Functional responses in habitat use: availability influences relative use in trade-off situations.
Habitat selection is an important feature of behavior and population dynamics, and it has therefore received much attention (e.g., Fretwell and Lucas 1970, Rosenzweig 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 Wittenberger 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 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 opportunities for all essential activities required for successful 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 exposure (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 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 Ostbye 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 concept 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 sometimes 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; Lucherini 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 Palomares 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, Thirgood 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.
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 adequate sample of N individuals from a target population of animals with well-defined home ranges (level 1) and a sample of ([n.sub.i], 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 [n.sub.i], the number of observations in habitat type A([n.sub.(A)i]) can be assumed to have a binomial distribution Bin([n.sub.i], [p.sub.(u)i]), where [p.sub.(u)i] is the probability for an individual i of being located in habitat A (which can be estimated as [Mathematical Expression Omitted] and [n.sub.i] = [n.sub.(A)i] + [n.sub.(B)i]. Our approach is to investigate whether [p.sub.(u)i] is conditional on the proportional availability of that habitat ([p.sub.(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.sub.(u)] against proportional availability ([p.sub.(A)]) for the target population. The regression approach requires that the predictor variable [p.sub.(a)] actually vary among the N individuals in the sample (see Discussion). Furthermore, we assume that [p.sub.(a)] can be mapped and quantified within a delineated home range based on the [n.sub.i] 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.sub.(u)] = log([p.sub.(u)]/[1 - [p.sub.(u)])
= [Alpha] + [Beta] log([p.sub.(a)]/[1 - [p.sub.(a)])
where [Alpha] (regression intercept; logit [p.sub.(a)] = 0 for [p.sub.(a)] = 0.5) and [Beta] (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 [Alpha] = 0 and [Beta] = 1. We expect [Beta] = 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.sub.(a)i] so that the expected (or fitted) proportion used is [p.sub.(u)] = exp([Alpha])/[1 + exp([Alpha])]. The situation [Alpha] [greater than] 0 and [Beta] [less than or equal to] 1 implies that habitat A is always selected (disproportionately more used than available). For [Beta] [greater than] 1 and [Alpha] [greater than] 0 the strength of habitat selection increases with [p.sub.(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.sub.(a)]. Specifically, 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 habitat, i.e., [Mathematical Expression Omitted]. Thus certain combinations of [Alpha] and [Beta] may indicate habitat selection in some part of the empirical range of [p.sub.(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 [[Alpha].sub.j] (j = 1, 2) (additive sex effect on a logit scale) and [[Beta].sub.i] (significant interaction between logit [p.sub.(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 [Mathematical Expression Omitted]. 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 imprecise radio-fix recordings; Springer 1979) may lead to biases when certain habitat types become increasingly rare and/or fragmented. Specifically, increasing fragmentation will lead to an increase in the number of incorrectly assigned fixes and possibly also a mismatch 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 carolinensis) and Ring-necked Pheasants (Phasianus colchicus). For an individual to be included in the analysis, we used the criterion that [greater than] 5% of the rarest habitat must be available within the home range.
Aebischer et al. (1993) considered initially five vegetation 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 predominantly 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 [greater than] 5% of open habitat available to them were included in the regression analysis. Squirrels were tracked in July 1979 on Elton Estate, Northamptonshire, 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 [greater than] 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 (5.7353.16% availability).
The regression model based on all individuals provided an appropriate fit to the data (Table 1, [ILLUSTRATION FOR FIGURE 1 OMITTED]). Thus our dichotomous classification of squirrel habitats seemed justified. The estimated value of the slope parameter ([Beta]) 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 [ILLUSTRATION FOR FIGURE 1 OMITTED], i.e., gray squirrels spent less time in open habitat as [TABULAR DATA FOR TABLE 1 OMITTED] availability increased. The regression curve and its confidence envelope indicated that selection for open habitat ([p.sub.(u)] where [p.sub.(a)] [greater than] [p.sub.(a)]) occurred only for [p.sub.(a)] [less than] 0.1 [ILLUSTRATION FOR FIGURE 1 OMITTED].
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 ([ILLUSTRATION FOR FIGURE 1 OMITTED], Table 1). To obtain an appropriate fit these three outlying individuals had to be removed from the analysis. Although 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.
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 violation of the assumption of independence will be identified 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. Furthermore, a dichotomous classification of the habitat as we have done may be too simplistic in a truly polychotomous 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 [ILLUSTRATION FOR FIGURE 2 OMITTED]. 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 [less than or equal to] 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 include the same amount of feeding habitat, then with increasing home range size, the ratio of food to cover in the home range decreases [ILLUSTRATION FOR FIGURE 2 OMITTED]. Thus, availabilities 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 correlation 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 movements between suitable habitats (i.e., transition habitat sensu Hansson  or traveling habitat sensu Rosenzweig ). 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 resemblance 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., [ILLUSTRATION FOR FIGURE 2 OMITTED]), 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 studies 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 estimating 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 categories. 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. Recent 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 similar to those made in theoretical models of habitat selection (i.e., Levins 1968, Rosenzweig 1981). Indeed, judicious simplification to achieve analytical tractability and a mechanistic understanding of ecological phenomena 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 justifications 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 emphasis 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 polychotomous response functions (McCullagh and Nelder 1989, Lunneborg 1994).
We thank Ivar Mysterud, Dana L. Thomas, Jerry Thomas Warren, and one anonymous referee for many valuable comments on an earlier draft of this paper.
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|Author:||Mysterud, Atle; Ims, Rolf Anker|
|Date:||Jun 1, 1998|
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