Intrachromosomal Gene Conversion and the Maintenance of Sequence Homogeneity among Repeated Genes

Intrachromosomal gene conversion is the non-reciprocal transfer of information between a pair of repeated genes on a single chromosome. This process produces eventual sequence homogeneity within a family of repeated genes. An evolutionary model for a single chromosome lineage was formulated and analyzed. Expressions were derived for the fixation probability, mean time to fixation or loss, and mean conditional fixation time for a variant repeat with an arbitrary initial frequency. It was shown that a small conversional advantage or disadvantage for the variant repeat (higher or lower probability of producing two variant genes by conversion than two wild-type genes) can have a dramatic effect on the probability of fixation. The results imply that intrachromosomal gene conversion can act sufficiently rapidly to be an important mechanism for maintaining sequence homogeneity among repeated genes.     

Fixation of Strategies for an Evolutionary Game in Finite Populations

A stochastic evolutionary dynamics of two strategies given by 2x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire population. The process is discussed in the framework of a random walk with site dependent hopping rates. The time of fixation is found to be identical for both strategies in any particular game. The asymptotic behavior of the fixation time and fixation probabilities in the large population size limit is also discussed. We show that fixation is fast when there is at least one pure evolutionary stable strategy (ESS) in the infinite population size limit, while fixation is slow when the ESS is the coexistence of the two strategies.     

Geographical invariance in population genetics

Various quantities of evolutionary interest are shown to be independent of geographical structure. A diploid, monoecious population is subdivided into a finite number of panmictic colonies that exchange migrants. The migration pattern is fixed and ergodic, but otherwise arbitrary. Generations are discrete and non-overlapping; the analysis is restricted to a single locus. Previous results are generalized in the neutral multiallelic case. With selection, it is assumed that there are only two alleles, dominance is absent, selection has the same intensity in all demes, migration does not change the subpopulation numbers, and all evolutionary forces are weak. A diffusion approximation is established for the gene frequencies, and the invariance of the fixation probability and of the moments of the conditional and unconditional total heterozygosities before absorption is demonstrated by a martingale argument.     

The fastest evolutionary trajectory

Given two mutants, A and B, separated by n mutational steps, what is the evolutionary trajectory which allows a homogeneous population of A to reach B in the shortest time? We show that the optimum evolutionary trajectory (fitness landscape) has the property that the relative fitness increase between any two consecutive steps is constant. Hence, the optimum fitness landscape between A and B is given by an exponential function. Our result is precise for small mutation rates and excluding back mutations. We discuss deviations for large mutation rates and including back mutations. For very large mutation rates, the optimum fitness landscape is flat and has a single peak at type B.     

Finite populations choose an optimal language

This paper studies the evolution of a proto-language in a finite population under the frequency-dependent Moran process. A proto-language can be seen as a collection of concept-to-sign mappings. An efficient proto-language is a bijective mapping from objects of communication to used signs and vice versa. Based on the comparison of fixation probabilities, a method for deriving conditions of evolutionary stability in a finite population [Nowak et al., 2004. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, 246-650], it is shown that efficient proto-languages are the only strategies that are protected by selection, which means that no mutant strategy can have a fixation probability that is greater than the inverse population size. In passing, the paper provides interesting results about the comparison of fixation probabilities as well as Maynard Smith's notion of evolutionary stability for finite populations [Maynard Smith, 1988. Can a mixed strategy be stable in a finite population? J. Theor. Biol. 130, 247-251] that are generally true for games with a symmetric payoff function.     

A novel analytical method for evolutionary graph theory problems

Evolutionary graph theory studies the evolutionary dynamics of populations structured on graphs. A central problem is determining the probability that a small number of mutants overtake a population. Currently, Monte Carlo simulations are used for estimating such fixation probabilities on general directed graphs, since no good analytical methods exist. In this paper, we introduce a novel deterministic framework for computing fixation probabilities for strongly connected, directed, weighted evolutionary graphs under neutral drift. We show how this framework can also be used to calculate the expected number of mutants at a given time step (even if we relax the assumption that the graph is strongly connected), how it can extend to other related models (e.g. voter model), how our framework can provide non-trivial bounds for fixation probability in the case of an advantageous mutant, and how it can be used to find a non-trivial lower bound on the mean time to fixation. We provide various experimental results determining fixation probabilities and expected number of mutants on different graphs. Among these, we show that our method consistently outperforms Monte Carlo simulations in speed by several orders of magnitude. Finally we show how our approach can provide insight into synaptic competition in neurology.     

