Effect of Mating Structure on Variation in Linkage Disequilibrium

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size (N_e) and the mating structure. Second, there is sampling of a finite number (n) of individuals to estimate the population disequilibrium.——Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of N_e, mating structure, n, and linkage or recombination parameter.——The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci.     

Inbreeding depression in an asexual population of Mimulus guttatus

The reproductive mechanism, that is whether an organism outcrosses, selfs or asexually reproduces, has a substantial impact on the amount and pattern of genetic variation. In this study, we estimate genetic variation and genetic load for a predominately asexual population of Mimulus guttatus, and then compare our results to other studies of predominately sexually reproducing (outcrossing and selfing) populations of M. guttatus. The asexual population had low levels of heterozygosity (H_e = 0.03) and low (but significantly non‐zero) inbreeding load, especially when compared with other M. guttatus populations. This differs greatly from the sexual populations of Mimulus that display substantial inbreeding depression. We discuss a variety of reasons why we see such low load in this study and suggest future research projects to further explore the questions.     

INBREEDING AND VARIANCE EFFECTIVE SIZES FOR NONRANDOM MATING POPULATIONS

Following an inbreeding approach and assuming discrete generations and autosomal inheritance involving genes that do not affect viability or reproductive ability, I have derived expressions for the inbreeding effective size, N_eI, for a finite diploid population with variable census sizes for three cases: monoecious populations with partial selfing; dioecious populations of equal numbers of males and females with partial sib mating; and unequal numbers of males and females with random mating. For the first two cases, recurrence equations for the inbreeding coefficient are also obtained, which allow inbreeding coefficients to be predicted exactly in both early and late generations. Following the variance of change in gene frequency approach, a general expression for variance effective size, N_eV, is obtained for a population with unequal numbers of male and female individuals, arbitrary family size distribution, and nonrandom mating. All the parameters involved are allowed to change over generations. For some special cases, the equation reduces to the simple expressions approximately as derived by previous authors. Comparisons are made between equations derived by the present study and those obtained by previous authors. Some of the published equations for N_eI and N_eV are shown to be incomplete or incorrect. Stochastic simulations are run to check the results where disagreements with others are involved.     

The use of agent-based modelling of genetics in conservation genetics studies

Animal Landscape and Man Simulation System a genetically explicit agent-based model was used to obtain measures for the genetic and demographic status of simulated populations. This investigation aimed to test the applicability of this approach for assessing the effect of environmental perturbations on populations’ temporal and spatial dynamics. This was achieved by assessing how three simple scenarios with increasing degree of environmental disturbance, simulated by populations bottlenecks repeated at different intervals, affected the genetic and demographic characteristics of the simulated population. Model outputs from a simplified landscape scenario concurred with theoretical expectations validating the model in a qualitative way. Differences in medians, means and coefficient of variation of the observed (H_o) and expected heterozygosity (H_e), population census size (N), effective population size (N_e), inbreeding coefficient (F) and N_e/N ratio were observed for simulated populations. Impacts occurred rapidly after simulated bottleneck events and genetic estimates were less variable, and therefore more reliable, than demographic estimates. Precise genetic consequences of the bottlenecks repeated at different intervals, and resulting population perturbations, are a complex balance between effects on population sub-structure, size and founding events. Agent-based models are appropriate tools to simulate these interactions, being sufficiently flexible to mimic real population processes under a range of environmental conditions. Such models incorporating explicit genetics provide a promising new approach to evaluate the impact of environmental changes on genetic composition of populations.     

gesp: A computer program for modelling genetic effective population size,inbreeding and divergence in substructured populations

The genetically effective population size (N_e) is of key importance for quantifying rates of inbreeding and genetic drift and is often used in conservation management to set targets for genetic viability. The concept was developed for single, isolated populations and the mathematical means for analysing the expected N_e in complex, subdivided populations have previously not been available. We recently developed such analytical theory and central parts of that work have now been incorporated into a freely available software tool presented here. gesp (Genetic Effective population size, inbreeding and divergence in Substructured Populations) is R‐based and designed to model short‐ and long‐term patterns of genetic differentiation and effective population size of subdivided populations. The algorithms performed by gesp allow exact computation of global and local inbreeding and eigenvalue effective population size, predictions of genetic divergence among populations (G_ST) as well as departures from random mating (F_IS, F_IT) while varying (i) subpopulation census and effective size, separately or including trend of the global population size, (ii) rate and direction of migration between all pairs of subpopulations, (iii) degree of relatedness and divergence among subpopulations, (iv) ploidy (haploid or diploid) and (v) degree of selfing. Here, we describe gesp and exemplify its use in conservation genetics modelling.     

