Genetic identity between populations when mutation rates vary within and across loci

A formula is derived for the probability that two genes taken at random from the same locus in two populations isolated at time t ago are of the same allelic type. The model assumed is a neutral one where there are possibly different mutation rates between different alleles. Inequalities are derived for this probability. A particular result is that for a fixed overall mutation rate, the probability is least for the infinite alleles model. Inequalities and approximations are found for Nei's genetic identity at one locus when mutation rates vary, and also for the identity across loci when the overall mutation rates per locus vary. Genetic identity at the molecular level is considered and a probability generating function found for the number of segregating sites between two randomly chosen gametes from two divergent populations, under various models.     

Genetic isolation of fragmented populations is exacerbated by drift and selection

Reduced genetic variation at marker loci in small populations has been well documented, whereas the relationship between quantitative genetic variation and population size has attracted little empirical investigation. Here we demonstrate that both neutral and quantitative genetic variation are reduced in small populations of a fragmented plant metapopulation, and that both drift and selective change are enhanced in small populations. Measures of neutral genetic differentiation (F(ST)) and quantitative genetic differentiation (Q(ST)) in two traits were higher among small demes, and Q(ST) between small populations exceeded that expected from drift alone. This suggests that fragmented populations experience both enhanced genetic drift and divergent selection on phenotypic traits, and that drift affects variation in both neutral markers and quantitative traits. These results highlight the need to integrate natural selection into conservation genetic theory, and suggests that small populations may represent reservoirs of genetic variation adaptive within a wide range of environments.     

Genetic variance and drift in selfed and intermated populations derived from backcrossing

Summary The genetic variance among random-mated lines derived from backcrossing (BC_gS₁ lines) depends upon the backcross generation (g) and the number (n) of BC_gF₁ plants crossed in generations 1 through g. There is little effect of n on genetic variance for n > 6. The genetic variance among BC_gF₂-derived lines is greater than that among BC_gS₁ lines for all g. If either BC_gF₂-derived or BC_gS₁ lines are used as a base population for recurrent selection, 8, 16, 32, and 64 BC₁F₁, BC₂F₁, BC₃F₁, and BC₄F₁ plants, respectively, should be used to avoid loss of donor alleles to drift.Joint contribution of USDA-ARS and Journal Paper No. J-11224 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2471Formerly Research Geneticist, USDA-ARS, Ames, Iowa, USA     

Spatial dynamics in fluctuating vole populations

Summary Patterns and consistency of distribution, spatial and temporal components, and the extent of spatial density-dependence were compared between semi-cyclic and cyclic populations of the vole species Clethrionomys glareolus and Microtus agrestis in south-central and north Sweden. Cyclic populations were less clumped and only C. glareolus showed a consistency in distribution between years. Spatial variation contributed little to the distributions in cyclic populations while the spatial and temporal variations were of the same magnitude in the semi-cyclic populations. The latter populations could be subdivided into areas with different spatial and temporal components. The spatial density-dependence increased from increase to decline years in C. glareolus but not in M. agrestis, which differed conspicuously between reregions in population development. The data imply that spatial dynamics should be considered as much as temporal ones for non-cyclic populations, that the same regulating or limiting factors may be at work in both spatial and temporal components and that, in addition, social behaviour may be important in explaining spatial dynamics. However, the latter effects may be fairly species-specific.     

Environmental variation, fluctuating selection and genetic drift in subdivided populations

Although there have many studies of the population genetical consequences of environmental variation, little is known about the combined effects of genetic drift and fluctuating selection in structured populations. Here we use diffusion theory to investigate the effects of temporally and spatially varying selection on a population of haploid individuals subdivided into a large number of demes. Using a perturbation method for processes with multiple time scales, we show that as the number of demes tends to infinity, the overall frequency converges to a diffusion process that is also the diffusion approximation for a finite, panmictic population subject to temporally fluctuating selection. We find that the coefficients of this process have a complicated dependence on deme size and migration rate, and that changes in these demographic parameters can determine both the balance between the dispersive and stabilizing effects of environmental variation and whether selection favors alleles with lower or higher fitness variance.     

