Genetic structures in finite, open-pollinated plant populations: a model and its application to seed orchards

A model has been constructed to investigate the consequences of the rate of self-fertilization, pollen-dispersal, population-size, and number of clones on the genetic structure of finite seed plant populations. Derivations have been performed for two different cases: A) Parental genetic structure explicitly given: inferences for the expected genetic structure of the resulting seed population; B) Extension of case A) to several non-overlapping generations. If random cross-fertilization is assumed for case A) the genetic composition does not change and the genetic distance between the corresponding Hardy-Weinberg-structure and the expected offspring-structure is 0 if the rate of self-fertilization is equal to 1/N (N = population-size); any deviation from 1/N causes an increase in genetic distance.in case B) the expected genetic structures have been derived for all generations and it was possible to establish a comparatively simple dependence on the coefficient of inbreeding. In addition the variance of the allele-frequency has been presented. All the above influential components can be summarized by a single quantity, called M. After proving that 1/M can be conceived as the effective population-size, all the results obtained could be presented depending on this effective size and the average rate of self-fertilization only.Applying the findings of the model to the situation realized approximately in a seed-orchard, the following statements can be made:Case A) Again assuming random cross-fertilization, a deviation of the parental population from the corresponding Hardy-Weinberg-proportions can, with increasing rate of self-fertilization, be exceeded by the respective deviation of the seed population. Case B) The influence of pollen dispersal on the effective population size has been investigated, assuming no variation of the individual rates of self-fertilization, pollen and seed production within the population. Only extremely small differences between effective and actual population size were obtained, which indicates that the influence of pollen dispersal is of minor importance in this case. For different rates of self-fertilization, significant differences in the increments per generation for the coefficients of inbreeding, as well as the frequency of homozygotes, were obtained for the first generation only. Decreasing number of clones influences the rate of self-fertilization and the effective population size simultaneously by increasing the first and decreasing the latter. This is transferred to the coefficient of inbreeding, frequency of the homozygotes and the variance of the allele frequency by an increase of increments for all generations.