Infinite Allele Model Research Articles

Pherotypes are driving genetic differentiation within Streptococcus pneumoniae

BackgroundThe boundaries of bacterial species and the mechanisms underlying bacterial speciation are matters of intense debate. Theoretical studies have shown that recombination acts as a strong cohesive force preventing divergence in bacterial populations. Streptococcus pneumoniae populations have the telltale signs of high recombination with competence implicated as the major driving force behind gene exchange. Competence in S. pneumoniae is triggered by a quorum-sensing mechanism controlled by the competence-stimulating peptide pheromone.ResultsWe studied the distribution of the two major pherotypes in the pneumococcal population and their association with serotype, antimicrobial resistance and genetic lineage. Using multilocus sequence data we evaluated pherotype influence on the dynamics of horizontal gene transfer. We show that pherotype is a clonal property of pneumococci. Standard population genetic analysis and multilocus infinite allele model simulations support the hypothesis that two genetically differentiated populations are defined by the major pherotypes.ConclusionSevere limitations to gene flow can therefore occur in bacterial species in the absence of geographical barriers and within highly recombinogenic populations. This departure from panmixia can have important consequences for our understanding of the response of pneumococci to human imposed selective pressures such as vaccination and antibiotic use.

The structure of the allelic partition of the total population for Galton–Watson processes with neutral mutations

We consider a (sub-)critical Galton–Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in terms of the distribution of the number of clone-children and the number of mutant-children of a typical individual. The approach combines an extension of Harris representation of Galton–Watson processes and a version of the ballot theorem. Some limit theorems related to the distribution of the allelic partition are also given.

Detecting bottlenecks using BOTTLENECK 1.2.02 in wild populations: the importance of the microsatellite structure

Reduced, or bottlenecked, populations are more prone to adverse events. Thus, the detection of genetic bottleneck signatures in wildlife is an important issue for conservation. BOTTLENECK 1.2.02 is a software commonly used for detecting genetic characteristics of past bottlenecks. Here we test the efficiency with which this software detects bottlenecks in two koala populations of known history. The sign test performed well for both populations, particularly under the infinite alleles model for mutation. This suggests this model could be the more realistic for marsupial microsatellites than other mutation models. Under the allele frequency distribution test, the two populations falsely appeared to be at mutation/drift equilibrium. However, this test could detect the bottleneck when only imperfect repeat microsatellites were included in the analysis. We thus recommend further investigation of imperfect repeat microsatellites, which could be more powerful for bottleneck detection. These results underline the cautious approach researchers and conservationists should take when studying the past of unknown populations.

Convergence time to the Ewens sampling formula in the infinite alleles Moran model

In this paper, we establish an upper bound for time to convergence to stationarity for the discrete time infinite alleles Moran model. If M is the population size and mu is the mutation rate, this bound gives a cutoff time of log(Mmu)/mu generations. The stationary distribution for this process in the case of sampling without replacement is the Ewens sampling formula. We show that the bound for the total variation distance from the generation t distribution to the Ewens sampling formula is well approximated by one of the extreme value distributions, namely, a standard Gumbel distribution. Beginning with the card shuffling examples of Aldous and Diaconis and extending the ideas of Donnelly and Rodrigues for the two allele model, this model adds to the list of Markov chains that show evidence for the cutoff phenomenon. Because of the broad use of infinite alleles models, this cutoff sets the time scale of applicability for statistical tests based on the Ewens sampling formula and other tests of neutrality in a number of population genetic studies.