A stochastic model for a single click of Muller's ratchet

This work presents a new approach to Muller's ratchet, where Haigh's model is approximately mapped into a simpler model that describes the behaviour of a population after a click of the ratchet, i.e., after loss of what was the fittest class. This new model predicts the distribution of times to the next click of the ratchet and is equivalent to a Wright-Fisher model for a population of haploid asexual individuals with one locus and two alleles. Within this model, the fittest members of a population correspond to carriers of one allele, while all other individuals have suboptimal fitness and are represented as carriers of the other allele. In this way, all suboptimal fitness individuals are amalgamated into a single “mutant” class.The approach presented here has some limitations and the potential for improvement. However, it does lead to results for the rate of the ratchet that, over a wide range of parameters, are accurate within one order of magnitude of simulation results. This contrasts with existing approaches, which are designed for only one or other of the two different parameter regimes known for the ratchet and are more accurate only in the parameter regime they were designed for.Numerical results are presented for the mean time between clicks of the ratchet for (i) the Wright-Fisher model, (ii) a diffusion approximation of this model and (iii) individually based simulations of a full model. The diffusion approximation is validated over a wide range of parameters by its close agreement with the Wright-Fisher model.The present work predicts that: (a) the time between clicks of the ratchet is insensitive to the value of the selection coefficient when the genomic mutation rate is large compared with the selection coefficient against a deleterious mutation, (b) the time interval between clicks of the ratchet has, approximately, an exponential distribution (or its discrete analogue). It is thus possible to determine the variance in times between clicks, given the expected time between clicks. Evidence for both (a) and (b) is seen in simulations.     

The Characteristic Trajectory of a Fixing Allele: A Consequence of Fictitious Selection That Arises from Conditioning

This work is concerned with the historical progression, to fixation, of an allele in a finite population. This progression is characterized by the average frequency trajectory of alleles that achieve fixation before a given time, T. Under a diffusion analysis, the average trajectory, conditional on fixation by time T, is shown to be equivalent to the average trajectory in an unconditioned problem involving additional selection. We call this additional selection “fictitious selection”; it plays the role of a selective force in the unconditioned problem but does not exist in reality. It is a consequence of conditioning on fixation. The fictitious selection is frequency dependent and can be very large compared with any real selection that is acting. We derive an approximation for the characteristic trajectory of a fixing allele, when subject to real additive selection, from an unconditioned problem, where the total selection is a combination of real and fictitious selection. Trying to reproduce the characteristic trajectory from the action of additive selection, in an infinite population, can lead to estimates of the strength of the selection that deviate from the real selection by >1000% or have the opposite sign. Strong evolutionary forces may be invoked in problems where conditioning has been carried out, but these forces may largely be an outcome of the conditioning and hence may not have a real existence. The work presented here clarifies these issues and provides two useful tools for future analyses: the characteristic trajectory of a fixing allele and the force that primarily drives this, namely fictitious selection. These should prove useful in a number of areas of interest including coalescence with selection, experimental evolution, time series analyses of ancient DNA, game theory in finite populations, and the historical dynamics of selected alleles in wild populations.     

Genetic variation in central and peripheral populations of Excoecaria agallocha from Indo-West Pacific

Genetic diversity and differentiation were studied in Excoecaria agallocha L., a mangrove species growing on the coastlines of the Indo-West Pacific region. Twenty natural populations of E. agallocha were sampled from the Malay Peninsula (central population), and in Southern China, North Australia, Sri Lanka and Southern Japan (peripheral populations). Our results showed that central populations from Malay Peninsula possessed significantly higher genetic diversity than the peripheral ones (P < 0.05). Analysis of molecular variation (AMOVA) revealed that genetic variability was partitioned at 22.9% among regions, 23.6% among populations within regions, and 53.5% within populations. Genetic differentiation (G_ST = 0.300) among the six central populations was stronger than those from peripheral regions. Populations from North Australia clustered closely together in the dendrogram and were distinct from the rest of the populations. Those from Southern Japan, Southern China and Sri Lanka also clustered closely together, respectively. However, populations from Malay Peninsula did not cluster by region. The east coast populations of Malay Peninsula (including Pasir population) were more genetically similar to the populations from Southern China than those from the west coastline of Malay Peninsula. Our study suggests that ocean currents, land barriers, limited dispersal ability of seeds, and founder effect may play important roles in the distribution of genetic diversity in E. agallocha.     