Finite Element Analysis of Minimal Invasive Transforaminal Lumbar Interbody Fusion

The purpose of our study is to develop and validate three-dimensional finite element models of transforaminal lumbar interbody fusion, and explore the most appropriate method of fixation and fusion by comparing biomechanical characteristics of different fixation method. We developed four fusion models: bilateral pedicle screws fixation with a single cage insertion model (A), bilateral pedicle screws fixation with two cages insertion model (B), unilateral pedicle screws fixation with a single cage insertion model (C), and unilateral pedicle screws fixation with two cages insertion model (D); the models were subjected to different forces including anterior bending, posterior extension, left bending, right bending, rotation, and axial compressive. The von Mises stress of the fusion segments on the pedicle screw and cages was recorded. Angular variation and stress of pedicle screw and cage were compared. There were differences of Von Mises peak stress among four models, but were within the range of maximum force. The angular variation in A, B, C, and D decreased significantly compared with normal. There was no significant difference of angular variation between A and B, and C and D. Bilateral pedicle screws fixation had more superior biomechanics than unilateral pedicle screws fixation. In conclusion, the lumbar interbody fusion models were established using varying fixation methods, and the results verified that unilateral pedicle screws fixation with a single cage could meet the stability demand in minimal invasive transforaminal interbody fusion.     

The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population

We study fixation probabilities and times as a consequence of neutral genetic drift in subdivided populations, motivated by a model of the cultural evolutionary process of language change that is described by the same mathematics as the biological process. We focus on the growth of fixation times with the number of subpopulations, and variation of fixation probabilities and times with initial distributions of mutants. A general formula for the fixation probability for arbitrary initial condition is derived by extending a duality relation between forwards- and backwards-time properties of the model from a panmictic to a subdivided population. From this we obtain new formulae(formally exact in the limit of extremely weak migration) for the mean fixation time from an arbitrary initial condition for Wright's island model, presenting two cases as examples. For more general models of population subdivision, formulae are introduced for an arbitrary number of mutants that are randomly located, and a single mutant whose position is known. These formulae contain parameters that typically have to be obtained numerically, a procedure we follow for two contrasting clustered models. These data suggest that variation of fixation time with the initial condition is slight, but depends strongly on the nature of subdivision. In particular, we demonstrate conditions under which the fixation time remains finite even in the limit of an infinite number of demes. In many cases-except this last where fixation in a finite time is seen--the time to fixation is shown to be in precise agreement with predictions from formulae for the asymptotic effective population size.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Chromosomal evolution of elements B and C in the Sophophora subgenus of Drosophila: evolutionary rate and polymorphism

The locations of 77 markers along the chromosomal elements B (41 markers) and C (36 markers) of Drosophila subobscura, D. pseudoobscura, and D. melanogaster were obtained by in situ hybridization on polytene chromosomes. In comparisons between D. subobscura and D. pseudoobscura, 10 conserved segments (accounting for 32% of the chromosomal length) were detected on element B and eight (17% of the chromosomal length) on element C. The fixation rate of paracentric inversions inferred by a maximum likelihood approach differs significantly between elements. Muller's element C (0.17 breakpoints/Mb/million years) is evolving two times faster than element B (0.08 breakpoints/Mb/million years). This difference in the evolutionary rate is paralleled by differences in the extent of chromosomal polymorphism in the corresponding lineages. Element C is highly polymorphic in D. subobscura, D. pseudoobscura, and in other obscura group species such as D. obscura and D. athabasca. In contrast, the level of polymorphism in element B is much lower in these species. The fixation rates of paracentric inversions estimated in the present study between species of the Sophophora subgenus are the highest estimates so far reported in the genus for the autosomes. At the subgenus level, there is also a parallelism between the high fixation rate and the classical observation that the species of the Sophophora subgenus tend to be more polymorphic than the species of the Drosophila subgenus. Therefore, the detected relationship between level of polymorphism and evolutionary rate might be a general characteristic of chromosomal evolution in the genus Drosophila.     

