Population Bottlenecks and Nonequilibrium Models in Population Genetics. II. Number of Alleles in a Small Population That Was Formed by a Recent Bottleneck

A model is presented in which a large population in mutation/drift equilibrium undergoes a severe restriction in size and subsequently remains at the small size. The rate of loss of genetic variability has been studied. Allelic loss occurs more rapidly than loss of genic heterozygosity. Rare alleles are lost especially rapidly. The result is a transient deficiency in the total number of alleles observed in samples taken from the reduced population when compared with the number expected in a sample from a steady-state population having the same observed heterozygosity. Alternatively, the population can be considered to possess excess gene diversity if the number of alleles is used as the statistical estimator of mutation rate. The deficit in allele number arises principally from a lack of those alleles that are expected to appear only once or twice in the sample. The magnitude of the allelic deficiency is less, however, than the excess that an earlier study predicted to follow a rapid population expansion. This suggests that populations that have undergone a single bottleneck event, followed by rapid population growth, should have an apparent excess number of alleles, given the observed level of genic heterozygosity and provided that the bottleneck has not occurred very recently. Conversely, such populations will be deficient for observed heterozygosity if allele number is used as the sufficient statistic for the estimation of 4Nev. Populations that have undergone very recent restrictions in size should show the opposite tendencies.     

The effective number of a population that varies cyclically in size. I. Discrete generations

We consider a dioecious population having numbers of males and females that vary over time in cycles of length k. It is shown that if k is small in comparison with the numbers of males and females in any generation of the cycle, the effective population number (or size), N(e), is approximately equal to the harmonic mean of the effective population sizes during any given cycle. This result holds whether the locus under consideration is autosomal or sex-linked and whether inbreeding effective population numbers or variance effective population numbers are involved in the calculation of N(e). If, however, only two successive generations in the cycle are considered and the population changes in size between these generations, the inbreeding effective population number, N(eI), differs from the variance effective population number, N(eV). The mutation effective population number turns out to be the same as the number derived using calculations involving probabilities of identity by descent. It is also shown that, at least in one special case, the eigenvalue effective population number is the same as N(eV).     

Historical Analysis of Genetic Variation Reveals Low Effective Population Size in a Northern Pike (Esox Lucius) Population

Effective population size (N(e)) of a natural fish population was estimated from temporal changes in allele frequencies at seven microsatellite loci. Use of a historical collection of fish scales made it possible to increase the precision of estimates by increasing the time interval between samples and to use an equation developed for discrete generations without correcting for demographic parameters. Estimates of N(e) for the time intervals 1961-1977 and 1977-1993 were 35 and 72, respectively. For the entire interval, 1961-1993, the estimate of N(e) was 48 when based on a weighted mean derived from the above two estimates or 125 when calculated from 1961 and 1993 samples only. Corresponding ratios of effective size to adult census size ranged from 0.03 to 0.14. An N(e) of 48 over a 32-year period would imply that this population lost as much as 8% of its heterozygosity in that time. Results suggest the potential for using genetic methods based on microsatellite loci data to compare historical trends in N(e) with population dynamic parameters. Such comparisons will help to evaluate the relationship between genetic diversity and long-term persistence of natural populations.     

Impact on Reindeer (Rangifer tarandus) Genetic Diversity from Two Parallel Population Bottlenecks Founded from a Common Source

Population bottlenecks and founder events reduce genetic diversity through stochastic processes associated with the sampling of alleles at the time of the bottleneck, and the recombination of alleles that are identical by descent. At the same time bottlenecks and founder events can structure populations through the stochastic distortion of allele frequencies. Here we undertake an empirical assessment of the impact of two independent bottlenecks of known size from a known source, and consider inference about evolutionary process in the context of simulations and theoretical expectations. We find a similar level of reduced variation in the parallel bottleneck events, with the greater impact on the population that began with the smaller number of females. The level of diversity remaining was consistent with model predictions, but only if re-growth of the population was essentially exponential and polygeny was minimal at the early stages. There was a high level of differentiation seen compared to the source population and between the two bottlenecked populations, reflecting the stochastic distortion of allele frequencies. We provide empirical support for the theoretical expectations that considerable diversity can remain following a severe bottleneck event, given rapid demographic recovery, and that populations founded from the same source can become quickly differentiated. These processes may be important during the evolution of population genetic structure for species affected by rapid changes in available habitat.     

