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.     

Selective phenotyping for increased efficiency in genetic mapping studies

The power of a genetic mapping study depends on the heritability of the trait, the number of individuals included in the analysis, and the genetic dissimilarity among them. In experiments that involve microarrays or other complex physiological assays, phenotyping can be expensive and time-consuming and may impose limits on the sample size. A random selection of individuals may not provide sufficient power to detect linkage until a large sample size is reached. We present an algorithm for selecting a subset of individuals solely on the basis of genotype data that can achieve substantial improvements in sensitivity compared to a random sample of the same size. The selective phenotyping method involves preferentially selecting individuals to maximize their genotypic dissimilarity. Selective phenotyping is most effective when prior knowledge of genetic architecture allows us to focus on specific genetic regions. However, it can also provide modest improvements in efficiency when applied on a whole-genome basis. Importantly, selective phenotyping does not reduce the efficiency of mapping as compared to a random sample in regions that are not considered in the selection process. In contrast to selective genotyping, inferences based solely on a selectively phenotyped population of individuals are representative of the whole population. The substantial improvement introduced by selective phenotyping is particularly useful when phenotyping is difficult or costly and thus limits the sample size in a genetic mapping study.     

Genetic progression and the waiting time to cancer

Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of cancer is complex and that individual cancers may evolve through mutations in as many as 20 different cancer-associated genes. We use data published by Sjöblom et al. (2006) to develop a new mathematical model for the somatic evolution of colorectal cancers. We employ the Wright-Fisher process for exploring the basic parameters of this evolutionary process and derive an analytical approximation for the expected waiting time to the cancer phenotype. Our results highlight the relative importance of selection over both the size of the cell population at risk and the mutation rate. The model predicts that the observed genetic diversity of cancer genomes can arise under a normal mutation rate if the average selective advantage per mutation is on the order of 1%. Increased mutation rates due to genetic instability would allow even smaller selective advantages during tumorigenesis. The complexity of cancer progression can be understood as the result of multiple sequential mutations, each of which has a relatively small but positive effect on net cell growth.     

Sexuality in a natural population of bacteria–Bacillus subtilis challenges the clonal paradigm

Reproduction by binary fission necessarily establishes a clonal genotypic structure in bacterial populations unless a high rate of genetic recombination opposes it. Several genetic properties were examined for a wild population of Bacillus subtilis in the Sonoran Desert of Arizona to assess the extent of recombination in a natural population. These properties included allozyme variation revealed by multilocus enzyme electrophoresis, phage and antibiotic resistance, and restriction fragment length polymorphism with Southern hybridization. Evidence of extensive genetic recombination was found along with evidence of modest clonal structure. Recombination must be frequent relative to binary fission in this population. This mixed population structure provides broader options for bacterial evolution than would a purely clonal structure.     

A MODULAR FRAMEWORK CHARACTERIZES MICRO‐ AND MACROEVOLUTION OF OLD WORLD MONKEY DENTITIONS

The study of modularity can provide a foundation for integrating development into studies of phenotypic evolution. The dentition is an ideal phenotype for this as it is developmentally relatively simple, adaptively highly significant, and evolutionarily tractable through the fossil record. Here, we use phenotypic variation in the dentition to test a hypothesis about genetic modularity. Quantitative genetic analysis of size variation in the baboon dentition indicates a genetic modular framework corresponding to tooth type categories. We analyzed covariation within the dentitions of six species of Old World monkeys (OWMs) to assess the macroevolutionary extent of this framework: first by estimating variance–covariance matrices of linear tooth size, and second by performing a geometric morphometric (GM) analysis of tooth row shape. For both size and shape, we observe across OWMs a framework of anterior and postcanine modules, as well as submodularity between the molars and premolars. Our results of modularity by tooth type suggest that adult variation in the OWM dentition is influenced by early developmental processes such as odontogenesis and jaw patterning. This study presents a comparison of genotypic modules to phenotypic modules, which can be used to better understand their action across evolutionary time scales.     

