Plant dispersal, neighbourhood size and isolation by distance

A theoretical relationship between isolation by distance or spatial genetic structure (SGS) and seed and pollen dispersal is tested using extensive spatial-temporal simulations. Although for animals Wright's neighbourhood size N(e) = 4pisigma(2)(t) has been ascertained also, where sigma(2)(t) is the axial variance of distances between parents and offspring, and it was recently confirmed that N(e) = 4pi(sigma(2)(f) + sigma(2)(m))/2 when dispersal of females and males differ, the situation for plants had not been established. This article shows that for a very wide range of conditions, neighbourhood size defined by Crawford's formula N(e) = 4pi(sigma(2)(s) + sigma(2)(p)/2) fully determines SGS, even when dispersal variances of seed (sigma(2)(s)) and pollen sigma(2)(p)) differ strongly. Further, self-fertilization with rate s acts as zero-distance pollen dispersal, and N(e) = 4pi[sigma(2)(s) + sigma(2)(p)(1 - s)/2] fully determines SGS, for most cases where there are both likely parameter values and substantial SGS. Moreover, for most cases, there is a loglinear relationship, I(1) = 0.587 - 0.117 ln(N(e)), between SGS, as measured by I(1), Moran's coefficient for adjacent individuals, and N(e). However, there are several biologically significant exceptions, namely for very low or large N(e), SGS exceeds the loglinear values. There are also important exceptions to Crawford's formula. First, plants with low seed dispersal, high outcross pollen dispersal and high selfing rate show larger SGS than predicted. Second, in plants with very low (near zero) seed dispersal, selfing decreases SGS, opposite expectations. Finally, in some cases seed dispersal is more critical than pollen dispersal, in a manner inconsistent with Crawford's formula.     

"Neighbourhood" size, dispersal and density estimates in the prickly forest skink (Gnypetoscincus queenslandiae) using individual genetic and demographic methods

Dispersal, or the amount of dispersion between an individual's birthplace and that of its offspring, is of great importance in population biology, behavioural ecology and conservation, however, obtaining direct estimates from field data on natural populations can be problematic. The prickly forest skink, Gnypetoscincus queenslandiae, is a rainforest endemic skink from the wet tropics of Australia. Because of its log-dwelling habits and lack of definite nesting sites, a demographic estimate of dispersal distance is difficult to obtain. Neighbourhood size, defined as 4piDsigma2 (where D is the population density and sigma2 the mean axial squared parent-offspring dispersal rate), dispersal and density were estimated directly and indirectly for this species using mark-recapture and microsatellite data, respectively, on lizards captured at a local geographical scale of 3 ha. Mark-recapture data gave a dispersal rate of 843 m2/generation (assuming a generation time of 6.5 years), a time-scaled density of 13 635 individuals * generation/km2 and, hence, a neighbourhood size of 144 individuals. A genetic method based on the multilocus (10 loci) microsatellite genotypes of individuals and their geographical location indicated that there is a significant isolation by distance pattern, and gave a neighbourhood size of 69 individuals, with a 95% confidence interval between 48 and 184. This translates into a dispersal rate of 404 m2/generation when using the mark-recapture density estimation, or an estimate of time-scaled population density of 6520 individuals * generation/km2 when using the mark-recapture dispersal rate estimate. The relationship between the two categories of neighbourhood size, dispersal and density estimates and reasons for any disparities are discussed.     

Spatial correlations at different spatial scales are themselves highly correlated in isolation by distance processes

Although many properties of spatial autocorrelation statistics are well characterized, virtually nothing is known about possible correlations among values at different spatial scales, which ultimately would influence how inferences about spatial genetics are made at multiple spatial scales. This article reports the results of stochastic space-time simulations of isolation by distance processes, having a very wide range of amounts of dispersal for plants or animals, and analyses of the correlations among Moran's I-statistics for different mutually exclusive distance classes. In general, the stochastic correlations are extremely large (>0.90); however, the correlations bear a complex relationship with level of dispersal, spatial scale and spatial lag between distance classes. The correlations are so large that any existing or conceived statistical method that employs more than one distance class (or spatial scale) should not ignore them. This result also suggests that gains in statistical power via increasing sample size are limited, and that increasing numbers of assayed loci generally should be preferred. To the extent that sampling error for real data sets can be treated as white noise, it should be possible to account for stochastic correlations in formulating more precise statistical methods. Further, while the current results are for isolation by distance processes, they provide some guidance for some more complex stochastic space-time processes of landscape genetics. Moreover, the results hold for several popular measures other than Moran's I. In addition, in the results, the signal to noise ratios strongly decreased with distance, which also has several implications for optimal statistical methods using correlations at multiple spatial scales.     