Cellular effects and epistasis among three determinants of adaptation in experimental populations of Saccharomyces cerevisiae

Epistatic interactions in which the phenotypic effect of an allele is conditional on its genetic background have been shown to play a central part in various evolutionary processes. In a previous study (J. B. Anderson et al., Curr. Biol. 20:1383-1388, 2010; J. R. Dettman, C. Sirjusingh, L. M. Kohn, and J. B. Anderson, Nature 447:585-588, 2007), beginning with a common ancestor, we identified three determinants of fitness as mutant alleles (each designated with the letter "e") that arose in replicate Saccharomyces cerevisiae populations propagated in two different environments, a low-glucose and a high-salt environment. In a low-glucose environment, MDS3e and MKT1e interacted positively to confer a fitness advantage. Also, PMA1e from a high-salt environment interacted negatively with MKT1e in a low-glucose environment, an example of a Dobzhansky-Muller incompatibility that confers reproductive isolation. Here we showed that the negative interaction between PMA1e and MKT1e is mediated by alterations in intracellular pH, while the positive interaction between MDS3e and MKT1e is mediated by changes in gene expression affecting glucose transporter genes. We specifically addressed the evolutionary significance of the positive interaction by showing that the presence of the MDS3 mutation is a necessary condition for the spread and fixation of the new mutations at the identical site in MKT1. The expected mutations in MKT1 rose to high frequencies in two of three experimental populations carrying MDS3e but not in any of three populations carrying the ancestral allele. These data show how positive and negative epistasis can contribute to adaptation and reproductive isolation.     

Molecular evolution of theSaccharomyces cerevisiae histone gene loci

Summary The core histone genes ofSaccharomyces cerevisiae are arranged as duplicate nonallelic sets of specifically paired genes. The identity of structural organization between the duplicated gene pairs would have its simplest evolutionary origin in the duplication of a complete locus in a single event. In such a case, the time since the duplication of one of the genes should be identical to that since duplication of the gene adjacent to it on the chromosome. A calculation of the evolutionary distances between the coding DNA sequences of the histone genes leads to a duplication paradox: The extents of sequence divergence in the silent component of third-base positions for adjacent pairs of genes are not identical. Estimates of the evolutionary distance between the two H3-H4 noncoding intergene DNA sequences are large; the divergence between the two separate sequences is indistinguishable from the divergence between either of the regions and a randomly generated permutation of itself. These results suggest that the duplication event may have occurred much earlier than previously estimated. The potential age of the duplication, and the attractive simplicity of the duplication of both the H3-H4 and the H2A-H2B gene pairs having taken place in a single event, leads to the hypothesis that modern haploidS. cerevisiae may have evolved by diploidization or fusion of two ancient fungi.     

Stochastic evolutionary dynamics on two levels

We consider a population that is subdivided into groups. Individuals reproduce proportional to their fitness. When a group reaches a certain size it has a probability to split into two groups while another group is eliminated. In this stochastic process, the number of groups is constant, while the total population size fluctuates between well-defined bounds. We calculate the fixation probability of newly introduced mutants under constant selection. We show that the described population structure acts as a suppressor of selection compared to an unstructured population of the same size. The maximum suppression of selection is obtained, when the number of groups equals the number of individuals per group. We also study opposing selection on two or more levels by analysing the evolutionary dynamics of hierarchically embedded Moran processes.     