Population correlation and population kinship

The processes of gene identity by descent and of allelic identities (or likenesses) between genes have been previously studied under a wide variety of migration and subdivision models of population evolution. Since the two processes follow probabilistically parallel paths, there has been a tendency to consider the two processes as equivalent, and to equate estimates of correlation of allele frequency with those of gene identity by descent. The adequacy of this procedure must depend upon the evolutionary history. Here, by distinguishing the processes and considering them jointly as a population evolves in time, we demonstrate the relationship between them in a simple situation, thus providing a basis for study of the extent to which observed allelic similarity between populations is a reflection of underlying gene identity.     

Population Structure of Barley Landrace Populations and Gene-Flow with Modern Varieties

Landraces are heterogeneous plant varieties that are reproduced by farmers as populations that are subject to both artificial and natural selection. Landraces are distinguished by farmers due to their specific traits, and different farmers often grow different populations of the same landrace. We used simple sequence repeats (SSRs) to analyse 12 barley landrace populations from Sardinia from two collections spanning 10 years. We analysed the population structure, and compared the population diversity of the landraces that were collected at field level (population). We used a representative pool of barley varieties for diversity comparisons and to analyse the effects of gene flow from modern varieties. We found that the Sardinian landraces are a distinct gene pool from those of both two-row and six-row barley varieties. There is also a low, but significant, mean level and population-dependent level of introgression from the modern varieties into the Sardinian landraces. Moreover, we show that the Sardinian landraces have the same level of gene diversity as the representative sample of modern commercial varieties grown in Italy in the last decades, even within population level. Thus, these populations represent crucial sources of germplasm that will be useful for crop improvement and for population genomics studies and association mapping, to identify genes, loci and genome regions responsible for adaptive variations. Our data also suggest that landraces are a source of valuable germplasm for sustainable agriculture in the context of future climate change, and that in-situ conservation strategies based on farmer use can preserve the genetic identity of landraces while allowing adaptation to local environments.     

Population size and time since island isolation determine genetic diversity loss in insular frog populations

Understanding the factors that contribute to loss of genetic diversity in fragmented populations is crucial for conservation measurements. Land‐bridge archipelagoes offer ideal model systems for identifying the long‐term effects of these factors on genetic variations in wild populations. In this study, we used nine microsatellite markers to quantify genetic diversity and differentiation of 810 pond frogs (Pelophylax nigromaculatus) from 24 islands of the Zhoushan Archipelago and three sites on nearby mainland China and estimated the effects of the island area, population size, time since island isolation, distance to the mainland and distance to the nearest larger island on reduced genetic diversity of insular populations. The mainland populations displayed higher genetic diversity than insular populations. Genetic differentiations and no obvious gene flow were detected among the frog populations on the islands. Hierarchical partitioning analysis showed that only time since island isolation (square‐root‐transformed) and population size (log‐transformed) significantly contributed to insular genetic diversity. These results suggest that decreased genetic diversity and genetic differentiations among insular populations may have been caused by random genetic drift following isolation by rising sea levels during the Holocene. The results provide strong evidence for a relationship between retained genetic diversity and population size and time since island isolation for pond frogs on the islands, consistent with the prediction of the neutral theory for finite populations. Our study highlights the importance of the size and estimated isolation time of populations in understanding the mechanisms of genetic diversity loss and differentiation in fragmented wild populations.     

Low genetic variability in a widely distributed and abundant clupeid species, Sardinella aurita. New empirical results and interpretations

Considering the wide geographic distribution and the catches of Sardinella aurita , the observed allozyme diversity (H=0·011) is strikingly small. Potential explanations for this low gene diversity, which include restrictions on effective population size owing to variance in reproductive success, demographic instability, historical bottlenecks in population size, selection, and technical artifacts are examined and quantified. This quantification, though rough, shows that no single factor can account for the lack of diversity. However, demographic instability of S. aurita , especially if this instability has persisted over evolutionary time scales, together with much greater than Poisson variance in individual reproductive success, could account reasonably for the results. Pleistocene reduction of population size seems also a necessary co-factor. Technical artifacts, mostly scoring difficulties linked to liver autolysis, are considered also and analysed in different clupeid species.     