Genetic variation of Picea jezoensis populations in South Korea revealed by chloroplast, mitochondrial and nuclear DNA markers

Genetic variation associated with Picea jezoensis populations of South Korea was investigated using chloroplast (cp), mitochondrial (mt) and nuclear DNA markers. In South Korea, P. jezoensis is distributed across a very restricted area, being found on the summits of three mountains: Mts. Jiri, Dokyu and Gyebang. Examination of five region restriction enzyme combinations for mtDNA and four for cpDNA revealed haplotypes endemic to South Korea. The Gyebang population, the most northerly and most isolated, was genetically distinct from the other populations. Nuclear microsatellite markers indicated, overall, a low level of genetic diversity (H (e) = 0.406) in South Korea; this could be attributed to genetic drift and/or founder effects associated with historical events. The Wilcoxon sign-rank test did not indicate a recent bottleneck in any of the populations irrespective of the model considered (infinite allele model, two-phased model of mutation, and stepwise mutation model). Microsatellite markers also demonstrated that the Gyebang population was distinct from the others. The results of this study could be used as the basis for conservation guidelines for the management of this species in South Korea.

Glacial survival, phylogeography, and a comparison of microsatellite evolution models for resolving population structure in two species of dwarf yams (Borderea, Dioscoreaceae) endemic to the central Pyrenees

Background: Borderea is a relict genus in the Pyrenees comprising only two extant allopolyploid species. The pre-Pyrenean, cliff-dweller B. chouardii is confined to a single critically endangered population, whereas the subalpine B. pyrenaica is more widely distributed in the mobile scree-habitats of the central Pyrenees and pre-Pyrenees. Aims: To determine the genetic structure and relationships among individuals and populations of both taxa to understand their origin. To compare two alternative evolutionary models, the Infinite Allele Model (IAM) and the Stepwise Mutation Model (SMM), in an examination of the primary factors responsible for population divergence during the Quaternary. Methods: A survey of nuclear microsatellite (Simple Sequence Repeat, SSR) variation was conducted to infer relationships among allelic phenotypes and genotypes and to evaluate the relative contributions of migration and mutation to population genetic structure. Results: The occurrence of shared ancestral alleles among populations of both Borderea species supported a presumably late-Tertiary divergence of the species in the low-altitudinal pre-Pyrenees. Borderea chouardii exhibited strong genetic differentiation between two sub-populations separated by only 150 m of vertical distance. In B. pyrenaica, populations from the pre-Pyrenees and southern Pyrenees showed greater genetic differentiation and more allelic diversity relative to populations from the northern Pyrenees. Conclusions: These results suggest that B. pyrenaica experienced glacial survival in warm southern pre-Pyrenean refugia followed by rapid postglacial migration towards the northern Pyrenees. Despite the a priori high suitability of the SMM for microsatellite markers, genotypic relationships among individuals and populations and genotypic assignments to predefined groups of B. pyrenaica were always better resolved by the IAM than by the SMM. This points towards the overwhelming influence of migration and genetic drift over mutation in the Quaternary history of the B. pyrenaica populations. However, for B. chouardii a similar pattern was shown by both evolutionary models, suggesting that sub-population divergence of this species could have also been favoured by mutation.

EFFECT OF MUTATION ON GENETIC DIFFERENTIATION AMONG NONEQUILIBRIUM POPULATIONS

The usefulness of GST and similar measures of genetic differentiation has been questioned repeatedly because of their dependence on the amount of heterozygosity within populations, creating problems when comparing degrees of divergence at loci with different mutation rates. Although the effect of mutation on GST is expected to be small in the early phases of divergence, it is unclear for how long after separation from a common ancestral population that GST is largely unaffected by mutation and by the resulting effect on heterozygosity. We address this question through analysis of the recursion equations for gene identity under the infinite allele model of mutation, and derive conditions describing when the effect of mutation on GST can be ignored under mutation-migration-drift equilibrium conditions and during the preceding transition phase. An important result is that during the transition phase GST is not only affected by mutation, but also by the heterozygosity in the base population from which the subpopulations diverged. The effect of mutation on GST is significant from the very start of the divergence process when initial heterozygosity is low, whereas GST is only weakly affected by mutation in the early phases of differentiation when initial heterozygosity is high. Thus, differentiation following a severe bottleneck is strongly dependent on mutation. The standardized measure of differentiation, G'ST, suggested by Hedrick (2005), may be helpful when comparing amounts of divergence at loci with different mutation rates under steady-state conditions, provided that migration is very low. In many other situations the use of G'ST might be misleading, however, and its application should be exercised with caution.

