How to account for behavioral states in step-selection analysis: a model comparison

Abstract

Step-selection models are widely used to study animals' fine-scale habitat selection based on movement data. Resource preferences and movement patterns, however, often depend on the animal's unobserved behavioral states, such as resting or foraging. As this is ignored in standard (integrated) step-selection analyses (SSA, iSSA), different approaches have emerged to account for such states in the analysis. The performance of these approaches and the consequences of ignoring the states in step-selection analysis, however, have rarely been quantified. We evaluate the recent idea of combining iSSAs with hidden Markov models (HMMs), which allows for a joint estimation of the unobserved behavioral states and the associated state-dependent habitat selection. Besides theoretical considerations, we use an extensive simulation study and a case study on fine-scale interactions of simultaneously tracked bank voles (Myodes glareolus) to compare this HMM-iSSA empirically to both the standard and a widely used classification-based iSSA (i.e., a two-step approach based on a separate prior state classification). Moreover, to facilitate its use, we implemented the basic HMM-iSSA approach in the R package HMMiSSA available on GitHub.

Keywords: Animal movement; Fine-scale interactions; Habitat selection; Hidden Markov models; Integrated step-selection analysis; Markov-switching regression; Movement behavior; State-switching.

Figure 1. Illustration of how behavioral states can affect animals’ habitat selection and movement patterns.

The state “foraging” is related to search for food such as small insects in an open landscape, while the state “resting” is associated with a retreat in its shelter. Usually, the behavioral states are unobserved, thus hidden, and serially correlated. This structure corresponds to the basic dependence structure of a hidden Markov step-selection model.

Figure 2. Gamma and von Mises distributions for step length and turning angle, respectively, as used in the simulation study (movement kernel).

Parameters are denoted by k (shape), r (rate) and κ (concentration). The distributions for state 1 are shown in blue and for state 2 in orange, except for Scenario 2 in which both states share the same movement kernel (in orange).

Figure 3. Boxplots of the parameter estimates across the 100 simulation runs for each applied method, simulation scenario and number of control locations M, respectively.

The rows refer to the estimated selection coefficient (β), the shape and rate of the gamma-distribution for step length and the concentration parameter (κ) of the von Mises distribution for turning angle, respectively. The columns refer to the three different simulation scenarios. For each method (iSSA, TS-iSSA and HMM-iSSA) and state (state 1: blue, state 2: orange, no state differentiation: black), the three adjacent boxplots refer the use of M = 20, M = 100 and M = 500 control locations per used location for the parameter estimation. Note that in Scenario 2, the TS-iSSA is naturally not capable to distinguish between two states as both share the same movement kernel. Thus, there are only results for a single state.

Figure 4. Estimated state-dependent gamma distributions for step length as implied by the fitted 2-state HMM-iSSAs for each individual in replicates 1–8, respectively.

The distributions are weighted by the relative state occupancy frequencies derived from the Viterbi sequence. The gray histograms in the background show the distribution of the observed step lengths.

Figure 5. (A–B) Estimated iSSA and HMM-iSSA selection coefficients (solid points/triangles) of interaction behavior between individuals of opposing sexes within the eight replicates (1–8), including 95% confidence intervals (solid lines).

Each replicate consisted of two males (male 1 and male 2) and one or two females (female 1 and female 2) such that each individual could respond to up to two opposite-sex individuals (dot: response to female/male 1, triangle: response to female/male 2 within a replicate). Non-significant coefficients (p-values below 0.05) are grayed out. The horizontal dashed line indicates zero (i.e., neutral behavior); positive coefficients indicate attraction, while negative coefficients would indicate avoidance.