Hidden Markov movement models reveal diverse seasonal movement patterns in two North American ungulates

Abstract

Animal movement is the mechanism connecting landscapes to fitness, and understanding variation in seasonal animal movements has benefited from the analysis and categorization of animal displacement. However, seasonal movement patterns can defy classification when movements are highly variable. Hidden Markov movement models (HMMs) are a class of latent-state models well-suited to modeling movement data. Here, we used HMMs to assess seasonal patterns of variation in the movement of pronghorn (Antilocapra americana), a species known for variable seasonal movements that challenge analytical approaches, while using a population of mule deer (Odocoileus hemionus), for whom seasonal movements are well-documented, as a comparison. We used population-level HMMs in a Bayesian framework to estimate a seasonal trend in the daily probability of transitioning between a short-distance local movement state and a long-distance movement state. The estimated seasonal patterns of movements in mule deer closely aligned with prior work based on indices of animal displacement: a short period of long-distance movements in the fall season and again in the spring, consistent with migrations to and from seasonal ranges. We found seasonal movement patterns for pronghorn were more variable, as a period of long-distance movements in the fall was followed by a winter period in which pronghorn were much more likely to further initiate and remain in a long-distance movement pattern compared with the movement patterns of mule deer. Overall, pronghorn were simply more likely to be in a long-distance movement pattern throughout the year. Hidden Markov movement models provide inference on seasonal movements similar to other methods, while providing a robust framework to understand movement patterns on shorter timescales and for more challenging movement patterns. Hidden Markov movement models can allow a rigorous assessment of the drivers of changes in movement patterns such as extreme weather events and land development, important for management and conservation.

Keywords: Hidden Markov movement model; migration; movement; mule deer; pronghorn.

FIGURE 1

Study areas for mule deer (a) and pronghorn (b) in Wyoming, USA. A random sample of animal locations (black dots) from 25 animals (for both mule deer, 197,824 locations, and pronghorn, 126,492 locations) indicates general space use across years, and the 95% isopleth of kernel density estimates for summer locations (generically defined as June–August, red), and winter locations (generically defined as December–February, blue) suggest broad seasonal space use patterns. The background colors denote elevation and range from approximately 1500–3900 m for mule deer, and 1400–3500 m for pronghorn.

FIGURE 2

Distributions of movement characteristics (step lengths and turning angles) for each movement state (state 1 equals short‐distance local movements; state 2 equals long‐distance movements) for pronghorn (a) and mule deer (b) from the estimated Hidden Markov movement model. A turning angle equal to 0 radians indicates a straight‐ahead movement path; a turning angle equal to $\pi$ radians indicates the opposite direction from the previous bearing.

FIGURE 3

Seasonal trends in the daily probabilities of transitioning among movement states (state 1 equal to short distance local movements; state 2 equal to long distance movements) in the HMM for pronghorn (purple) and mule deer (green). The solid line indicates the median and the ribbon indicates the 90% HDPI. The flexible, spline‐based approach to modeling seasonal movements did not guarantee July–July probabilities be equal, and the minor differences in probabilities arose from the tradeoff between flexibility and simplicity in the model form. Note the differences in scale for the y‐axes in both panels.

FIGURE 4

Marginal probabilities of animals being in movement state 2 (long distance movements) on each day of the year for mule deer (green, top panel) and pronghorn (purple, bottom panel). The solid line indicates the median and the ribbon indicates the 90% HDPI. We defined seasonal events as the maximum rate of change in the transition probabilities and estimated the timing of these events using the approximate posterior. The dashed line indicates the median day, and the gray interval indicates the 90% HDPI.