INCREASED PROBABILITY OF EXTINCTION DUE TO DECREASED GENETIC EFFECTIVE POPULATION SIZE: EXPERIMENTAL POPULATIONS OF CLARKIA PULCHELLA

We established replicated experimental populations of the annual plant Clarkia pulchella to evaluate the existence of a causal relationship between loss of genetic variation and population survival probability. Two treatments differing in the relatedness of the founders, and thus in the genetic effective population size (N_e), were maintained as isolated populations in a natural environment. After three generations, the low N_e treatment had significantly lower germination and survival rates than did the high N_e treatment. These lower germination and survival rates led to decreased mean fitness in the low N_e populations: estimated mean fitness in the low N_e populations was only 21% of the estimated mean fitness in the high N_e populations. This inbreeding depression led to a reduction in population survival: at the conclusion of the experiment, 75% of the high N_e populations were still extant, whereas only 31% of the low N_e populations had survived. Decreased genetic effective population size, which leads to both inbreeding and the loss of alleles by genetic drift, increased the probability of population extinction over that expected from demographic and environmental stochasticity alone. This demonstrates that the genetic effective population size can strongly affect the probability of population persistence.     

Inbreeding and extinction: Effects of rate of inbreeding

Deleterious alleles may be removed (purged) bynatural selection in populations undergoinginbreeding. However, there is controversyregarding the effectiveness of selection inreducing the risk of extinction due toinbreeding, especially in relation to the rateof inbreeding. We evaluated the effect of therate of inbreeding on reducing extinction risk,in populations of Drosophila melanogastermaintained using full-sib mating (160replicates), or at effective population sizes(N _e) of 10 (80) or 20 (80).Extinction rates in the populations maintainedusing full-sib mating occurred at lower levelsof inbreeding than in the larger populations,whereas the two larger populations did notdiffer significantly from each other.Inbreeding coefficients at 50% extinction were0.62, 0.79 and 0.77 for the full-sib (N _e = 2.6), N _e = 10 and N _e = 20 treatments, respectively. Populations of N _e = 20 that remained extant after 60 generations, showed inbreeding depression, with the mean fitness of these populations being only 45% of the outbredcontrols. There was considerable variationamong the 31 inbred populations in fitness, butnone of the N _e = 20 populations hadfitness that was higher than the outbredcontrol. We conclude that purging may slow therate of extinction slightly, but it cannot berelied on to eliminate the deleterious effectsof inbreeding.     

Genetic diversity, mating system, and conservation of a Mexican subalpine relict, Picea mexicana Martínez

Mexican spruce (Picea mexicana Martínez), an endangered species of the highest sky islands in México's Sierra Madre Oriental and Sierra Madre Occidental, is threatened by fire, grazing, and global warming. Its conservation depends on whether it also is threatened by inbreeding and loss of genic diversity. We used 18 isozyme markers in 12 enzyme systems to assay genic diversity, characterize the mating system, and test for recent bottlenecks in three known populations. Unbiased, expected heterozygosity (H _e ) averaged 0.125. Despite a separation of 676 km between populations in the Sierra Madre Oriental and the Sierra Madre Occidental, Wright's F _ST , the proportion of total genic diversity among populations, was only 6.9%. Nei's genetic distance was 0.001 between the populations in the Sierra Madre Oriental and more than an order of magnitude greater, 0.019, between the Sierra Madre Oriental and Sierra Madre Occidental. However, both values point to relatively recent divergence. Mating systems were predominantly outcrossing, but with significant selfing. Multilocus estimates of selfing varied from 19% to 41%, and the means of single-locus estimates were higher, suggesting that additional inbreeding occurred by mating among relatives. Despite significant inbreeding, observed heterozygosity was as high as or higher than H _e ; Wright's fixation index, F _IS , was –0.107. Under the observed level of selfing, positive values of F _IS were expected. Therefore, selection against inbreds and homozygotes must be intense. Cornuet-Luikart tests indicate recent bottlenecks in at least two of the three populations. The results suggest that Mexican spruce is a genetically viable species, and threats are primarily environmental.     

