A simple method of removing the effect of a bottleneck and unequal population sizes on pairwise genetic distances

In this paper, we derive the expectation of two popular genetic distances under a model of pure population fission allowing for unequal population sizes. Under the model, we show that conventional genetic distances are not proportional to the divergence time and generally overestimate it due to unequal genetic drift and to a bottleneck effect at the divergence time. This bias cannot be totally removed even if the present population sizes are known. Instead, we present a method to estimate the divergence times between populations which is based on the average number of nucleotide differences within and between populations. The method simultaneously estimates the divergence time, the ancestral population size and the relative sizes of the derived populations. A simulation study revealed that this method is essentially unbiased and that it leads to better estimates than traditional approaches for a very wide range of parameter values. Simulations also indicated that moderate population growth after divergence has little effect on the estimates of all three estimated parameters. An application of our method to a comparison of humans and chimpanzee mitochondrial DNA diversity revealed that common chimpanzees have a significantly larger female population size than humans.     

Estimating the Rate of Adaptive Molecular Evolution When the Evolutionary Divergence Between Species is Small

We investigate the extent by which the estimates of the rate of adaptive molecular evolution obtained by extending the McDonald-Kreitman test are biased if the species, subjected to analysis, diverged recently. We show that estimates can be biased if the nucleotide divergence between the species is low relative to within species variation, and that the magnitude of the bias depends on the rate of adaptive evolution and the distribution of fitness effects of new mutations. Bias appears to be because of three factors: (1) misattribution of polymorphism to divergence; (2) the contribution of ancestral polymorphism to divergence; and (3) different rates of fixation of neutral and advantageous mutations. If there is little adaptive molecular evolution, then slightly deleterious mutations inflate estimates of the rate of adaptive evolution, because these contribute proportionately more to polymorphism than to nucleotide divergence than neutral mutations. However, if there is substantial adaptive evolution, polymorphism contributing to apparent divergence may downwardly bias estimates. We propose a simple method for correcting the different contributions of slightly deleterious and neutral mutations to polymorphism and divergence, and apply it to datasets from several species. We find that estimates of the rate of adaptive molecular evolution from closely related species may be underestimates by ~10% or more. However, after the contribution of polymorphism to divergence is removed, the rate of adaptive evolution may still be overestimated as a consequence of ancestral polymorphism and time for fixation effects. This bias may be substantial if branch lengths are less than 10N (e) generations.     

Positive and negative selection on the human genome.

The distinction between deleterious, neutral, and adaptive mutations is a fundamental problem in the study of molecular evolution. Two significant quantities are the fraction of DNA variation in natural populations that is deleterious and destined to be eliminated and the fraction of fixed differences between species driven by positive Darwinian selection. We estimate these quantities using the large number of human genes for which there are polymorphism and divergence data. The fraction of amino acid mutations that is neutral is estimated to be 0.20 from the ratio of common amino acid (A) to synonymous (S) single nucleotide polymorphisms (SNPs) at frequencies of > or =15%. Among the 80% of amino acid mutations that are deleterious at least 20% of them are only slightly deleterious and often attain frequencies of 1-10%. We estimate that these slightly deleterious mutations comprise at least 3% of amino acid SNPs in the average individual or at least 300 per diploid genome. This estimate is not sensitive to human population history. The A/S ratio of fixed differences is greater than that of common SNPs and suggests that a large fraction of protein divergence is adaptive and driven by positive Darwinian selection.     

Synonymous Nucleotide Divergence: What Is ``saturation''?

The nucleotide divergence at synonymous third sites between two lineages will increase with time since the latest common ancestor, up to some saturation level. The ``null-hypothesis divergence' is defined as the percentage of difference predicted at synonymous third sites, allowing for amino acid composition and codon bias, but assuming that codon bias is the same at all sites occupied by a given amino acid, when equilibrium has been reached between forward and backward substitutions. For two highly expressed genes, gapA and ompA, in the enterobacteria, the estimated values of the null-hypothesis divergence are 39.3 and 38.15%, respectively, compared to estimated values of saturation divergence of 19.0 and 25.4%. A possible explanation for this discrepancy is that different codons for a given amino acid are favored at different sites in the same gene.     

