A two-locus mutation—Selection model and some of its evolutionary implications

The deterministic properties of a two-locus model with mutation and selection have been investigated. The mutation process is unidirectional, and the model is so constructed that the genetic variation at one locus is selectively neutral in the absence of a mutant allele at the other locus. All genotypes with three or four mutant alleles are deleterious, while the double heterozygotes may have the same fitness as the standard genotype. If one of the mutant alleles becomes fixed in the population, then the other locus will show a regular one-locus mutation-selection balance. Such a boundary equilibrium may be unstable or stable in the full two-locus setting. In the symmetric case, which is analyzed in details, the population will either go to one of the two boundary equilibria, or to a fully polymorphic equilibrium at which both the mutant alleles are rare. The origin of reproductive separation between two populations via the fixation of complementary deleterious mutants at different loci, and the fixation of nonfunctional alleles at duplicated loci, are two biological processes which both can be studied with the present model. In the last part of the paper we show how the results from the deterministic analysis can be used to predict how different factors will influence the rates of evolution in these systems.     

Multilocus self-recognition systems in fungi as a cause of trans-species polymorphism

Trans-species polymorphism, meaning the presence of alleles in different species that are more similar to each other than they are to alleles in the same species, has been found at loci associated with vegetative incompatibility in filamentous fungi. If individuals differ at one or more of these loci (termed het for heterokaryon), they cannot form stable heterokaryons after vegetative fusion. At the het-c locus in Neurospora crassa and related species there is clear evidence of trans-species polymorphism: three alleles have persisted for approximately 30 million years. We analyze a population genetic model of multilocus vegetative incompatibility and find the conditions under which trans-species polymorphism will occur. In the model, several unlinked loci determine the vegetative compatibility group (VCG) of an individual. Individuals of different VCGs fail to form productive heterokaryons, while those of the same VCG form viable heterokaryons. However, viable heterokaryon formation between individuals of the same VCG results in a loss in fitness, presumably via transfer of infectious agents by hyphal fusion or exploitation by aggressive genotypes. The result is a form of balancing selection on all loci affecting an individual's VCG. We analyze this model by making use of a Markov chain/strong selection, weak mutation (SSWM) approximation. We find that trans-species polymorphism of the type that has been found at the het-c locus is expected to occur only when the appearance of new incompatibility alleles is strongly constrained, because the rate of mutation to such alleles is very low, because the number of possible incompatibility alleles at each locus is restricted, or because the number of incompatibility loci is limited.     

The evolution of recombination in permanent translocation heterozygotes

The evolution of a selectively neutral locus that controls the degree to which alleles at a single selected locus are linked with a particular set of chromosomes in a permanent translocation heterozygote is studied. With complete selfing and fitness overdominance a new allele at the modifying locus will increase in frequency if it increases the linkage of all alleles at the selected locus to a particular set of chromosomes. With random mating a new allele at the modifying locus will increase when rare if it increases the linkage of alleles at the selected locus to a particular set of chromosomes. In addition, a parameter analogous to the coefficient of linkage disequilibrium in usual two-locus models with random mating must be nonzero if a new allele at the modifying locus is to increase in frequency at a geometric rate when rare. With mixed selfing and random mating a new allele at the modifying locus will apparently increase when rare only if it increases the linkage of alleles at the selected locus to a particular set of chromosomes.     

Identifying Signatures of Selection in Genetic Time Series

Both genetic drift and natural selection cause the frequencies of alleles in a population to vary over time. Discriminating between these two evolutionary forces, based on a time series of samples from a population, remains an outstanding problem with increasing relevance to modern data sets. Even in the idealized situation when the sampled locus is independent of all other loci, this problem is difficult to solve, especially when the size of the population from which the samples are drawn is unknown. A standard χ²-based likelihood-ratio test was previously proposed to address this problem. Here we show that the χ²-test of selection substantially underestimates the probability of type I error, leading to more false positives than indicated by its P-value, especially at stringent P-values. We introduce two methods to correct this bias. The empirical likelihood-ratio test (ELRT) rejects neutrality when the likelihood-ratio statistic falls in the tail of the empirical distribution obtained under the most likely neutral population size. The frequency increment test (FIT) rejects neutrality if the distribution of normalized allele-frequency increments exhibits a mean that deviates significantly from zero. We characterize the statistical power of these two tests for selection, and we apply them to three experimental data sets. We demonstrate that both ELRT and FIT have power to detect selection in practical parameter regimes, such as those encountered in microbial evolution experiments. Our analysis applies to a single diallelic locus, assumed independent of all other loci, which is most relevant to full-genome selection scans in sexual organisms, and also to evolution experiments in asexual organisms as long as clonal interference is weak. Different techniques will be required to detect selection in time series of cosegregating linked loci.     

