Limits to adaptation in asexual populations

In asexual populations, the rate of adaptation is basically limited by the frequency and properties of spontaneous beneficial mutations. Hence, knowledge of these mutational properties and how they are affected by particular evolutionary conditions is a precondition for understanding the process of adaptation. Here, we address how the rate of adaptation of asexual populations is limited by its population size and mutation rate, as well as by two factors affecting the fraction of mutations that confer a benefit, i.e. the initial adaptedness of the population and the variability of the environment. These factors both influence which mutations are likely to occur, as well as the probability that they will ultimately contribute to adaptation. We attempt to separate the consequences of these basic population features in terms of their effect on the rate of adaptation by using results from evolution experiments with microorganisms.     

Genetic covariance structure of growth in the salamander Ambystoma macrodactylum

The size of an organism at any point during ontogeny often has fitness consequences through either direct selection on size or through selection on size-related morphological, performance, or life history traits. However, the evolutionary response to selection on size across ontogeny (a growth trajectory) may be limited by genetic correlations across ages. Here we characterize the phenotypic and genetic covariance structure of length and mass growth trajectories in a natural population of larval Ambystoma macrodactylum using function-valued quantitative genetic analyses and principal component decomposition. Most of the phenotypic and genetic variation in both growth trajectories appears to be confined to a single principal component describing a pattern of positive covariation among sizes across all ages. Higher order principal components with no significant associated genetic variation were identified for both trajectories, suggesting that evolution towards certain patterns of negative covariation between sizes across ages is constrained. The well-characterized positive relationship between size at metamorphosis and fitness in pond-breeding amphibians predicts that the across-age covariance structure will strongly limit evolution only if there is negative selection on size prior to metamorphosis. The pattern of genetic covariation observed in this study is similar to that observed in other vertebrate taxa, indicating that size may often be highly genetically and phenotypically integrated across ontogeny. Additionally, we find that phenotypic and genetic analyses of growth trajectories can yield qualitatively similar patterns of covariance structure.     

The parasite capacity of the host population

The estimation of parasitic pressure on the host populations is frequently required in parasitological investigations. The empirical values of prevalence of infection are used for this, however the latter one as an estimation of parasitic pressure on the host population is insufficient. For example, the same prevalence of infection can be insignificant for the population with high reproductive potential and excessive for the population with the low reproductive potential. Therefore the development of methods of an estimation of the parasitic pressure on the population, which take into account the features the host population, is necessary. Appropriate parameters are to be independent on view of the researcher, have a clear biological sense and be based on easily available characteristics. The methods of estimation of parasitic pressure on the host at the organism level are based on various individual viability parameters: longevity, resistance to difficult environment etc. The natural development of this approach for population level is the analysis of viability parameters of groups, namely, the changing of extinction probability of host population under the influence of parasites. Obviously, some critical values of prevalence of infection should exist; above theme the host population dies out. Therefore the heaviest prevalence of infection, at which the probability of host population size decreases during the some period is less than probability of that increases or preserves, can serve as an indicator of permissible parasitic pressure on the host population. For its designation the term "parasite capacity of the host population" is proposed. The real parasitic pressure on the host population should be estimated on the comparison with its parasite capacity. Parasite capacity of the host population is the heaviest possible prevalence of infection, at which, with the generation number T approaching infinity, there exists at least one initial population size ni(0) for which the probability of size decrease through T generations is less than the probability of its increase. [formula: see text] The estimation of the probabilities of host population size changes is necessary for the parasite capacity determination. The classical methods for the estimation of extinction probability of population are unsuitable in this case, as these methods require the knowledge of population growth rates and their variances for all possible population sizes. Thus, the development methods of estimate of extinction probability of population, based on the using of available parameters (sex ratio, fecundity, mortality, prevalence of infection PI) is necessary. The population size change can be considered as the Markov process. The probabilities of all changes of population size for a generation in this case are described by a matrix of transition probabilities of Markov process (pi) with dimensions Nmax x Nmax (maximum population size). The probabilities of all possible size changes for T generations can be calculated as pi T. Analyzing the behaviour matrix of transition at various prevalence of infection, it is possible to determine the parasite capacity of the host population. In constructing of the matrix of transition probabilities, should to be taken into account the features the host population and the influence of parasites on its reproductive potential. The set of the possible population size at a generation corresponds to each initial population size. The transition probabilities for the possible population sizes at a generation can be approximated to the binomial distribution. The possible population sizes at a generation nj(t + 1) can be calculated as sums of the number of survived parents N1 and posterities N2; their probabilities--as P(N1) x P(N2). The probabilities of equal sums N1 + N2 and nj(t + 1) > or = Nmax are added. The number of survived parents N1 may range from 0 to (1-PI) x ni(t). The survival probabilities can be estimated for each N1 as [formula: see text] The number of survived posterities N2 may range from 0 to N2max (the maximum number of posterities). N2max is [formula: see text] and the survival probabilities for each N2, is defined as [formula: see text] where [formula: see text], ni(t) is the initial population size (including of males and infected specimens of host), PI is the prevalence of infection, Q1 is the survival probabilities of parents, Pfemales is the frequency of females in the host population, K is the number of posterities per a female, and Q2 is the survival probabilities of posterities. When constructing matrix of transition probabilities of Markov process (pi), the procedure outlined above should be repeated for all possible initial population size. Matrix of transition probabilities for T generations is defined as pi T. This matrix (pi T) embodies all possible transition probabilities from the initial population sizes to the final population sizes and contains a wealth of information by itself. From the practical point of view, however, the plots of the probability of population size decrease are more suitable for analysis. They can be received by summing the probabilities within of lines of matrix from 0 to ni--1 (ni--the population size, which corresponds to the line of the matrix). Offered parameter has the number of advantages. Firstly, it is independent on a view of researcher. Secondly, it has a clear biological sense--this is a limit of prevalence, which is safe for host population. Thirdly, only available parameters are used in the calculation of parasite capacity: population size, sex ratio, fecundity, mortality. Lastly, with the availability of modern computers calculations do not make large labour. Drawbacks of this parameter: 1. The assumption that prevalence of infection, mortality, fecundity and sex ratio are constant in time (the situations are possible when the variability of this parameters can not be neglected); 2. The term "maximum population size" has no clear biological sense; 3. Objective restrictions exist for applications of this mathematical approach for populations with size, which exceeds 1000 specimens (huge quantity of computing operations--order Nmax 3*(T-1), work with very low probabilities). The further evolution of the proposed approach will allow to transfer from the probabilities of size changes of individual populations to be probabilities of size changes of population systems under the influence of parasites. This approach can be used at the epidemiology and in the conservation biology.     

