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.     

Antagonism between local dispersal and self-incompatibility systems in a continuous plant population

Many self-incompatible plant species exist in continuous populations in which individuals disperse locally. Local dispersal of pollen and seeds facilitates inbreeding because pollen pools are likely to contain relatives. Self-incompatibility promotes outbreeding because relatives are likely to carry incompatible alleles. Therefore, populations can experience an antagonism between these forces. In this study, a novel computational model is used to explore the effects of this antagonism on gene flow, allelic diversity, neighbourhood sizes, and identity by descent. I confirm that this antagonism is sensitive to dispersal levels and linkage. However, the results suggest that there is little to no difference between the effects of gametophytic and sporophytic self-incompatibility systems (GSI and SSI) on unlinked loci. More importantly, both GSI and SSI affect unlinked loci in a manner similar to obligate outcrossing without mating types. This suggests that the primary evolutionary impact of self-incompatibility systems may be to prevent selfing, and prevention of biparental inbreeding might be a beneficial side-effect.     

Evolution of the distribution of dispersal distance under distance‐dependent cost of dispersal

Abstract We analyse the evolution of the distribution of dispersal distances in a stable and homogeneous environment in one‐ and two‐dimensional habitats. In this model, dispersal evolves to avoid the competition between relatives although some cost might be associated with this behaviour. The evolutionarily stable dispersal distribution is characterized by an equilibration of the fitness gains among all the different dispersal distances. This cost‐benefit argument has heuristic value and facilitates the comprehension of results obtained numerically. In particular, it explains why some minimal or maximal probability of dispersal may evolve at intermediate distances when the cost of dispersal function is an increasing function of distance. We also show that kin selection may favour long range dispersal even if the survival cost of dispersal is very high, provided the survival probability does not vanish at long distances.     

The effects of ecological and genetic neighbourhood size on the evolution of two competing species

Summary Individual-based simulations were conducted to examine the effect of a small ecological neighbourhood (an area in which ecological processes such as density-dependent factors operate) and the genetic neighbourhood size (the size of an area from which the parents may be assumed to be drawn at random) on the coevolution of two competing species. For the simulations, individuals of two consumer species compete for two types of food organisms. Different genotypes (one locus and two alleles) have different efficiencies of food acquisition for different food types. Individual consumer organisms search for food within their home ranges and reproduce depending on the amount of food eaten. The dispersal distance of the offspring follows a normal distribution with a zero mean and _d standard deviation. Simulations were conducted by varying the home range size, mating area (area from where individuals choose their mates), standard deviation of dispersal distance, food generation time, the reproductive rates of food populations and the sizes and number of independent food populations. Food organisms reproduce either within one population or independently within 16 spatially divided populations. For all the simulations, competitive exclusion was the most frequent outcome and character displacement was the least frequent outcome. Through a 200-generation simulation, the two consumer species could co-exist longer and maintain a polymorphic resource use longer when the home range and mating size were small in 16 spatially divided populations than when random mating and homogeneous interaction occurred within a community (perfect mixing population). For perfect mixing populations, the frequency of character displacement increased as the food generation time became short and the reproductive rates of food decreased. It follows from the results that the sizes of the genetic and ecological neighbourhoods and the mode of resource dynamics can affect the evolution of two competing species.     

IBDSim: a computer program to simulate genotypic data under isolation by distance

IBDSim is a package for the simulation of genotypic data under isolation by distance. It is based on a backward 'generation by generation' coalescent algorithm allowing the consideration of various isolation by distance models with discrete subpopulations as well as continuous populations. Many dispersal distributions can be considered as well as heterogeneities in space and time of the demographic parameters. Typical applications of our program include (i) the study of the effect of various sampling, mutational and demographic factors on the pattern of genetic variation; and (ii) the production of test data sets to assess the influence of these factors on inferential methods available to analyse genotypic data.     

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.     

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.     