Genetic variation,population structure and cryptic species within the black mudfish,Neochanna diversus,an endemic galaxiid from New Zealand

To investigate the phylogenetic relationships and geographical structure among landlocked populations of the black mudfish, Neochanna diversus, mitochondrial DNA nucleotide sequence data were sampled from seven populations from the Waikato and Northland regions of New Zealand. The complete D-loop region was sequenced from 70 individuals, with 913 bp from the tRNA-pro end used in population and phylogenetic analysis. A tandem repeat array, which ranged in size up to 200 bp, was found in most populations at the 3′ end of the D-loop that was not able to be aligned for analysis. Of the seven sites sampled, two from Northland exhibited significant sequence divergence from all other sites. There was also a clear distinction among remaining Northland sites and those from the Waikato. An additional 518 bp segment of the 16S region was sequenced from all sites and compared with the other New Zealand mudfish species, N. apoda, N. burrowsius and the Tasmanian mudfish Galaxias (Neochanna) cleaveri using Galaxias maculatus as an outgroup. Both D-loop and 16S sequence data provided strong evidence for a cryptic species of mudfish present in Northland. The significant genetic structure apparent in the black mudfish appears most probably to be attributed to geological conditions during the Pliocene, where peat wetlands became apparent in the Waikato while Northland consisted of disjunct ‘islands’. Conservation and management of these populations must take into account the historical processes that have shaped these patterns of genetic diversity.     

Genetic differentiation and diversity of Acacia koa populations in the Hawaiian Islands

Acacia koa A. Gray (koa) is a leguminous tree endemic to the Hawaiian Islands and can be divided into morphologically distinguishable groups of A. koaia Hillebrand, A. koa and populations that are intermediate between these extremes. The objectives of this investigation were to distinguish among divergent groups of koa at molecular levels, and to determine genetic diversity within and among the groups. Phylogenetic analyses using the ITS/5.8S rDNA and trnK intron sequences did not separate the representative koa types into distinct clusters. An unweighted pair group method with arithmetic mean cluster analysis and principal coordinate analysis, based on allele profiles of 12 microsatellite loci for 215 individual koa samples, separated the population into three distinct clusters consistent with their morphology, A. koaia, A. koa and intermediate forms. There was an average of 8.8 alleles per polymorphic locus (AP) among all koa and koaia individuals. The intermediate populations had the highest genetic diversity (H′ = 1.599), AP (7.9) and total number of unique alleles (21), whereas A. koaia and A. koa showed similar levels of genetic diversity (H′ = 0.965 and 0.943, respectively). No correlation was observed between geographic distance and genetic distance as determined by a Mantel test (r = 0.027, P = 0.91). The data presented here support previous recommendations that morphological variation within koa should be recognized at the subspecific level rather than as distinct species.     

Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N_e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

Genetic structure of expanding wolf (Canis lupus) populations in Italy and Croatia,and the early steps of the recolonization of the Eastern Alps

After centuries of range contraction and demographic declines wolves are now expanding in Europe, colonizing regions from where they have been absent for centuries. Wolf colonizing the western Alps originate by the expansion of the Italian population. Vagrant wolves of Italian and Dinaric-Balkan origins have been recently observed in the Eastern Alps. In this study we compared the genetic structure of wolf populations in Italy and Croatia, aiming to identify the sources of the ongoing recolonization of the Eastern Alps. DNA samples, extracted from 282 Italian and 152 Croatian wolves, were genotyped at 12 autosomal microsatellites (STR), four Y-linked STR and at the hypervariable part of the mitochondrial DNA control-region (mtDNA CR1). Wolves in Croatia and Italy underwent recent demographic bottlenecks, but they differ in genetic diversity and population structure. Wolves in Croatia were more variable at STR loci (N_A = 7.4, H_O = 0.66, H_E = 0.72; n = 152) than wolves in Italy (N_A = 5.3, H_O = 0.57, H_E = 0.58; n = 282). We found four mitochondrial DNA (mtDNA CR1) and 11 Y-STR haplotypes in Croatian wolves, but only one mtDNA CR1 and three Y-STR haplotypes in Italy. Wolves in Croatia were subdivided into three genetically distinct subpopulations (in Dalmatia, Gorski kotar and Lika regions), while Italian wolves were not sub-structured. Assignment testing shows that the eastern and central Alps are recolonized by wolves dispersing from both the Italian and Dinaric populations. The recolonization of the Alps will predictably continue in the future and the new population will be genetically admixed and very variable with greater opportunities for local adaptations and survival.     