Ecosystem size predicts the probability of speciation in migratory freshwater fish

Predicting speciation is a fundamental goal of research in evolutionary ecology. The probability of speciation is often positively correlated with ecosystem size. Although the mechanisms driving this correlation are generally difficult to identify, a shared geographical and ecological context provides a suitable condition to study the mechanisms that promote speciation in large ecosystems by reducing the number of factors to be considered. Here, we determined the correlation between speciation and ecosystem size, and discuss the underlying mechanisms of this relationship, using a probable parallel ecotype formation for freshwater fish. Our population genetic analysis revealed that speciation of the landlocked goby, Rhinogobius sp. YB, of the Ryukyu Archipelago, Japan, from its migratory ancestor, R. brunneus, occurred in parallel across five islands. Logistic regression analysis showed that speciation probability could be predicted using island size. The results suggest that ecosystem size predicts the occurrence of adaptation and reproductive isolation, probably through its association with three possible factors: divergent selection strength, population persistence, and occurrence probability of habitat separation.     

Constrained sex allocation in a parasitoid due to variation in male quality

The theory of constrained sex allocation posits that when a fraction of females in a haplodiploid population go unmated and thus produce only male offspring, mated females will evolve to lay a female-biased sex ratio. I examined evidence for constrained sex ratio evolution in the parasitic hymenopteran Uscana semifumipennis. Mated females in the laboratory produced more female-biased sex ratios than the sex ratio of adults hatching from field-collected eggs, consistent with constrained sex allocation theory. However, the male with whom a female mated affected her offspring sex ratio, even when sperm was successfully transferred, suggesting that constrained sex ratios can occur even in populations where all females succeed in mating. A positive relationship between sex ratio and fecundity indicates that females may become sperm-limited. Variation among males occurred even at low fecundity, however, suggesting that other factors may also be involved. Further, a quantitative genetic experiment found significant additive genetic variance in the population for the sex ratio of offspring produced by females. This has only rarely been demonstrated in a natural population of parasitoids, but is a necessary condition for sex ratio evolution. Finally, matings with larger males produced more female-biased offspring sex-ratios, suggesting positive selection on male size. Because the great majority of parasitic hymenoptera are monandrous, the finding of natural variation among males in their capacity to fertilize offspring, even after mating successfully, suggests that females may often be constrained in the sex allocation by inadequate number or quality of sperm transferred.     

