Loss of alleles in a haploid population with varying environment

The evolution of populations may be affected by a number of factors. The basic forces of migration, mutation, and selection are self-explanatory. However, finite populations are also known to be subject to the fundamental undirected force of genetic drift—the random fluctuation of gene frequencies. It is this random effect which will be investigated via the consideration of discrete stochastic models.     

Low RAPD Variation and Female-Biased Sex Ratio Indicate Genetic Drift in Small Populations of the Dioecious Conifer Taxus Baccata in Switzerland

Small populations are prone to genetic drift as a consequence of random sampling effects. We investigated whether we could detect such random sampling effects in the English yew (Taxus baccata), a dioecious conifer species occurring in scattered populations in Switzerland. Seven pairs of small and large populations were analyzed using random amplified polymorphic DNA (RAPD) marker bands from 20 individuals per population. Several genetic parameters (mean marker band frequency deviation, molecular variance, population differentiation) indicated that small populations experienced genetic drift. These genetic differences between small and large populations of yew were paralleled by an increased sex ratio bias towards a higher number of females in the small populations. Our findings support earlier assumptions that the Swiss occurrences of yew may be described as metapopulation dynamics, characterized by local colonization and extinction events leading to the observed genetic drift.     

The variance of sample heterozygosity

The variance of sample heterozygosity, averaged over several loci, is studied in a variety of situations. The variance depends on the sampling implicit in the mating system as well as on that explicit in the loci scored and individuals sampled. There are also effects of allelic distributions over loci and of linkage or linkage disequilibrium between pairs of loci. Results are obtained for populations in drift and mutation balance, for infinite populations undergoing mixed self and random mating, and for finite monoecious populations with or without selfing. For unlinked loci in drift/mutation balance, variances appear to be lessened more by increasing the number of loci scored than by increasing the number of individuals sampled. For infinite populations under the mixed self and random mating system, however, the reverse is true. Methods for estimating the variance of sample heterozygosity are discussed, with attention being paid to unbalanced data where not all loci are scored in all individuals.     

Population genetics of the population in the European north of the RSFSR. V. An evaluation of the virtual size of the population by computer simulation of marriage and migration processes

The paper deals with the effect of assortative matings on some parameters of population structure. To solve this problem, two rural populations near Archangelsk (river Peosa region) were used. Some genetic and demographic characteristics of these populations were described in previous publications. A comparison between random matches through a random number generator and true marriages was made by computer estimation of the spouses kinship coefficients. Significant avoidance of first and second cousins marriages in real populations was discovered. As a consequence of this avoidance of consanguinity, the effective breeding size of villages is increased twofold. Similar results were obtained by estimation os isonymy.     

A genetic affinity analysis of human populations

Genetic affinity of human populations based on allele frequency data was studied from two viewpoints. (1) The effect of the number of polymorphic loci on the reconstruction of a phylogenetic tree of human populations was empirically investigated. Genetic affinity trees were constructed based on data for 1–12 polymorphic loci, by using the neighbor-joining method. Geographical clustering of populations gradually appeared when the number of loci was increased. A new classification and terminology of higher order human population clusters is proposed based on these and other studies. (2) A new method of estimating the absolute divergence time of two populations is proposed, which is based on a diffusion equation that describes random genetic drift.     

Geneland: a computer package for landscape genetics

Geneland is a computer package that allows to make use of georeferenced individual multilocus genotypes for the inference of the number of populations and of the spatial location of genetic discontinuities between those populations. Main assumptions of the method are: (i) the number of populations is unknown and all values are considered a priori equally likely, (ii) populations are spread over areas given by a union of some polygons of unknown location in the spatial domain, (iii) Hardy–Weinberg equilibrium is assumed within each population and (iv) allele frequencies in each population are unknown and treated as random variable either following the so‐called Dirichlet model or Falush model. Different algorithms implemented in Geneland to perform inferences are first briefly presented. Then major running steps and outputs (i.e. histogram of number of populations and map of posterior probabilities of population membership) are illustrated from the analysis of a simulated data set, which was also produced by Geneland.     

Differential admixture shapes morphological variation among invasive populations of the lizard Anolis sagrei

The biological invasion of the lizard Anolis sagrei provides an opportunity to study evolutionary mechanisms that produce morphological differentiation among non-native populations. Because the A. sagrei invasion represents multiple native-range source populations, differential admixture as well as random genetic drift and natural selection, could shape morphological evolution during the invasion. Mitochondrial DNA (mtDNA) analyses reveal seven distinct native-range source populations for 10 introduced A. sagrei populations from Florida, Louisiana and Texas (USA), and Grand Cayman, with 2-5 native-range sources contributing to each non-native population. These introduced populations differ significantly in frequencies of haplotypes from different native-range sources and in body size, toepad-lamella number, and body shape. Variation among introduced populations for both lamella number and body shape is explained by differential admixture of various source populations; mean morphological values of introduced populations are correlated with the relative genetic contributions from different native-range source populations. The number of source populations contributing to an introduced population correlates with body size, which appears independent of the relative contributions of particular source populations. Thus, differential admixture of various native-range source populations explains morphological differences among introduced A. sagrei populations. Morphological differentiation among populations is compatible with the hypothesis of selective neutrality, although we are unable to test the hypothesis of interdemic selection among introductions from different native-range source populations.     

