Fumio Tajima

EVOLUTION OF COADAPTATION IN A TWO-LOCUS EPISTATIC SYSTEM

Abstract Although recent advances in genome biology have dramatically increased our understanding of the contribution of gene interactions to the development of complex phenotypes, we still lack general agreement on the process and mechanisms responsible for the evolution of epistatic systems. Even if genes in a species are indeed integrated into coadapted complexes of interacting components, simple additive evolution may eventually result in epistatic differentiation of populations. Consequently, the prevalence of epistatic gene action does not tell us anything about the role of epistatic selection in the history of population divergence. To elucidate the contribution of epistatic selection in the evolution of coadaptation, we investigate the fixation process of two mutations that interact synergistically to enhance fitness. We show by diffusion analysis and simulations that epistatic selection on cosegregating variants does not by itself promote the evolution of epistatic systems; rather, accumulation of neutral mutations may play a crucial role, creating an appropriate genetic milieu for adaptive evolution in the future generations.

Infinite-allele model and infinite-site model in population genetics

Both the infinite-allele model and infinite-site model have contributed to development of population genetics. Although the former is a model mainly for protein polymorphism and the latter is mainly for DNA polymorphism, these two models are related: the expected heterozygosity and homozygosity can be obtained from the infinite-site model, and the expectation of the amount of DNA polymorphism can be obtained from the infinite-allele model.

Measuring epistasis in fitness landscapes: The correlation of fitness effects of mutations

Genotypic fitness landscapes are constructed by assessing the fitness of all possible combinations of a given number of mutations. In the last years, several experimental fitness landscapes have been completely resolved. As fitness landscapes are high-dimensional, simple measures of their structure are used as statistics in empirical applications. Epistasis is one of the most relevant features of fitness landscapes. Here we propose a new natural measure of the amount of epistasis based on the correlation of fitness effects of mutations. This measure has a natural interpretation, captures well the interaction between mutations and can be obtained analytically for most landscape models. We discuss how this measure is related to previous measures of epistasis (number of peaks, roughness/slope, fraction of sign epistasis, Fourier-Walsh spectrum) and how it can be easily extended to landscapes with missing data or with fitness ranks only. Furthermore, the dependence of the correlation of fitness effects on mutational distance contains interesting information about the patterns of epistasis. This dependence can be used to uncover the amount and nature of epistatic interactions in a landscape or to discriminate between different landscape models.

A statistical test for the difference in the amounts of DNA variation between two populations

A statistical test for the difference in the amounts of DNA variation between two populations is developed. The test statistic involves the covariance of the amount of variation between two populations, which is given by a function of their divergence time, T0. Accordingly, the power (rejection probability) of the test depends on T0. In this article, T0 is treated as unknown because it is very difficult to estimate. The test is most conservative when T0 = infinity is assumed because the covariance is zero. If T0 = 0 is assumed, the largest value of the rejection probability is obtained. Thus, the test provides a range of rejection probability unless we have a reliable estimate of T0. The test is applied to the PgiC region in three mustard species: Leavenworthia stylosa, L. crassa and L. uniflora. The results of our test show that the level of variation in L. stylosa is significantly higher than those in the other species.

Effect of non-random sampling on the estimation of parameters in population genetics

The amount and pattern of genetic variation in a population can be estimated from genes or DNA sequences sampled from the population. Although random sampling is assumed in almost all cases, we often do not know whether sampling is random or not. Using a simple non-random sampling model, the effects of non-random sampling on the estimation of parameters in population genetics were investigated. This non-random sampling model assumes that n genes are randomly sampled with replacement from m genes which were randomly sampled from a large random mating population, and various degrees of non-randomness can be generated by changing the value of m. The results obtained show that the effect of non-random sampling on the number of alleles and the number of segregating sites is substantially large whereas the effect of non-random sampling on heterozygosity and the average number of nucleotide differences is negligibly small unless non-randomness is extremely large. The effects of non-random sampling on the tests of neutrality were also investigated, and the results obtained indicate that the effect of non-random sampling is stronger on Fu and Lis tests than on Tajimas test.

The amount and pattern of DNA polymorphism under the neutral mutation hypothesis

The amount and pattern of DNA polymorphism can give useful information on the maintenance mechanism of genetic variation at the DNA level. In this note we have shown the amount and pattern of DNA polymorphism expected under the neutral theory. The amount of DNA polymorphism can be estimated from the average number of nucleotide differences per site, the proportion of segregating sites, and so on. We have shown how to estimate from these quantities, where =4 is the effective population size and is the mutation rate per site per generation. We have also shown the expectations of the nucleotide variation within and between allelic classes.

New Weighting Methods for Phylogenetic Tree Reconstruction Using Multiple Loci

Efficient determination of evolutionary distances is important for the correct reconstruction of phylogenetic trees. The performance of the pooled distance required for reconstructing a phylogenetic tree can be improved by applying large weights to appropriate distances for reconstructing phylogenetic trees and small weights to inappropriate distances. We developed two weighting methods, the modified Tajima–Takezaki method and the modified least-squares method, for reconstructing phylogenetic trees from multiple loci. By computer simulations, we found that both of the new methods were more efficient in reconstructing correct topologies than the no-weight method. Hence, we reconstructed hominoid phylogenetic trees from mitochondrial DNA using our new methods, and found that the levels of bootstrap support were significantly increased by the modified Tajima–Takezaki and by the modified least-squares method.

Evolutionary constraints in fitness landscapes

In the last years, several genotypic fitness landscapes—combinations of a small number of mutations—have been experimentally resolved. To learn about the general properties of “real” fitness landscapes, it is key to characterize these experimental landscapes via simple measures of their structure, related to evolutionary features. Some of the most relevant measures are based on the selectively acessible paths and their properties. In this paper, we present some measures of evolutionary constraints based on (i) the similarity between accessible paths and (ii) the abundance and characteristics of “chains” of obligatory mutations, that are paths going through genotypes with a single fitter neighbor. These measures have a clear evolutionary interpretation. Furthermore, we show that chains are only weakly correlated to classical measures of epistasis. In fact, some of these measures of constraint are non-monotonic in the amount of epistatic interactions, but have instead a maximum for intermediate values. Finally, we show how these measures shed light on evolutionary constraints and predictability in experimentally resolved landscapes.

The amount of DNA polymorphism when population size changes linearly

Population size is one of the main factors that determine the amount of DNA polymorphism. We examined a model under which the population size changed linearly. Because of the simplicity of this model, we could analytically obtain the expectation of nucleotide diversity, E(π), and the expectation of the amount of DNA polymorphism, E(θ), based on the number of segregating sites. The results suggest that E(π) is larger than E(θ) when the population size decreased and that E(π) is smaller than E(θ) when the population size increased. The expected time to the most recent common ancestor could also be obtained under this model.