Population size and fragmentation thresholds for the maintenance of genetic diversity in the herbaceous endemic Scutellaria montana (Lamiaceae)

Abstract.-The level and distribution of genetic variation is thought to be affected primarily by the size of individual populations and by gene flow among populations. Although the effects of population size have frequently been examined, the contributions of regional gene flow to levels of genetic variation are less well known. Here I examine the effects of population size and the number of neighboring populations (metapopulation density) on the distribution and maintenance of genetic diversity in an endemic herbaceous perennial. Reductions in the proportion of polymorphic loci and the effective number of alleles per locus were apparent for many populations with a census size of less than 100 individuals, but no effects of population size on levels of inbreeding were detected. I assess the effects of regional population density on levels of diversity and inbreeding using stepwise regression analysis of metapopulation diameter (i.e., the size of a circle within which population density is estimated). This procedure provides a spatially explicit evaluation of the effects of metapopulation size on population genetic parameters and indicates the critical number of neighboring populations (fragmentation threshold) for the regional maintenance of genetic diversity. Stepwise regression analyses revealed fragmentation thresholds at two levels; at a scale of 2 km, where small metapopulations resulted in greater levels of selfing or sibling mating, and at a scale of 8 km, where metapopulation size was positively associated with higher levels of genetic diversity. I hypothesize that the smaller fragmentation threshold may reflect higher levels of selfing in isolated populations because of the absence of pollinators. The larger threshold probably indicates the maximum distance over which pollen dispersal rates are high enough to counteract genetic drift. This study demonstrates that the regional distribution of populations can be an important factor for the long-term maintenance of genetic variation.     

Maintenance of genetic diversity in cyclic populations-a longitudinal analysis in Myodes glareolus

Conspicuous cyclic changes in population density characterize many populations of small northern rodents. The extreme crashes in individual number are expected to reduce the amount of genetic variation within a population during the crash phases of the population cycle. By long-term monitoring of a bank vole (Myodes glareolus) population, we show that despite the substantial and repetitive crashes in the population size, high heterozygosity is maintained throughout the population cycle. The striking population density fluctuation in fact only slightly reduced the allelic richness of the population during the crash phases. Effective population sizes of vole populations remained also relatively high even during the crash phases. We further evaluated potential mechanisms contributing to the genetic diversity of the population and found that the peak phases are characterized by both a change in spatial pattern of individuals and a rapid accession of new alleles probably due to migration. We propose that these events act together in maintaining the high genetic diversity within cyclical populations.     

Factors important in evolutionary shaping of immunoglobulin gene loci

Background

The extraordinary diversity characterizing the antibody repertoire is generated by both evolution and lymphocyte development. Much of this diversity is due to the existence of immunoglobulin (Ig) variable region gene segment libraries, which were diversified during evolution and, in higher vertebrates, are used in generating the combinatorial diversity of antibody genes. The aim of the present study was to address the following questions: What evolutionary parameters affect the size and structure of gene libraries? Are the number of genes in libraries of contemporary species, and the corresponding gene locus structure, a random result of evolutionary history, or have these properties been optimized with respect to individual or population fitness? If a larger number of genes or different genome structures do not increase the fitness, then the current structure is probably optimized.

Results

We used a simulation of variable region gene library evolution. We measured the effect of different parameters on gene library size and diversity, and the corresponding fitness. We found compensating relationships between parameters, which optimized Ig library size and diversity.

Conclusions

We conclude that contemporary species' Ig libraries have been optimized by evolution in terms of Ig sequence lengths, the number and diversity of Ig genes, and antibody-antigen affinities.     

The Genetic Structure of a Tribal Population, the Yanomama Indians. VI. Analysis by F-Statistics (Including a Comparison with the Makiritare and Xavante

The infra-structure of three relatively undisturbed tribes of American Indians (Yanomama, Makiritare, Xavante) has been investigated by means of the F-statistics of Wright, using 8, 9 and 6 codominant systems respectively. The data for the first two mentioned tribes are much more extensive (37 and 7 villages) than for the third (3 villages), and much of the argument is based on the first two. An additive model partitioning F(IS) into an average effect (F(A)) and deviations due to deme size, systems effects, village effects, and random error has been employed. The Cannings-Edwards formulation suggests that the small size of the demes alone would result in an F(IS) of -0.008 for the Yanomama and -0.007 for the Makiritare. There is no evidence for significant village or systems effects. Despite considerable scatter, F(A) values are not significantly heterogeneous and tend to be negative (-0.012 to -0.023). On the basis of a computer simulation model, it appears that there is an excess of consanguineous marriage over random expectation, i.e. the negative F(A) values are probably not due to avoidance of close inbreeding in a subdivided population in which demes are small. Aspects of population structure which could contribute to negative F(A) values are identified. These include unequal gene frequencies in the sexes and occasional marked differential fertility. It is at this point unnecessary to introduce overdominance as a cause of the negative F(A) values, since a computer simulation program which does not incorporate selection satisfactorily reproduces the observed F(IS) values. If population breeding structure alone can result in negative F(IS) values, then this may constitute a mechanism for retarding random fixation.-Mean F(ST) values are 0.063 for the Yanomama and 0.036 for the Makiritare. While truly comparable data are lacking, it seems likely these will be found to be relatively high values for human populations. F(IT) values have been calculated by both direct and indirect approaches. The direct approach yields a value of 0.045 for the Yanomama and -0.009 for the Makiritare; the respective indirect values are 0.085 and 0.017. The primary identifiable reason for this difference between tribes is the greater genetic heterogeneity among Yanomama villages. The assumptions underlying the indirect approach to the calculation of F(IT) do not appear to be met in these populations.     

