On the application of statistical physics to evolutionary biology

There is a close analogy between statistical thermodynamics and the evolution of allele frequencies under mutation, selection and random drift. Wright's formula for the stationary distribution of allele frequencies is analogous to the Boltzmann distribution in statistical physics. Population size, 2N, plays the role of the inverse temperature, 1/kT, and determines the magnitude of random fluctuations. Log mean fitness, , tends to increase under selection, and is analogous to a (negative) energy; a potential function, U, increases under mutation in a similar way. An entropy, S_H, can be defined which measures the deviation from the distribution of allele frequencies expected under random drift alone; the sum gives a free fitness that increases as the population evolves towards its stationary distribution. Usually, we observe the distribution of a few quantitative traits that depend on the frequencies of very many alleles. The mean and variance of such traits are analogous to observable quantities in statistical thermodynamics. Thus, we can define an entropy, S_Ω, which measures the volume of allele frequency space that is consistent with the observed trait distribution. The stationary distribution of the traits is ; this applies with arbitrary epistasis and dominance. The entropies S_Ω, S_H are distinct, but converge when there are so many alleles that traits fluctuate close to their expectations. Populations tend to evolve towards states that can be realised in many ways (i.e., large S_Ω), which may lead to a substantial drop below the adaptive peak; we illustrate this point with a simple model of genetic redundancy. This analogy with statistical thermodynamics brings together previous ideas in a general framework, and justifies a maximum entropy approximation to the dynamics of quantitative traits.     

Evolutionarily stable mutation rate in a periodically changing environment

Evolution of mutation rate controlled by a neutral modifier is studied for a locus with two alleles under temporally fluctuating selection pressure. A general formula is derived to calculate the evolutionarily stable mutation rate μ(ess) in an infinitely large haploid population, and following results are obtained. (I) For any fluctuation, periodic or random: (1) if the recombination rate r per generation between the modifier and the main locus is 0, μ(ess) is the same as the optimal mutation rate μ(op) which maximizes the long-term geometric average of population fitness; and (2) for any r, if the strength s of selection per generation is very large, μ(ess) is equal to the reciprocal of the average number T of generations (duration time) during which one allele is persistently favored than the other. (II) For a periodic fluctuation in the limit of small s and r, μ(ess)T is a function of sT and rT with properties: (1) for a given sT, μ(ess)T decreases with increasing rT; (2) for sT </= 1, μ(ess)T is almost independent of sT, and depends on rT as μ(ess)T & 1.6 for rT << 1 and μ(ess)T & 6/rT for rT >> 1; and (3) for sT >/= 1, and for a given rT, μ(ess)T decreases with increasing sT to a certain minimum less than 1, and then increases to 1 asymptotically in the limit of large sT. (III) For a fluctuation consisting of multiple Fourier components (i.e., sine wave components), the component with the longest period is the most effective in determining μ(ess) (low pass filter effect). (IV) When the cost c of preventing mutation is positive, the modifier is nonneutral, and μ(ess) becomes larger than in the case of neutral modifier under the same selection pressure acting at the main locus. The value of c which makes μ(ess) equal to μ(op) of the neutral modifier case is calculated. It is argued that this value gives a critical cost such that, so long as the actual cost exceeds this value, the evolution rate at the main locus must be smaller than its mutation rate μ(ess).     

Evolutionary rates for multivariate traits: the role of selection and genetic variation

A fundamental question in evolutionary biology is the relative importance of selection and genetic architecture in determining evolutionary rates. Adaptive evolution can be described by the multivariate breeders'' equation (), which predicts evolutionary change for a suite of phenotypic traits () as a product of directional selection acting on them (β) and the genetic variance–covariance matrix for those traits (G). Despite being empirically challenging to estimate, there are enough published estimates of G and β to allow for synthesis of general patterns across species. We use published estimates to test the hypotheses that there are systematic differences in the rate of evolution among trait types, and that these differences are, in part, due to genetic architecture. We find some evidence that sexually selected traits exhibit faster rates of evolution compared with life-history or morphological traits. This difference does not appear to be related to stronger selection on sexually selected traits. Using numerous proposed approaches to quantifying the shape, size and structure of G, we examine how these parameters relate to one another, and how they vary among taxonomic and trait groupings. Despite considerable variation, they do not explain the observed differences in evolutionary rates.     

Chromosome Rearrangements Recovered following Transformation of Neurospora Crassa

Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, γ, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When γ = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as γ changes. The effects of γ on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.     

