Random Drift Model Research Articles

Analysis of Key Comparison Data: Unstable Travelling Standards

A procedure for the analysis of key comparison data is proposed in the case where the travelling standard shows a deterministic or random drift. It is assumed that some parametric model such as a linear trend is appropriate for modelling the deterministic part of the drift. The random part of the drift is assumed to be adequately described by a random walk model. The chosen drift model is determined by least squares and a model check is carried out. If the model check is satisfied, the derived drift model is applied to determine degrees of equivalence. A star-type sequence is required for the comparison in order to check the adequacy of the random drift model. The procedure is illustrated by its application to simulated data.

Molecular changes in the maize composite EPS12 during selection for resistance to pink stem borer

The pink stem borer (Sesamia nonagrioides Lefèvbre) is the most important pest of maize (Zea mays L.) throughout the Mediterranean area. The maize composite EPS12 has been chosen as the base population for a breeding program based on its resistance to pink stem borer, with the main selection criterion being resistance to stem tunneling. Yield was taken as a secondary selection criterion to avoid any unwanted negatively correlated response on this character. The aims of investigation were: (1) to monitor the effects of selection for resistance to pink stem borer on allele frequency at 70 simple sequence repeat (SSR) markers and their impact on the genetic structure of EPS12 and (2) to identify loci at which allelic frequencies changed significantly due to directional selection. Genetic diversity was reduced during the selection process (as expected since random genetic drift as well as selection could reduce genetic variability), but not significantly so. Although the loss of genetic variation was generally consistent with that expected in a model in which random genetic drift acts alone on neutral alleles, the changes observed in the frequency of five alleles were significantly greater than expected. Further, the linear trend of the departure from the random genetic drift model was significant for some allelic versions of two SSR markers, umc1329 and phi076; directional selection was therefore acting on these loci. The significant effect of directional selection on those markers suggests the presence of quantitative trait loci (QTLs) for tunnel length and/or for yield under artificial infestation with Sesamia nonagrioides on the long arm of chromosome 4.

Random drift and large shifts in popularity of dog breeds

A simple model of random copying among individuals, similar to the population genetic model of random drift, can predict the variability in the popularity of cultural variants. Here, we show that random drift also explains a biologically relevant cultural phenomenon--changes in the distributions of popularity of dog breeds in the United States in each of the past 50 years. There are, however, interesting deviations from the model that involve large changes in the popularity of certain breeds. By identifying meaningful departures from our null model, we show how it can serve as a foundation for studying culture change quantitatively, using the tools of population genetics.

Excess of rare amino acid polymorphisms in the Toll-like receptor 4 in humans.

The Toll-like receptor 4 protein acts as the transducing subunit of the lipopolysaccharide receptor complex and assists in the detection of Gram-negative pathogens within the mammalian host. Several lines of evidence support the view that variation at the TLR4 locus may alter host susceptibility to Gram-negative infection or the outcome of infection. Here, we surveyed TLR4 sequence variation in the complete coding region (2.4 kb) in 348 individuals from several population samples; in addition, a subset of the individuals was surveyed at 1.1 kb of intronic sequence. More than 90% of the chromosomes examined encoded the same structural isoform of TLR4, while the rest harbored 12 rare amino acid variants. Conversely, the variants at silent sites (intronic and synonymous positions) occur at both low and high frequencies and are consistent with a neutral model of mutation and random drift. The spectrum of allele frequencies for amino acid variants shows a significant skew toward lower frequencies relative to both the neutral model and the pattern observed at linked silent sites. This is consistent with the hypothesis that weak purifying selection acted on TLR4 and that most mutations affecting TLR4 protein structure have at least mildly deleterious phenotypic effects. These results may imply that genetic variants contributing to disease susceptibility occur at low frequencies in the population and suggest strategies for optimizing the design of disease-mapping studies.

Dynamics of Cytonuclear Disequilibria in Subdivided Populations

The purpose of this report is to understand the effects of hybrid zone architecture and genetic drift on cytonuclear genotypic disequilibria. We also study the exact dynamics of the expected values of the cytonuclear genotypic disequilibria for both the homozygotes and heterozygotes in a finite population containing reproductively isolated subpopulations under random drift alone and random drift along with mutation, respectively. We study the dynamics of the between-population component of the disequilibrium for the homozygotes. The dynamics of the variances of these disequilibria under the random drift model are studied by Monte Carlo simulations. The asymptotic formulas for both the expectations and variances are obtained. The results are contrasted with those for a single undivided population and their biological significances are discussed. Approximate normality of the disequilibria measures are also demonstrated by Monte Carlo simulations.