Consequences of multiple mating‐system shifts for population and range‐wide genetic structure in a coastal dune plant

Evolutionary transitions from outcrossing to selfing can strongly affect the genetic diversity and structure of species at multiple spatial scales. We investigated the genetic consequences of mating‐system shifts in the North American, Pacific coast dune endemic plant Camissoniopsis cheiranthifolia (Onagraceae) by assaying variation at 13 nuclear (n) and six chloroplast (cp) microsatellite (SSR) loci for 38 populations across the species range. As predicted from the expected reduction in effective population size (N_e) caused by selfing, small‐flowered, predominantly selfing (SF) populations had much lower nSSR diversity (but not cpSSR) than large‐flowered, predominantly outcrossing (LF) populations. The reduction in nSSR diversity was greater than expected from the effects of selfing on N_e alone, but could not be accounted for by indirect effects of selfing on population density. Although selfing should reduce gene flow, SF populations were not more genetically differentiated than LF populations. We detected five clusters of nSSR genotypes and three groups of cpSSR haplotypes across the species range consisting of parapatric groups of populations that usually (but not always) differed in mating system, suggesting that selfing may often initiate ecogeographic isolation. However, lineage‐wide genetic variation was not lower for selfing clusters, failing to support the hypothesis that selection for reproductive assurance spurred the evolution of selfing in this species. Within three populations where LF and SF plants coexist, we detected genetic differentiation among diverged floral phenotypes suggesting that reproductive isolation (probably postzygotic) may help maintain the striking mating‐system differentiation observed across the range of this species.     

Estimating effective population size from linkage disequilibrium: severe bias in small samples

Effective population size (N _e) is a central concept in evolutionary biology and conservation genetics. It predicts rates of loss of neutral genetic variation, fixation of deleterious and favourable alleles, and the increase of inbreeding experienced by a population. A method exists for the estimation of N _e from the observed linkage disequilibrium between unlinked loci in a population sample. While an increasing number of studies have applied this method in natural and managed populations, its reliability has not yet been evaluated. We developed a computer program to calculate this estimator of N _e using the most widely used linkage disequilibrium algorithm and used simulations to show that this estimator is strongly biased when the sample size is small (<‰100) and below the true N _e. This is probably due to the linkage disequilibrium generated by the sampling process itself and the inadequate correction for this phenomenon in the method. Results suggest that N _e estimates derived using this method should be regarded with caution in many cases. To improve the method’s reliability and usefulness we propose a way to determine whether a given sample size exceeds the population N _e and can therefore be used for the computation of an unbiased estimate.     

Do estimates of contemporary effective population size tell us what we want to know?

Estimation of effective population size (N_e) from genetic marker data is a major focus for biodiversity conservation because it is essential to know at what rates inbreeding is increasing and additive genetic variation is lost. But are these the rates assessed when applying commonly used N_e estimation techniques? Here we use recently developed analytical tools and demonstrate that in the case of substructured populations the answer is no. This is because the following: Genetic change can be quantified in several ways reflecting different types of N_e such as inbreeding (N_eI), variance (N_eV), additive genetic variance (N_eAV), linkage disequilibrium equilibrium (N_eLD), eigenvalue (N_eE) and coalescence (N_eCo) effective size. They are all the same for an isolated population of constant size, but the realized values of these effective sizes can differ dramatically in populations under migration. Commonly applied N_e‐estimators target N_eV or N_eLD of individual subpopulations. While such estimates are safe proxies for the rates of inbreeding and loss of additive genetic variation under isolation, we show that they are poor indicators of these rates in populations affected by migration. In fact, both the local and global inbreeding (N_eI) and additive genetic variance (N_eAV) effective sizes are consistently underestimated in a subdivided population. This is serious because these are the effective sizes that are relevant to the widely accepted 50/500 rule for short and long term genetic conservation.  The bias can be infinitely large and is due to inappropriate parameters being estimated when applying theory for isolated populations to subdivided ones.     