Evolution of the polymorphism at molecular markers in QTL and non-QTL regions in selected chicken lines (Open Access publication)

We investigated the joint evolution of neutral and selected genomic regions in three chicken lines selected for immune response and in one control line. We compared the evolution of polymorphism of 21 supposedly neutral microsatellite markers versus 30 microsatellite markers located in seven quantitative trait loci (QTL) regions. Divergence of lines was observed by factor analysis. Five supposedly neutral markers and 12 markers in theQTL regions showed F_st values greater than 0.15. However, the non-significant difference (P > 0.05) between matrices of genetic distances based on genotypes at supposedly neutral markers on the one hand, and at markers in QTL regions, on the other hand, showed that none of the markers in the QTL regions were influenced by selection. A supposedly neutral marker and a marker located in the QTL region on chromosome 14 showed temporal variations in allele frequencies that could not be explained by drift only. Finally, to confirm thatmarkers located inQTL regions on chromosomes 1, 7 and 14were under the influence of selection, simulations were performed using haplotype dropping along the existing pedigree. In the zone located on chromosome 14, the simulation results confirmed that selection had an effect on the evolution of polymorphism of markers within the zone.     

The genetical theory of social behaviour

We survey the population genetic basis of social evolution, using a logically consistent set of arguments to cover a wide range of biological scenarios. We start by reconsidering Hamilton''s (Hamilton 1964 J. Theoret. Biol. 7, 1–16 (doi:10.1016/0022-5193(64)90038-4)) results for selection on a social trait under the assumptions of additive gene action, weak selection and constant environment and demography. This yields a prediction for the direction of allele frequency change in terms of phenotypic costs and benefits and genealogical concepts of relatedness, which holds for any frequency of the trait in the population, and provides the foundation for further developments and extensions. We then allow for any type of gene interaction within and between individuals, strong selection and fluctuating environments and demography, which may depend on the evolving trait itself. We reach three conclusions pertaining to selection on social behaviours under broad conditions. (i) Selection can be understood by focusing on a one-generation change in mean allele frequency, a computation which underpins the utility of reproductive value weights; (ii) in large populations under the assumptions of additive gene action and weak selection, this change is of constant sign for any allele frequency and is predicted by a phenotypic selection gradient; (iii) under the assumptions of trait substitution sequences, such phenotypic selection gradients suffice to characterize long-term multi-dimensional stochastic evolution, with almost no knowledge about the genetic details underlying the coevolving traits. Having such simple results about the effect of selection regardless of population structure and type of social interactions can help to delineate the common features of distinct biological processes. Finally, we clarify some persistent divergences within social evolution theory, with respect to exactness, synergies, maximization, dynamic sufficiency and the role of genetic arguments.     

The Mechanisms Underlying α-Amanitin Resistance in Drosophila melanogaster: A Microarray Analysis

The rapid evolution of toxin resistance in animals has important consequences for the ecology of species and our economy. Pesticide resistance in insects has been a subject of intensive study; however, very little is known about how Drosophila species became resistant to natural toxins with ecological relevance, such as α-amanitin that is produced in deadly poisonous mushrooms. Here we performed a microarray study to elucidate the genes, chromosomal loci, molecular functions, biological processes, and cellular components that contribute to the α-amanitin resistance phenotype in Drosophila melanogaster. We suggest that toxin entry blockage through the cuticle, phase I and II detoxification, sequestration in lipid particles, and proteolytic cleavage of α-amanitin contribute in concert to this quantitative trait. We speculate that the resistance to mushroom toxins in D. melanogaster and perhaps in mycophagous Drosophila species has evolved as cross-resistance to pesticides, other xenobiotic substances, or environmental stress factors.     

Words as alleles: connecting language evolution with Bayesian learners to models of genetic drift

Scientists studying how languages change over time often make an analogy between biological and cultural evolution, with words or grammars behaving like traits subject to natural selection. Recent work has exploited this analogy by using models of biological evolution to explain the properties of languages and other cultural artefacts. However, the mechanisms of biological and cultural evolution are very different: biological traits are passed between generations by genes, while languages and concepts are transmitted through learning. Here we show that these different mechanisms can have the same results, demonstrating that the transmission of frequency distributions over variants of linguistic forms by Bayesian learners is equivalent to the Wright–Fisher model of genetic drift. This simple learning mechanism thus provides a justification for the use of models of genetic drift in studying language evolution. In addition to providing an explicit connection between biological and cultural evolution, this allows us to define a ‘neutral’ model that indicates how languages can change in the absence of selection at the level of linguistic variants. We demonstrate that this neutral model can account for three phenomena: the s-shaped curve of language change, the distribution of word frequencies, and the relationship between word frequencies and extinction rates.     