Mathematical Modelling of Mycobacterium tuberculosis VNTR Loci Estimates a Very Slow Mutation Rate for the Repeats

Minisatellites are highly variable tandem repeats used for over 20 years in humans for DNA fingerprinting. In prokaryotes fingerprinting techniques exploiting VNTR (variable number of tandem repeats) polymorphisms have become widely used recently in bacterial typing. However although many investigations into the mechanisms underlying minisatellite variation in humans have been performed, relatively little is known about the processes that mediate bacterial minisatellite polymorphism. An understanding of this is important since it will influence how the results from VNTR experiments are interpreted. The minisatellites of Mycobacterium tuberculosis are well characterized since they are some of the few polymorphic loci in what is otherwise a very homogeneous organism. Using VNTR results from a well-defined and characterized set of M. tuberculosis strains we show that the repeats at a locus are likely to evolve by stepwise contraction or expansion in the number of repeats. A stochastic continuous-time population mathematical model was developed to simulate the evolution of the repeats. This allowed estimation of the tendency of the repeats to increase or decrease and the rate at which they change. The majority of loci tend to lose rather than gain repeats. All of the loci mutate extremely slowly, with an average rate of 2.3 x 10(-8), which is 350 times slower than that of a set of VNTR repeats with similar diversity observed experimentally in Escherichia coli. This suggests that the VNTR profile of a strain of M. tuberculosis will be indicative of its clonal lineage and will be unlikely to vary in epidemiologically-related strains.     

Evolutionary consequences of asymmetric dispersal rates

We study the consequences of asymmetric dispersal rates (e.g., due to wind or current) for adaptive evolution in a system of two habitat patches. Asymmetric dispersal rates can lead to overcrowding of the "downstream" habitat, resulting in a source-sink population structure in the absence of intrinsic quality differences between habitats or can even cause an intrinsically better habitat to function as a sink. Source-sink population structure due to asymmetric dispersal rates has similar consequences for adaptive evolution as a source-sink structure due to habitat quality differences: natural selection tends to be biased toward the source habitat. We demonstrate this for two models of adaptive evolution: invasion of a rare allele that improves fitness in one habitat but reduces it in the other and antagonistic selection on a quantitative trait determined by five additive loci. If a habitat can sustain a population without immigration, the conditions for adaptation to that habitat are most favorable if there is little or no immigration from the other habitat; the influence of emigration depends on the magnitude of the allelic effects involved and other parameters. If, however, the population is initially unable to persist in a given habitat without immigration, our model predicts that the population will be most likely to adapt to that habitat if the dispersal rates in both directions are high. Our results highlight the general message that the effect of gene flow upon local adaptation should depend profoundly on the demographic context of selection.     

ON EVOLUTION UNDER SEXUAL AND VIABILITY SELECTION: A TWO-LOCUS DIPLOID MODEL

A two-locus diploid model of sexual selection is presented in which the two loci govern, respectively, a trait limited in expression in one sex (generally male) and the mating preferences of the other sex (generally female). The viability of a male depends on its genotype at the trait locus. In contrast, all females are equally viable and all individuals are equally fertile with respect to the two loci. Near fixation at both loci, evolution at the mating locus is neutral and hence a new mating preference allele will increase only through random genetic drift or through a correlated response to the increase of a new advantageous trait allele. If, however, a polymorphism is already maintained at the trait locus through overdominance in fitness then the increase of a rare preference allele depends only on the recombination rate between the loci and not on the new preference scheme.     

