Investigating movement within irregularly shaped patches: Analysis of markrelease-recapture data using randomization procedures

The analysis of net-displacement data extracted from mark-release-recapture (MRR) Studies is usually based on the assumption that movement follows a random walk in homogeneous space. Yet given sufficient time, within-patch movement cannot conform to this assumption, as maximum net-displacement must be limited by the patch's dimension. We thus suggest a pragmatic protocol for analyzing such MRR data: (1) Test for correlation between the time intervals between captures and displacement distance; if such a correlation is weak, displacement does not follow the rules of a random walk. (2) Test whether net-displacement observed approaches an even density distribution (null-model). (3) Estimate whether net-displacement is limited by the individual's tendency to restrict movement to sub-regions of a patch. For this purpose we developed two randomization algorithms that generate patch-specific distance distributions given that (i) displacement distances converge to an even distribution and habitat use is homogeneous within patches, or that (ii) the spatial distribution of capture points is heterogeneous. Both methods are expanded to account for the influence of potential movement restrictions beyond those imposed by the patch's dimension. The sequential comparison of empirical distributions with distributions generated by these algorithms allows drawing conclusions about the rules underlying withinpatch movement. We exemplarily apply our protocol to an empirical MRR data set on the butterfly Maculinea teleius. The analysis indicates that habitat use within patches is heterogeneous and that Maculinea possibly establishes home ranges. Such analyses may convey important information about the biology of species and help to develop appropriate conservation strategies.