Multiple-Trait Genomic Selection Methods Increase Genetic Value Prediction Accuracy

Genetic correlations between quantitative traits measured in many breeding programs are pervasive. These correlations indicate that measurements of one trait carry information on other traits. Current single-trait (univariate) genomic selection does not take advantage of this information. Multivariate genomic selection on multiple traits could accomplish this but has been little explored and tested in practical breeding programs. In this study, three multivariate linear models (i.e., GBLUP, BayesA, and BayesCπ) were presented and compared to univariate models using simulated and real quantitative traits controlled by different genetic architectures. We also extended BayesA with fixed hyperparameters to a full hierarchical model that estimated hyperparameters and BayesCπ to impute missing phenotypes. We found that optimal marker-effect variance priors depended on the genetic architecture of the trait so that estimating them was beneficial. We showed that the prediction accuracy for a low-heritability trait could be significantly increased by multivariate genomic selection when a correlated high-heritability trait was available. Further, multiple-trait genomic selection had higher prediction accuracy than single-trait genomic selection when phenotypes are not available on all individuals and traits. Additional factors affecting the performance of multiple-trait genomic selection were explored.     

Identification and Analysis of Genome-Wide SNPs Provide Insight into Signatures of Selection and Domestication in Channel Catfish (Ictalurus punctatus)

Domestication and selection for important performance traits can impact the genome, which is most often reflected by reduced heterozygosity in and surrounding genes related to traits affected by selection. In this study, analysis of the genomic impact caused by domestication and artificial selection was conducted by investigating the signatures of selection using single nucleotide polymorphisms (SNPs) in channel catfish (Ictalurus punctatus). A total of 8.4 million candidate SNPs were identified by using next generation sequencing. On average, the channel catfish genome harbors one SNP per 116 bp. Approximately 6.6 million, 5.3 million, 4.9 million, 7.1 million and 6.7 million SNPs were detected in the Marion, Thompson, USDA103, Hatchery strain, and wild population, respectively. The allele frequencies of 407,861 SNPs differed significantly between the domestic and wild populations. With these SNPs, 23 genomic regions with putative selective sweeps were identified that included 11 genes. Although the function for the majority of the genes remain unknown in catfish, several genes with known function related to aquaculture performance traits were included in the regions with selective sweeps. These included hypoxia-inducible factor 1β· HIFιβ ¨ and the transporter gene ATP-binding cassette sub-family B member 5 (ABCB5). HIF1β· is important for response to hypoxia and tolerance to low oxygen levels is a critical aquaculture trait. The large numbers of SNPs identified from this study are valuable for the development of high-density SNP arrays for genetic and genomic studies of performance traits in catfish.     

Environmental stability affects phenotypic evolution in a globally distributed marine picoplankton

Marine phytoplankton can evolve rapidly when confronted with aspects of climate change because of their large population sizes and fast generation times. Despite this, the importance of environment fluctuations, a key feature of climate change, has received little attention—selection experiments with marine phytoplankton are usually carried out in stable environments and use single or few representatives of a species, genus or functional group. Here we investigate whether and by how much environmental fluctuations contribute to changes in ecologically important phytoplankton traits such as C:N ratios and cell size, and test the variability of changes in these traits within the globally distributed species Ostreococcus. We have evolved 16 physiologically distinct lineages of Ostreococcus at stable high CO₂ (1031±87 μatm CO₂, SH) and fluctuating high CO₂ (1012±244 μatm CO₂, FH) for 400 generations. We find that although both fluctuation and high CO₂ drive evolution, FH-evolved lineages are smaller, have reduced C:N ratios and respond more strongly to further increases in CO₂ than do SH-evolved lineages. This indicates that environmental fluctuations are an important factor to consider when predicting how the characteristics of future phytoplankton populations will have an impact on biogeochemical cycles and higher trophic levels in marine food webs.     

