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Stochastic dispersal processes in plant populations. (English) Zbl 0889.92026
Summary: A dispersal model for airborne pollen based on assumptions about wind directionality, gravity, and a wind threshold at which pollen is taken by the wind is developed, using a three dimensional diffusion approximation. The bivariate probability distribution of pollen receipt by flowers at the same height as the pollen source is derived. Gravity, vertical random movements, and vegetation density turn out to have similar effects on this distribution. Maximum likelihood methods for estimating the combined parameters from data with multiple point or continuous pollen sources, and one or more plant varieties, are developed. Using an example data set from the literature, it is shown that our model gives a better fit than more traditional descriptive dispersal models of the form \(e^{-a{r^b}}\). We also show that estimates of important properties of the dispersal distribution, such as the variances, become considerably smaller using our model than for the more traditional models. Finally, we discuss potential extensions and evolutionary implications of these types of models.

MSC:
92D40 Ecology
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
62P10 Applications of statistics to biology and medical sciences; meta analysis
Software:
bootstrap; Maple
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