Measurement error and estimates of population extinction risk

It is common to estimate the extinction probability for a vulnerable population using methods that are based on the mean and variance of the long‐term population growth rate. The numerical values of these two parameters are estimated from time series of population censuses. However, the proportion of a population that is registered at each census is typically not constant but will vary among years because of stochastic factors such as weather conditions at the time of sampling. Here, we analyse how such sampling errors influence estimates of extinction risk and find sampling errors to produce two opposite effects. Measurement errors lead to an exaggerated overall variance, but also introduce negative autocorrelations in the time series (which means that estimates of annual growth rates tend to alternate in size). If time series data are treated properly these two effects exactly counter balance. We advocate routinely incorporating a measure of among year correlations in estimating population extinction risk.     

Population demography and heterozygosity–fitness correlations in natural guppy populations: An examination using sexually selected fitness traits

Heterozygosity–fitness correlations (HFCs) have been examined in a wide diversity of contexts, and the results are often used to infer the role of inbreeding in natural populations. Although population demography, reflected in population‐level genetic parameters such as allelic diversity or identity disequilibrium, is expected to play a role in the emergence and detectability of HFCs, direct comparisons of variation in HFCs across many populations of the same species, with different genetic histories, are rare. Here, we examined the relationship between individual microsatellite heterozygosity and a range of sexually selected traits in 660 male guppies from 22 natural populations in Trinidad. Similar to previous studies, observed HFCs were weak overall. However, variation in HFCs among populations was high for some traits (although these variances were not statistically different from zero). Population‐level genetic parameters, specifically genetic diversity levels (number of alleles, observed/expected heterozygosity) and measures of identity disequilibrium (g2 and heterozygosity–heterozygosity correlations), were not associated with variation in population‐level HFCs. This latter result indicates that these metrics do not necessarily provide a reliable predictor of HFC effect sizes across populations. Importantly, diversity and identity disequilibrium statistics were not correlated, providing empirical evidence that these metrics capture different essential characteristics of populations. A complex genetic architecture likely underpins multiple fitness traits, including those associated with male fitness, which may have reduced our ability to detect HFCs in guppy populations. Further advances in this field would benefit from additional research to determine the demographic contexts in which HFCs are most likely to occur.     

Bottlenecks, drift and differentiation: the population structure and demographic history of sika deer (Cervus nippon) in the Japanese archipelago

We assessed genetic differentiation and diversity in 14 populations of sika deer (Cervus nippon) from Japan and four populations of sika deer introduced to the UK, using nine microsatellite loci. We observed extreme levels of differentiation and significant differences in diversity between populations. Our results do not support morphological subspecies designations, but are consistent with previous mitochondrial DNA analyses which suggest the existence of two genetically distinct lineages of sika deer in Japan. The source of sika introduced to the UK was identified as Kyushu. The underlying structure of Japanese populations probably derives from drift in separate glacial refugia and male dispersal limited by distance. This structure has been perturbed by bottlenecks and habitat fragmentation, resulting from human activity from the mid-nineteenth century. Most current genetic differentiation and differences in diversity among populations probably result from recent drift. Coalescent model analysis suggests sika on each of the main Japanese islands have experienced different recent population histories. Hokkaido, which has large areas of continuous habitat, has maintained high levels of gene flow. In Honshu the population is highly fragmented and is likely to have been evolving by drift alone. In Kyushu there has been a balance between gene flow and drift but all the populations have experienced high levels of drift. Habitat fragment size was not significantly associated with genetic diversity in populations but there was a significant correlation between habitat fragment size and effective population size.     

Population structure in Arabidopsis lyrata: evidence for divergent selection on trichome production

Leaf trichomes may serve several biological functions including protection against herbivores, drought, and UV radiation; and their adaptive value can be expected to vary among environments. The perennial, self-incompatible herb Arabidopsis lyrata is polymorphic for trichome production, and occurs in a glabrous and a trichome-producing form. Controlled crosses indicate that the polymorphism is governed by a single gene, with trichome production being dominant. We examined the hypothesis that trichome production is subject to divergent selection (i.e., directional selection favoring different phenotypes in different populations) by comparing patterns of variation at the locus coding for glabrousness and at eight putatively neutral isozyme loci in Swedish populations of A. lyrata. The genetic diversity (He) and allele number at isozyme loci tended to increase with population size and decreased with latitude of origin, whereas genetic diversity at the locus coding for glabrousness did not vary with population size and increased with latitude of origin. The degree of genetic differentiation at the glabrousness locus was much higher than that at isozyme loci. Genetic identity at isozyme loci was negatively related to geographic distance, suggesting isolation by distance. In contrast, there was no significant correlation between genetic identity at the glabrousness locus and at isozyme loci. The results are consistent with the hypothesis that divergent selection contributes to population differentiation in trichome production in A. lyrata.     

