Emerging strains of watermelon mosaic virus in Southeastern France: model-based estimation of the dates and places of introduction.

Where and when alien organisms are successfully introduced are central questions to elucidate biotic and abiotic conditions favorable to the introduction, establishment and spread of invasive species. We propose a modelling framework to analyze multiple introductions by several invasive genotypes or genetic variants, in competition with a resident population, when observations provide knowledge on the relative proportions of each variant at some dates and places. This framework is based on a mechanistic-statistical model coupling a reaction-diffusion model with a probabilistic observation model. We apply it to a spatio-temporal dataset reporting the relative proportions of five genetic variants of watermelon mosaic virus (WMV, genus Potyvirus, family Potyviridae) in infections of commercial cucurbit fields. Despite the parsimonious nature of the model, it succeeds in fitting the data well and provides an estimation of the dates and places of successful introduction of each emerging variant as well as a reconstruction of the dynamics of each variant since its introduction.

Partial genotyping at polymorphic markers can improve heritability estimates in sibling groups.

Accurate estimates of heritability (h2) are necessary to assess adaptive responses of populations and evolution of fitness-related traits in changing environments. For plants, h2 estimates generally rely on maternal progeny designs, assuming that offspring are either half-sibs or unrelated. However, plant mating systems often depart from half-sib assumptions, this can bias h2 estimates. Here, we investigate how to accurately estimate h2 in nonmodel species through the analysis of sibling designs with a moderate genotyping effort. We performed simulations to investigate how microsatellite marker information available for only a subset of offspring can improve h2 estimates based on maternal progeny designs in the presence of nonrandom mating, inbreeding in the parental population or maternal effects. We compared the basic family method, considering or not adjustments based on average relatedness coefficients, and methods based on the animal model. The animal model was used with average relatedness information, or with hybrid relatedness information: associating one-generation pedigree and family assumptions, or associating one-generation pedigree and average relatedness coefficients. Our results highlighted that methods using marker-based relatedness coefficients performed as well as pedigree-based methods in the presence of nonrandom mating (i.e. unequal male reproductive contributions, selfing), offering promising prospects to investigate in situ heritabilities in natural populations. In the presence of maternal effects, only the use of pairwise relatednesses through pedigree information improved the accuracy of h2 estimates. In that case, the amount of father-related offspring in the sibling design is the most critical. Overall, we showed that the method using both one-generation pedigree and average relatedness coefficients was the most robust to various ecological scenarios.

Using genetic data to estimate diffusion rates in heterogeneous landscapes.

Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to increase the survival of endangered species. In this paper, we propose a mechanistic-statistical method to estimate space-dependent diffusion parameters of spatially-explicit models based on stochastic differential equations, using genetic data. Dividing the total population into subpopulations corresponding to different habitat patches with known allele frequencies, the expected proportions of individuals from each subpopulation at each position is computed by solving a system of reaction-diffusion equations. Modelling the capture and genotyping of the individuals with a statistical approach, we derive a numerically tractable formula for the likelihood function associated with the diffusion parameters. In a simulated environment made of three types of regions, each associated with a different diffusion coefficient, we successfully estimate the diffusion parameters with a maximum-likelihood approach. Although higher genetic differentiation among subpopulations leads to more accurate estimations, once a certain level of differentiation has been reached, the finite size of the genotyped population becomes the limiting factor for accurate estimation.

Disentangling the causes of heterogeneity in male fecundity in gynodioecious Beta vulgaris ssp. maritima.

Variation among individuals in reproductive success is advocated as a major process driving evolution of sexual polymorphisms in plants, such as gynodioecy where females and hermaphrodites coexist. In gynodioecious Beta vulgaris ssp. maritima, sex determination involves cytoplasmic male sterility (CMS) genes and nuclear restorers of male fertility. Both restored CMS and non-CMS hermaphrodites co-occur. Genotype-specific differences in male fitness are theoretically expected to explain the maintenance of cytonuclear polymorphism. Using genotypic information on seedlings and flowering plants within two metapopulations, we investigated whether male fecundity was influenced by ecological, phenotypic and genetic factors, while taking into account the shape and scale of pollen dispersal. Along with spatially restricted pollen flow, we showed that male fecundity was affected by flowering synchrony, investment in reproduction, pollen production and cytoplasmic identity of potential fathers. Siring success of non-CMS hermaphrodites was higher than that of restored CMS hermaphrodites. However, the magnitude of the difference in fecundity depended on the likelihood of carrying restorer alleles for non-CMS hermaphrodites. Our results suggest the occurrence of a cost of silent restorers, a condition supported by scarce empirical evidence, but theoretically required to maintain a stable sexual polymorphism in gynodioecious species.

Genetic inferences about the population dynamics of codling moth females at a local scale.