EFFECTIVE POPULATION SIZE AND GENETIC DRIFT IN TRISTYLOUS EICHHORNIA PANICULATA (PONTEDERIACEAE)

Populations of the tristylous, annual Eichhornia paniculata are markedly differentiated with respect to frequency of mating types. This variation is associated with evolutionary changes in mating system, from predominant outcrossing to high self-fertilization. To assess the potential influence of genetic drift acting on this variation, we estimated effective population size in 10 populations from northeastern Brazil using genetic and demographic methods. Effective size (N_e) was inferred from temporal changes in allele frequency at two to eight isozyme loci and also calculated using five demographic variables: 1) the number of flowering individuals (N); 2) temporal fluctuations in N; 3) variance in flower number; 4) frequency of mating types; and 5) selfing rate. Average N_e based on isozyme data was 15.8, range 3.4–70.6, and represented a fraction (mean N_e/N = 0.106) of the census number of individuals (mean N = 762.8; range: 30.5–5,040). Temporal variation in N and variance in flower number each reduced N_e to about a half of N whereas mating type frequencies and selfing rate caused only small reductions in N_e relative to N. All estimates of N_e based on demographic variables were considerably larger than those obtained from genetic data. The two kinds of estimates were in general agreement, however, when all demographic variables were combined into a single measure. Monte Carlo simulations indicated that effective size must be fewer than about 40 for drift to overcome the frequency-dependent selection that maintains the polymorphism for mating type. Applying the average N_e/N value to 167 populations censused in northeastern Brazil indicated that 72% had effective sizes below this number. This suggests that genetic drift is likely to play a dominant role in natural populations of E. paniculata.     

Effects of population characteristics and structure on estimates of effective population size in a house sparrow metapopulation

Effective population size (N_e) is a key parameter to understand evolutionary processes and the viability of endangered populations as it determines the rate of genetic drift and inbreeding. Low N_e can lead to inbreeding depression and reduced population adaptability. In this study, we estimated contemporary N_e using genetic estimators (LDNE, ONeSAMP, MLNE and CoNe) as well as a demographic estimator in a natural insular house sparrow metapopulation. We investigated whether population characteristics (population size, sex ratio, immigration rate, variance in population size and population growth rate) explained variation within and among populations in the ratio of effective to census population size (N_e/N_c). In general, N_e/N_c ratios increased with immigration rates. Genetic N_e was much larger than demographic N_e, probably due to a greater effect of immigration on genetic than demographic processes in local populations. Moreover, although estimates of genetic N_e seemed to track N_c quite well, the genetic N_e‐estimates were often larger than N_c within populations. Estimates of genetic N_e for the metapopulation were however within the expected range (<N_c). Our results suggest that in fragmented populations, even low levels of gene flow may have important consequences for the interpretation of genetic estimates of N_e. Consequently, further studies are needed to understand how N_e estimated in local populations or the total metapopulation relates to actual rates of genetic drift and inbreeding.     

Asymmetric gene flow and the evolutionary maintenance of genetic diversity in small,peripheral Atlantic salmon populations

Small populations may be expected to harbour less genetic variation than large populations, but the relation between census size (N), effective population size (N _e), and genetic diversity is not well understood. We compared microsatellite variation in four small peripheral Atlantic salmon populations from the Iberian peninsula and three larger populations from Scotland to test whether genetic diversity was related to population size. We also examined the historical decline of one Iberian population over a 50-year period using archival scales in order to test whether a marked reduction in abundance was accompanied by a decrease in genetic diversity. Estimates of effective population size (N _e) calculated by three temporal methods were consistently low in Iberian populations, ranging from 12 to 31 individuals per generation considering migration, and from 38 to 175 individuals per generation if they were regarded as closed populations. Corresponding N _e/N ratios varied from 0.02 to 0.04 assuming migration (mean=0.03) and from 0.04 to 0.18 (mean=0.10) assuming closed populations. Population bottlenecks, inferred from the excess of heterozygosity in relation to allelic diversity, were detected in all four Iberian populations, particularly in those year classes derived from a smaller number of returning adults. However, despite their small size and declining status, Iberian populations continue to display relatively high levels of heterozygosity and allelic richness, similar to those found in larger Scottish populations. Furthermore, in the R. Asón no evidence was found for a historical loss of genetic diversity despite a marked decline in abundance during the last five decades. Thus, our results point to two familiar paradigms in salmonid conservation: (1)␣endangered populations can maintain relatively high levels of genetic variation despite their small size, and (2) marked population declines may not necessarily result in a significant loss of genetic diversity. Although there are several explanations for such results, microsatellite data and physical tagging suggest that high levels of dispersal and asymmetric gene flow have probably helped to maintain genetic diversity in these peripheral populations, and thus to avoid the negative consequences of inbreeding.     

