An application of upscaled optimal foraging theory using hidden Markov modelling: year-round behavioural variation in a large arctic herbivore

Abstract

Background: In highly seasonal environments, animals face critical decisions regarding time allocation, diet optimisation, and habitat use. In the Arctic, the short summers are crucial for replenishing body reserves, while low food availability and increased energetic demands characterise the long winters (9-10 months). Under such extreme seasonal variability, even small deviations from optimal time allocation can markedly impact individuals' condition, reproductive success and survival. We investigated which environmental conditions influenced daily, seasonal, and interannual variation in time allocation in high-arctic muskoxen (Ovibos moschatus) and evaluated whether results support qualitative predictions derived from upscaled optimal foraging theory.

Methods: Using hidden Markov models (HMMs), we inferred behavioural states (foraging, resting, relocating) from hourly positions of GPS-collared females tracked in northeast Greenland (28 muskox-years). To relate behavioural variation to environmental conditions, we considered a wide range of spatially and/or temporally explicit covariates in the HMMs.

Results: While we found little interannual variation, daily and seasonal time allocation varied markedly. Scheduling of daily activities was distinct throughout the year except for the period of continuous daylight. During summer, muskoxen spent about 69% of time foraging and 19% resting, without environmental constraints on foraging activity. During winter, time spent foraging decreased to 45%, whereas about 43% of time was spent resting, mediated by longer resting bouts than during summer.

Conclusions: Our results clearly indicate that female muskoxen follow an energy intake maximisation strategy during the arctic summer. During winter, our results were not easily reconcilable with just one dominant foraging strategy. The overall reduction in activity likely reflects higher time requirements for rumination in response to the reduction of forage quality (supporting an energy intake maximisation strategy). However, deep snow and low temperatures were apparent constraints to winter foraging, hence also suggesting attempts to conserve energy (net energy maximisation strategy). Our approach provides new insights into the year-round behavioural strategies of the largest Arctic herbivore and outlines a practical example of how to approximate qualitative predictions of upscaled optimal foraging theory using multi-year GPS tracking data.

Keywords: Activity budgets; Arctic ungulate; Behavioural state classification; Hidden Markov modelling; Optimal foraging theory; Seasonality.

Fig. 1

a Map indicating the study area (black rectangle) in northeast Greenland (white). b Map of the study area in detail (WGS 84, UTM zone 27), showing the distribution of landcover types (note that in the statistical models, lakes, non-vegetated and bare ground were pooled to ‘bare ground’). For the distribution of remaining static covariates, see Additional file 1: Fig. S1. c Muskox tracks during the snow-free summer and d snow-covered winter period across years, colour-coded by animal ID (within season). For an overview of muskox observations per season and year, see Additional file 1: Figs. S2-S3

Fig. 2

Histograms of step length and turning angle between hourly relocations, respectively, for the summer a, b and winter c, d season, overlaid with the state-dependent distributions as estimated by the HMMs selected by BIC. The state-dependent distributions were weighted according to the proportion of time spent in the different states, as inferred by the Viterbi sequence. Dashed black lines indicate the associated marginal observation distributions. Note that the x- and y-axes for step length were truncated at the upper range limit to facilitate visualisation (maximum observed step length was 3486 m for summer, and 3897 m for winter). Tables included in panels provide parameter estimates per state and model (mean step length with standard deviation; mean turning angle (phi) and angle concentration (kappa))

Fig. 3

Example of state-decoded step lengths for the a summer and b winter season, showing a period of 18 days for one individual female, respectively. For all state-decoded muskox locations, see Additional file 1: Fig. S15. c Monthly boxplots for the individual-based mean duration of behavioural bouts

Fig. 4

Behavioural time allocation in female muskoxen in northeast Greenland depending on a day of the year, aggregated by month, b time of day during different light seasons (polar night = period of 24 h of darkness, midnight sun = period of 24 h daylight), c year and d landcover type (bare ground, sparse or dense vegetation). Note that in c year t denotes the winter season t-1 to t, i.e. for instance 2014 is the winter 2013–2014. For behavioural time allocation by Julian day, i.e. not aggregated by month, see Additional file 1: Fig. S11 D

Fig. 5

Stationary probabilities (mean and 95% CI) of behavioural state occupancy as a function of the environmental covariates included in the final HMMs for the a summer and b-f winter season. According to BIC model selection, the final summer model included light, landcover type, terrain ruggedness and Julian day as covariates; the final winter model included Julian day, time of day, landcover type, terrain ruggedness, snow depth, light, ambient temperature, year, distance to coast and wind speed. Probabilities were calculated for each covariate and state by fixing the values of the remaining continuous environmental covariates at their respective seasonal mean. Continuous temporal covariates were set to Julian Day 213 (i.e. August 1st) and 91 (i.e. April 1st) for summer and winter, respectively, and to12 o’clock for time of day. Categorical covariates were set to their corresponding reference categories, i.e. to bare ground (landcover type), daylight, and, for the winter model, winter 2013–2014 (year). Monte Carlo simulation from the estimator’s approximate multivariate normal distribution was used to obtain pointwise 95% CIs. Coefficients of the multinomial logistic regression underlying this figure, as well as figures for probabilities of behavioural state occupancy for different categories (e.g. sparse/dense vegetation, darkness), are provided in the supplementary materials (Additional file 1: Tables S2-S3, Figs. S12-S14)