Divergence between Human Populations Estimated from Linkage Disequilibrium

Observed linkage disequilibrium (LD) between genetic markers in different populations descended independently from a common ancestral population can be used to estimate their absolute time of divergence, because the correlation of LD between populations will be reduced each generation by an amount that, approximately, depends only on the recombination rate between markers. Although drift leads to divergence in allele frequencies, it has less effect on divergence in LD values. We derived the relationship between LD and time of divergence and verified it with coalescent simulations. We then used HapMap Phase II data to estimate time of divergence between human populations. Summed over large numbers of pairs of loci, we find a positive correlation of LD between African and non-African populations at levels of up to ~0.3 cM. We estimate that the observed correlation of LD is consistent with an effective separation time of approximately 1,000 generations or ~25,000 years before present. The most likely explanation for such relatively low separation times is the existence of substantial levels of migration between populations after the initial separation. Theory and results from coalescent simulations confirm that low levels of migration can lead to a downward bias in the estimate of separation time.     

Estimating divergence time with the use of microsatellite genetic distances: impacts of population growth and gene flow

Genetic distances play an important role in estimating divergence time of bifurcated populations. However, they can be greatly affected by demographic processes, such as migration and population dynamics, which complicate their interpretation. For example, the widely used distance for microsatellite loci, (deltamu)2, assumes constant population size, no gene flow, and mutation-drift equilibrium. It is shown here that (deltamu)2 strongly underestimates divergence time if populations are growing and/or connected by gene flow. In recent publications, the average estimate of divergence time between African and non-African populations obtained by using (deltamu)2 is about 34,000 years, although archaeological data show a much earlier presence of modern humans out of Africa. I introduce a different estimator of population separation time based on microsatellite statistics, T(D), that does not assume mutation-drift equilibrium, is independent of population dynamics in the absence of gene flow, and is robust to weak migration flow for growing populations. However, it requires a knowledge of the variance in the number of repeats at the beginning of population separation, V(0). One way to overcome this problem is to find minimal and maximal bounds for the variance and thus obtain the earliest and latest bounds for divergence time (this is not a confidence interval, and it simply reflects an uncertainty about the value of V(0) in an ancestral population). Another way to avoid the uncertainty is to choose from among present populations a reference whose variation is presumably close to what it might have been in an ancestral population. A different approach for using T(D) is to estimate the time difference between adjacent nodes on a phylogenetic population tree. Using data on variation at autosomal short tandem repeat loci with di-, tri-, and tetranucleotide repeats in worldwide populations, T(D) gives an estimate of 57,000 years for the separation of the out-of-Africa branch of modern humans from Africans based on the value of V(0) in the Southern American Indian populations; the earliest bound for this event has been estimated to be about 135,000 years. The data also suggest that the Asian and European populations diverged from each other about 20,000 years, after the occurrence of the out-of-Africa branch.     

Microsatellite allele sizes: a simple test to assess their significance on genetic differentiation

The mutation process at microsatellite loci typically occurs at high rates and with stepwise changes in allele sizes, features that may introduce bias when using classical measures of population differentiation based on allele identity (e.g., F(ST), Nei's Ds genetic distance). Allele size-based measures of differentiation, assuming a stepwise mutation process [e.g., Slatkin's R(ST), Goldstein et al.'s (deltamu)(2)], may better reflect differentiation at microsatellite loci, but they suffer high sampling variance. The relative efficiency of allele size- vs. allele identity-based statistics depends on the relative contributions of mutations vs. drift to population differentiation. We present a simple test based on a randomization procedure of allele sizes to determine whether stepwise-like mutations contributed to genetic differentiation. This test can be applied to any microsatellite data set designed to assess population differentiation and can be interpreted as testing whether F(ST) = R(ST). Computer simulations show that the test efficiently identifies which of F(ST) or R(ST) estimates has the lowest mean square error. A significant test, implying that R(ST) performs better than F(ST), is obtained when the mutation rate, mu, for a stepwise mutation process is (a) >/= m in an island model (m being the migration rate among populations) or (b) >/= 1/t in the case of isolated populations (t being the number of generations since population divergence). The test also informs on the efficiency of other statistics used in phylogenetical reconstruction [e.g., Ds and (deltamu)(2)], a nonsignificant test meaning that allele identity-based statistics perform better than allele size-based ones. This test can also provide insights into the evolutionary history of populations, revealing, for example, phylogeographic patterns, as illustrated by applying it on three published data sets.     

