The estimation of neighbourhood parameters for plant populations

Abstract

SUMMARYSewall Wright's neighbourhood model indicates that the area containing a panmictic unit within a continuous and uniform array of organisms can be estimated by 4iro2 where a-2 is the parent-offspring dispersal variance measured around a zero mean and relative to a single reference axis passing through the population. The method has proved popular in studies on higher plants but the literature is confused as to how the two components of dispersal variance, for pollen and seeds, should be combined. It is argued that o2 o' ÷o-, where o and o are pollen and seed dispersal variances already corrected to give axial variances. The consequences of using different methods are compared and some puzzling aspects of the previous literature are discussed.

Relative strength of fine-scale spatial genetic structure in paternally vs biparentally inherited DNA in a dioecious plant depends on both sex proportions and pollen-to-seed dispersal ratio

“…Because half of the nuclear genes are dispersed through pollen (as haploid gametes) and the second (Crawford, 1984). For paternally transmitted DNA, s 2 pat ¼ s 2 s þ s 2 p , because all genes are dispersed first through pollen (from male to female) and then through seeds (from female to offspring).…”

“…In sexually reproducing plants, SGS measured at neutral genomic regions is shaped mainly by two factors: gene dispersal capability and effective population density (Hardy and Vekemans, 1999;Rousset, 2000). Among others, the effective density depends on the effective number of parents (Vekemans and Hardy, 2004) and thus can differ substantially among different plant populations because of differences in distributions of individual reproductive success (Lyons et al, 1989), whereas gene dispersal capability depends on seed and pollen dispersal distances (Crawford, 1984).…”

Effect of balancing selection on spatial genetic structure within populations: theoretical investigations on the self-incompatibility locus and empirical studies in Arabidopsis halleri

“…We assumed that the dispersal of seeds and pollen followed an isotropic bivariate normal distribution (that is, normal distribution in a two-dimensional space with equal dispersal in all directions), with standard deviation s s and s p (s represents the axial standard deviation of dispersal distances in units of grid steps, that is, the standard deviation of dispersal distances measured around a zero mean and relative to a single reference axis passing through the population). The axial variance of overall gene dispersal can be computed as s t 2 ¼ s p 2 /2 þ s s 2 (Crawford, 1984 to the observed level of population genetic structure based on a survey of microsatellite data in 65 populations covering the whole geographical distribution of A. halleri, F ST E 0.25; M Pauwels, unpublished results) when investigating the effect of variation in other parameters. To determine genotypes of each individual i across the grid at generation t, we used a forward simulation algorithm that searched potential parents of i in the grid at generation tÀ1.…”

Genetic neighbourhoods in plants with diverse systems of mating and different patterns of growth

“…The use of incorrect formulae for the calulation of genetic neighbourhoods by previous workers has been pointed out by Crawford (1984b). The failure to take account of growth or vegetative "reproduction" can also lead to serious errors and (a) th<l, are not transmitted through pollen, their parentoffspring dispersal variance, o-, is given by: which will always be smaller than that of the nuclear genes.…”

“…The method by which these two components may be combined is given by Crawford (1984b). In plant species which show significant amounts of vegetative growth prior to flowering, it is necessary to consider this growth as a component of dispersal.…”