Wright-Fisher revisited: the case of fertility correlation

We study the non-genetic inheritance of fertility from parents to offspring. For this purpose, we propose an exchangeable extension of the Wright-Fisher model. This extension allows us to introduce non-genetic fertility correlation in the forward in time process and to study its effects on the genealogies of individuals (or genes) samples. Since it is independent of the gene considered, this effect is uniform on the genome, even in diploid populations. For values of fertility correlation observed in human populations, we show that coalescence times are strongly but inhomogenously reduced and that the shape of gene genealogies is markedly unbalanced. Despite the fact that our simulations concern stationary populations, the former non-genetic effect is very similar to what has been described for populations of variable size such as populations passing through demographic bottleneck. However, additional strong tree imbalance due to non-genetic causes is reported here for the first time.

Sampling within the genome for measuring within-population diversity: trade-offs between markers

Experimental results of diversity estimates in a set of populations often exhibit contradictory patterns when different marker systems are used. Using simulations we identified potential causes for these discrepancies. These investigations aimed also to detect whether different sampling strategies of markers within the genome resulted in different estimates of the diversity at the whole genome level. The simulations consisted in generating a set of populations undergoing various evolutionary scenarios which differed by population size, migration rate and heterogeneity of gene flow. Population diversity was then computed for the whole genome and for subsets of loci corresponding to different marker techniques. Rank correlation between the two measures of diversity were investigated under different scenarios. We showed that the heterogeneity of genetic diversity either between loci (genomic heterogeneity, GH) or among populations (population heterogeneity, PH) varied greatly according to the evolutionary scenario considered. Furthermore, GH and PH were major determinants of the level of rank correlation between estimates of genetic diversities obtained using different kinds of markers. We found a strong positive relationship between the level of the correlation and PH, whatever the marker system. It was also shown that, when GH values were constantly low during generations, a reduced number of microsatellites was enough to predict the diversity of the whole genome, whereas when GH increased, more loci were needed to predict the diversity and amplified fragment length polymorphism markers would be more recommended in this case. Finally the results are discussed to recommend strategies for gene diversity surveys.

Two-generation analysis of pollen flow across a landscape. IV. Estimating the dispersal parameter

The distance of pollen movement is an important determinant of the neighborhood area of plant populations. In earlier studies, we designed a method for estimating the distance of pollen dispersal, on the basis of the analysis of the differentiation among the pollen clouds of a sample of females, spaced across the landscape. The method was based solely on an estimate of the global level of differentiation among the pollen clouds of the total array of sampled females. Here, we develop novel estimators, on the basis of the divergence of pollen clouds for all pairs of females, assuming that an independent estimate of adult population density is available. A simulation study shows that the estimators are all slightly biased, but that most have enough precision to be useful, at least with adequate sample sizes. We show that one of the novel pairwise methods provides estimates that are slightly better than the best global estimate, especially when the markers used have low exclusion probability. The new method can also be generalized to the case where there is no prior information on the density of reproductive adults. In that case, we can jointly estimate the density itself and the pollen dispersal distance, given sufficient sample sizes. The bias of this last estimator is larger and the precision is lower than for those estimates based on independent estimates of density, but the estimate is of some interest, because a meaningful independent estimate of the density of reproducing individuals is difficult to obtain in most cases.

Two-generation analysis of pollen flow across a landscape. III. Impact of adult population structure

The rate and distance of instantaneous pollen flow in a population are parameters of considerable current interest for plant population geneticists and conservation biologists. We have recently developed an estimator (phi ft) of differentiation between the inferred pollen clouds that fertilize several females, sampled within a single population. We have shown that there is a simple relation between phi ft and the average pollen dispersal distance (delta) for the case of a population with no geographic structure. Though forest trees usually show considerable pollen flow, assuming an absence of spatially distributed genetic structure is not always wise. Here, we develop analytical theory for the relation between phi ft and delta, for the case where the probability of Identity by Descent (IBD) for two individuals decreases with the physical distance between them. This analytical theory allows us to provide an effective method for estimating pollen dispersal distance in a population with adult genetic structure. Using real examples, we show that estimation errors can be large if genetic structure is not taken into account, so it is wise to evaluate adult genetic structure simultaneously with estimation of phi ft for the pollen clouds. We show that the results are only moderately affected by changes in the decay function, a result of some importance since no completely established theory is available for this function.