Genetic variability and population differentiation in captive baird's Tapirs (Tapirus bairdii)

The objectives of this study were to assess the level of genetic variability and population differentiation within captive populations of an endangered large mammal, Baird's tapir (Tapirus bairdii). We genotyped 37 captive animals from North American (NA) and Central American (CA) zoos and conservation ranches using six polymorphic microsatellite loci. Standard indices of genetic variability (allelic richness and diversity, and heterozygosity) were estimated and compared between captive populations, and between captive and wild population samples. In addition, we evaluated levels of population differentiation using Weir and Cockerham's version of Wright's F-statistics. The results indicate that the NA and CA captive populations of Baird's tapirs have retained levels of genetic variability similar to that measured in a wild population. However, inbreeding coefficients estimated from the molecular data indicate that the CA captive population is at increased risk of losing genetic variability due to inbreeding. Despite this, estimated levels of population differentiation indicate limited divergence of the CA captive population from the wild population. Careful management appears to have kept inbreeding coefficients low in the NA captive population; however, population differentiation levels indicate that the NA population has experienced increased divergence from wild populations due to a founder effect and isolation. Based on these results, we conclude that intermittent exchanges of Baird's tapirs between the NA and CA captive populations will benefit both populations by increasing genetic variability and effective population size, while reducing inbreeding and divergence from wild populations. Zoo Biol 23:521–531, 2004. © 2004 Wiley-Liss, Inc.     

Allele frequency divergence reveals ubiquitous influence of positive selection in Drosophila

Resolving the role of natural selection is a basic objective of evolutionary biology. It is generally difficult to detect the influence of selection because ubiquitous non-selective stochastic change in allele frequencies (genetic drift) degrades evidence of selection. As a result, selection scans typically only identify genomic regions that have undergone episodes of intense selection. Yet it seems likely such episodes are the exception; the norm is more likely to involve subtle, concurrent selective changes at a large number of loci. We develop a new theoretical approach that uncovers a previously undocumented genome-wide signature of selection in the collective divergence of allele frequencies over time. Applying our approach to temporally resolved allele frequency measurements from laboratory and wild Drosophila populations, we quantify the selective contribution to allele frequency divergence and find that selection has substantial effects on much of the genome. We further quantify the magnitude of the total selection coefficient (a measure of the combined effects of direct and linked selection) at a typical polymorphic locus, and find this to be large (of order 1%) even though most mutations are not directly under selection. We find that selective allele frequency divergence is substantially elevated at intermediate allele frequencies, which we argue is most parsimoniously explained by positive—not negative—selection. Thus, in these populations most mutations are far from evolving neutrally in the short term (tens of generations), including mutations with neutral fitness effects, and the result cannot be explained simply as an ongoing purging of deleterious mutations.     

Noise does not equal bias in assessing the evolutionary history of the angiosperm flora of China: A response to Qian (2019)

In response to our paper on the evolutionary history of the Chinese flora, Qian suggests that certain features of the divergence time estimation employed might have led to biased conclusions in Lu et al (2018). Here, we consider Qian's specific criticisms, explore the extent of uncertainty in the data and demonstrate that (i) no systematic bias toward dates that are too young or too old is detected in Lu et al.; (ii) constraint of the crown age of angiosperms does not bias the generic ages estimated by Lu et al.; and (iii) ages derived from the Chinese regional phylogeny do not bias the conclusions reported by Lu et al. All these analyses confirm that the conclusions reported previously are robust. We argue that, like many large-scale biodiversity analyses, sources of noise in divergence time estimation are to be expected, but these should not be confused with bias.     