Small-scale spatial genetic structure in the Central African rainforest tree species Aucoumea klaineana: a stepwise approach to infer the impact of limited gene dispersal, population history and habitat fragmentation

Under the isolation-by-distance model, the strength of spatial genetic structure (SGS) depends on seed and pollen dispersal and genetic drift, which in turn depends on local demographic structure. SGS can also be influenced by historical events such as admixture of differentiated gene pools. We analysed the fine-scale SGS in six populations of a pioneer tree species endemic to Central Africa, Aucoumea klaineana. To infer the impacts of limited gene dispersal, population history and habitat fragmentation on isolation by distance, we followed a stepwise approach consisting of a Bayesian clustering method to detect differentiated gene pools followed by the analysis of kinship-distance curves. Interestingly, despite considerable variation in density, the five populations situated under continuous forest cover displayed very similar extent of SGS. This is likely due to an increase in dispersal distance with decreased tree density. Admixture between two gene pools was detected in one of these five populations creating a distinctive pattern of SGS. In the last population sampled in open habitat, the genetic diversity was in the same range as in the other populations despite a recent habitat fragmentation. This result may due to the increase of gene dispersal compensating the effect of the disturbance as suggested by the reduced extent of SGS estimated in this population. Thus, in A. klaineana, the balance between drift and dispersal may facilitate the maintenance of genetic diversity. Finally, from the strength of the SGS and population density, an indirect estimate of gene dispersal distances was obtained for one site: the quadratic mean parent-offspring distance, sigma(g), ranged between 210 m and 570 m.     

Estimating seed vs. pollen dispersal from spatial genetic structure in the common ash

Spatial genetic structure was analysed with five highly polymorphic microsatellite loci in a Romanian population of common ash (Fraxinus excelsior L.), a wind-pollinated and wind-dispersed tree species occurring in mixed deciduous forests over almost all of Europe. Contributions of seed and pollen dispersal to total gene flow were investigated by analysing the pattern of decrease in kinship coefficients among pairs of individuals with geographical distance and comparing it with simulation results. Plots of kinship against the logarithm of distance were decomposed into a slope and a shape component. Simulations showed that the slope is informative about the global level of gene flow, in agreement with theoretical expectations, whereas the shape component was correlated with the relative importance of seed vs. pollen dispersal. Hence, our results indicate that insights into the relative contributions of seed and pollen dispersal to overall gene flow can be gained from details of the pattern of spatial genetic structure at biparentally inherited loci. In common ash, the slope provided an estimate of total gene dispersal in terms of Wright's neighbourhood size of Nb = 519 individuals. No precise estimate of seed vs. pollen flow could be obtained from the shape because of the stochasticity inherent to the data, but the parameter combinations that best fitted the data indicated restricted seed flow, sigmas pound 14 m, and moderate pollen flow, 70 m pound sigmap pound 140 m.     

Comparative analysis of the within-population genetic structure in wild cherry (Prunus avium L.) at the self-incompatibility locus and nuclear microsatellites

Gametophytic self-incompatibility (SI) systems in plants exhibit high polymorphism at the SI controlling S-locus because individuals with rare alleles have a higher probability to successfully pollinate other plants than individuals with more frequent alleles. This process, referred to as frequency-dependent selection, is expected to shape number, frequency distribution, and spatial distribution of self-incompatibility alleles in natural populations. We investigated the genetic diversity and the spatial genetic structure within a Prunus avium population at two contrasting gene loci: nuclear microsatellites and the S-locus. The S-locus revealed a higher diversity (15 alleles) than the eight microsatellites (4-12 alleles). Although the frequency distribution of S-alleles differed significantly from the expected equal distribution, the S-locus showed a higher evenness than the microsatellites (Shannon's evenness index for the S-locus: E = 0.91; for the microsatellites: E = 0.48-0.83). Also, highly significant deviations from neutrality were found for the S-locus whereas only minor deviations were found for two of eight microsatellites. A comparison of the frequency distribution of S-alleles in three age-cohorts revealed no significant differences, suggesting that different levels of selection acting on the S-locus or on S-linked sites might also affect the distribution and dynamics of S-alleles. Autocorrelation analysis revealed a weak but significant spatial genetic structure for the multilocus average of the microsatellites and for the S-locus, but could not ascertain differences in the extent of spatial genetic structure between these locus types. An indirect estimate of gene dispersal, which was obtained to explain this spatial genetic pattern, indicated high levels of gene dispersal within our population (sigma(g) = 106 m). This high gene dispersal, which may be partly due to the self-incompatibility system itself, aids the effective gene flow of the microsatellites, thereby decreasing the contrast between the neutral microsatellites and the S-locus.     

