Pollen dispersai is a critical process that shapes genetic diversity in natural populations of plants. Estimating the pollen dispersal curve can provide insight into the evolutionary dynamics of populations and is essential background for making predictions about changes induced by perturbations. Specifically, we would like to know whether the dispersal curve is exponential, thin-tailed (decreasing faster than exponential), or fat-tailed (decreasing slower than the exponential). In the latter case, rare events of long-distance dispersal will be much more likely. Here we generalize the previously developed TWOGENER method, assuming that the pollen dispersal curve belongs to particular one-or two-parameter families of dispersal curves and estimating simultaneously the parameters of the dispersal curve and the effective density of reproducing individuals in the population. We tested this method on simulated data, using an exponential power distribution, under thin-tailed, exponential and fat-tailed conditions. We find that even if our estimates show some bias and large mean squared error (MSE), we are able to estimate correctly the general trend of the curve • thin-tailed or fat-tailed • and the effective density. Moreover, the mean distance of dispersal can be correctly estimated with low bias and MSE, even if another family of dispersal curve is used for the estimation. Finally, we consider three case studies based on forest tree species. We find that dispersal is fat-tailed in all cases, and that the effective density estimated by our model is below the measured density in two of the cases. This latter result may reflect the difficulty of estimating two parameters, or it may be a biological consequence of variance in reproductive success of males in the population. Both the simulated and empirical findings demonstrate the strong potential of TWOGENER for evaluating the shape of the dispersal curve and the effective density of the population (d^).

Knowing the extent of gene movements from parents to offspring is essential to understand the potential of a species to adapt rapidly to a changing environment, and to design appropriate conservation strategies. In this study, we develop a nonlinear statistical model to jointly estimate the pollen dispersal kernel and the heterogeneity in fecundity among phenotypically or environmentally defined groups of males. This model uses genotype data from a sample of fruiting plants, a sample of seeds harvested on each of these plants, and all males within a circumscribed area. We apply this model to a scattered, entomophilous woody species, Sorbus torminalis (L.) Crantz, within a natural population covering more than 470 ha. We estimate a high heterogeneity in male fecundity among ecological groups, both due to phenotype (size of the trees and flowering intensity) and landscape factors (stand density within the neighbourhood). We also show that fat-tailed kernels are the most appropriate to depict the important abilities of long-distance pollen dispersal for this species. Finally, our results reveal that the spatial position of a male with respect to females affects as much its mating success as ecological determinants of male fecundity. Our study thus stresses the interest to account for the dispersal kernel when estimating heterogeneity in male fecundity, and reciprocally.

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.

SummaryThe evolutionary potential of long-lived species, such as forest trees, is fundamental for their local persistence under climate change (CC). Genome-environment association (GEA) analyses reveal if species in heterogeneous environments at the regional scale are under differential selection resulting in populations with potential preadaptation to CC within this area.In 79 natural Fagus sylvatica populations, neutral genetic patterns were characterized using 12 simple sequence repeat (SSR) markers, and genomic variation (144 single nucleotide polymorphisms (SNPs) out of 52 candidate genes) was related to 87 environmental predictors in the latent factor mixed model, logistic regressions and isolation by distance/environmental (IBD/IBE) tests.SSR diversity revealed relatedness at up to 150 m intertree distance but an absence of large-scale spatial genetic structure and IBE. In the GEA analyses, 16 SNPs in 10 genes responded to one or several environmental predictors and IBE, corrected for IBD, was confirmed. The GEA often reflected the proposed gene functions, including indications for adaptation to water availability and temperature.Genomic divergence and the lack of large-scale neutral genetic patterns suggest that gene flow allows the spread of advantageous alleles in adaptive genes. Thereby, adaptation processes are likely to take place in species occurring in heterogeneous environments, which might reduce their regional extinction risk under CC.

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