Simultaneous estimation of the temporal and spatial extent of animal migration using step lengths and turning angles.

BACKGROUND: Animals of many different species, trophic levels, and life history strategies migrate, and the improvement of animal tracking technology allows ecologists to collect increasing amounts of detailed data on these movements. Understanding when animals migrate is important for managing their populations, but is still difficult despite modelling advancements. METHODS: We designed a model that parametrically estimates the timing of migration from animal tracking data. Our model identifies the beginning and end of migratory movements as signaled by change-points in step length and turning angle distributions. To this end, we can also use the model to estimate how an animal's movement changes when it begins migrating. In addition to a thorough simulation analysis, we tested our model on three datasets: migratory ferruginous hawks (Buteo regalis) in the Great Plains, barren-ground caribou (Rangifer tarandus groenlandicus) in northern Canada, and non-migratory brown bears (Ursus arctos) from the Canadian Arctic. RESULTS: Our simulation analysis suggests that our model is most useful for datasets where an increase in movement speed or directional autocorrelation is clearly detectable. We estimated the beginning and end of migration in caribou and hawks to the nearest day, while confirming a lack of migratory behaviour in the brown bears. In addition to estimating when caribou and ferruginous hawks migrated, our model also identified differences in how they migrated; ferruginous hawks achieved efficient migrations by drastically increasing their movement rates while caribou migration was achieved through significant increases in directional persistence. CONCLUSIONS: Our approach is applicable to many animal movement studies and includes parameters that can facilitate comparison between different species or datasets. We hope that rigorous assessment of migration metrics will aid understanding of both how and why animals move.

Next-generation matrices for marine metapopulations: The case of sea lice on salmon farms.

Classifying habitat patches as sources or sinks and determining metapopulation persistence requires coupling connectivity between habitat patches with local demographic rates. While methods to calculate sources, sinks, and metapopulation persistence exist for discrete-time models, there is no method that is consistent across modeling frameworks. In this paper, we show how next-generation matrices, originally popularized in epidemiology to calculate new infections after one generation, can be used in an ecological context to calculate sources and sinks as well as metapopulation persistence in marine metapopulations. To demonstrate the utility of the method, we construct a next-generation matrix for a network of sea lice populations on salmon farms in the Broughton Archipelago, BC, an intensive salmon farming region on the west coast of Canada where certain salmon farms are currently being removed under an agreement between local First Nations and the provincial government. The column sums of the next-generation matrix can determine if a habitat patch is a source or a sink and the spectral radius of the next-generation matrix can determine the persistence of the metapopulation. With respect to salmon farms in the Broughton Archipelago, we identify the salmon farms which are acting as the largest sources of sea lice and show that in this region the most productive sea lice populations are also the most connected. The farms which are the largest sources of sea lice have not yet been removed from the Broughton Archipelago, and warming temperatures could lead to increased sea louse growth. Calculating sources, sinks, and persistence in marine metapopulations using the next-generation matrix is biologically intuitive, mathematically equivalent to previous methods, and consistent across different modeling frameworks.

Timing and probability of arrival for sea lice dispersing between salmon farms.

Sea lice are a threat to the health of both wild and farmed salmon and an economic burden for salmon farms. With a free-living larval stage, sea lice can disperse tens of kilometres in the ocean between salmon farms, leading to connected sea louse populations that are difficult to control in isolation. In this paper, we develop a simple analytical model for the dispersal of sea lice (Lepeophtheirus salmonis) between two salmon farms. From the model, we calculate the arrival time distribution of sea lice dispersing between farms, as well as the level of cross-infection of sea lice. We also use numerical flows from a hydrodynamic model, coupled with a particle tracking model, to directly calculate the arrival time of sea lice dispersing between two farms in the Broughton Archipelago, British Columbia, in order to fit our analytical model and find realistic parameter estimates. Using the parametrized analytical model, we show that there is often an intermediate interfarm spacing that maximizes the level of cross-infection between farms, and that increased temperatures will lead to increased levels of cross-infection.

A Next-Generation Approach to Calculate Source-Sink Dynamics in Marine Metapopulations.

In marine systems, adult populations confined to isolated habitat patches can be connected by larval dispersal. Source-sink theory provides effective tools to quantify the effect of specific habitat patches on the dynamics of connected populations. In this paper, we construct the next-generation matrix for a marine metapopulation and demonstrate how it can be used to calculate the source-sink dynamics of habitat patches. We investigate the effect of environmental variables on the source-sink dynamics and demonstrate how the next-generation matrix can provide useful biological insight into transient as well as asymptotic dynamics of the model.