Bromodeoxyuridine labeling and flow cytometric identification of replicating Saccharomyces cerevisiae cells: lengths of cell cycle phases and population variability at specific cell cycle positions.

An immunofluorescent staining procedure has been developed to identify, with flow cytometry, replicating cells of Saccharomyces cerevisiae after incorporation of bromodeoxyuridine (BrdUrd) into the DNA. Incorporation of BrdUrd is made possible by using yeast strains with a cloned thymidine kinase gene from the herpes simplex virus. An exposure time of 4 min to BrdUrd results in detectable labeling of the DNA. The BrdUrd/DNA double staining procedure has been optimized and the flow cytometry measurements yield histograms comparable to data typically obtained for mammalian cells. On the basis of the accurate assessment of cell fractions in individual cell cycle phases of the asynchronously growing cell population, the average duration of the cell cycle phases has been evaluated. For a population doubling time of 100 min it was found that cells spend in average 41 min in the replicating phase and 24 min in the G2+M cell cycle period. Assuming that mother cells immediately reenter the S phase after cell division, daughter cells spend 65 min in the G1 cell cycle phase. Together with the single cell fluorescence parameters, the forward-angle light scattering intensity (FALS) has been determined as an indicator of cell size. Comparing different temporal positions within the cell cycle, the determined FALS distributions show the lowest variability at the beginning of the S phase. The developed procedure in combination with multiparameter flow cytometry should be useful for studying the kinetics and regulation of the budding yeast cell cycle.     

Population genetics of rhizobia: construction and analysis of an "Infection and Release" model

A mathematical model is created to assess the inputs of sym gene transfer of in planta multiplication and of interstrain competition into dynamics of the rhizobia populations. Their microevolution is presented as a series of the "infection and release" cycles; each cycle includes transfer of sym genes from virulent initial symbionts to avirulent local bacteria yielding the virulent novel symbionts; competition between initial symbionts and novel symbionts for the host nodulation; multiplication of initial symbionts and novel symbionts in planta and their release into soil; competition between the released novel symbionts and resident local bacteria for ex planta survival. A recurrent equation is created to determine the number of novel symbionts at each cycle of evolution of the closed bacteria-plant system. Its analysis demonstrates that under certain, really allowable values of the introduced parameters two major effects may occur: (a) rapid multiplication of novel symbionts arisen from sym gene transfer; and (b) increase of frequency of rare local bacteria genotypes after acquisition of virulence. Multiplication of very rare strains (p<10(-19)) in the plant-associated bacteria population is possible at certain parameters of the system. Variation of the sizes of bacteria populations and of the parameters for interstrain competition may influence the evolutionary rate of the bacteria population. The "infection and release" model represents a selective mechanism which may be responsible for a high taxonomic diversity of rhizobia and for a panmictic structure of their populations.     

Population dynamics of a selfish B chromosome neutralized by the standard genome in the grasshopper Eyprepocnemis plorans

Effects of the B chromosome polymorphism of the grasshopper Eyprepocnemis plorans were analyzed in two natural populations. Postmating sexual selection, female fertility, and survival were studied. The B chromosome lacks drive and has no detectable effects on fitness. A neutral B cannot invade a population and establish a polymorphism, but the confidence limits on our estimates cannot exclude the possibility that the polymorphism is maintained by a balance between weak drive and weak selection against individuals with two and three B's. However, other lines of evidence favor the following model of the dynamics of the B in E. plorans. In a newly invaded population, the B has substantial drive, but the evolution of drive suppressor genes in the A chromosomes neutralizes the B drive so that it becomes near-neutral and begins a random walk toward extinction by stochastic loss. Because the B is common by the time drive disappears, the random walk is likely to continue for a long time. If in the course of the random walk a variant B with greater drive appears, then it will displace the original variant, and a new cycle of drive suppression and drift to extinction occurs. A simulation model of this process suggested that the mean time to extinction is proportional to the two-thirds power of the population size; it is much less affected by subpopulation size or the number of populations in a subdivided population.