Genetic characterization of Kenai brown bears (Ursus arctos): microsatellite and mitochondrial DNA control region variation in brown bears of the Kenai Peninsula, south central Alaska

We collected data from 20 biparentally inherited microsatellite loci, and nucleotide sequence from the maternally inherited mitochondrial DNA (mtDNA) control region, to determine levels of genetic variation of the brown bears ( Ursus arctos L., 1758) of the Kenai Peninsula, south central Alaska. Nuclear genetic variation was similar to that observed in other Alaskan peninsular populations. We detected no significant inbreeding and found no evidence of population substructuring on the Kenai Peninsula. We observed a genetic signature of a bottleneck under the infinite alleles model (IAM), but not under the stepwise mutation model (SMM) or the two-phase model (TPM) of microsatellite mutation. Kenai brown bears have lower levels of mtDNA haplotypic diversity relative to most other brown bear populations in Alaska.

Microsatellites reveal a high population structure in Triatoma infestans from Chuquisaca, Bolivia.

BackgroundFor Chagas disease, the most serious infectious disease in the Americas, effective disease control depends on elimination of vectors through spraying with insecticides. Molecular genetic research can help vector control programs by identifying and characterizing vector populations and then developing effective intervention strategies.Methods and FindingsThe population genetic structure of Triatoma infestans (Hemiptera: Reduviidae), the main vector of Chagas disease in Bolivia, was investigated using a hierarchical sampling strategy. A total of 230 adults and nymphs from 23 localities throughout the department of Chuquisaca in Southern Bolivia were analyzed at ten microsatellite loci. Population structure, estimated using analysis of molecular variance (AMOVA) to estimate FST (infinite alleles model) and RST (stepwise mutation model), was significant between western and eastern regions within Chuquisaca and between insects collected in domestic and peri-domestic habitats. Genetic differentiation at three different hierarchical geographic levels was significant, even in the case of adjacent households within a single locality (R ST = 0.14, F ST = 0.07). On the largest geographic scale, among five communities up to 100 km apart, R ST = 0.12 and F ST = 0.06. Cluster analysis combined with assignment tests identified five clusters within the five communities.ConclusionsSome houses are colonized by insects from several genetic clusters after spraying, whereas other households are colonized predominately by insects from a single cluster. Significant population structure, measured by both R ST and F ST, supports the hypothesis of poor dispersal ability and/or reduced migration of T. infestans. The high degree of genetic structure at small geographic scales, inferences from cluster analysis and assignment tests, and demographic data suggest reinfesting vectors are coming from nearby and from recrudescence (hatching of eggs that were laid before insecticide spraying). Suggestions for using these results in vector control strategies are made.

Importance Sampling for the Infinite Sites Model

Importance sampling or Markov Chain Monte Carlo sampling is required for state-of-the-art statistical analysis of population genetics data. The applicability of these sampling-based inference techniques depends crucially on the proposal distribution. In this paper, we discuss importance sampling for the infinite sites model. The infinite sites assumption is attractive because it constraints the number of possible genealogies, thereby allowing for the analysis of larger data sets. We recall the Griffiths-Tavaré and Stephens-Donnelly proposals and emphasize the relation between the latter proposal and exact sampling from the infinite alleles model. We also introduce a new proposal that takes knowledge of the ancestral state into account. The new proposal is derived from a new result on exact sampling from a single site. The methods are illustrated on simulated data sets and the data considered in Griffiths and Tavaré (1994).

