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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.

Patterns of habitat use are commonly studied in horizontal space, but this does not capture the four-dimensional nature of ocean habitats (space, depth, and time). Deep-diving marine animals encounter varying oceanographic conditions, particularly at the poles, where there is strong seasonal variation in vertical ocean structuring. This dimension of space use is hidden if we only consider horizontal movement. To identify different diving behaviours and usage patterns of vertically distributed habitat, we use hidden Markov models fitted to telemetry data from an air-breathing top predator, the Weddell seal, in the Weddell Sea, Antarctica. We present evidence of overlapping use of high-density, continental shelf water masses by both sexes, as well as important differences in their preferences for oceanographic conditions. Males spend more time in the unique high-salinity shelf water masses found at depth, while females also venture off the continental shelf and visit warmer, shallower water masses. Both sexes exhibit a diurnal pattern in diving behaviour (deep in the day, shallow at night) that persists from austral autumn into winter. The differences in habitat use in this resident, sexually monomorphic Antarctic top predator suggest a different set of needs and constraints operating at the intraspecific level, not driven by body size.

State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend these approaches to address the case of multiple observation sequences whose underlying state variables interact. In this article, we provide an overview of the modelling techniques related to coupling in state-switching models, thereby forming a rich and flexible statistical framework particularly useful for modelling correlated time series. Simulation experiments demonstrate the relevance of being able to account for an asynchronous evolution as well as interactions between the underlying latent processes. The models are further illustrated using two case studies related to (a) interactions between a dolphin mother and her calf as inferred from movement data and (b) electronic health record data collected on 696 patients within an intensive care unit.

Patterns of habitat use are commonly studied in horizontal space, but this does not capture the four-10 dimensional nature of ocean habitats. There is strong seasonal variation in vertical ocean structuring, 11 particularly at the poles, and deep-diving marine animals encounter a range of oceanographic condi-12 tions. We use hidden Markov models fitted to telemetry data from an air-breathing top predator to 13 identify different diving behaviours and understand usage patterns of vertically distributed habitat. 14 We show that preference for oceanographic conditions in the Weddell Sea, Antarctica, varies by sex in 15 Weddell seals, and present the first evidence that both sexes use high-density, continental shelf water 16 masses. Males spend more time in the colder, unique high-salinity shelf water masses found at depth, 17 while females also venture off the continental shelf and visit warmer, shallower pelagic water masses. 18 Both sexes exhibit a diurnal pattern in diving behaviour that persists from austral autumn into win-19 ter. These findings provide insights into the Weddell Sea shelf and open ocean ecosystem from a top 20 predator perspective. The differences in habitat use in a resident, sexually monomorphic Antarctic 21 top predator suggest a different set of needs and constraints operating at the intraspecific level, which 22 are not driven by body size. 23 Keywords: diving behaviour, density regime, water mass, continental shelf, Weddell Sea, Weddell 24 seal, sex-specific variation, hidden Markov model 25 1 2 Background 26Understanding what parts of an ecosystem are important for species is a cornerstone of ecological 27 research. Important habitat is often detected by proxy; if a species regularly occurs in a habitat, it 28 must fulfill a life-history function. For large marine vertebrates, occurrence is usually measured using 29 location data from animal-attached instruments. However, identifying the drivers of marine population 30 distributions from horizontal location data alone can be problematic for air-breathing deep-diving 31 marine animals [1, 2]. This group spend most of their time underwater and are intrinsically difficult 32 to observe. Depth is a fundamental dimension of their movement, and information is lost if dives are 33 not considered. Vertical structuring of ocean habitats can enhance productivity and create predictable 34 concentrations of resources across trophic levels (e.g., [3, 4, 5]). Deep-divers can benefit from this 35 increased productivity and prey density at steep physical gradients [6, 7, 8, 9, 10, 11, 12, 13] and track 36 its seasonality [14], which is especially strong at the poles (e.g., [15]). For most species of deep-diving 37 wide-ranging marine vertebrates, we do not have a detailed understanding of what prey they consume 38 nor the structure and functioning of the ecosystems that support them. 39For air-breathing divers like pinnipeds, seabirds and cetaceans, dives are the result of the separation 40 of two basic resources: air at the surface and pre...