Studies on the Second Emerson Effect in the Hill Reaction in Algal Cells

This paper shows that the “second Emerson effect”¹ exists not only in photosynthesis, but also in the quinone reduction (Hill reaction), in Chlorella pyrenoidosa and Anacystis nidulans. The peaks at 650 mμ, 600 mμ, 560 mμ, 520 mμ, and 480 mμ, observed in the action spectrum of this effect in the Hill reaction in Chorella, are attributable to chlorophyll b; the occurrence of an additional peak at 670 mμ, 620 mμ, and of two (or three) peaks in the blueviolet region suggests that (at least) one form of chlorophyll a contributes to it. In analogy to suggestions made previously in the interpretation of the Emerson effect in photosynthesis, these results are taken as indicating that excitation by light preferentially absorbed by one (or two) forms of chlorophyll a (Chl a 690 + 700), needs support by simultaneous absorption of light in another form of chlorophyll a (Chl a 670)—directly or via energy transfer from chlorophyll b—in order to produce the Hill reaction with its full quantum yield. In Anacystis, the participation of phycocyanin in the Emerson effect in the Hill reaction is revealed by the occurrence, in the action spectrum of this effect, of peaks at about 560 mμ, 610 mμ, and 640 mμ; a peak at 670 mμ, due to Chl a 670, also is present.     

Effect of Monensin and Lasalocid-Sodium on the Growth of Methanogenic and Rumen Saccharolytic Bacteria

It is thought that monensin increases the efficiency of feed utilization by cattle by altering the rumen fermentation. We studied the effect of monensin and the related ionophore antibiotic lasalocid-sodium (Hoffman-LaRoche) on the growth of methanogenic and rumen saccharolytic bacteria in a complex medium containing rumen fluid. Ruminococcus albus, Ruminococcus flavefaciens, and Butyrivibrio fibrisolvens were inhibited by 2.5 μg of monensin or lasalocid per ml. Growth of Bacteroides succinogenes and Bacteroides ruminicola was delayed by 2.5 μg of monensin or lasalocid per ml. Populations of B. succinogenes and B. ruminicola that were resistant to 20 μg of either drug per ml were rapidly selected by growth in the presence of each drug at 5.0 μg/ml. Selenomonas ruminantium was insensitive to 40 μg of monensin or lasalocid per ml. Either antibiotic (10 μg/ml) inhibited Methanobacterium MOH, Methanobacterium formicicum, and Methanosarcina barkeri MS. Methanobacterium ruminantium PS was insensitive to 40 μg of monensin or 20 μg of lasalocid per ml. The methanogenic strain 442 was insensitive to 40 μg of monensin but sensitive to 10 μg of lasalocid per ml. The results suggest that monensin or lasalocid acts in the rumen by selecting for succinate-forming Bacteroides and for S. ruminantium, a propionate producer that decarboxylates succinate to propionate. The selection could lead to an increase in rumen propionate formation. Selection against H₂ and formate producers, e.g. R. albus, R. flavefaciens, and B. fibrisolvens, could lead to a depression of methane production in the rumen.     

Chromosomal Gene Inactivation in the Green Sulfur Bacterium Chlorobium tepidum by Natural Transformation

Conditions for inactivating chromosomal genes of Chlorobium tepidum by natural transformation and homologous recombination were established. As a model, mutants unable to perform nitrogen fixation were constructed by interrupting nifD with various antibiotic resistance markers. Growth of wild-type C. tepidum at 40°C on agar plates could be completely inhibited by 100 μg of gentamicin ml⁻¹, 2 μg of erythromycin ml⁻¹, 30 μg of chloramphenicol ml⁻¹, or 1 μg of tetracycline ml⁻¹ or a combination of 300 μg of streptomycin ml⁻¹ and 150 μg of spectinomycin ml⁻¹. Transformation was performed by spotting cells and DNA on an agar plate for 10 to 20 h. Transformation frequencies on the order of 10⁻⁷ were observed with gentamicin and erythromycin markers, and transformation frequencies on the order of 10⁻³ were observed with a streptomycin-spectinomycin marker. The frequency of spontaneous mutants resistant to gentamicin, erythromycin, or spectinomycin-streptomycin was undetectable or significantly lower than the transformation frequency. Transformation with the gentamicin marker was observed when the transforming DNA contained 1 or 3 kb of total homologous flanking sequence but not when the transforming DNA contained only 0.3 kb of homologous sequence. Linearized plasmids transformed at least an order of magnitude better than circular plasmids. This work forms a foundation for the systematic targeted inactivation of genes in C. tepidum, whose 2.15-Mb genome has recently been completely sequenced.     