Recombination Rate and Selection Strength in HIV Intra-patient Evolution

The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known. While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data. However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution. Yet, little is known about the distribution of selection differentials between individual viruses and the impact of single polymorphisms on viral fitness. Here, we estimate the rate of recombination and the distribution of selection coefficients from time series sequence data tracking the evolution of HIV within single patients. By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be ρ = 1.4±0.6×10⁻⁵ recombinations per site and generation. Furthermore, we provide evidence that the selection coefficients of at least 15% of the observed non-synonymous polymorphisms exceed 0.8% per generation. These results provide a basis for a more detailed understanding of the evolution of HIV. A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations. With the methods developed here, more precise and more detailed studies will be possible as soon as data with higher time resolution and greater sample sizes are available.     

The probability of parallel genetic evolution from standing genetic variation

Parallel evolution is often assumed to result from repeated adaptation to novel, yet ecologically similar, environments. Here, we develop and analyse a mathematical model that predicts the probability of parallel genetic evolution from standing genetic variation as a function of the strength of phenotypic selection and constraints imposed by genetic architecture. Our results show that the probability of parallel genetic evolution increases with the strength of natural selection and effective population size and is particularly likely to occur for genes with large phenotypic effects. Building on these results, we develop a Bayesian framework for estimating the strength of parallel phenotypic selection from genetic data. Using extensive individual‐based simulations, we show that our estimator is robust across a wide range of genetic and evolutionary scenarios and provides a useful tool for rigorously testing the hypothesis that parallel genetic evolution is the result of adaptive evolution. An important result that emerges from our analyses is that existing studies of parallel genetic evolution frequently rely on data that is insufficient for distinguishing between adaptive evolution and neutral evolution driven by random genetic drift. Overcoming this challenge will require sampling more populations and the inclusion of larger numbers of loci.     

Evolutionary rescue can prevent extinction following environmental change

The ubiquity of global change and its impacts on biodiversity poses a clear and urgent challenge for evolutionary biologists. In many cases, environmental change is so widespread and rapid that individuals can neither accommodate to them physiologically nor migrate to a more favourable site. Extinction will ensue unless the population adapts fast enough to counter the rate of decline. According to theory, whether populations can be rescued by evolution depends upon several crucial variables: population size, the supply of genetic variation, and the degree of maladaptation to the new environment. Using techniques in experimental evolution we tested the conditions for evolutionary rescue (ER). Hundreds of yeast populations were exposed to normally lethal concentrations of salt in conditions, where the frequency of rescue mutations was estimated and population size was manipulated. In a striking match with theory, we show that ER is possible, and that the recovery of the population may occur within 25 generations. We observed a clear threshold in population size for ER whereby the ancestral population size must be sufficiently large to counter stochastic extinction and contain resistant individuals. These results demonstrate that rapid evolution is an important component of the response of small populations to environmental change.     

Natural Selection for within-Generation Variance in Offspring Number

In this paper it is shown that natural selection can act on the within-generation variance in offspring number. The fitness of a genotype will increase as its variance in offspring number decreases. The intensity of selection on the variance component is inversely proportional to population size, although the fixation probability of a gene which differs from its allele only in the variance in its offspring number is independent of population size. The concept of effective population size is shown to be of limited use when there is genetic variation in the variance in offspring number.     

On some Markov models of certain interacting populations

We give a stochastic foundation to the Volterra prey-predator population in the following case. We take Volterra's predator equations and let a free host birth and death process support the evolution of the predator population. The purpose of this article is to present a rigorous population sample path construction of this interacted predator process and study the properties of this interacted process. The constructions yields a strong Markov process. The existence of steady-state distribution for the interacted predator process means the existence of equilibrium population level. We find a necessary and sufficient condition for the existence of a steady-state distribution. Next we see that if the host process possesses a steady-state distribution, so does the interacted predator process and this distribution satisfies a difference equation. For special choices of the auto death and interaction parametersa andb of the predator, whenever the host process visits the particular statea ^*=a/b the predator takes rest (saturates) from its evolution. We find the probability of asymptotic saturating of the predator.     

Existence of steady-state probability distributions in multilocus models for genotype evolution

It is shown that a representative Fisher-Wright model withn(≥3) diallelic loci admits a necessary condition for existence of a time-independent steady-state probability distribution. This necessary condition states that a global integral depending on the phenotype fitness functions of natural selection must be larger than a certain quantity depending on the parameters associated with genetic drift.     