A statistical test of a neutral model using the dynamics of cytonuclear disequilibria.

In this paper we use cytonuclear disequilibria to test the neutrality of mtDNA markers. The data considered here involve sample frequencies of cytonuclear genotypes subject to both statistical sampling variation as well as genetic sampling variation. First, we obtain the dynamics of the sample cytonuclear disequilibria assuming random drift alone as the source of genetic sampling variation. Next, we develop a test statistic using cytonuclear disequilibria via the theory of generalized least squares to test the random drift model. The null distribution of the test statistic is shown to be approximately chi-squared using an asymptotic argument as well as computer simulation. Power of the test statistic is investigated under an alternative model with drift and selection. The method is illustrated using data from cage experiments utilizing different cytonuclear genotypes of Drosophila melanogaster. A program for implementing the neutrality test is available upon request.

Diagnostics and a Statistical Test of Neutrality Hypotheses Using the Dynamics of Cytonuclear Disequilibria

We use cytonuclear disequilibria to test the neutrality of mtDNA markers. First we propose the dynamics of cytonuclear disequilibria as diagnostic tools for checking a random drift model. Next we develop a formal test statistic to test the random drift model. The approximate sampling distribution of the test statistic under the random drift model is determined for large effective population sizes. The theoretical result is validated by a small sample simulation. Power of the test statistic is investigated under an alternative model with drift and migration. The method is illustrated using a data set collected by Scribner and Avise (1994, Evolution 48, 155-171).

Patterns of morphological variation among cardueline finches (Fringillidae: Carduelinae)

Patterns of variation in five morphological traits in cardueline finches were analysed. Among species, bill characters were the most and tail length the least variable. Species differed primarily in terms of body size, whereas genera differed in terms of bill size. Cardueline finches were far less variable compared with the amount of variation expected under a model of neutral random drift. This indicates that this group of birds is under strong stabilizing selection pressure. This could conform to models of stasis where populations are thought to travel only between adjacent adaptive peaks separated by shallow valleys. Changes in body size are correlated with speciation, whereas changes in bill morphology are correlated with divergences leading to the erection of new genera.

The maximum non-unit eigenvalue for the Wright-Fisher model of random genetic drift incorporating selection

The largest non-unit eigenvalue λ of the transition matrix for the Wright-Fisher Markov chain model of random genetic drift is found numerically with selective advantages of genotypes taken into account. Polynomials in the selection coefficients are fitted to λ in order to summarize the behaviour of λ with varying selection. Also found are the values of the selective advantages which give rise to an acceleration to the rate of fixation of alleles. These values are compared to results for the diffusion approximation to the Wright-Fisher model.

Possibility of extensive neutral evolution under stabilizing selection with special reference to nonrandom usage of synonymous codons.

The rate of evolution in terms of the number of mutant substitutions in a finite population is investigated assuming a quantitative character subject to stabilizing selection, which is known to be the most prevalent type of natural selection. It is shown that, if a large number of segregating loci (or sites) are involved, the average selection coefficient per mutant under stabilizing selection may be exceedingly small. These mutants are very slightly deleterious but nearly neutral, so that mutant substitutions are mainly controlled by random drift, although the rate of evolution may be lower as compared with the situation in which all the mutations are strictly neutral. This is treated quantitatively by using the diffusion equation method in population genetics. A model of random drift under stabilizing selection is then applied to the problem of "nonrandom" or unequal usage of synonymous codons, and it is shown that such nonrandomness can readily be understood within the framework of the neutral mutation--random drift hypothesis (the neutral theory, for short) of molecular evolution.

ALLOZYME FREQUENCY CHANGES ASSOCIATED WITH SELECTION FOR INCREASED GRAIN YIELD IN MAIZE (ZEA MAYS L.)

Frequency changes of alleles at eight enzyme loci were monitored in four long-term maize selection experiments. The results indicate that changes in frequencies of the alleles at these loci are associated with changes due to selection for improved grain yield. The frequencies changed more than is consistent with the hypothesis of selective neutrality. In addition, significant deviations from a random-drift model were nearly always accompanied by significant linear trends as would result if allozyme frequencies respond to directional selection. Evaluations of linkages and linkage disequilibria in the selected populations indicate that the eight enzyme loci responded independently as selection progressed.