Compatible genetic and ecological estimates of dispersal rates in insect (Coenagrion mercuriale: Odonata: Zygoptera) populations: analysis of 'neighbourhood size' using a more precise estimator

Genetic and demographic estimates of dispersal are often thought to be inconsistent. In this study, we use the damselfly Coenagrion mercuriale (Odonata: Zygoptera) as a model to evaluate directly the relationship between estimates of dispersal rate measured during capture-mark-recapture fieldwork with those made from the spatial pattern of genetic markers in linear and two-dimensional habitats. We estimate the 'neighbourhood size' (Nb) - the product of the mean axial dispersal rate between parent and offspring and the population density - by a previously described technique, here called the regression method. Because C. mercuriale is less philopatric than species investigated previously by the regression method we evaluate a refined estimator that may be more applicable for relatively mobile species. Results from simulations and empirical data sets reveal that the new estimator performs better under most situations, except when dispersal is very localized relative to population density. Analysis of the C. mercuriale data extends previous results which demonstrated that demographic and genetic estimates of Nb by the regression method are equivalent to within a factor of two at local scales where genetic estimates are less affected by habitat heterogeneity, stochastic processes and/or differential selective regimes. The corollary is that with a little insight into a species' ecology the pattern of spatial genetic structure provides quantitative information on dispersal rates and/or population densities that has real value for conservation management.     

Comparing direct vs. indirect estimates of gene flow within a population of a scattered tree species

The comparison between historical estimates of gene flow, using variance in allelic frequencies, and contemporary estimates of gene flow, using parentage assignment, is expected to provide insights into ecological and evolutionary processes at work within and among populations. Genetic variation at six microsatellite loci was used to quantify genetic structure in the insect-pollinated, animal-dispersed, low-density tree Sorbus torminalis L. Crantz, and to derive historical estimates of gene flow. The neighbourhood size and root-mean-squared dispersal distance inferred from seedling genotypes ( N _b  = 70 individuals, σ _e  = 417 m) were similar to those inferred from adult genotypes ( N _b  = 114 individuals, σ _e  = 472 m). We also used parentage analyses and a neighbourhood model approach after an evaluation of the statistical properties of this method on simulated data. From our data, we estimated even contributions of seed- and pollen-mediated dispersal to the genetic composition of established seedlings, with both fat-tailed pollen and seed dispersal kernels, and slightly higher mean distance of pollen dispersal (248 m) as compared to seed dispersal (135 m). The resulting contemporary estimate of gene dispersal distance (σ _c  = 211 m) was ∼twofold smaller than the historical estimates. Besides different assumptions and statistical nuances of both approaches, this discrepancy is likely to reflect a recent restriction in the scale of gene flow which requires manager's attention in a context of increasing forest fragmentation.     

Spatial population genetic structure and limited dispersal in a Rocky Mountain alpine stream insect

Using the mitochondrial cytochrome oxidase I (COI) gene, we assessed the phylogeographic structure of Prosimulium neomacropyga, a black fly (Simuliidae) whose distribution in the US Southern Rockies ecoregion is limited to alpine tundra streams. Given high habitat specificity, lack of hydrological connection between streams, and a terrestrial environment restrictive to insect flight, we hypothesized limited gene flow. A spatially nested sampling design showed that grouping populations according to high-elevation 'islands' of alpine tundra (which typically include headwater streams of > 1 watershed) explained a significant proportion of genetic variation while grouping streams according to major watershed (across islands) did not. Nested clade analysis and isolation-by-distance (IBD) relationships further implicated limited ongoing gene flow within but not among the isolated alpine islands. IBD was strong among five streams within an individual island using each of four alternative models of pairwise landscape connectivity for flying insects. Results of all landscape models were positively correlated, suggesting that straight-line distance is an acceptable surrogate for presumably more biologically meaningful connectivity measures in this system. IBD was significantly weaker across the entire study area, comprised of three separate islands. Overall, population structure was significant with F(ST) = 0.38, suggesting limited dispersal across a small spatial extent.