Phylogeography of Stable Fly (Diptera: Muscidae) Estimated by Diversity at Ribosomal <I>16S</I> and <I>Cytochrome Oxidase I</I> Mitochondrial Genes

The blood-feeding cosmopolitan stable fly, Stomoxys calcitrans L. (Diptera: Muscidae), is thought to disperse rapidly and widely, and earlier studies of allozyme variation were consistent with high vagility in this species. The geographic origins of New World populations are unknown. Diversity at mitochondrial loci r16S and cytochrome oxidase I was examined in 277 stable flies from 11 countries, including five zoogeographical regions. Of 809 nucleotides, 174 were polymorphic and 133 were parsimony informative. Seventy-six haplotypes were found in frequencies consistent with the Wright-Fisher infinite allele model. None were shared among four or more zoogeographical regions. The null hypothesis of mutation neutrality was not rejected, thereby validating the observed distribution. Fifty-nine haplotypes were singular, eight were private and confined to the Old World, and three of 76 haplotypes were shared between the Old and New World. Only 19 haplotypes were found in the New World, 14 of which were singletons. Haplotype and nucleotide diversities were heterogeneous among countries and regions. The most diversity was observed in sub-Saharan Africa. Regional differentiation indices were C(RT) = 0.26 and N(RT) = 0.31, indicating populations were highly structured macrogeographically. Palearctic and New World flies were the least differentiated from each other. There were strong genetic similarities among populations in the Nearctic, Neotropical, and Palearctic regions, and it is most likely that New World populations were derived from the Palearctic after 1492 CE, in the colonial era.

Phylogeography of Stable Fly (Diptera: Muscidae) Estimated by Diversity at Ribosomal16SandCytochrome Oxidase IMitochondrial Genes

The blood-feeding cosmopolitan stable fly, Stomoxys calcitrans L. (Diptera: Muscidae), is thought to disperse rapidly and widely, and earlier studies of allozyme variation were consistent with high vagility in this species. The geographic origins of New World populations are unknown. Diversity at mitochondrial loci r16S and cytochrome oxidase I was examined in 277 stable flies from 11 countries, including five zoogeographical regions. Of 809 nucleotides, 174 were polymorphic and 133 were parsimony informative. Seventy-six haplotypes were found in frequencies consistent with the Wright–Fisher infinite allele model. None were shared among four or more zoogeographical regions. The null hypothesis of mutation neutrality was not rejected, thereby validating the observed distribution. Fifty-nine haplotypes were singular, eight were private and confined to the Old World, and three of 76 haplotypes were shared between the Old and New World. Only 19 haplotypes were found in the New World, 14 of which were singletons. Haplotype and nucleotide diversities were heterogeneous among countries and regions. The most diversity was observed in sub-Saharan Africa. Regional differentiation indices were GRT = 0.26 and NRT = 0.31, indicating populations were highly structured macrogeographically. Palearctic and New World flies were the least differentiated from each other. There were strong genetic similarities among populations in the Nearctic, Neotropical, and Palearctic regions, and it is most likely that New World populations were derived from the Palearctic after 1492 CE, in the colonial era.

Steady state of homozygosity and [formula omitted] for the island model

We examine homozygosity and G st for a subdivided population governed by the finite island model. Assuming an infinite allele model and strong mutation we show that the steady state distributions of G st and homozygosity have asymptotic expansions in the mutation rate. We use this observation to derive asymptotic expansions for various moments of homozygosity and to derive rigorous formulas for the mean and variance of G st . We show that G st ≈ 1 / ( 1 + 2 Nm ) , similarly to the well known formula of Wright for the infinite island model, and that the variance of G st goes to zero as mutation increases.

Genetic structure and evidence for recent population decline in Eurasian otter populations in the Czech and Slovak Republics: implications for conservation

AbstractOver the latter part of the 20th century, Eurasian otter Lutra lutra populations suffered dramatic declines, resulting in extinction or fragmentation of populations in many western and central European countries. Part of the Czech otter population became totally isolated while the Slovak population remained partly connected to the relatively continuous central and eastern European otter distribution range. This paper examines the genetic structure and past demographic history of otters in the Czech and Slovak Republics, using microsatellite nuclear markers amplified from DNA extracted from tissue and faecal samples. A relatively high level of genetic differentiation was found between the Czech and Slovak populations (FST=0.154, P=0.0002), supported by a perfect assignment in Bayesian cluster analysis. Both the Czech and Slovak populations showed significant heterozygosity excess (assuming an infinite allele model), indicating recent population bottlenecks. A very recent population decline was also suggested by coalescent analysis, inferring a drop to c. 25% of past effective population size in both populations. The timing of the decline was in accordance with published data from otter surveys, suggesting that the strongest decline probably occurred between the 1970s and the mid‐1990s. The results of this study confirm that otter populations remain vulnerable to any violent demographic change and, despite the claims of fish‐farmers and anglers for legal culls, it is highly desirable that they remain a strongly protected species in both countries. The spreading and re‐connection of otter populations observed recently is essential for the future health of the populations, and should be supported through habitat conservation.