Genetic diversity and structuring of the grey wolf population from the Central Balkans based on mitochondrial DNA variation

The Dinaric-Balkan grey wolf population used to be at a border between the large remaining Eastern European populations and the largely eradicated Western European populations. During the last few decades we have witnessed the Western European wolf population recovery. Substantial genetic variation has previously been reported in the Balkan wolf population, but rigorous genetic characterization has not been done for its central parts. The aims of this research were to determine genetic diversity based on mtDNA sequence variability, to infer possible population structuring, to find genetic signals of population expansions or bottlenecks and to evaluate phylogenetic position of the grey wolf population from the Central Balkans. Six haplotypes were detected, of which three have only been found in the Balkan region. These haplotypes belong to both haplogroups previously determined in Europe. Based on our mtDNA sequence analyses, the Dinaric-Balkan wolf population is vertically differentiated into “western” (Croatia/Bosnia and Herzegovina) and “eastern” (Serbia/Macedonia) subpopulations. None of the results support assumption of population expansion. Instead, significantly positive values for Tajima's D and Fu's Fs may suggest recent population bottleneck. Obtained data may be helpful in observation to which extent gene pool from the Balkans contribute to newly founded populations in Western Europe.     

Drift load in populations of small size and low density

According to theory, drift load in randomly mating populations is determined by past population size, because enhanced genetic drift in small populations causes accumulation and fixation of recessive deleterious mutations of small effect. In contrast, segregating load due to mutations of low frequency should decline in smaller populations, at least when mutations are highly recessive and strongly deleterious. Strong local selection generally reduces both types of load. We tested these predictions in 13 isolated, outcrossing populations of Arabidopsis lyrata that varied in population size and plant density. Long-term size was estimated by expected heterozygosity at 20 microsatellite loci. Segregating load was assessed by comparing performance of offspring from selfings versus within-population crosses. Drift load was the heterosis effect created by interpopulation outbreeding. Results showed that segregating load was unrelated to long-term size. However, drift load was significantly higher in populations of small effective size and low density. Drift load was mostly expressed late in development, but started as early as germination and accumulated thereafter. The study largely confirms predictions of theory and illustrates that mutation accumulation can be a threat to natural populations.     

Allele frequencies of 6 autosomal STR loci in the Xibo nationality with phylogenetic structure among Chinese populations

In the present study, we investigated the genetic polymorphisms of 6 autosomal STR loci Hum-CSF1PO, D13S317, D5S818, D16S539, TH01, and TPOX in the Xibo population of Liaoning, northeastern China as well as its genetic relationships with other populations in China. No significant deviations from Hardy-Weinberg equilibrium could be found for all loci. Allele frequencies in the Xibo population ranged from 0.001 to 0.507. Among all the 6 loci, D16S539 had the highest polymorphism (PIC = 0.8632), whereas TPOX had the lowest (PIC = 0.5179). A phylogenic tree was constructed using Poptree 2 software. In the phylogenic tree, Xibo population has a distant relationship with the other populations.     

Coalescent process with fluctuating population size and its effective size

We consider a Wright-Fisher model whose population size is a finite Markov chain. We introduce a sequence of two-dimensional discrete time Markov chains whose components describe the coalescent process and the fluctuation of population size. For the limiting process of the sequence of Markov chains, the relationship of the expectation of coalescence time to the harmonic and the arithmetic means of population sizes is shown, and the Laplace transform of the distribution of coalescence time is calculated. We define the coalescence effective population size (cEPS) by the expectation of coalescence time. We show that cEPS is strictly larger (resp. smaller) than the harmonic (resp. arithmetic) mean. As the population size fluctuates more quickly (resp. slowly), cEPS is closer to the harmonic (resp. arithmetic) mean. For the case of a two-valued Markov chain, we show the explicit expression of cEPS and its dependency on the sample size.     

植物居群遗传变异的空间自相关分析

本文介绍了植物遗传变异空间自相关分析的理论、方法与应用 ,包括将基因型作为绝对型数据与等位基因频率作为连续型数据进行自相关分析的基本方法等。并对影响植物居群遗传变异空间结构的因素以及研究居群内遗传结构的重要意义作了评述     

Genetic polymorphisms in three Alpine populations (Visp valleys,Switerland)

Phenotype distributions and allele frequencies of 13 blood proteins are presented for the populations of the three Visp valleys, situated in the Swiss Alps. Blood samples of a total of 883 individuals were electrophoretically analysed. The three populations were statistically compared with each other, and with an additional sample from the literature thought to be representative of the entire Swiss population. Statistical differences are revealed and genetic distances are presented. These results are interpreted in connection with differences between the Visp valleys in topological situation.