Two-generation analysis of pollen flow across a landscape. II. Relation between phi(ft), pollen dispersal and interfemale distance

We study the behavior of Phi(ft), a recently introduced estimator of instantaneous pollen flow, which is basically the intraclass correlation of inferred pollen cloud genetic frequencies among a sample of females drawn from a single population. Using standard theories of identity by descent and spatial processes, we show that Phi(ft) depends on the average distance of pollen dispersal (delta) and on the average distance between sampled mothers (x(1)). Provided that mothers are sampled far enough apart (x(1) > 5delta), Phi(ft) becomes independent of x(1) and is then inversely proportional to the square of delta. Provided that this condition is fulfilled, delta is directly estimable from Phi(ft). Even when x(1) < 5delta, estimation can easily be achieved via numerical evaluation. We show that the relation between Phi(ft) and delta is only modestly affected by the shape of the distribution function, a result of importance, since this shape is generally unknown. We also study the impact of adult density within the population on Phi(ft), showing that to achieve the correct inference of delta from Phi(ft) it must be taken into account, but that it has no effect on the distance at which mothers must be sampled.

Allelic association is increased by correlation of effective family size

In a previous study, we showed that the observation of high frequencies of certain inherited disorders in the population of Saguenay Lac Saint Jean (SLSJ) in Quebec can be explained in terms of the variance and the auto-correlation of effective family size (EFS) across generations. Correlated EFS, across generations, allows alleles introduced as a single copy to reach very high frequencies in about 12 generations. Here, we investigate the impact of this same demographic process on allelic association between a disease locus and closely linked neutral markers. We model the fate of a disease allele, introduced as a single copy, and of its surrounding haplotype. We show that the auto-correlation of EFS across generations increases the expected proportion of individuals who carry the ancestral haplotype in the present generation. Thus, the length of a shared haplotype is longer, making this population useful for coarse mapping. But this autocorrelation decreases the estimated value; thus ignoring the auto-correlation in EFS leads to an underestimate of the recombination rate. This result is of importance, since socio-demographic processes such as auto-correlation of EFS across generations have been described in other human populations.

Impact of demographic distribution and population growth rate on haplotypic diversity linked to a disease gene and their consequences for the estimation of recombination rate: example of a French Canadian population

A disease gene introduced into a rapidly growing population by a single individual remains in strong linkage disequilibrium with the surrounding molecular markers. Mapping strategies taking advantage of this phenomenon allow increased mapping resolution as compared to pedigree analysis. Demographic models underlying these strategies usually assume the population exponential growth approximated by Poisson distribution of the number of children per individual. Knowing the real demographic distribution in the studied French-Canadian population, we analyzed the validity of the Poisson approximation. We adapted the existing model of the Poisson branching process to the case of a rapidly growing population and to non-Poisson distributions. In consequence, we were able to apply maximum-likelihood methods to estimate the recombination rate under various demographic scenarios. Our analysis shows that the growth rate has a higher impact on the estimation of recombination rate than the shape of the demographic distribution. The choice of the demographic model (Poisson vs. non-Poisson) has little effect on the estimation of the recombination rate but affects the expected distribution of haplotype frequencies. This distribution, however, depends much more on the population growth rate. Finally, we also demonstrate the usefulness of the Luria-Delbrück method, which gives a correct estimation of the recombination rate in a growing population, provided the sampling error is taken into account in the confidence intervals.

Effects of colonization processes on genetic diversity: differences between annual plants and tree species

Tree species are striking for their high within-population diversity and low among-population differentiation for nuclear genes. In contrast, annual plants show much more differentiation for nuclear genes but much less diversity than trees. The usual explanation for this difference is that pollen flow, and therefore gene flow, is much higher for trees. This explanation is problematic because it relies on equilibrium hypotheses. Because trees have very recently recolonized temperate areas, they have experienced many foundation events, which usually reduce within-population diversity and increase differentiation. Only extremely high levels of gene flow could counterbalance these successive founder effects. We develop a model to study the impact of life cycle of forest trees, in particular of the length of their juvenile phase, on genetic diversity and differentiation during the glacial period and the following colonization period. We show that both a reasonably high level of pollen flow and the life-cycle characteristics of trees are needed to explain the observed structure of genetic diversity. We also show that gene flow and life cycle both have an impact on maternally inherited cytoplasmic genes, which are characterized both in trees and annual species by much less diversity and much more differentiation than nuclear genes.

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.

Social transmission of reproductive behavior increases frequency of inherited disorders in a young-expanding population

The observation of high frequencies of certain inherited disorders in the population of Saguenay-Lac Saint Jean can be explained in terms of the variance and the correlation of effective family size (EFS) from one generation to the next. We have shown this effect by using the branching process approach with real demographic data. When variance of EFS is included in the model, despite its profound effect on mutant allele frequency, any mutant introduced in the population never reaches the known carrier frequencies (between 0.035 and 0.05). It is only when the EFS correlation between generations is introduced into the model that we can explain the rise of the mutant alleles. This correlation is described by a c parameter that reflects the dependency of children's EFS on their parents' EFS. The c parameter can be considered to reflect social transmission of demographic behavior. We show that such social transmission dramatically reduces the effective population size. This could explain particular distributions in allele frequencies and unusually high frequency of certain inherited disorders in some human populations.