On the Theory of Partially Inbreeding Finite Populations. I. Partial Selfing

Some stochastic theory is developed for monoecious populations of size N in which there are probabilities beta and 1 - beta of reproduction by selfing and by random mating. It is assumed that beta much greater than N-1. Expressions are derived for the inbreeding coefficient of one random individual and the coefficient of kinship of two random separate individuals at time t. The mean and between-lines variance of the fraction of copies of a locus that are identical in two random separate individuals in an equilibrium population are obtained under the assumption that there is an infinite number of possible alleles. It is found that the theory for random mating populations holds if the effective population number is Ne = N'/(1 + FIS), where FIS is the inbreeding coefficient at equilibrium when N is infinite and N' is the reciprocal of the probability that two gametes contributing to random separate adults come from the same parent. When there is a binomial distribution of successful gametes emanating from each adult, N' = N. An approximation to the probability that an allele A survives if it is originally present in one AA heterozygote is found to be 2(N'/N)(FISS1 + (1 - FIS)S2), where S1 and S2 are the selective advantages of AA and AA in comparison with AA. In the last section it is shown that if there is partial full sib mating and binomial offspring distributions Ne = N/(1 + 3FIS).     

Assessing the nucleotide diversity of three aphid species by RAPD

A method is presented for the estimation of nucleotide diversity and genetic structure of populations from RAPD (random amplified polymorphic DNA) data. It involves a modification of the technique developed by Lynch and Crease (1990) for the case of restriction sites as survey data. As new elements the method incorporates (i) dominance correction, (ii) values of asexual reproduction of the populations sampled, and (iii) an analytical variance of the number of nucleotide substitutions per site. Sampling was carried out at two geographic scales for three aphid species. At a macrogeographic scale, populations of Rhopalosiphum padi did not show statistical genetic differentiation. Aphis gossypii and Myzus persicae, which were sampled at a microgeographic scale, showed a higher genetic differentiation than R. padi, it being statistically significant in M. persicae. The major sources of sampling variance within- and between-populations were found to be nucleotide (i.e., the number of alleles used as a function of the number of primers used) and population (i.e., sample size) sampling. Extremely low estimates of nucleotide diversity were obtained for the species studied here. This result is consistent with previous reports on genetic diversity for the same or other aphid species which were based on allozyme polymorphism, mitochondrial DNA variation and qualitative analyses of RAPDs.     

A generalized chain binomial model with application to HIV infection

The original Reed-Frost formulation of the chain binomial model is mathematically equivalent to a stochastic model allowing a Poisson number of effective contacts in a time interval. Their formulation cannot accommodate survey data that necessarily correspond to more complex distributions of partners or contacts, or to large populations where complete random mixing is unlikely. This paper generalizes the Reed-Frost model to accommodate these situations in both the one- and two-population settings. The extension to multiple populations is also outlined. Using the model to predict HIV incidence in San Francisco's homosexual population, we show that the total number of contacts over all partners is more important than the distribution of contacts among partners in determining the number of infected.     

The over-dispersion between cells of chromosomal aberrations

A survey of the literature suggests that random dispersion of radiation induced aberrations occurs only when uniform fields of predominantly low LET radiations act on cell populations which are homogeneous with regard to cell type, cycle stage and intrinsic radiosensitivity. The in vitro irradiation of unstimulated human lymphocytes with X- or γ-rays is an example of this. Over-dispersion is observed in all other cases where sufficient data have been obtained and where there are a sufficient number of chromosomes per cell to prevent underdispersion through distortion.The observation is made that the sum of two or more Poisson populations with different means gives an over-dispersed population. This is used to make a unified explanation of the various observations of overdispersion of aberrations between cells.     

