Pollen flow in the wildservice tree, Sorbus torminalis (L.) Crantz. IV. Whole interindividual variance of male fecundity estimated jointly with the dispersal kernel

Abstract

Interindividual variance of male reproductive success (MRS) contributes to genetic drift, which in turn interacts with selection and migration to determine the short-term response of populations to rapid changes in their environment. Individual relative MRS can be estimated through paternity analysis and can be further dissected into fecundity and spatial components. Existing methods to achieve this decomposition either rely on the strong assumption of a random distribution of pollen donors (TwoGener) or estimate only the part of the variance of male fecundity that is explained by few covariates. We developed here a method to estimate jointly the whole variance of male fecundity and the pollen dispersal curve from the genotypic information of sampled seeds and their putative fathers and geographical information of all individuals in the study area. We modelled the relative individual fecundities as a log-normally distributed random effect. We used a Bayesian approach, well suited to the hierarchical nature of the model, to estimate these fecundities. When applied to Sorbus torminalis, the estimated variance of male fecundity corresponded to an effective density of trees 13 times lower than the observed density (d(obs)/d(ep ) approximately 13). This value is between the value (approximately 2) estimated with a classical mating model including three covariates (neighbourhood density, diameter, flowering intensity) that affect fecundity and the value (approximately 30) estimated with TwoGener. The estimated dispersal kernel was close to previous results. This approach allows fine monitoring of ongoing genetic drift in natural populations, and quantitative dissection of the processes contributing to drift, including human actions.

Size advantage for male function and size‐dependent sex allocation inAmbrosia artemisiifolia, a wind‐pollinated plant

“…We selected sets of seeds and parents genotyped at least for five of the six loci. For paternity analysis, we employed the program NM+ v. 1.1 (Chybicki & Burczyk, 2010, 2012) instead of MEMM (Klein, Desassis, & Oddou‐Muratorio, 2008) because the former enables us to estimate not only pollen dispersal kernel but also selection gradients on MRS in which we can evaluate relative contribution of height and MRI; we applied a neighborhood model (Burczyk, Adams, Moran, & Griffin, 2002) implemented in the program NM+ to 2,102 seeds which were genotyped. On the other hand, NM+ does not estimate individual reproductive success and we need to examine how it could vary with the effects of the spatial position of individual plants in the experimental population.…”

Impact of negative frequency-dependent selection on mating pattern and genetic structure: a comparative analysis of the S-locus and nuclear SSR loci in Prunus lannesiana var. speciosa

“…For the standardized variables, corresponding parameters were estimated. Parameters of pollen dispersal and male fecundity have often been estimated on the basis of the neighborhood model using maximum likelihood (Burczyk et al, 2002) or Bayesian methods (Klein et al, 2008). In our mating model, the results of paternity assignment were used to simplify the model (Tani et al, 2009), and an exponential power function (Oddou-Muratorio et al, 2005) was applied to a dispersal kernel.…”

“…Effects of the SI system on male-female pair fecundity were evaluated using a Bayesian model (Klein et al, 2008, Tani et al, 2009, discriminating between factors such as spatial distance, kinship coefficient, flowering synchrony between mates and floral abundance of pollen donors. The SI score s between the mother trees and the candidate pollen donors was allocated a value of 0 when they were compatible (no S-alleles were shared), 0.5 when halfcompatible (one of two alleles at the S-locus were shared) and 1 when incompatible (both S-alleles were shared).…”

A statistical-reaction–diffusion approach for analyzing expansion processes

“…Like many other models in ecology this parameter results from the intertwined effects of several factors and cannot be directly measured. However, it can be estimated using observations of the population dynamics of interest (Klein et al, 2008;Soubeyrand et al, 2009a,b); here, we use observations of the position of PPM nests at the study sites.…”