A method for the estimation of gene flow parameters from a population structure caused by restricted gene flow and genetic drift

Abstract

A method has been developed which enables the estimation of the plant gene flow parameters σp (pollen dispersal), σs (seed dispersal) and t (outcrossing rate) from a selection-free continuously structured population in equilibrium. The method uses Wright's F-coefficients and introduces a new F-function which describes the genetic similarity as a function of the spatial distance. The method has been elaborated for wind pollinated plant species but can be modified for insect pollination and for animal species. In practice allozymes will provide for the necessary neutral genetic variation. The more loci used and the more intermediate the gene frequencies, the more reliable the results. For the estimation of σp and t together (when the outcrossing rate is not known) at least two chromosomally unlinked loci are required. The method for estimating σs depends on whether the plant species is annual or perennial. The mechanism of selfing has been analysed by the explanation of the value of t by three components: population density (d), pollen flow (σp) and relative fertilization potential of own pollen (Z). The concepts of neighbourhood size and isolation by distance, developed by Wright, who used a single gene flow parameter σ, have been extended to the situation which is realistic for seed plants, using all three parameters σp, σs and t. When σp is large with respect to σs, σs largely determines the value of the neighbourhood size, whereas σp is the most dominating factor in isolation by distance. The use of "local effective population size" and "mean gene transport per generation" instead of "neighbourhood size" and "neighbourhood area", respectively, is proposed to avoid confusion. Computer simulations have been carried out to check the validity and the reliability of the method. Populations of 200 plants, using two or three loci with intermediate allele frequencies, gave good results in the calculation of σp with known value of t and of σs and Ne. With unknown t, especially with lower values of t, larger populations of at least 1,000 plants are necessary to obtain reasonably accurate results for σp and mean gene transport per generation M.