Process-based functions for seed retention on animals: a test of improved descriptions of dispersal using multiple data sets

Studies of external seed transport on animals usually assume that the probability of detachment is constant, so that seed retention should show a simple exponential relationship with time. This assumption has not been tested explicitly, and may lead to inaccurate representation of long distance seed dispersal by animals. We test the assumption by comparing the fit to empirical data of simple, two-parameter functions. Fifty-two data sets were obtained from five published studies, describing seed retention of 32 plant species on sheep, cattle, deer, goats and mice. Model selection suggested a simple exponential function was adequate for data sets in which seed retention was followed for short periods (<48 h). The data gathered over longer periods (49-219 days) were best described by the power exponential function, a form of the stretched exponential which allows a changing dropping rate. In these cases the power exponential showed that seed dropping rate decreased with time, suggesting that seeds vary in attachment, with some seeds becoming deeply buried or wound up in the animal's coat. Comparison of fitted parameters across all the data sets also confirmed that seeds with adhesive structures have lower dropping rates than those without. We conclude that the seed dropping rate often changes with time during external transport on animals and that the power exponential is an effective function to describe this change. We advise that, to analyse seed dropping rates adequately, retention should be measured over reasonable time periods - until most seeds are dropped - and both the simple and power exponential functions should be fitted to the resulting data. To increase its utility, we provide functions describing the seed dropping rate and the dispersal kernel resulting from the power exponential relationship.