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

Abstract

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.

Seed‐Parent Fecundity Distributions in Bee‐Pollinated Forage Legume Polycrosses

“…There was, however, a significant positive linear relationship between a polycross's l and its 50th quantile estimated l from 169 polycross l estimates assuming a lognormal distribution 1.166 -1.090 -50th quantile estimated l from 169 polycross l estimates assuming a gamma distribution 1.189 -1.095 - † Estimated k value based on k = 0.1019l 5 − 0.9441l 4 + 3.4386l 3 − 6.2398l 2 + 5.7585l − 1.0662. distributions (Riday et al, 2015). The first relationship measured was between a polycross's l and its N. No significant linear relationship was determined (P = 0.295, r 2 = 0.007).…”

“…Using empirical measures of pollen-parent fecundity distributions in 10 forage legume polycrosses, k and l were estimated to be 1.126 and 1.524, respectively (Riday et al, 2015). Riday and Peel (2016) demonstrated that Eq.…”

“…To estimate k and l from empirical data and for graphing purposes, the following Weibull inverse cumulative distribution function (Forbes et al, 2011) equation was used (Riday et al, 2015):…”

“…In general, plants to be crossed in polycrosses were transferred from the greenhouse to a field site in April of a given year and, after having grown a little, were mulched and staked up (for a detailed description of a set of polycrosses, see Riday, 2011). A portion of polycrosses used in this study have previously been described in more detail (Riday, 2008(Riday, , 2009(Riday, , 2011(Riday, , 2016Riday and Krohn, 2010;AOSCA, 2015;Riday et al, 2015). Pollination usually proceeded for ~2 mo, after which polycrosses were opened and seed was harvested from individual plants in late August or early September.…”

“…57, may-june 2017 RESEARCH R andom mating or panmixis is a fundamental concept in quantitative genetic theory (Weismann, 1883), although it is recognized that, theoretically, random mating rarely occurs in nature (Clegg, 1980;Allard, 1999). Furthermore, by defining the fecundity distribution in terms of panmixis, a single empirical model dependent only on polycross size can be developed (Riday et al, 2015): Furthermore, by defining the fecundity distribution in terms of panmixis, a single empirical model dependent only on polycross size can be developed (Riday et al, 2015):…”