Linkage analysis of a cluster-based quantitative phenotype constructed from pulmonary function test data in 27 multigenerational families with multiple asthmatic members

OBJECTIVE: To identify genes involved in phenotypes that increase one's risk for developing asthma, a complex disease that is likely genetically heterogeneous. Unlike other approaches to locus discovery in the presence of heterogeneity, this method seeks loci that segregate in all or most ascertained families while recognizing that other genes and environmental factors that modify the action of the common gene may vary across families. METHODS: The method is based on seeking groups of families that differ, between groups, in the way affected individuals express the genotype. Then we use the distance of each individual to the cluster center for his family to define a quantitative trait. This quantitative trait is then subjected to a genome scan using variance components methods. RESULTS: The method is applied to a data set of 27 multigenerational families with asthma, and a novel locus at 2q33 (at 210 cM) is identified. CONCLUSIONS: The proposed method has the potential to identify loci near genes that increase risk for asthma related phenotypes. The method could be used for other complex disorders that exhibit locus heterogeneity.     

ON THE INSTABILITY OF POLYGENIC SEX DETERMINATION: THE EFFECT OF SEX-SPECIFIC SELECTION

A combination of analytical and simulation models is used to explore the initial evolution of genic sex determination from polygenic sex determination. Prior studies have indicated that polygenic sex determination is rare or absent in extant species but that it has likely played an important intermediate role in the evolution of other genetic sex-determination systems. This study explores why polygenic sex determination does not persist. Two possibilities are considered. First it is assumed that a major sex-determining gene also pleiotropically increases fitness. Second it is assumed that the sex-determining gene is neutral but linked to another locus segregating for a rare selectively favored allele. The major conclusion from the models is that sex-specific natural selection will cause polygenic sex determination to be a transient state in most populations. Polygenic sex determination may be an important intermediate step in the evolution of genetically controlled sexual differentiation, but it is unlikely to persist unless there is some selective advantage compared to genic sex determination. This may in part explain the relatively small number of extant species that have polygenic sex determination.     

GENETIC CONSEQUENCES OF RARITY IN ASTER FURCATUS (ASTERACEAE), A THREATENED,SELF-INCOMPATIBLE PLANT

Aster furcatus is a rare, self-incompatible plant with fewer than 50 known populations throughout its range. We verified self-incompatibility in A. furcatus by conducting experimental self- and cross-pollinations and by examining seed set in a small population comprised of a single clonal genet. We examined variation at 22 electrophoretic loci in 23 populations of A. furcatus from across its range in Wisconsin, Illinois, Indiana, and Missouri. Except for two rare alleles found in single individuals in three populations, all loci but one of those examined were fixed for single alleles. The only variable locus (triosephosphate isomerase, TPI-1) tended to exhibit genotype frequencies in Hardy-Weinberg equilibrium or with a slight excess of heterozygotes. Although overall gene diversity was extremely low, TPI genotype frequencies were indicative of an outcrossing plant. We examined the subpopulation genetic structure among clonal plants within one Wisconsin population in greater detail. F statistics indicated that much of the genetic variation at the polymorphic TPI locus was due to differentiation among populations. We discuss the implications of self-incompatibility and low levels of genetic variation for the evolution and conservation of Aster furcatus and other rare plants with similar breeding systems.     

Sex ratio and gamete size across eastern North America in Dictyostelium discoideum,a social amoeba with three sexes

Theory indicates that numbers of mating types should tend towards infinity or remain at two. The social amoeba, Dictyostelium discoideum, however, has three mating types. It is therefore a mystery how this species has broken the threshold of two mating types, but has not increased towards a much higher number. Frequency‐dependent selection on rare types in combination with isogamy, a form of reproduction involving gametes similar in size, could explain the evolution of multiple mating types in this system. Other factors, such as drift, may be preventing the evolution of more than three. We first looked for evidence of isogamy by measuring gamete size associated with each type. We found no evidence of size dissimilarities between gametes. We then looked for evidence of balancing selection, by examining mating type distributions in natural populations and comparing genetic differentiation at the mating type locus to that at more neutral loci. We found that mating type frequency varied among the three populations we examined, with only one of the three showing an even sex ratio, which does not support balancing selection. However, we found more population structure at neutral loci than the mating type locus, suggesting that the three mating types are indeed maintained at intermediate frequencies by balancing selection. Overall, the data are consistent with balancing selection acting on D. discoideum mating types, but with a sufficiently weak rare sex advantage to allow for drift, a potential explanation for why these amoebae have only three mating types.     

