A framework for understanding semi-permeable barrier effects on migratory ungulates

By studying animal movements, researchers can gain insight into many of the ecological characteristics and processes important for understanding population-level dynamics. We developed a Brownian bridge movement model (BBMM) for estimating the expected movement path of an animal, using discrete location data obtained at relatively short time intervals. The BBMM is based on the properties of a conditional random walk between successive pairs of locations, dependent on the time between locations, the distance between locations, and the Brownian motion variance that is related to the animal's mobility. We describe two critical developments that enable widespread use of the BBMM, including a derivation of the model when location data are measured with error and a maximum likelihood approach for estimating the Brownian motion variance. After the BBMM is fitted to location data, an estimate of the animal's probability of occurrence can be generated for an area during the time of observation. To illustrate potential applications, we provide three examples: estimating animal home ranges, estimating animal migration routes, and evaluating the influence of fine-scale resource selection on animal movement patterns.

1. Animal migration has long intrigued scientists and wildlife managers alike, yet migratory species face increasing challenges because of habitat fragmentation, climate change and over-exploitation. Central to the understanding migratory species is the objective discrimination between migratory and nonmigratory individuals in a given population, quantifying the timing, duration and distance of migration and the ability to predict migratory movements. 2. Here, we propose a uniform statistical framework to (i) separate migration from other movement behaviours, (ii) quantify migration parameters without the need for arbitrary cut-off criteria and (iii) test predictability across individuals, time and space. 3. We first validated our novel approach by simulating data based on established theoretical movement patterns. We then formulated the expected shapes of squared displacement patterns as nonlinear models for a suite of movement behaviours to test the ability of our method to distinguish between migratory movement and other movement types. 4. We then tested our approached empirically using 108 wild Global Positioning System (GPS)-collared moose Alces alces in Scandinavia as a study system because they exhibit a wide range of movement behaviours, including resident, migrating and dispersing individuals, within the same population. Applying our approach showed that 87% and 67% of our Swedish and Norwegian subpopulations, respectively, can be classified as migratory. 5. Using nonlinear mixed effects models for all migratory individuals we showed that the distance, timing and duration of migration differed between the sexes and between years, with additional individual differences accounting for a large part of the variation in the distance of migration but not in the timing or duration. Overall, the model explained most of the variation (92%) and also had high predictive power for the same individuals over time (69%) as well as between study populations (74%). 6. The high predictive ability of the approach suggests that it can help increase our understanding of the drivers of migration and could provide key quantitative information for understanding and managing a broad range of migratory species. © 2010 The Authors. Journal compilation © 2010 British Ecological Society.