Why we do not expect dispersal probability density functions based on a single mechanism to fit real seed shadows

Bullock et al. (Journal of Ecology 105:6-19, 2017) have suggested that the theory behind the Wald Analytical Long Distance (WALD) model for wind dispersal from a point source needs to be re-examined. This is on the basis that an inverse Gaussian probability density function (pdf) does not provide the best fit to seed shadows around individual source plants known to be dispersed by wind.
We present two reasons why we would not necessarily expect any of the standard mechanistically derived pdfs to fit real seed shadows any better than empirical functions.
Firstly, the derivation of “off-the-shelf” pdfs such as the Gaussian, exponential and inverse Gaussian involves only one of the processes and factors that together generate a real seed shadow. It is implausible to expect that a single-process model, no matter how sophisticated in detail, will capture the behaviour of an entire, complex system, which may involve a number of sequential random processes, or a superposition of parallel ran...