Association between host's genetic diversity and parasite burden in damselflies

Recent research indicates that low genetic variation in individuals can increase susceptibility to parasite infection, yet evidence from natural invertebrate populations remains scarce. Here, we studied the relationship between genetic heterozygosity, measured as AFLP‐based inbreeding coefficient f_AFLP, and gregarine parasite burden from eleven damselfly, Calopteryx splendens, populations. We found that in the studied populations, 5–92% of males were parasitized by endoparasitic gregarines (Apicomplexa: Actinocephalidae). Number of parasites ranged from none to 47 parasites per male, and parasites were highly aggregated in a few hosts. Mean individual f_AFLP did not differ between populations. Moreover, we found a positive association between individual's inbreeding coefficient and parasite burden. In other words, the more homozygous the individual, the more parasites it harbours. Thus, parasites are likely to pose strong selection pressure against inbreeding and homozygosity. Our results support the heterozygosity‐fitness correlation hypothesis, which suggests the importance of heterozygosity for an individual's pathogen resistance.     

Effect of recurrent selfing on inbreeding depression and mating system evolution in an autopolyploid plant

Genome duplication resulting in polyploidy can have significant consequences for the evolution of mating systems. Most theory predicts that self‐fertilization will be selectively favored in polyploids; however, many autopolyploids are outcrossing or mixed‐mating. Here, we examine the hypothesis that the evolution of selfing is restricted in autopolyploids because the genetic cost of selfing (i.e., inbreeding depression) increases monotonically with successive generations of inbreeding. Using the herbaceous, autotetraploid plant Chamerion angustifolium, we generated populations with different inbreeding coefficients (F= 0, 0.17 and 0.36) through three consecutive generations of selfing and compared their magnitudes of inbreeding depression in a common environment. Mating system estimates for four natural populations confirmed that tetraploid selfing rates (s_m= 0.25, SE = 0.02) are similar to those of diploids (s_m= 0.12, SE = 0.12; F_1,2= 1.34, P= 0.37) indicating that both cytotypes are predominantly outcrossing. Compared to an outbred control line, mean inbreeding depression for seed production, survival, and height (vegetative and total) in the inbred line differed among generations (inbreeding coefficients). Across all stages, inbreeding depression (relative to control) was positively related to generation (inbreeding coefficient). Although the initial costs of inbreeding in extant and newly synthesized polyploids may be low compared to diploids, the monotonic increase in inbreeding depression with repeated inbreeding may limit the extent to which selfing variants are favored.     

Microsatellite variation in simulated and natural founder populations of the Laysan finch (Telespiza cantans)

Historical and demographic data were used in a computer model tosimulate neutral genetic change in populations of the Laysanfinch (Telespiza cantans), an insular passerine bird that hasundergone documented founder events at Pearl and Hermes reef(PHR). Measures of genetic variation in the natural PHRpopulations generally matched those in the simulated populations,except that heterozygosity on Southeast Island was lower than themodel predicted, and the heterozygote excess in the naturalpopulations had a low probability of occurrence in the simulatedpopulations. The estimate of effective population size (N _e) fromthe stochastic demographic model matched the estimate fromgenetic data for two populations, but the demographic estimatewas higher than the genetic estimate for Southeast Island. Smallfounder number was rejected as a possible explanation for thereduced genetic variation on Southeast. We suggest that N _e wasoverestimated in part because we assumed seasonal variance inreproductive success. Additional variance components need to bemeasured in the field and incorporated into the model. Accounting for the heterozygote excess also requires furthertheoretical and field investigations. Possible explanations forthe excess include inbreeding depression, incest avoidance, andthe effect of polygyny on heterozygote excess in smallpopulations. We concluded that the Pearl and Hermes reefpopulation will continue to lose genetic variation at a highrate, and translocations from the native population on Laysan maybe required to maintain a viable population on the reef.     