Inference of population structure under a Dirichlet process model

Inferring population structure from genetic data sampled from some number of individuals is a formidable statistical problem. One widely used approach considers the number of populations to be fixed and calculates the posterior probability of assigning individuals to each population. More recently, the assignment of individuals to populations and the number of populations have both been considered random variables that follow a Dirichlet process prior. We examined the statistical behavior of assignment of individuals to populations under a Dirichlet process prior. First, we examined a best-case scenario, in which all of the assumptions of the Dirichlet process prior were satisfied, by generating data under a Dirichlet process prior. Second, we examined the performance of the method when the genetic data were generated under a population genetics model with symmetric migration between populations. We examined the accuracy of population assignment using a distance on partitions. The method can be quite accurate with a moderate number of loci. As expected, inferences on the number of populations are more accurate when theta = 4N(e)u is large and when the migration rate (4N(e)m) is low. We also examined the sensitivity of inferences of population structure to choice of the parameter of the Dirichlet process model. Although inferences could be sensitive to the choice of the prior on the number of populations, this sensitivity occurred when the number of loci sampled was small; inferences are more robust to the prior on the number of populations when the number of sampled loci is large. Finally, we discuss several methods for summarizing the results of a Bayesian Markov chain Monte Carlo (MCMC) analysis of population structure. We develop the notion of the mean population partition, which is the partition of individuals to populations that minimizes the squared partition distance to the partitions sampled by the MCMC algorithm.     

Hidden Genetic Variability within Electromorphs in Finite Populations

The amount of hidden genetic variability within electromorphs in finite populations is studied by using the infinite site model and stepwise mutation model simultaneously. A formula is developed for the bivariate probability generating function for the number of codon differences and the number of electromorph state differences between two randomly chosen cistrons. Using this formula, the distribution as well as the mean and variance of the number of codon differences between two identical or nonidentical electromorphs are studied. The distribution of the number of codon differences between two randomly chosen identical electromorphs is similar to the geometric distribution but more leptokurtic. Studies are also made on the number of codon differences between two electromorphs chosen at random one from each of two populations which have been separated for an arbitrary number of generations. It is shown that the amount of hidden genetic variability is very large if the product of effective population size and mutation rate is large.     

Two complementary perspectives on inter-individual genetic distance

This paper examines population structure through the prism of pairwise genetic distances. Two complementary perspectives, framed as two simple questions, are explored: Q1: What is the probability that a random pair of individuals from the same local population is more genetically dissimilar than a random pair from two distinct populations? Q2: On average, how genetically different are two individuals from the same local population, in comparison with two individuals chosen from any two distinct populations? Models are developed to provide quantitative answers for the two questions, given allele frequencies across any number of markers from two diploid populations. The probability from Q1 is shown to drop to zero with increasing number of genetic markers even for very closely-related populations and rare alleles. The average genetic dissimilarity of two individuals from distinct populations diverges from the average dissimilarity of two individuals from the same population by a percentage dependent on estimates of population differentiation. This perspective also suggests a measure of population distance based on the intuitive notion of pairwise genetic distance, along with a simple method of estimation. Results from recent empirical research on inter-individual genetic distance in human populations are analyzed in the context of the theoretical framework.     

Evaluation of the SNP tagging approach in an independent population sample—array-based SNP discovery in Sami

Significant efforts have been made to determine the correlation structure of common SNPs in the human genome. One method has been to identify the sets of tagSNPs that capture most of the genetic variation. Here, we evaluate the transferability of tagSNPs between populations using a population sample of Sami, the indigenous people of Scandinavia. Array-based SNP discovery in a 4.4 Mb region of 28 phased copies of chromosome 21 uncovered 5,132 segregating sites, 3,188 of which had a minimum minor allele frequency (mMAF) of 0.1. Due to the population structure and consequently high LD, the number of tagSNPs needed to capture all SNP variation in Sami is much lower than that for the HapMap populations. TagSNPs identified from the HapMap data perform only slightly better in the Sami than choosing tagSNPs at random from the same set of common SNPs. Surprisingly, tagSNPs defined from the HapMap data did not perform better than selecting the same number of SNPs at random from all SNPs discovered in Sami. Nearly half (46%) of the Sami SNPs with a mMAF of 0.1 are not present in the HapMap dataset. Among sites overlapping between Sami and HapMap populations, 18% are not tagged by the European American (CEU) HapMap tagSNPs, while 43% of the SNPs that are unique to Sami are not tagged by the CEU tagSNPs. These results point to serious limitations in the transferability of common tagSNPs to capture random sequence variation, even between closely related populations, such as CEU and Sami. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Genetic similarities within and between human populations

The proportion of human genetic variation due to differences between populations is modest, and individuals from different populations can be genetically more similar than individuals from the same population. Yet sufficient genetic data can permit accurate classification of individuals into populations. Both findings can be obtained from the same data set, using the same number of polymorphic loci. This article explains why. Our analysis focuses on the frequency, omega, with which a pair of random individuals from two different populations is genetically more similar than a pair of individuals randomly selected from any single population. We compare omega to the error rates of several classification methods, using data sets that vary in number of loci, average allele frequency, populations sampled, and polymorphism ascertainment strategy. We demonstrate that classification methods achieve higher discriminatory power than omega because of their use of aggregate properties of populations. The number of loci analyzed is the most critical variable: with 100 polymorphisms, accurate classification is possible, but omega remains sizable, even when using populations as distinct as sub-Saharan Africans and Europeans. Phenotypes controlled by a dozen or fewer loci can therefore be expected to show substantial overlap between human populations. This provides empirical justification for caution when using population labels in biomedical settings, with broad implications for personalized medicine, pharmacogenetics, and the meaning of race.     

