All dispersal functions are wrong, but many are useful: A response to Cousens et al.

Abstract

Abstract To address the lack of information about the shape and extent of real dispersal kernels, Bullock et al. (Journal of Ecology 105:6‐19, 2017) synthesised empirical information on seed dispersal distances. Testing the fit of a variety of probability density functions, they found no function was the best‐fitting for all datasets but some outperformed others. Cousens et al. (Journal of Ecology, 2017) focus on the specific finding of the generally poor fit of the WALD function to wind dispersal data and use this to argue that mechanistically derived functions would not be expected to fit data particularly well. We agree in part with this argument and discuss the issues that may lead to poor fit, including the simplifying assumptions of the WALD and the complexity of the dispersal process. We explain the fundamental linkage between the mechanistic form of the WALD and the derived function used for fitting to data. We demonstrate, however, that the logic that a mechanistically based function could fit to data is valid, under the hypothesis that it encompasses the key processes determining the dispersal kernel. This argument is supported by the facts that: (1) our analyses and others have shown the WALD performs well in a number of cases; and (2) the WALD is the best‐fitting function for an example in which we simulate dispersal data using a realistic representation of variability in the wind dispersal process. Synthesis. While there are reasons that mechanistically derived functions may not fit well to empirical data, they do in some empirical and simulated cases and this suggests they can capture the dispersal behaviour of real systems. Mechanistic functions should be explored along with other more general functions when describing empirical data to investigate their simplifying assumptions and to add to our arsenal of functions for analysing dispersal data. Analyses using these functions are critical if we are to move from simply describing the system in which the data were gathered to gaining more general insights into dispersal and predicting its consequences.