A simple model for pollen-parent fecundity distributions in bee-pollinated forage legume polycrosses

A simple Weibull distribution based empirical model that predicts pollen-parent fecundity distributions based on polycross size alone has been developed in outbred forage legume species for incorporation into quantitative genetic theory. Random mating or panmixis is a fundamental assumption in quantitative genetic theory. Random mating is sometimes thought to occur in actual fact, although a large body of empirical work shows that this is often not the case in nature. Models have been developed to explain many non-random mating phenomena. This paper measured pollen-parent fecundity distributions among outbred perennial forage legume species [autotetraploid alfalfa (Medicago sativa L.), autohexaploid kura clover (Trifolium ambiguum M. Bieb.), and diploid red clover (Trifolium pratense L.)] in ten polycrosses ranging in size (N) from 9 to 94 pollinated with bee pollinators [Bumble Bees (Bombus impatiens Cr.) and leafcutter bees (Megachile rotundata F.)]. A Weibull distribution best fit the observed pollen-parent fecundity distributions. After standardizing data among the 10 polycrosses, a single Weibull distribution-based model was obtained with an R (2) of 0.978. The model is able to predict pollen-parent fecundity distributions based on polycross size alone. The model predicts that the effective polycross size will be approximately 9 % smaller than under random mating (i.e., N e/N ~ 0.91). The model is simple and can easily be incorporated into other models or simulations requiring a pollen-parent fecundity distribution. Further work is needed to determine how widely applicable the model is.