Plant dispersal, neighbourhood size and isolation by distance


Bryan K. Epperson, Fax: (517) 432-1143; E-mail:


A theoretical relationship between isolation by distance or spatial genetic structure (SGS) and seed and pollen dispersal is tested using extensive spatial-temporal simulations. Although for animals Wright's neighbourhood size inline image has been ascertained also, where inline image is the axial variance of distances between parents and offspring, and it was recently confirmed that inline image when dispersal of females and males differ, the situation for plants had not been established. This article shows that for a very wide range of conditions, neighbourhood size defined by Crawford's formula inline image fully determines SGS, even when dispersal variances of seed (inline image) and pollen (inline image) differ strongly. Further, self-fertilization with rate s acts as zero-distance pollen dispersal, and inline image fully determines SGS, for most cases where there are both likely parameter values and substantial SGS. Moreover, for most cases, there is a loglinear relationship, I(1) = 0.587 – 0.117 ln(Ne), between SGS, as measured by I(1), Moran's coefficient for adjacent individuals, and Ne. However, there are several biologically significant exceptions, namely for very low or large Ne, SGS exceeds the loglinear values. There are also important exceptions to Crawford's formula. First, plants with low seed dispersal, high outcross pollen dispersal and high selfing rate show larger SGS than predicted. Second, in plants with very low (near zero) seed dispersal, selfing decreases SGS, opposite expectations. Finally, in some cases seed dispersal is more critical than pollen dispersal, in a manner inconsistent with Crawford's formula.