 1982a. Goshawk hunting behaviour, and range size as a function of food and habitat availability. Journal of Animal Ecology 51:69-80.

1982b. Techniques for monitoring the behaviour of gray squirrels by radio. Symposium of the Zoological So- ciety of London 49:175-196.

Kotler, B. P., and L. Blaustein. 1995. Titrating food and safety in a heterogenous environment: when are the risky and safe patches of equal value? Oikos 74:251-258.

Levins, R. 1968. Evolution in changing environments. Princeton University Press, Princeton, New Jersey, USA.

Lima, S. L. 1985. Maximizing feeding efficiency and min- imizing time exposed to predators: a trade-off in the black- capped chickadee. Oecologia 66:60-67.

Lima, S. L., and L. M. Dill. 1990. Behavioral decisions made under the risk of predation: a review and prospectus. Ca- nadian Journal of Zoology 68:619-640.

Lima, S. L., T. J. Valone, and T. Caraco. 1985. Foraging- efficiency-predation risk trade-off in the gray squirrel. An- imal Behaviour 33:155-165.

Lucherini, M., S. Lovari, and G. Crema. 1995. Habitat use and ranging behaviour of the red fox (Vulpes vulpes) in a Mediterranean rural area: Is shelter availability a key factor? Journal of Zoology 237:577-591.

Lunneborg, C. E. 1994. Modeling experimental and obser- vational data. Duxbury, Belmont, California, USA.

Manly, B. F J., L. L. McDonald, and D. L. Thomas. 1993. Resource selection by animals: statistical design and analysis for field studies. Chapman and Hall, London, UK.

Maynard Smith, J. 1974. Models in ecology. Cambridge Uni- versity Press, Cambridge, UK.

McCullagh, P., and N. A. Nelder. 1989. Generalized linear models. Chapman and Hall, London, UK.

McNay, J., A. Morgan, and F L. Bunnell. 1994. Character- izing independence of observations in the movement of Columbian black-tailed deer. Journal of Wildlife Manage- ment 58:22-429.

Milinski, M., and R. Heller. 1978. Influence of a predator on the optimal behaviour of sticklebacks (Gasterosteus acu- leatus L.). Nature 275:642-644.

Mohr, C. 0. 1947. Table of equivalent populations of North American small mammals. American Midland Naturalist 37:223-249.

Moody, A. L., A. I. Houston, and J. M. McNamara. 1996. Ideal free distributions under predation risk. Behavioral Ecology and Sociobiology 38:131-143.

Morris, D. W. 1987. Ecological scale and habitat use. Ecol- ogy 68:362-369.

Mysterud, A., and E. 0stbye. 1995. Bed-site selection by European roe deer (Capreolus capreolus) in southern Nor- way during winter. Canadian Journal of Zoology 73:924- 932.

Neu, C. W., C. R. Byers, and J. M. Peek. 1974. A technique for analysis of utilization-availability data. Journal of Wild- life Management 38:541-545.

Orians, G. H., and J. E Wittenberger. 1991. Spatial and tem- poral scales in habitat selection. American Naturalist 137: 29-49.

Palomares, E, and M. Delibes. 1992. Data analysis and potential bias in radio-tracking studies of animal habitat use. Acta Oecologia 13:221-226.

Robertson, P. A. 1986. The ecology and management of hand-reared and wild pheasants (Phasianus colchicus) in Ireland. Dissertation. National University of Ireland, Dub- lin, Ireland.

Rosenzweig, M. L. 1981. A theory of habitat selection. Ecol- ogy 62:327-335.

Schmitz, 0. Z. 1991. Thermal constraints and optimization of winter feeding and habitat choice in white-tailed deer. Holarctic Ecology 14:104- 111.

Schoener, T. W. 1981. An empirically based estimate of home range. Theoretical Population Biology 20:281-325.

Sih, A. 1980. Optimal behavior: Can foragers balance two conflicting demands? Science 210:1041-1043.

. 1982. Foraging strategies and the avoidance of predation by an aquatic insect, Notonecta hoffmanni. Ecology 63:786-796.

Sih, A., J. Krupa, and S. Travers. 1990. An experimental study on the effects of predation risk and feeding regime on the mating behavior of the water strider. American Nat- uralist 135:284-290.

Springer, J. T. 1979. Some sources of bias and sampling error in radio triangulation. Journal of Wildlife Management 43: 926-935.

Swihart, R. K., and N. A. Slade. 1985. Testing for independence of observations in animal movement. Ecology 66: 1176-1184.

Thirgood, S. J. 1995. The effects of sex, season and habitat availability on patterns of habitat use by fallow deer (Dama dama). Journal of Zoology 235:645-659.

Thomas, D. L., and E. J. Taylor. 1990. Study designs and tests for comparing resource use and availability. Journal of Wildlife Management 54:322-330.

Venables, W. N., and B. D. Ripley. 1994. Modern applied statistics with S-Plus. Springer-Verlag, New York, New York, USA.

Westneat, D. E 1994. To guard mates or go forage: conflicting demands affect the paternity of male red-winged black- birds. American Naturalist 144:343-354.

White, G. C., and R. A. Garrott, editors. 1990. Home range estimation. Pages 145-183 in Analysis of wildlife radio tracking data. Academic Press, New York, New York, USA.

Wiens. J. A. 1976. Population responses to patchy environments. Annual Review of Ecology and Systematics 7:81- 120.



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Functional Responses in Habitat Use: Availability Influences Relative Use in Trade-Off Situations