POPULATION STRUCTURE OF DIPODOMYS INGENS (HETEROMYIDAE): THE ROLE OF SPATIAL HETEROGENEITY IN MAINTAINING GENETIC DIVERSITY

The giant kangaroo rat, Dipodomys ingens (Heteromyidae), is an endangered rodent that inhabits approximately 3% of its estimated historic range. Its current distribution is centered in two geographic areas, situated about 150 km apart, in south-central California. We sequenced a 293 base-pair fragment at the 5' end of the control region in 95 giant kangaroo rats from nine localities to examine the genetic structure of extant populations. We determine that mutations in this section of the control region follow a negative binominal distribution, rather than a Poisson. However, the distance between haplotypes is small enough that the difference between a tree that corrects for the non-Poisson distribution of mutations and one that does not, is minimal. This implies that the use of methods that assume a Poisson distribution of mutations, such as those based on coalescent theory, are justified. We find that the correlation between levels of genetic diversity and estimated census size is poor. This suggests that population sizes have fluctuated over time or that populations have not been isolated from one another, or both. We also examine the hierarchical structure of populations and find that the southern populations are not genetically subdivided but that there is significant subdivision between northern and southern populations and between some northern subpopulations. The phylogeographic relationship between northern and southern populations can primarily be attributed to isolation by distance, although the time since divergence between them appears to be less than the age of either. To examine the phylogeographic relationships in more detail we construct a minimum spanning tree based on Tamura-Nei gamma-corrected distances and superimpose on it the geographic position of haplotypes. This reveals that there is more genetic distance between some northern haplotypes than between any northern and southern haplotypes, despite the geographic distance separating north from south and the larger size of the southern population. It also reveals that one northern population, in the Panoche Valley, contains old allelic lineages and shares ancestral polymorphism with several other populations. It also shows that two, small, geographically remote populations contain a surprising amount of genetic diversity, but that different population/geographic processes have affected the structure of that diversity. We estimate the average migration rate among all populations to be 7.5 per generation, and conclude that a disproportionate number of migration events involve gene flow with one northern population, the Panoche Valley. We find evidence for the hypothesis that there has been an increase in population size in the remaining populations in the north and suggest that the Panoche Valley could play a role in these expansions. Finally we discuss the probabilitiy that the genetic structure of the southern populations has been affected by fluctuations in size. These results are briefly compared to other studies on the genetic structure of rodent populations.     

Measures of divergence between populations and the effect of forces that reduce variability

Wright's FST and related statistics are often used to measure the extent of divergence among populations of the same species relative to the net genetic diversity within the species. This paper compares several definitions of FST which are relevant to DNA sequence data, and shows that these must be used with care when estimating migration parameters. It is also pointed out that FST is strongly influenced by the level of within-population diversity. In situations where factors such as selection on closely linked sites are expected to have stronger effects on within-population diversity at some loci than at others, differences among loci can result entirely from differences in within- population diversities. It is shown that several published cases of differences in FST among regions of high and low recombination in Drosophila may be caused in this way. For the purpose of comparisons of levels of between-population differences among loci or species which are subject to different intensities of forces that reduce variability within local populations, absolute measures of divergence between populations should be used in preference to relative measures such as FST.      

Bayesian analysis of an admixture model with mutations and arbitrarily linked markers

We introduce here a Bayesian analysis of a classical admixture model in which all parameters are simultaneously estimated. Our approach follows the approximate Bayesian computation (ABC) framework, relying on massive simulations and a rejection-regression algorithm. Although computationally intensive, this approach can easily deal with complex mutation models and partially linked loci, and it can be thoroughly validated without much additional computation cost. Compared to a recent maximum-likelihood (ML) method, the ABC approach leads to similarly accurate estimates of admixture proportions in the case of recent admixture events, but it is found superior when the admixture is more ancient. All other parameters of the admixture model such as the divergence time between parental populations, the admixture time, and the population sizes are also well estimated, unlike the ML method. The use of partially linked markers does not introduce any particular bias in the estimation of admixture, but ML confidence intervals are found too narrow if linkage is not specifically accounted for. The application of our method to an artificially admixed domestic bee population from northwest Italy suggests that the admixture occurred in the last 10-40 generations and that the parental Apis mellifera and A. ligustica populations were completely separated since the last glacial maximum.     

ADAPTIVE RADIATION ALONG GENETIC LINES OF LEAST RESISTANCE

Are measurements of quantitative genetic variation useful for predicting long-term adaptive evolution? To answer this question, I focus on g_max, the multivariate direction of greatest additive genetic variance within populations. Original data on threespine sticklebacks, together with published genetic measurements from other vertebrates, show that morphological differentiation between species has been biased in the direction of g_max for at least four million years, despite evidence that natural selection is the cause of differentiation. This bias toward the direction of evolution tends to decay with time. Rate of morphological divergence between species is inversely proportional to θ, the angle between the direction of divergence and the direction of greatest genetic variation. The direction of greatest phenotypic variance is not identical with g_max, but for these data is nearly as successful at predicting the direction of species divergence. I interpret the findings to mean that genetic variances and covariances constrain adaptive change in quantitative traits for reasonably long spans of time. An alternative hypothesis, however, cannot be ruled out: that morphological differentiation is biased in the direction g_max because divergence and g_max are both shaped by the same natural selection pressures. Either way, the results reveal that adaptive differentiation occurs principally along “genetic lines of least resistance.”     

