A hidden Markov model to identify and adjust for selection bias: an example involving mixed migration strategies

Estimating the movements of terrestrial animal populations using broad-scale occurrence data

As human and automated sensor networks collect increasingly massive volumes of animal observations, new opportunities have arisen to use these data to infer or track species movements. Sources of broad scale occurrence datasets include crowdsourced databases, such as eBird and iNaturalist, weather surveillance radars, and passive automated sensors including acoustic monitoring units and camera trap networks. Such data resources represent static observations, typically at the species level, at a given location. Nonetheless, by combining multiple observations across many locations and times it is possible to infer spatially continuous population-level movements. Population-level movement characterizes the aggregated movement of individuals comprising a population, such as range contractions, expansions, climate tracking, or migration, that can result from physical, behavioral, or demographic processes. A desire to model population movements from such forms of occurrence data has led to an evolving field that has created new analytical and statistical approaches that can account for spatial and temporal sampling bias in the observations. The insights generated from the growth of population-level movement research can complement the insights from focal tracking studies, and elucidate mechanisms driving changes in population distributions at potentially larger spatial and temporal scales. This review will summarize current broad-scale occurrence datasets, discuss the latest approaches for utilizing them in population-level movement analyses, and highlight studies where such analyses have provided ecological insights. We outline the conceptual approaches and common methodological steps to infer movements from spatially distributed occurrence data that currently exist for terrestrial animals, though similar approaches may be applicable to plants, freshwater, or marine organisms.

Uncovering state-dependent relationships in shallow lakes using Bayesian latent variable regression

Ecosystems sometimes undergo dramatic shifts between contrasting regimes. Shallow lakes, for instance, can transition between two alternative stable states: a clear state dominated by submerged aquatic vegetation and a turbid state dominated by phytoplankton. Theoretical models suggest that critical nutrient thresholds differentiate three lake types: highly resilient clear lakes, lakes that may switch between clear and turbid states following perturbations, and highly resilient turbid lakes. For effective and efficient management of shallow lakes and other systems, managers need tools to identify critical thresholds and state-dependent relationships between driving variables and key system features. Using shallow lakes as a model system for which alternative stable states have been demonstrated, we developed an integrated framework using Bayesian latent variable regression (BLR) to classify lake states, identify critical total phosphorus (TP) thresholds, and estimate steady state relationships between TP and chlorophyll a (chl a) using cross-sectional data. We evaluated the method using data simulated from a stochastic differential equation model and compared its performance to k-means clustering with regression (KMR). We also applied the framework to data comprising 130 shallow lakes. For simulated data sets, BLR had high state classification rates (median/mean accuracy >97%) and accurately estimated TP thresholds and state-dependent TP-chl a relationships. Classification and estimation improved with increasing sample size and decreasing noise levels. Compared to KMR, BLR had higher classification rates and better approximated the TP-chl a steady state relationships and TP thresholds. We fit the BLR model to three different years of empirical shallow lake data, and managers can use the estimated bifurcation diagrams to prioritize lakes for management according to their proximity to thresholds and chance of successful rehabilitation. Our model improves upon previous methods for shallow lakes because it allows classification and regression to occur simultaneously and inform one another, directly estimates TP thresholds and the uncertainty associated with thresholds and state classifications, and enables meaningful constraints to be built into models. The BLR framework is broadly applicable to other ecosystems known to exhibit alternative stable states in which regression can be used to establish relationships between driving variables and state variables.

Behavioural flexibility in migratory behaviour in a long-lived large herbivore

Migratory animals are predicted to enhance lifetime fitness by obtaining higher quality forage and/or reducing predation risk compared to non-migratory conspecifics. Despite evidence for behavioural flexibility in other taxa, previous research on large mammals has often assumed that migratory behaviour is a fixed behavioural trait. Migratory behaviour may be plastic for many species, although few studies have tested for individual-level flexibility using long-term monitoring of marked individuals, especially in large mammals such as ungulates. We tested variability in individual migratory behaviour using a 10-year telemetry data set of 223 adult female elk (Cervus elaphus) in the partially migratory Ya Ha Tinda population in Alberta, Canada. We used net squared displacement (NSD) to classify migratory strategy for each individual elk-year. Individuals switched between migrant and resident strategies at a mean rate of 15% per year, and migrants were more likely to switch than residents. We then tested how extrinsic (climate, elk/wolf abundance) and intrinsic (age) factors affected the probability of migrating, and, secondly, the decision to switch between migratory strategies. Over 630 individual elk-years, the probability of an individual elk migrating increased following a severe winter, in years of higher wolf abundance, and with increasing age. At an individual elk level, we observed 148 switching events of 430 possible transitions in elk monitored at least 2 years. We found switching was density-dependent, where migrants switched to a resident strategy at low elk abundance, but residents switched more to a migrant strategy at high elk abundance. Precipitation during the previous summer had a weak carryover effect, with migrants switching slightly more following wetter summers, whereas residents showed the opposite pattern. Older migrant elk rarely switched, whereas resident elk switched more frequently to migrate at older ages. Our results show migratory behaviour in ungulates is an individually variable trait that can respond to intrinsic, environmental and density-dependent forces. Different strategies had opposing responses to density-dependent and intrinsic drivers, providing a stabilizing mechanism for the maintenance of partial migration and demographic fitness in this population.