Evolution of a species' range

Gene flow from the center of a species' range can stymie adaptation at the periphery and prevent the range from expanding outward. We study this process using simple models that track both demography and the evolution of a quantitative trait in a population that is continuously distributed in space. Stabilizing selection acts on the trait and favors an optimum phenotype that changes linearly across the habitat. One of three outcomes is possible: the species will become extinct, expand to fill all of the available habitat, or be confined to a limited range in which it is sufficiently adapted to allow population growth. When the environment changes rapidly in space, increased migration inhibits local adaptation and so decreases the species' total population size. Gene flow can cause enough maladaptation that the peripheral half of a species' range acts as a demographic sink. The trait's genetic variance has little effect on species persistence or the size of the range when gene flow is sufficiently strong to keep population densities far below the carrying capacity throughout the range, but it can increase the range width and population size of an abundant species. Under some conditions, a small parameter change can dramatically shift the balance between gene flow and local adaptation, allowing a species with a limited range to suddenly expand to fill all the available habitat.     

Quantitative genetics of growth and cryptic evolution of body size in an island population

While evolution occurs when selection acts on a heritable trait, empirical studies of natural systems have frequently reported phenotypic stasis under these conditions. We performed quantitative genetic analyses of weight and hindleg length in a free-living population of Soay sheep (Ovis aries) to test whether genetic constraints can explain previously reported stasis in body size despite evidence for strong positive directional selection. Genetic, maternal and environmental covariance structures were estimated across ontogeny using random regression animal models. Heritability increased with age for weight and hindleg length, though both measures of size were highly heritable across ontogeny. Genetic correlations among ages were generally strong and uniformly positive, and the covariance structures were also highly integrated across ontogeny. Consequently, we found no constraint to the evolution of larger size itself. Rather we expect size at all ages to increase in response to positive selection acting at any age. Consistent with expectation, predicted breeding values for age-specific size traits have increased over a twenty-year period, while maternal performance for offspring size has declined. Re-examination of the phenotypic data confirmed that sheep are not getting larger, but also showed that there are significant negative trends in size at all ages. The genetic evolution is therefore cryptic, with the response to selection presumably being masked at the phenotypic level by a plastic response to changing environmental conditions. Density-dependence, coupled with systematically increasing population size, may contribute to declining body size but is insufficient to completely explain it. Our results demonstrate that an increased understanding of the genetic basis of quantitative traits, and of how plasticity and microevolution can occur simultaneously, is necessary for developing predictive models of phenotypic change in nature.     

High mitochondrial and nuclear genetic diversity in one of the world’s most endangered seabirds,the Chatham Island Taiko (<Emphasis Type="Italic">Pterodroma magentae</Emphasis>)

Interpreting the levels of genetic diversity in organisms with diverse life and population histories can be difficult. The processes and mechanisms regulating this diversity are complex and still poorly understood. However, endangered species typically have low genetic variation as a consequence of the effects of genetic drift in small populations. In this study we examine genetic variation in the critically endangered Chatham Island Taiko (Tchaik, Pterodroma magentae), one of the world’s rarest seabirds. The Taiko has a very small population size of between 120 and 150 individuals, including just 8–15 breeding pairs. We report surprisingly high mitochondrial and nuclear genetic diversity in this critically endangered long-lived species. We hypothesise that the present Taiko population has retained a significant proportion of its past genetic diversity. However, it is also possible that undiscovered birds are breeding in unknown areas, which could increase the population size estimate. Importantly, from a conservation perspective, we show that the high level of variation is unlikely to be maintained in the future since chicks currently being born have only a limited number of the mitochondrial DNA haplotypes found in adults. Reduced genetic variation will mean that our ability to infer past events and the population history of Taiko using genetics could soon be lost and the power to determine, for example, parentage and other close order relationships will be diminished. Therefore, the maintenance of genetic diversity in future generations is an important consideration for conservation management of the Taiko.     

