Dispersal kernels of butterflies: Power-law functions are invariant to marking frequency

Abstract

Summary Despite recent developments of sophisticated dispersal modelling, simple regression-based models remain useful for estimating frequencies of long-distance movements of animals. Since the inverse power function, IPF (ln I=ln C−m ln D), but not the negative exponential function, NEF (ln I=ln a−k D), exhibits the property of self-similarity, it should be robust against variation in effort invested into mark-recapture studies. We illustrate this using three data sets on movements of butterflies (Lepidoptera): Euphydryas aurinia, year 2002 (better fitted by IPF), E. aurinia, year 2003 (better fitted by NEF) and Parnassius mnemosyne (better fitted by NEF). By simulated reductions of numbers of animals, numbers of marking days, and marking effort, we show that IPF withstands severe decline in marking frequency without a change of parameters of regressions based on reduced data. In contrast, parameters of NEFs fitted to the reduced data widely varied and differed from functions based on unreduced data. Owing to the robust performance of IPF, reliable dispersal estimates may be obtained at relatively small field effort, which may facilitate quick and efficient comparisons of movement patterns among species, locations and populations.