Common pearl oysters in China, Japan, and Australia are conspecific: evidence from ITS sequences and AFLP

To elucidate the species status of Pinctada fucata in China, P. fucata martensii in Japan and P. imbricata in Australia, one population of each taxon was studied using internal transcribed spacer 1 and 2 (ITS1, and ITS2) and amplified fragment length polymorphism (AFLP) markers. ITS1 and ITS2 were 401–405 and 229–237 bp long, respectively. Twenty-nine ITS1 and 15 ITS2 unique genotypes were obtained from 44 and 34 individuals, respectively, with some genotypes shared by two or three populations. In AFLP analysis, each individual exhibited a distinct phenotype. No population had diagnostic markers. Mean genetic divergences within and among the three populations were very low and overlapped (between-population: 0.7–0.9% for ITS1, 0.9–1.3% for ITS2, and 53.3–55.6% for AFLP; within-population: 0.5–0.9% for ITS1, 0.8–1.2% for ITS2, and 50.4–53.6% for AFLP). Low levels of genetic differentiation were observed among the three populations while the Australian population is partially genetically isolated. Unter an infinite allele model, genetic differentiation among populations was not significant based on a permutation test. Under an infinite site model, most F ST values were not significant for ITS data although they were significant for AFLP data. Network analysis using ITS data indicated that individuals from the same population did not cluster together. Analysis of molecular variance (AMOVA) demonstrated that >94% variation was contributed by within-population variation. These findings suggest that the three taxa are conspecific and Pinctada fucata is the correct name.

Wide‐range analysis of genetic structure of Betula maximowicziana, a long‐lived pioneer tree species and noble hardwood in the cool temperate zone of Japan

Betula maximowicziana is a long-lived pioneer tree species in Japanese cool temperate forests that plays an important role in maintenance of the forest ecosystem and has high economic value. Here we assess the wide-range genetic structure of 23 natural populations of B. maximowicziana using 11 simple sequence repeat (SSR) loci. Genetic diversity within populations was relatively low in all populations (mean H(E), 0.361; mean allelic richness, 2.80; mean rare allelic richness, 1.02). The population differentiation was also relatively low (F(ST), 0.062). Genetic distance-based and Bayesian clustering analysis revealed that the populations examined here could be divided into a southern group and a northern group. Analysis of rare allelic richness and Bayesian clustering revealed evidence for both southern and northern refugia during the last glacial period. Furthermore, a comparison of regional genetic diversity revealed significant clines in allelic richness. In spatial genetic structure evaluation, significant isolation by distance (IBD) was detected among the 23 populations, but not within regions. Moreover, significant population bottlenecks were found in all populations under infinite allele model (IAM) assumptions. These unusual, significant bottlenecks might be because of the processes of postglacial colonization and the species' characters and/or life history as a long-lived pioneer tree species. The wide-range, regional genetic structure found in this study provides an important baseline for conservation and forest management, including the identification of evolutionarily significant units (ESUs) and/or management units (MUs) of B. maximowicziana.