Genetic interference reduces the evolvability of modular and non-modular visual neural networks

The aim of this paper is to propose an interdisciplinary evolutionary connectionism approach for the study of the evolution of modularity. It is argued that neural networks as a model of the nervous system and genetic algorithms as simulative models of biological evolution would allow us to formulate a clear and operative definition of module and to simulate the different evolutionary scenarios proposed for the origin of modularity. I will present a recent model in which the evolution of primate cortical visual streams is possible starting from non-modular neural networks. Simulation results not only confirm the existence of the phenomenon of neural interference in non-modular network architectures but also, for the first time, reveal the existence of another kind of interference at the genetic level, i.e. genetic interference, a new population genetic mechanism that is independent from the network architecture. Our simulations clearly show that genetic interference reduces the evolvability of visual neural networks and sexual reproduction can at least partially solve the problem of genetic interference. Finally, it is shown that entrusting the task of finding the neural network architecture to evolution and that of finding the network connection weights to learning is a way to completely avoid the problem of genetic interference. On the basis of this evidence, it is possible to formulate a new hypothesis on the origin of structural modularity, and thus to overcome the traditional dichotomy between innatist and empiricist theories of mind.     

Density-Dependent Selection Incorporating Intraspecific Competition. II. a Diploid Model

A diploid model is introduced and analyzed in which intraspecific competition is incorporated within the context of density-regulated selection. It is assumed that each genotype has a unique carrying capacity corresponding to the equilibrium population size when only that type is present. Each genotypic fitness at a single diallelic autosomal locus is a decreasing function of a distinctive effective population size perceived as a result of intraspecific competition. The resulting fitnesses are both density and frequency dependent with selective advantage determined by a balance between genotypic carrying capacity and sensitivity to intraspecific competition. A major finding is that intergenotypic interactions may allow genetic variation to be more easily maintained than in the corresponding model of purely density-dependent selection. In addition, numerical study confirms the possible existence of multiple interior equilibria and that neither overdominance in fitness nor carrying capacity is necessary for stability. The magnitude of the equilibrium population size and optimization principles are also discussed.     

Demographic processes shaping genetic variation

Demographic processes modulate genome-wide levels and patterns of genetic variation via impacting effective population size independently of natural selection. Such processes include the perturbation of population distributions from external events shaping habitat landscape and internal factors shaping the probability of contemporaneous alleles in a population (coalescence). Several patterns have recently emerged: spatial and temporal heterogeneity in population structure have different influences on the persistence of new mutations and genetic variation, multi-locus analyses indicate that gene flow continues to occur during speciation and the incorporation of demographic processes into models of molecular evolution and association genetics approaches has improved statistical power to detect deviations from neutral-equilibrium expectations and decreased false positive rates.     

Parallel Genetic Evolution Within and Between Bacteriophage Species of Varying Degrees of Divergence

Parallel evolution is the acquisition of identical adaptive traits in independently evolving populations. Understanding whether the genetic changes underlying adaptation to a common selective environment are parallel within and between species is interesting because it sheds light on the degree of evolutionary constraints. If parallel evolution is perfect, then the implication is that forces such as functional constraints, epistasis, and pleiotropy play an important role in shaping the outcomes of adaptive evolution. In addition, population genetic theory predicts that the probability of parallel evolution will decline with an increase in the number of adaptive solutions—if a single adaptive solution exists, then parallel evolution will be observed among highly divergent species. For this reason, it is predicted that close relatives—which likely overlap more in the details of their adaptive solutions—will show more parallel evolution. By adapting three related bacteriophage species to a novel environment we find (1) a high rate of parallel genetic evolution at orthologous nucleotide and amino acid residues within species, (2) parallel beneficial mutations do not occur in a common order in which they fix or appear in an evolving population, (3) low rates of parallel evolution and convergent evolution between species, and (4) the probability of parallel and convergent evolution between species is strongly effected by divergence.     

Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.     

Impact of ancestral populations on postzygotic isolation in allopatric speciation

Postzygotic isolation evolves due to an accumulation of substitutions (potentially deleterious alleles in hybrids) in populations that have become geographically isolated. These potentially deleterious alleles might also be maintained in ancestral populations before geographic isolation. We used an individual-based model to examine the effect of the genetic state of an ancestral population on the evolution of postzygotic isolation after geographic isolation of a population. The results showed that the number of loci at which degenerative alleles are fixed in an ancestral population at equilibrium significantly affects the evolutionary rates of postzygotic isolation between descendant allopatric populations. Our results suggest that: (1) a severe decrease in population size (e.g., less than ten individuals) is not necessary for the rapid evolution of postzygotic isolation (e.g., <10,000 generation); (2) rapid speciation can occur when there is a large difference in the equilibrium number of accumulated degenerative alleles between ancestral and descendant populations; and (3) in an ancestral population maintained at a small effective population size for a long period of time, postzygotic isolation rarely evolves if back mutations that restore the function of degenerative alleles are limited.