Holling meets habitat selection: functional response of large herbivores revisited

Background Holling (Can Entomol 91(5):293–320, 1959) was the first to describe a functional response between a predator’s consumption-rate and the density of its prey. The same concept can be applied to the habitat selection of herbivores, specifically, the change in relative habitat use with the change in habitat availability. Functional responses in habitat selection at a home-range scale have been reported for several large herbivores. However, a link to Holling’s original functional response types has never been drawn, although it could replace the current phenomenological view with a more mechanistically based understanding of functional responses. Methods In this study, discrete choice models were implemented as mixed-effects baseline-category logit models to analyze the variation in habitat selection of a large herbivore at seasonal and diurnal scales. Thus, changes in the use of land cover types with respect to their availability were investigated by monitoring 11 land cover types commonly used by roe deer (Capreolus capreolus) in the Bavarian Forest National Park, Germany. Functional response curves were then fitted using Holling’s formulas. Results Strong evidence of non-linear functional responses was obtained for almost all of the examined land cover types. The shape of the functional response curves varied depending on the season, the time of day, and in some cases between sexes. These responses could be referenced to Holling’s types, with a predominance of type II. Conclusions Our results indicate that Holling’s types can be applied to describe general patterns of the habitat selection behavior of herbivores. Functional responses in habitat selection may occur in situations requiring a trade-off in the selection of land cover types offering different resources, such as due to the temporally varying physiological needs of herbivores. Moreover, two associated parameters defining the curves (prey density and predation rate) can aid in the identification of temporal variations and in determinations of the strength of the cost-benefit ratio for a specific land cover type. Application of our novel approach, using Holling’s equations to describe functional responses in the habitat selection of herbivores, will allow the assignment of general land cover attraction values, independent of availability, thus facilitating the identification of suitable habitats.

Before thinning, 172,507 xes were obtained for 52 roe deer (26 males, 26 females), ranging from 136 to 17,044 xes per individual (mean: 3,317, SD: 2,897), over a period of 142,081 days (mean: 484, SD: 397). The average spatial accuracy of the xes was 10 m, with a maximum recorded error of 16.3 m (Stache, Löttker & Heurich, 2012). Spatial autorcorrelation was analysed using variograms (Fleming et al., 2014). For the monthly habitat selection, it is assumed that successive locations are independent at the scale of the home range, i.e. that the animal might have crossed the home range between successive steps. In the variogram, this condition is found at the time interval between successive steps where the squared displacement distance (approximately) levels o. Variograms were calculated using the package ctmm (Fleming & Calabrese, 2015) and visually inspected the variograms.
In our data this interval was approximately 25 h. Only data from individuals with > 70 recordings were included. Per month, only the individuals with at least 10 recordings were taken into account. Thus, the nal analysis consisted of 15,267 locations of 17 females and 19 males.

Appendix 1b. Model selection & model t
Nineteen dierent models f i (x) that estimated the eects of the above mentioned variables on the odds that roe deer select habitat type i over K, were estimated for each habitat type i = 1, . . . , K. To take into account the problem of overtting, the prediction performance of all models was measured by applying cross-validation, which is nding the model f i (x) that can best predict the choice behaviour of the animals when choosing between habitat i and K at time m. Hence, models for habitats that are selected dierently over time, compared to the baseline category, will in general obtain a better prediction performance. Cross-validation was applied by splitting the data into ten subgroups, ensuring that a) the data of one individual were evenly spread over all ten subgroups and b) within groups, data for all times of the year and day were available (Wiens et al., 2008).
As the prediction involved a probability and the observed variable was binary, a receiver op-   the table on the bottom of the gure. All models included the variable id (for individual) and year as random eects. Abbrevations: rel.avail, relative avialability of habitat type; s, smooth term, for hour and month it is a cyclic smooth function; te, cyclic tensor product smooth term; by, a replicate of the smooth is produced for each factor level of sex or season or interaction of both, respectively.
Appendix S2: Holling's equation as applied to habitat selection Calculating the point of switch when use equals availability for Holling type II.
Calculating the point of switch when use equals availability for Holling type III.
Calculating the inection point for Holling type III.
First derivative Inection point: Appendix S4: Shapes of functional response curves Figure S4.  Appendix S5: Overview of optimal models describing Holling types Given Holling's equations for type I: h I (x) = ax, where x is the availability of a habitat, a value between 0 and 1; for type II: h II (x) = ax b+x and for type III: h III (x) = ax 2 b 2 +x 2 and the estimated curves for functional response the optimal values for a and b are evaluated that minimizes the distance between the estimated curves and one of the Holling functions. The optimal values are listed in the following tables for dierent times of the year (month: June or December) and day (noon or midnight) and for males and females. Furthermore, the fraction a b indicates the selection strength independent of availability of a habitat: the greater the value the greater the general use. x * for Holling type II is the availability at which use equals availability, hence the value of relative availability at which no selection occurs, which is the tipping point when selection switches to avoidance of a habitat.

Habitat
Sex  Figure S1: Appendix S6. Overview of the eect of varying parameters a and b of the Holling's type II on the functional response curve, linking the proportion of availability of a habitat with the proportion of its use.