Genetic variability and population structure in Cypriot chukar partridges (Alectorischukar cypriotes) as determined by microsatellite analysis

For the first time, microsatellite loci were used to study the genetic structure in Alectoris chukar cypriotes. Four of the ten tested microsatellite loci were found to be polymorphic in 33 individuals from four regions of Cyprus. The differentiation test between all the pairs of samples gave non-differentiation exact P values in every case (P>0.05). The posterior probability distribution on the number of source populations indicated only one population (P=0.977); also, a high Bayes factor value (130.020) was obtained. Posterior co-assignment probabilities (measures of similarity) for all pairs of individuals ranged from 0.984 to 1. The global FIS value was not found to be significant. A recent bottleneck of the Cypriot total partridge population is suggested and this is supported by a significant Wilcoxon test (P=0.031) under the Infinite Alleles Model (IAM) and shifted mode in the alleles frequencies distribution. The results suggest that all the individuals studied belong to only one randomly mating (panmictic) population, with low genetic variation and evidence of recent effective population size reduction (genetic bottleneck). A big hunting pressure exists on the island and about 200,000 captive-bred birds are released every year; these individuals are descendant from a small number of eggs collected in a small area of Cyprus in 1986 and this founder effect could explain the existence of a bottleneck and the low genetic variability.

Variogram Analysis of the Spatial Genetic Structure of Continuous Populations Using Multilocus Microsatellite Data

A geostatistical perspective on spatial genetic structure may explain methodological issues of quantifying spatial genetic structure and suggest new approaches to addressing them. We use a variogram approach to (i) derive a spatial partitioning of molecular variance, gene diversity, and genotypic diversity for microsatellite data under the infinite allele model (IAM) and the stepwise mutation model (SMM), (ii) develop a weighting of sampling units to reflect ploidy levels or multiple sampling of genets, and (iii) show how variograms summarize the spatial genetic structure within a population under isolation-by-distance. The methods are illustrated with data from a population of the epiphytic lichen Lobaria pulmonaria, using six microsatellite markers. Variogram-based analysis not only avoids bias due to the underestimation of population variance in the presence of spatial autocorrelation, but also provides estimates of population genetic diversity and the degree and extent of spatial genetic structure accounting for autocorrelation.

Detecting Holocene divergence in the anadromous–freshwater three‐spined stickleback (Gasterosteus aculeatus) system

The anadromous-freshwater three-spined stickleback (Gasterosteus aculeatus) system allows for inferring the role of adaptation in speciation with a high level of accuracy because the freshwater ecotype has evolved multiple times from a uniform anadromous ancestor. A cause for concern is that independent evolution among drainages is not guaranteed in areas with a poorly resolved glacial history. This is the case for the west European great rivers, whose downstream valleys flanked the southern limit of the late Pleistocene ice sheet. We tested for independent and postglacial colonization of these valleys hypothesizing that the relationships among anadromous and freshwater sticklebacks correspond to a raceme structure. We compared the reduction in plate number accompanying this colonization to the genetic differentiation using 13 allozyme and five microsatellite loci in 350 individuals. Overall microsatellite differentiation (F(ST) = 0.147) was twice as large as allozyme differentiation (F(ST) = 0.066). Although habitat-specific gene flow may mask the ancestral relationships among both ecotypes, levels of microsatellite differentiation supported the hypothesis of raceme-like divergence, reflecting independent colonizations rather than the presence of two distinct evolutionary clades. Under an infinite alleles model and in the absence of gene flow, the observed freshwater divergence might be reached after 440 (microsatellites) to 4500 (allozymes) generations. Hence, the anadromous-freshwater stickleback system most likely diverged postglacially. We conclude that the reduction in plate number in two freshwater basins probably occurred independently, and that its considerable variation among populations is not in agreement with the time since divergence.

Solvable null model for the distribution of word frequencies

Zipf's law asserts that in all natural languages the frequency of a word is inversely proportional to its rank. The significance, if any, of this result for language remains a mystery. Here we examine a null hypothesis for the distribution of word frequencies, a so-called discourse-triggered word choice model, which is based on the assumption that the more a word is used, the more likely it is to be used again. We argue that this model is equivalent to the neutral infinite-alleles model of population genetics and so the degeneracy of the different words composing a sample of text is given by the celebrated Ewens sampling formula [Theor. Pop. Biol. 3, 87 (1972)]], which we show to produce an exponential distribution of word frequencies.