The Inbreeding Effective Population Number and the Expected Homozygosity for an X-Linked Locus

Assuming random mating and discrete nonoverlapping generations, the inbreeding effective population number, (see PDF), is calculated for an X-linked locus. For large populations, the result agrees with the variance effective population number. As an application, the maintenance of genetic variability by the joint action of mutation and random drift is investigated. It is shown that, if every allele mutates at rate u to new types, then the probabilities of identity in state (and hence the expected homozygosity of females) converge to the approximate value (see PDF) at the approximate asymptotic rate (see PDF).     

On flexible finite polygenic models for multiple-trait evaluation

Finite polygenic models (FPM) might be an alternative to the infinitesimal model (TIM) for the genetic evaluation of pedigreed multiple-generation populations for multiple quantitative traits. I present a general flexible Bayesian method that includes the number of genes in the FPM as an additional random variable. Markov-chain Monte Carlo techniques such as Gibbs sampling and the reversible jump sampler are used for implementation. Sampling of genotypes of all genes in the FPM is done via the use of segregation indicators. A broad range of FPM models, some combined with TIM, are empirically tested for the estimation of variance components and the number of genes in the FPM. Four simulation scenarios were studied, including genetic models with 5 or 50 additive independent diallelic genes affecting the traits, and random selection or selection on one of the traits was performed. The results in this study were based on ten replicates per simulation scenario. In the case of random selection, uniform priors on additive gene effects led to posterior mean estimates of genetic variance that were positively correlated with the number of genes fitted in the FPM. In the case of trait selection, assuming normal priors on gene effects also led to genetic variance estimates for the selected trait that were negatively correlated with the number of genes in the FPM. This negative correlation was not observed for the unselected trait. Treating the number of genes in the FPM as random revealed a positive correlation between prior and posterior mean estimates of this number, but the prior hardly affected the posterior estimates of genetic variance. Posterior inferences about the number of genes should be considered to be indicative where trait selection seems to improve the power of distinguishing between TIM and FPM. Based on the results of this study, I suggest not replacing TIM by the FPM, but combining TIM and FPM with the number of genes treated as random, to facilitate a highly flexible and thereby robust method for variance component estimation in pedigreed populations. Further study is required to explore the full potential of these models under different genetic model assumptions.     

Pattern formation by the global limits of a nonlinear competitive interaction in n dimensions

Summary This paper describes a class of nonlinear systems that include processes of pattern formation, short term memory, interpopulation competition, and parallel processing. These systems show how continuously fluctuating data patterns can be processed by noisy populations having finitely many excitable sites. Particular examples are found in vertebrate retina and sensory cortex, as well as certain nonneural developing tissues.After an initial period of seemingly random behavior, that is described by a finite series of iterated decisions or enhancement steps, a global consensus or asymptotic pattern is reached. This is true given any number of competing populations, any mean competition function, and any number of random factors determining interpopulation signals. Which pattern will be chosen can depend on initial data and system structure in a complicated fashion. The results demonstrate a robust design that joins together the dynamics of mass action, the geometry of interpopulation competition, and the statistics of signal generation.Supported in part by the Advanced Research Projects Agency of the Office of Naval Research (N00014-70-C-0350).     

Conservation of the Lake Kasumigaura population of Nymphoides indica (L.) Kuntze based on genetic evaluation using microsatellite markers

We compared the genetic diversity of the Lake Kasumigaura population of Nymphoides indica with that of pond populations in Hyogo and Kagawa Prefectures, which are thought to maintain high genetic diversity, to elucidate the current genetic diversity and occurrence of distinctive alleles in the Lake Kasumigaura population. The genetic diversity, as measured by the mean number of alleles per polymorphic locus, effective number of alleles per locus, mean observed heterozygosity, mean expected heterozygosities, total gene diversity, and number of multilocus genotypes was lower in the Lake Kasumigaura population than in the Hyogo and Kagawa populations. In addition, the inbreeding coefficient suggests that random mating does not occur in the Lake Kasumigaura population. The degree of genetic differentiation between the Lake Kasumigaura population and the Hyogo and Kagawa populations suggests that the Lake Kasumigaura population is largely genetically distinct. We found five genotypes in the Lake Kasumigaura population that were absent from the Hyogo and Kagawa populations. These results demonstrate that the Lake Kasumigaura population is an important component of the overall genetic diversity of N. indica in Japan.