Effects of fragmentation phenomena on the genetic structure and gene flow in Centaurea cineraria group (Asteraceae) in the Mediterranean Basin

The complex history of the Mediterranean region illustrates how ancient and recent phenomena are closely associated with species distribution and the creation of phylogeographic divisions within Mediterranean flora. A good model to explore the genetic consequences of fragmentation can be found in Centaurea cineraria and its close relatives. We applied simple sequence repeat molecular markers to a dense population sampling throughout the distribution area of all C. cineraria taxa to study how fragmentation has altered the genetic structure and distribution of C. cineraria. The average gene diversity (H_e) was 0.286, and the average allelic richness (A_r) was 3.65 and ranged from 2.15 (C. gymnocarpa) to 5.25 (C. busambarensis). The F_IS averaged a relatively high 0.223, ranging from ? 0.724 in C. aeolica subsp. aeolica to 0.589 in C. leucadea. Our results indicate that habitat fragmentation over several generations reduced heterozygosity due to random genetic drift in populations of C. cineraria. This heterozygosity erosion becomes more severe when the inbreeding coefficient is positive and the outcrossing rates show a significant increase. The results observed for outcrossing rates and inbreeding coefficient could also indirectly support the possibility of disrupted gene flow or mating pattern changes in fragmented C. cineraria populations.     

Inbreeding depression and drift load in small populations at demographic disequilibrium

Inbreeding depression is a major driver of mating system evolution and has critical implications for population viability. Theoretical and empirical attention has been paid to predicting how inbreeding depression varies with population size. Lower inbreeding depression is predicted in small populations at equilibrium, primarily due to higher inbreeding rates facilitating purging and/or fixation of deleterious alleles (drift load), but predictions at demographic and genetic disequilibrium are less clear. In this study, we experimentally evaluate how lifetime inbreeding depression and drift load, estimated by heterosis, vary with census (N_c) and effective (estimated as genetic diversity, H_e) population size across six populations of the biennial Sabatia angularis as well as present novel models of inbreeding depression and heterosis under varying demographic scenarios at disequilibrium (fragmentation, bottlenecks, disturbances). Our experimental study reveals high average inbreeding depression and heterosis across populations. Across our small sample, heterosis declined with H_e, as predicted, whereas inbreeding depression did not vary with H_e and actually decreased with N_c. Our theoretical results demonstrate that inbreeding depression and heterosis levels can vary widely across populations at disequilibrium despite similar H_e and highlight that joint demographic and genetic dynamics are key to predicting patterns of genetic load in nonequilibrium systems.     

Estimating effective population size using RADseq: Effects of SNP selection and sample size

Effective population size (N_e) is a key parameter of population genetics. However, N_e remains challenging to estimate for natural populations as several factors are likely to bias estimates. These factors include sampling design, sequencing method, and data filtering. One issue inherent to the restriction site‐associated DNA sequencing (RADseq) protocol is missing data and SNP selection criteria (e.g., minimum minor allele frequency, number of SNPs). To evaluate the potential impact of SNP selection criteria on N_e estimates (Linkage Disequilibrium method) we used RADseq data for a nonmodel species, the thornback ray. In this data set, the inbreeding coefficient F_IS was positively correlated with the amount of missing data, implying data were missing nonrandomly. The precision of N_eestimates decreased with the number of SNPs. Mean N_e estimates (averaged across 50 random data sets with2000 SNPs) ranged between 237 and 1784. Increasing the percentage of missing data from 25% to 50% increased N_e estimates between 82% and 120%, while increasing the minor allele frequency (MAF) threshold from 0.01 to 0.1 decreased estimates between 71% and 75%. Considering these effects is important when interpreting RADseq data‐derived estimates of effective population size in empirical studies.