Tissue-specific co-expression and in vitro heteropolymer formation of the two small branchiostoma intermediate filament proteins A3 and B2

The two small intermediate filament (IF) proteins A3 and B2 of the cephalochordate Amphioxus were investigated. Blot overlays indicated a heterotypic interaction pattern of the recombinant proteins. While the individual proteins formed only aggregates, the stoichiometric mixture formed obligatory heteropolymeric filaments. Mutant proteins with a single cysteine residue in equivalent positions gave rise to filaments that oxidize to the disulfide-linked heterodimer, which can again form IF. Thus the A3/B2 filaments, which are expressed in the intestinal epithelium, are based on a hetero coiled coil. This keratin-like assembly process of A3 plus B2 was unexpected, since previous evolutionary tree calculations performed by two laboratories on the various Amphioxus IF proteins identified keratin I and II orthologs but left the A/B group as a separate branch. We discuss obvious evolutionary aspects of the Amphioxus IF multigene family, including the previously made observation that B1, the closest relative of B2, forms homopolymeric IF in vitro and is, like vertebrate type III proteins, expressed in mesodermally derived tissues.     

Successive waves of fixation of B1 variants in rodent lineage history

Summary A new method of analyzing phylogenetic relations among members of sequence family (Quentin 1988) discriminates at least six possible B1 subfamilies in the mouse genome. Several additional and independent observations suggest that these grouping have evolutionary significance, and that successive waves of fixation of new variants occur during rodent lineage history. We have reason to believe that, in a genome, the founder sequences of different families of retroposons are in competition with regard to the amplification/fixation process.     

Rapid evolutionary escape by large populations from local fitness peaks is likely in nature

Fitness interactions between loci in the genome, or epistasis, can result in mutations that are individually deleterious but jointly beneficial. Such epistasis gives rise to multiple peaks on the genotypic fitness landscape. The problem of evolutionary escape from such local peaks has been a central problem of evolutionary genetics for at least 75 years. Much attention has focused on models of small populations, in which the sequential fixation of valley genotypes carrying individually deleterious mutations operates most quickly owing to genetic drift. However, valley genotypes can also be subject to mutation while transiently segregating, giving rise to copies of the high fitness escape genotype carrying the jointly beneficial mutations. In the absence of genetic recombination, these mutations may then fix simultaneously. The time for this process declines sharply with increasing population size, and it eventually comes to dominate evolutionary behavior. Here we develop an analytic expression for N(crit), the critical population size that defines the boundary between these regimes, which shows that both are likely to operate in nature. Frequent recombination may disrupt high-fitness escape genotypes produced in populations larger than N(crit) before they reach fixation, defining a third regime whose rate again slows with increasing population size. We develop a novel expression for this critical recombination rate, which shows that in large populations the simultaneous fixation of mutations that are beneficial only jointly is unlikely to be disrupted by genetic recombination if their map distance is on the order of the size of single genes. Thus, counterintuitively, mass selection alone offers a biologically realistic resolution to the problem of evolutionary escape from local fitness peaks in natural populations.     

Fixation probabilities for the Moran process in evolutionary games with two strategies: graph shapes and large population asymptotics

This paper is based on the complete classification of evolutionary scenarios for the Moran process with two strategies given by Taylor et al. (Bull Math Biol 66(6):1621–1644, 2004. https://doi.org/10.1016/j.bulm.2004.03.004). Their classification is based on whether each strategy is a Nash equilibrium and whether the fixation probability for a single individual of each strategy is larger or smaller than its value for neutral evolution. We improve on this analysis by showing that each evolutionary scenario is characterized by a definite graph shape for the fixation probability function. A second class of results deals with the behavior of the fixation probability when the population size tends to infinity. We develop asymptotic formulae that approximate the fixation probability in this limit and conclude that some of the evolutionary scenarios cannot exist when the population size is large.

     

活跃连接下Wright-Fisher过程的演化动态

在活跃连接下讨论了2×2对称博弈中频率相依Wright-Fisher过程的演化动力学,得到弱选择下策略的固定概率.利用固定概率讨论囚徒困境与雪堆博弈的演化动态,给出促使合作行为的条件.最后对所得结果进行数值模拟,发现活跃连接可以有效地促进合作行为.     

Ecological public goods games: cooperation and bifurcation

The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.