Interactions between environmental factors can hide isolation by distance patterns: a case study of Ctenomys rionegrensis in Uruguay

Identifying the factors responsible for the structuring of genetic diversity is of fundamental importance for biodiversity conservation. However, arriving at such understanding is difficult owing to the many factors involved and the potential interactions between them. Here, we present an example of how such interactions can preclude us from arriving at a complete characterization of the demographic history and genetic structure of a species. Ctenomys rionegrensis is a species with restricted dispersal abilities and, as such, should exhibit an isolation by distance (IBD) pattern, which previous studies were unable to uncover. It was therefore concluded that this species underwent a recent population expansion. Using a novel hierarchical Bayesian method, we show that the inability to detect the IBD pattern is due to the interaction between elevation and geographical distance. We posit that populations in low areas suffer periodic floods that may reduce local population sizes, increasing genetic drift, a process that masks the effect of distance on genetic differentiation. Our results do not refute the possibility that the populations of C. rionegrensis underwent a recent population expansion but they indicate that an alternative scenario described by a metapopulation model at or near migration-drift equilibrium cannot be excluded either.     

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.     

Influence of mutational and sampling factors on the estimation of demographic parameters in a "continuous" population under isolation by distance

In numerous species, individual dispersal is restricted in space so that "continuous" populations evolve under isolation by distance. A method based on individual genotypes assuming a lattice population model was recently developed to estimate the product Dsigma2, where D is the population density and sigma2 is the average squared parent-offspring distance. We evaluated the influence on this method of both mutation rate and mutation model, with a particular reference to microsatellite markers, as well as that of the spatial scale of sampling. Moreover, we developed and tested a nonparametric bootstrap procedure allowing the construction of confidence intervals for the estimation of Dsigma2. These two objectives prompted us to develop a computer simulation algorithm based on the coalescent theory giving individual genotypes for a continuous population under isolation by distance. Our results show that the characteristics of mutational processes at microsatellite loci, namely the allele size homoplasy generated by stepwise mutations, constraints on allele size, and change of slippage rate with repeat number, have little influence on the estimation of Dsigma2. In contrast, a high genetic diversity (approximately 0.7-0.8), as is commonly observed for microsatellite markers, substantially increases the precision of the estimation. However, very high levels of genetic diversity (>0.85) were found to bias the estimation. We also show that statistics taking into account allele size differences give unreliable estimations (i.e., high variance of Dsigma2 estimation) even under a strict stepwise mutation model. Finally, although we show that this method is reasonably robust with respect to the sampling scale, sampling individuals at a local geographical scale gives more precise estimations of Dsigma2.     

Female philopatry and male-biased dispersal in a direct-developing salamander, Plethodon cinereus

The local resource competition hypothesis and the local mate competition hypothesis were developed based on avian and mammalian systems to explain sex-biased dispersal. Most avian species show a female bias in dispersal, ostensibly due to resource defence, and most mammals show a male bias, ostensibly due to male-male competition. These findings confound phylogeny with mating strategy; little is known about sex-biased dispersal in other taxa. Resource defence and male-male competition are both intense in Plethodon cinereus, a direct-developing salamander, so we tested whether sex-biased dispersal in this amphibian is consistent with the local resource competition hypothesis (female-biased) or the local mate competition hypothesis (male-biased). Using fine-scale genetic spatial autocorrelation analyses, we found that females were philopatric, showing significant positive genetic structure in the shortest distance classes, with stronger patterns apparent when only territorial females were tested. Males showed no spatial genetic structure over the shortest distances. Mark-recapture observations of P. cinereus over 5 years were consistent with the genetic data: males dispersed farther than females during natal dispersal and 44% of females were recaptured within 1 m of their juvenile locations. We conclude that, in this population of a direct-developing amphibian, females are philopatric and dispersal is male-biased, consistent with the local mate competition hypothesis.     

The ecological genetics of introduced populations of the giant toad, Bufo marinus (Amphibia: Anura): dispersal and neighbourhood size

The pattern of colonization of the Moreton Bay region in southeast Queensland, Australia, by the giant toad, Bufo marinus , is described. Estimates are made of the rates of colonization in this and other regions. The mean values obtained range from 2.5 km/year in the south to 15.1 km/year in the north. The analysis suggests that colonization has been discontinuous in many areas, probably as a result of occasional, long-distance transportation of toads by humans. The variation in colonization rate is related in a predictable way to variation in environmental factors such as temperature and topography. In areas where discontinuities are least likely, colonization rates are used to estimate rates of continuous dispersal. These are combined with estimates of population density, sex ratios and offspring number variance to obtain estimates of genetic neighbourhood size. These are much greater than estimates of the effective size of B. marinus populations determined from gene frequency variances. The reasons for and implications of this discrepancy are discussed.