Molecular population genetics of male accessory gland proteins in the Drosophila simulans complex

Accessory gland proteins are a major component of Drosophila seminal fluid. These proteins have a variety of functions and may be subject to sexual selection and/or antagonistic evolution between the sexes. Most population genetic data from these proteins are from D. melanogaster and D. simulans. Here, we extend the population genetic analysis of Acp genes to the other simulans complex species, D. mauritiana and D. sechellia. We sequenced population samples of seven Acp's from D. mauritiana, D. sechellia, and D. simulans. We investigated the population genetics of these genes on individual simulans complex lineages and compared Acp polymorphism and divergence to polymorphism and divergence from a set of non-Acp loci in the same species. Polymorphism and divergence data from the simulans complex revealed little evidence for adaptive protein evolution at individual loci. However, we observed a dramatically inflated index of dispersion for amino acid substitutions in the simulans complex at Acp genes, but not at non-Acp genes. This pattern of episodic bursts of protein evolution in Acp's provides the strongest evidence to date that the population genetic mechanisms driving Acp divergence are different from the mechanisms driving evolution at most Drosophila genes.     

Characteristics of loci and individuals are associated with germline microsatellite mutation rates in lesser kestrels (Falco naumanni)

Although microsatellites are one of the most popular tools in genetic studies, their mutational dynamics and evolution remain unclear. Here, we apply extensive pedigree genotyping to identify and analyze the patterns and factors associated with de novo germline mutations across nine microsatellite loci in a wild population of lesser kestrels (Falco naumanni). A total of 10 germline mutations events were unambiguously identified in four loci, yielding an average mutation rate of 2.96x10(-3). Across loci, mutation rate was positively correlated with locus variability and average allele size. Mutations were primarily compatible with a stepwise mutation model, although not exclusively involved single-step changes. Unexpectedly, we found an excess of maternally transmitted mutations (male-to-female ratio of 0.1). One of the analyzed loci (Fn2.14) resulted hypermutable (mutation rate=0.87%). This locus showed a size-dependent mutation bias, with longer alleles displaying deletions or additions of a small number of repeat than shorter alleles. Mutation probability at Fn2.14 was higher for females and increased with parental (maternal) age but was not associated with individual physical condition, multilocus heterozygosity, allele length or allele span. Overall, our results do not support the male-biased mutation rate described in other organisms and suggest that mutation dynamics at microsatellite loci are a complex process which requires further research.     

The evolutionary dynamics of direct phenotypic overdominance: emergence possible, loss probable

An evolutionary dynamical system with explicit diploid genetics is used to investigate the likelihood of observing phenotypically overdominant heterozygotes versus heterozygous phenotypes that are intermediate between the homozygotes. In this model, body size evolves in a population with discrete demographic episodes and with competition limiting reproduction. A genotype-phenotype map for body size is used that can generate the two qualitative types of dominance interactions (overdominance versus intermediate dominance). It is written as a single-locus model with one focal locus and parameters summarizing the effects of alleles at other loci. Two types of evolutionarily stable strategy (ESS; continuously stable strategy, CSS) occur. The ESS is generated either (1) by the population ecology; or (2) by a local maximum of the genotype-phenotype map. Overdominant heterozygotes are expected to arise if the population evolves toward the second type of ESS, where nearly maximum body sizes are found. When other loci with partially dominant inheritance also evolve, the location of the maximum in the genotype-phenotype map repeatedly changes. It is unlikely that an evolving population will track these changes; ESSs of the second type now are at best quasi-stationary states of the evolutionary dynamics. Considering the restrictions on its probability, a pattern of phenotypic overdominance is expected to be rare.     

