A framework for modelling range shifts and migrations: asking when, whither, whether and will it return.

Many animals undertake movements that are longer scaled and more directed than their typical home ranging behaviour. These movements include seasonal migrations (e.g. between breeding and feeding grounds), natal dispersal, nomadic range shifts and responses to local environmental disruptions. While various heuristic tools exist for identifying range shifts and migrations, none explicitly model the movement of the animals within a statistical framework that facilitates quantitative comparisons. We present the mechanistic range shift analysis (MRSA), a method to estimate a suite of range shift parameters: times of initiation, duration of transitions, centroids and areas of respective ranges. The method can take the autocorrelation and irregular sampling that is characteristic of much movement data into account. The mechanistic parameters suggest an intuitive measure, the range shift index, for the extent of a range shift. The likelihood based estimation further allows for statistical tests of several relevant hypotheses, including a range shift test, a stopover test and a site fidelity test. The analysis tools are provided in an R package (marcher). We applied the MRSA to a population of GPS tracked roe deer (Capreolus capreolus) in the Italian Alps between 2005 and 2008. With respect to seasonal migration, this population is extremely variable and difficult to classify. Using the MRSA, we were able to quantify the behaviours across the population and among individuals across years, identifying extents, durations and locations of seasonal range shifts, including cases that would have been ambiguous to detect using existing tools. The strongest patterns were differences across years: many animals simply did not perform a seasonal migration to wintering grounds during the mild winter of 2006-2007, even though some of these same animals did move extensively in other, harsher winters. For seasonal migrants, however, site fidelity across years was extremely high, even after skipping an entire seasonal migration. These results suggest that for roe deer behavioural plasticity and tactical responses to immediate environmental cues are reflected in the decision of whether rather than where to migrate. The MRSA also revealed a trade-off between the probability of migrating and the size of a home range.