Estimation of demographic parameters is important for understanding the functioning of natural populations and the underlying ecological and evolutionary processes that may impact their dynamics. Here, we used sibship assignment methods to shed light on the local dynamics of codling moth females in eight orchards in a 90-ha domain near Valence, France. Based on full-sib inference among 1,063 genotyped moths, we estimated (1) the effective number of females that had offspring, (2) their fertility and (3) the distribution of their oviposition sites within and among orchards. The average number of females in all the orchards increased between the first (~130) and the second (~235) annual generations. The average fertilities of the females were similar at each generation according to the host plant considered (apple, pear, or walnut), but differed between commercial (~10) and non-treated (~25) apple orchards. Females mainly clustered their eggs on contiguous trees along orchard borders, but they also occasionally dispersed their eggs among different orchards independently of the cultivated host plants or the inter-orchard distances (up to 698 m) during the second annual generation. The mean distance between two oviposition sites was 30 m. Sibship estimates of both the effective number of females and the inter-orchard migration rates (~5%) were in agreement with the observed genetic differentiation among the eight orchards (0.006 < F ( st ) < 0.013). These results confirm and extend previous field and laboratory observations in Cydia pomonella, and they demonstrate that sibship assignments based on genetic data are an interesting alternative to mark-release-recapture methods for inferring insect population dynamics.

Pollen and seed dispersal inferred from seedling genotypes: the Bayesian revolution has passed here too.

Understanding precisely how plants disperse their seeds and pollen in their neighbourhood is a central question for both ecologists and evolutionary biologists because seed and pollen dispersal governs both the rate of spread of an expanding population and gene flow within and among populations. The concept of a 'dispersal kernel' has become extremely popular in dispersal ecology as a tool that summarizes how dispersal distributes individuals and genes in space and at a given scale. In this issue of Molecular Ecology, the study by Moran & Clark (2011) (M&C in the following) shows how genotypic and spatial data of established seedlings can be analysed in a Bayesian framework to estimate jointly the pollen and seed dispersal kernels and finally derive a parentage analysis from a full-probability approach. This approach applied to red oak shows important dispersal of seeds (138 m on average) and pollen (178 m on average). For seeds, this estimate contrasts with previous results from inverse modelling on seed trap data (9.3 m). This research gathers several methodological advances made in recent years in two research communities and could become a cornerstone for dispersal ecology.

Recolonisation by diffusion can generate increasing rates of spread.

Diffusion is one of the most frequently used assumptions to explain dispersal. Diffusion models and in particular reaction-diffusion equations usually lead to solutions moving at constant speeds, too slow compared to observations. As early as 1899, Reid had found that the rate of spread of tree species migrating to northern environments at the beginning of the Holocene was too fast to be explained by diffusive dispersal. Rapid spreading is generally explained using long distance dispersal events, modelled through integro-differential equations (IDEs) with exponentially unbounded (EU) kernels, i.e. decaying slower than any exponential. We show here that classical reaction-diffusion models of the Fisher-Kolmogorov-Petrovsky-Piskunov type can produce patterns of colonisation very similar to those of IDEs, if the initial population is EU at the beginning of the considered colonisation event. Many similarities between reaction-diffusion models with EU initial data and IDEs with EU kernels are found; in particular comparable accelerating rates of spread and flattening of the solutions. There was previously no systematic mathematical theory for such reaction-diffusion models with EU initial data. Yet, EU initial data can easily be understood as consequences of colonisation-retraction events and lead to fast spreading and accelerating rates of spread without the long distance hypothesis.

Rapid changes in plasticity across generations within an expanding cedar forest.

We investigated the inter-individual variation of phenotypic plasticity and its evolution across three generations within an expanding forest. Plasticity was assessed in situ from dendrochronological data as the response of radial growth to summer rainfall. A linear mixed model was used to account for spatial effects (environment and stand structure), temporal factors (stand dynamics) and the variation with age. Beyond these effects, our results reveal a significant inter-individual variance of growth and plasticity within each generation. We also show that the mean values and variances of growth and plasticity changed significantly across generations, with different patterns for both traits. The possible environmental and genetic drivers of these changes are discussed. Contrasting with the trade-off between stress tolerance and plasticity generally observed among populations, we detected a positive covariance at the individual level, which does not support the cost of plasticity hypothesis in this case.

Long distance dispersal and the fate of a gene from the colonization front.

There is an increasing recognition that long distance dispersal (LDD) plays a key role in establishing spatial genetic structure during colonization. Recent works, focused on short distance dispersal, demonstrated that a neutral mutation arising at the colonization front can either 'surf' with the wave front and reach high frequencies or stay near its place of origin at low frequencies. Here, we examine how LDD, and more generally the shape of the dispersal kernel, modifies this phenomenon and how the width of the colonization corridor affects the fate of the mutation. We demonstrate that when LDD events are more frequent, the 'surfing phenomenon' is less frequent, probably because any alleles can get far ahead from the colonization front and preclude the invasion by others alleles, thus leading to an attenuation of the diversity loss. We also demonstrate that the width of the colonization corridor influences the fate of the mutation, wide spaces decreasing the probability of invasion. Overall, the genetic structure of diversity resulted not only from LDD but also particularly from the shape of the dispersal kernel.