Rapid evolution of goat and sheep globin genes following gene duplication

Statistical analyses of DNA sequences of globin genes (beta A, beta C, and gamma) from goat and sheep (including new sequence information for the second intron of sheep beta A and gamma, kindly provided by A. Davis and A. W. Nienhuis) indicate that the rates of nonsynonymous substitution in these genes have been greatly accelerated following the gene duplication separating gamma and the ancestor of beta A and beta C and the gene duplication separating beta A and beta C. In both cases the acceleration was apparently due to relaxation of purifying selection (functional constraints) rather than advantageous mutations because acceleration occurred only in less important parts of the beta globin chain. The rates of nonsynonymous substitution in these genes are estimated to be about 2.3 x 10(-9) per site per year, which is three times higher than that for the divergence between human beta and mouse beta major globin genes. Our analyses further suggest that the rate of synonymous substitution in functional genes and the rate of substitution in pseudogenes are approximately equal and are between 2.8 x 10(-9) and 5.0 x 10(-9) and that the rate of substitution in introns is about 3.0 x 10(-9). The divergence time between beta A and beta C and that between gamma and the beta A-beta C pair are about 12 and 30 million years, respectively. The proportion of transition mutations is estimated to be 64%, two times higher than expected under random mutation but considerably lower than the 96% estimated for animal mitochondrial DNA.      

Evolutionary divergence in Dolichopoda cave crickets: A comparison of single copy DNA hybridization data with allozymes and morphometric distances

In this paper we attempt to investigate relationships between the amount of genetic divergence in nuclear genes and the degree of morphological differentiation for different sets of characters in Dolichopoda cave crickets. Six populations representing five Dolichopoda species from Central and Southern Italy have been studied. The overall genetic divergence at nuclear genes was estimated both by single copy DNA-DNA hybridization and allozyme frequencies at 26 loci. Euclidean distances for two multivariate sets of morphometric variables: one describing body and appendage morphology, the other male epiphallus shape. Results showed a close agreement between the branching patterns of ΔTm values from DNA hybridization and Nei's allozyme distance values. On the other hand, patterns of morphological divergence revealed independent trends, although the branching pattern based on epiphallus morphology matched to some extent the phylogenies inferred from molecular data. The relative value of molecular and morphological characters as reliable phylogenetic tracers was evaluated in relation to their dependence on evolutionary factors. Implications of these findings on the calibration of molecular clocks are also discussed. The absolute rate of molecular change based on scDNA was estimated to be at least 0.98% divergence/my/lineage. This result is in agreement with calibrations attempted on other insects. Estimates of time of divergence based on allozymes (Nei's D) were highly consistent with the estimate from geological data.     

Natural selection on synonymous sites is correlated with gene length and recombination in Drosophila.

Evolutionary analysis of codon bias in Drosophila indicates that synonymous mutations are not neutral, but rather are subject to weak selection at the translation level. Here we show that the effectiveness of natural selection on synonymous sites is strongly correlated with the rate of recombination, in accord with the nearly neutral hypothesis. This correlation, however, is apparent only in genes encoding short proteins. Long coding regions have both a lower codon bias and higher synonymous substitution rates, suggesting that they are affected less efficiently by selection. Therefore, both the length of the coding region and the recombination rate modulate codon bias. In addition, the data indicate that selection coefficients for synonymous mutations must vary by a minimum of one or two orders of magnitude. Two hypotheses are proposed to explain the relationship among the coding region length, the codon bias, and the synonymous divergence and polymorphism levels across the range of recombination rates in Drosophila. The first hypothesis is that selection coefficients on synonymous mutations are inversely related to the total length of the coding region. The second hypothesis proposes that interference among synonymous mutations reduces the efficacy of selection on these mutations. We investigated this second hypothesis by carrying out forward simulations of weakly selected mutations in model populations. These simulations show that even with realistic recombination rates, this interference, which we call the "small-scale" Hill-Robertson effect, can have a moderately strong influence on codon bias.     