MicNeSs: genotyping microsatellite loci from a collection of (NGS) reads

Microsatellites are widely used in population genetics to uncover recent evolutionary events. They are typically genotyped using capillary sequencer, which capacity is usually limited to 9, at most 12 loci for each run, and which analysis is a tedious task that is performed by hand. With the rise of next‐generation sequencing (NGS), a much larger number of loci and individuals are available from sequencing: for example, on a single run of a GS Junior, 28 loci from 96 individuals are sequenced with a 30X cover. We have developed an algorithm to automatically and efficiently genotype microsatellites from a collection of reads sorted by individual (e.g. specific PCR amplifications of a locus or a collection of reads that encompass a locus of interest). As the sequencing and the PCR amplification introduce artefactual insertions or deletions, the set of reads from a single microsatellite allele shows several length variants. The algorithm infers, without alignment, the true unknown allele(s) of each individual from the observed distributions of microsatellites length of all individuals. MicNeSs, a python implementation of the algorithm, can be used to genotype any microsatellite locus from any organism and has been tested on 454 pyrosequencing data of several loci from fruit flies (a model species) and red deers (a nonmodel species). Without any parallelization, it automatically genotypes 22 loci from 441 individuals in 11 hours on a standard computer. The comparison of MicNeSs inferences to the standard method shows an excellent agreement, with some differences illustrating the pros and cons of both methods.     

Lower-than-expected linkage disequilibrium between tightly linked markers in humans suggests a role for gene conversion

Understanding the pattern of linkage disequilibrium (LD) in the human genome is important both for successful implementation of disease-gene mapping approaches and for inferences about human demographic histories. Previous studies have examined LD between loci within single genes or confined genomic regions, which may not be representative of the genome; between loci separated by large distances, where little LD is seen; or in population groups that differ from one study to the next. We measured LD in a large set of locus pairs distributed throughout the genome, with loci within each pair separated by short distances (average 124 bp). Given current models of the history of the human population, nearly all pairs of loci at such short distances would be expected to show complete LD as a consequence of lack of recombination in the short interval. Contrary to this expectation, a significant fraction of pairs showed incomplete LD. A standard model of recombination applied to these data leads to an estimate of effective human population size of 110,000. This estimate is an order of magnitude higher than most estimates based on nucleotide diversity. The most likely explanation of this discrepancy is that gene conversion increases the apparent rate of recombination between nearby loci.     

A simple model of co-evolutionary dynamics caused by epistatic selection

Epistasis is the dependency of the effect of a mutation on the genetic background in which it occurs. Epistasis has been widely documented and implicated in the evolution of species barriers and the evolution of genetic architecture. Here we propose a simple model to formalize the idea that epistasis can also lead to co-evolutionary patterns in molecular evolution of interacting genes. This model epistasis is represented by the influence of one gene substitution on the fitness rank of the resident allele at another locus. We assume that increasing or decreasing fitness rank occur equally likely. In simulations we show that this form of epistasis leads to co-evolution in the sense that the length of an adaptive walk between interacting loci is highly correlated. This effect is caused by episodes of elevated rate of evolution in both loci simultaneously. We find that the influence of epistasis on these measures of co-evolutionary dynamics is relatively robust to the details of the model. The main factor influencing the correlation in evolutionary rates is the probability that a substitution will have an epistatic effect, but the strength of epistasis or the asymmetry of the initial fitness ranks of the alleles have only a minor effect. We suggest that covariance in rates of evolution among loci could be used to detect epistasis among loci.     

Speciation: more likely through a genetic or through a learned habitat preference?

A problem in understanding sympatric speciation is establishing how reproductive isolation can arise when there is disruptive selection on an ecological trait. One of the solutions that has been proposed is that a habitat preference evolves, and that mates are chosen within the preferred habitat. We present a model where the habitat preference can evolve either by means of a genetic mechanism or by means of learning. Employing an adaptive-dynamical analysis, we show that evolution proceeds either to a single population of specialists with a genetic preference for their optimal habitat, or to a population of generalists without a habitat preference. The generalist population subsequently experiences disruptive selection. Learning promotes speciation because it increases the intensity of disruptive selection. An individual-based version of the model shows that, when loci are completely unlinked and learning confers little cost, the presence of disruptive selection most probably leads to speciation via the simultaneous evolution of a learned habitat preference. For high costs of learning, speciation is most likely to occur via the evolution of a genetic habitat preference. However, the latter only happens when the effect of mutations is large, or when there is linkage between genes coding for the different traits.