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

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.

Modelling and estimating pollen movement in oilseed rape (Brassica napus) at the landscape scale using genetic markers.

Understanding patterns of pollen movement at the landscape scale is important for establishing management rules following the release of genetically modified (GM) crops. We use here a mating model adapted to cultivated species to estimate dispersal kernels from the genotypes of the progenies of male-sterile plants positioned at different sampling sites within a 10 x 10-km oilseed rape production area. Half of the pollen clouds sampled by the male-sterile plants originated from uncharacterized pollen sources that could consist of both large volunteer and feral populations, and fields within and outside the study area. The geometric dispersal kernel was the most appropriate to predict pollen movement in the study area. It predicted a much larger proportion of long-distance pollination than previously fitted dispersal kernels. This best-fitting mating model underestimated the level of differentiation among pollen clouds but could predict its spatial structure. The estimation method was validated on simulated genotypic data, and proved to provide good estimates of both the shape of the dispersal kernel and the rate and composition of pollen issued from uncharacterized pollen sources. The best dispersal kernel fitted here, the geometric kernel, should now be integrated into models that aim at predicting gene flow at the landscape level, in particular between GM and non-GM crops.

High diversity of oilseed rape pollen clouds over an agro-ecosystem indicates long-distance dispersal.

Abstract Estimating the frequency of long-distance pollination is important in cultivated species, particularly to assess the risk of gene transfer following the release of genetically modified crops. For this purpose, we estimated the diversity and origin of fertilizing pollen in a 10 x 10 km French oilseed rape production area. First, the cultivar grown in each field was identified through surveys to farmers and using microsatellite markers. Examination of the seed set in fields indicated high rates of seed contamination (8.7%) and pollination from other sources (5%). Then, male-sterile plants were scattered over the study area and their seed genotyped using the same markers. Most pollination was local: 65% of the seeds had a compatible sire in the closest field, i.e. at 50 or 300 m depending on site, but the nearest compatible field was found more than 1000 m away for 13% of the seeds. To assess the diversity of fertilizing pollen, each seed was assigned to the nearest putative siring cultivar. The observed diversity of pollen was then compared to that predicted by simulations using three empirical dispersal models with increasing proportion of long-distance pollination. The diversity was sensitive to the dispersal kernel used in the simulations, fatter-tailed functions predicting higher diversities. The dispersal kernel that was more consistent with our data predicted more long-distance dispersal than the exponential function.

Using seed purity data to estimate an average pollen mediated gene flow from crops to wild relatives.

Gene flow from crops to wild related species has been recently under focus in risk-assessment studies of the ecological consequences of growing transgenic crops. However, experimental studies addressing this question are usually temporally or spatially limited. Indirect population-structure approaches can provide more global estimates of gene flow, but their assumptions appear inappropriate in an agricultural context. In an attempt to help the committees providing advice on the release of transgenic crops, we present a new method to estimate the quantity of genes migrating from crops to populations of related wild plants by way of pollen dispersal. This method provides an average estimate at a landscape level. Its originality is based on the measure of the inverse gene flow, i.e. gene flow from the wild plants to the crop. Such gene flow results in an observed level of impurities from wild plants in crop seeds. This level of impurity is usually known by the seed producers and, in any case, its measure is easier than a direct screen of wild populations because crop seeds are abundant and their genetic profile is known. By assuming that wild and cultivated plants have a similar individual pollen dispersal function, we infer the level of pollen-mediated gene flow from a crop to the surrounding wild populations from this observed level of impurity. We present an example for sugar beet data. Results suggest that under conditions of seed production in France (isolation distance of 1,000 m) wild beets produce high numbers of seeds fathered by cultivated plants.

Some statistical improvements for estimating population size and mutation rate from segregating sites in DNA sequences.

In population genetics, under a neutral Wright-Fisher model, the scaling parameter straight theta=4Nmu represents twice the average number of new mutants per generation. The effective population size is N and mu is the mutation rate per sequence per generation. Watterson proposed a consistent estimator of this parameter based on the number of segregating sites in a sample of nucleotide sequences. We study the distribution of the Watterson estimator. Enlarging the size of the sample, we asymptotically set a Central Limit Theorem for the Watterson estimator. This exhibits asymptotic normality with a slow rate of convergence. We then prove the asymptotic efficiency of this estimator. In the second part, we illustrate the slow rate of convergence found in the Central Limit Theorem. To this end, by studying the confidence intervals, we show that the asymptotic Gaussian distribution is not a good approximation for the Watterson estimator.