The Deep Phylogeny of Land Plants Inferred from a Full Analysis of Nucleotide Base Changes in Terms of Mutation and Selection

The occurrence frequencies of nucleotide bases are biased to those of T and A bases even at third codon positions for conserved amino acid residues with fourfold degeneracy in the chloroplasts of land plants. Regarding this bias as the result of selection, the base changes at these positions are fully analyzed theoretically in terms of mutation and selection. Although the degree of bias is considerably different depending on the lineages of land plants, the theoretical curves considering the influence of selection in the respective lineages provide a reasonable set of evolutionary distances for the relative base change probabilities estimated empirically from base changes enumerated in the comparison of rbcL genes. By using the fossil records of earliest seed plants in the Late Devonian and of uniaperturate and triaperturate pollen types in the early stage of the Cretaceous as calibration points, the divergence of Marchantiidae and a common ancestor of other land plants is estimated to have occurred 509 Mya, together with the estimation of a mutation rate of 1.45 × 10^–9 year^–1 per site. The other bryophytes such as Bryopsida, Anthocerotopsida, and Jungermanniidae are sister groups to tracheophytes, the divergence of bryophytes and tracheophytes being estimated to have occurred 483 Mya. The evolutionary distance of Gnetopsida from Coniferopsida and Magnoliophyta is concluded to be decisively longer than the distance between Coniferopsida and Magnoliophyta, i.e., the former divergence corresponds to 286 Mya and the latter to 211 Mya.     

Delimiting shades of gray: phylogeography of the Northern Fulmar,Fulmarus glacialis

The Northern Fulmar (Fulmarus glacialis) is a common tube‐nosed seabird with a disjunct Holarctic range. Taxonomic divisions within the Northern Fulmar have historically been muddled by geographical variation notably including highly polymorphic plumage. Recent molecular analyses (i.e., DNA barcoding) have suggested that genetic divergence between Atlantic and Pacific populations could be on par with those typically observed between species. We employ a multigene phylogenetic analysis to better explore the level of genetic divergence between these populations and to test an old hypothesis on the origin of the modern distribution of color morphs across their range. Additionally, we test whether mutations in the melanocortin‐1 receptor gene (MC1R) are associated with dark plumage in the Northern Fulmar. We confirmed that mitochondrial lineages in the Atlantic and Pacific populations are highly divergent, but nuclear markers revealed incomplete lineage sorting. Genetic divergence between these populations is consistent with that observed between many species of Procellariiformes and we recommend elevating these two forms to separate species. We also find that MC1R variation is not associated with color morph but rather is better explained by geographical divergence.     

The Distribution of Mutation Effects on Viability in Drosophila Melanogaster

Parameters of continuous distributions of effects and rates of spontaneous mutation for relative viability in Drosophila are estimated by maximum likelihood from data of two published experiments on accumulation of mutations on protected second chromosomes. A model of equal mutant effects gives a poor fit to the data of the two experiments; higher likelihoods are obtained with leptokurtic distributions or for models in which there is more than one class of mutation effect. Minimum estimates of mutation rates (events per generation) at polygenes affecting viability on chromosome 2 are 0.14 and 0.068, but estimates are strongly confounded with other parameters in the model. Separate information on rates of molecular divergence between Drosophila species and from rates of movement of transposable elements is used to infer the overall genomic mutation rate in Drosophila, and the viability data are analyzed with mutation rate as a known parameter. If, for example, a mutation rate for chromosome 2 of 0.4 is assumed, maximum likelihood estimates of mean mutant effect on relative viability are 0.4% and 1%, but the majority of mutations have very much smaller effects than these values as distributions are highly leptokurtic. The methodology is applied to estimate viability effects of single P element insertional mutations. The mean effect per insertion is found to be higher, and their distribution is found to be less leptokurtic than for spontaneous mutations. The equilibrium genetic variance of viability predicted by a mutation-selection balance model with parameters estimated from the mutation accumulation experiments is similar to laboratory estimates of genetic variance of viability from natural populations of Drosophila.