An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment

The evolution of population dynamics in a stochastic environment is analysed under a general form of density-dependence with genetic variation in r and K, the intrinsic rate of increase and carrying capacity in the average environment, and in σ_e², the environmental variance of population growth rate. The continuous-time model assumes a large population size and a stationary distribution of environments with no autocorrelation. For a given population density, N, and genotype frequency, p, the expected selection gradient is always towards an increased population growth rate, and the expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Long-term evolution maximizes the expected value of the density-dependence function, averaged over the stationary distribution of N. In the θ-logistic model, where density dependence of population growth is a function of N^θ, long-term evolution maximizes E[N^θ]=[1−σ_e²/(2r)]K^θ. While σ_e² is always selected to decrease, r and K are always selected to increase, implying a genetic trade-off among them. By contrast, given the other parameters, θ has an intermediate optimum between 1.781 and 2 corresponding to the limits of high or low stochasticity.     

一个基于熵的精细定位数量性状位点的指数

针对数量性状位点的精细定位,本文采用群体的极端样本,利用稠密的标记位点,通过比较标记的熵和条件熵,给出了一个基于熵的指数。该指数是标记基因和性状位点间连锁不平衡系数的函数,它不依赖于标记基因的频率。该指数对应我们之前提出的数量性状位点精细定位的哈迪-温伯格不平衡(HWD)指数,但在精细定位数量性状位点时,本文提出的指数的效能要高于哈迪-温伯格不平衡(HWD)指数。通过计算机模拟,文章调查了不同遗传参数下该指数的性质。模拟结果表明该指数用作精细定位是有效的。     

The Spread of an Advantageous Allele across a Barrier: The Effects of Random Drift and Selection against Heterozygotes

A local barrier to gene flow will delay the spread of an advantageous allele. Exact calculations for the deterministic case show that an allele that is favorable when rare is delayed very little even by a strong barrier: its spread is slowed by a time proportional to log ((B/σ) &2S)/S, where B is the barrier strength, σ the dispersal range, and fitnesses are 1:1 + S:1 + 2S. However, when there is selection against heterozygotes, such that the allele cannot increase from low frequency, a barrier can cause a much greater delay. If gene flow is reduced below a critical value, spread is entirely prevented. Stochastic simulations show that with additive selection, random drift slows down the spread of the allele, below the deterministic speed of σ &2S. The delay to the advance of an advantageous allele caused by a strong barrier can be substantially increased by random drift and increases with B/(2Sρσ(2)) in a one-dimensional habitat of density ρ. However, with selection against heterozygotes, drift can facilitate the spread and can free an allele that would otherwise be trapped indefinitely by a strong barrier. We discuss the implications of these results for the evolution of chromosome rearrangements.     

Estimation of the Amount of DNA Polymorphism When the Neutral Mutation Rate Varies among Sites

Knowing the amount of DNA polymorphism is essential to understand the mechanism of maintaining DNA polymorphism in a natural population. The amount of DNA polymorphism can be measured by the average number of nucleotide differences per site (π), the proportion of segregating (polymorphic) site (s) and the minimum number of mutations per site (s*). Since the latter two quantities depend on the sample size, θ is often used as a measure of the amount of DNA polymorphism, where θ = 4Nμ, N is the effective population size and μ is the neutral mutation rate per site per generation. It is known that θ estimated from π, s and s* under the infinite site model can be biased when the mutation rate varies among sites. We have therefore developed new methods for estimating θ under the finite site model. Using computer simulations, it has been shown that the new methods give almost unbiased estimates even when the mutation rate varies among sites substantially. Furthermore, we have also developed new statistics for testing neutrality by modifying Tajima's D statistic. Computer simulations suggest that the new test statistics can be used even when the mutation rate varies among sites.     

Frequency Distribution of Esterase-5 Alleles in Two Populations of DROSOPHILA PSEUDOOBSCURA

Statistical tests comparing allele frequencies in natural populations with those predicted by various theories of genic variation depend critically on the accurate enumeration of alleles. This study used a series of five sequential electrophoretic conditions to characterize the allele frequency distributions of esterase-5 in two large population samples of Drosophila pseudoobscura from California. In Standard chromosome lines 12 electromorphs were discriminated using a single electrophoretic condition. When four additional criteria were used, the number of electromorphs increased to 41, 33 in one population and 22 in the other. Both populations had the same two alleles in high frequency, with other alleles present in frequencies of 6% or less. Although each population had a number of unique alleles, a χ² contingency test demonstrated no significant genetic divergence between them. A statistical comparison of allele frequencies in both populations with that predicted by neutral models suggests that the individual and combined distributions deviate from neutrality in the direction of purifying selection.—Sex-Ratio chromosomes differed markedly from Standard chromosomes in both allelic content and diversity. In 32 Sex-Ratio chromosomes from one population only three alleles were found, all of which were detected under the initial "standard" electrophoretic conditions. Moreover, none of these alleles was found in the Standard chromosome lines.