Constraint and opportunity: the genetic basis and evolution of modularity in the cichlid mandible

Modular variation, whereby the relative degree of connectivity varies within a system, is thought to evolve through a process of selection that favors the integration of certain traits and the decoupling of others. In this way, modularity may facilitate the pace of evolution and determine evolvability. Alternatively, conserved patterns of modularity may act to constrain the rate and direction of evolution by preventing certain functions from evolving. A comprehensive understanding of the potential interplay between these phenomena will require knowledge of the inheritance and the genetic basis of modularity. Here we explore these ideas in the cichlid mandible by investigating patterns of modularity at the clade and species levels and through the introduction of a new approach, the individual level. Specifically, we assessed patterns of covariation in Lake Malawi cichlid species that employ alternate "biting" and "suction-feeding" modes of feeding and in a hybrid cross between these two ecotypes. Across the suction-feeding clade, patterns of modularity were largely conserved and reflected a functionally based pattern. In contrast, the biting species displayed a pattern of modularity that more closely matched developmental modules. The pattern of modularity present in our F2 population was very similar to the pattern exhibited by the biter, suggesting a role for dominant inheritance. We demonstrate that our individual-level metric of modularity (IMM) is a valid quantitative trait that has a nonlinear relationship with shape. IMMs for each model were used as quantitative characters to map quantitative trait loci (QTL) that underlie modularity. Our QTL analysis offers new insights into the genetic basis of modularity in these fishes that may eventually lead to the discovery of the genetic processes that delineate particular modules. In all, our findings suggest that modularity is both a constraining and an evolvable force in cichlid evolution, as distinct patterns occur between species and variation exists among individuals.     

The Wright-Fisher model with temporally varying selection and population size

The Wright-Fisher model is considered in the case where the population size is random and the magnitude of the selective advantage of one of the alleles varies with time. The central question addressed is the possibility of ultimate genetic polymorphism. Partial results are obtained in the general case and complete results in the case where the population size and selective advantage are not density dependent. Bounds on the fixation probability are obtained when the selective advantage is constant.     

The Impact of Random and Lineal Fission on the Genetic Divergence of Small Human Groups: A Case Study among the Yanomama

Most of the genetic divergence that currently separates populations of Homo sapiens must have arisen during that long period when the local village (or band) was the basic unit of biological evolution. Studies of tribally intact Amerindian groups exhibiting such small-group organization have demonstrated marked genetic divergence between nearby villages. Some of this genetic radiation can be attributed to the effects of random genetic drift over time within these small demes. Some of it, however, might be better ascribed to the consequences of nonrandom genetic assortment at the time of village fission, a recurring event for such groups. Even random genetic assortment at the time of fission would lead to some genetic divergence, due to the finite size of the parent gene pool. We term the genetic consequences of random assortment the random fission effect. Routinely, village fission occurs along family lines, leading to even greater genetic divergence between the daughter villages. We use the term lineal fission effect to describe the genetic consequences of nonrandom assortment and contrast these results with those derived from random assortment.——A formal treatment of random and lineal fission effects is developed, first for the single-locus case, then for the multiple-locus extension. Using this formulation, three Yanomama fission events were examined. Fission in the Yanomama often involves a great deal of mutual hostility between the two factions, so that subsequent gene flow between the two daughter villages is minimal. The first two examples are typical of the Yanomama behavior norm, and are accompanied by a minimum of subsequent gene flow between the daughter villages. In these two cases, the observed divergence values are very large and are also very unlikely under random fission. The lineal fission effect is pronounced. The net impact of lineal fission is to reduce the effective size of the village at the time of fission by a factor of four, relative to expectation from random fission. The third example, however, involved an unusually amicable split of a village, followed by free genetic exchange between the fission products. This "friendly fission" yields an observed divergence value not much in excess of the expectation from random fission.—The long-term consequences of such fission bottlenecks in effective population size are discussed for both intra- and inter-tribal genetic diversity. It appears that the rate of genetic divergence for tribal and subtribal groups may have been somewhat greater than would be expected from classical drift arguments.     

Evolution of microbial genomes: sequence acquisition and loss

We present models describing the acquisition and deletion of novel sequences in populations of microorganisms. We infer that most novel sequences are neutral. Thus, sequence duplications and gene transfer between organisms sharing the same environment are rarely expected to generate adaptive functions. Two classes of models are considered: (1) a homogeneous population with constant size, and (2) an island model in which the population is subdivided into patches that are in contact through slow migration. Distributions of gene frequencies are derived in a Moran model with overlapping generations. We find that novel, neutral or near-neutral coding sequences in microorganisms will not be fixed globally because they offer large target sizes for mutations and because the populations are so large. At most, such genes may have a transient presence in only a small fraction of the population. Consequently, a microbial population is expected to have a very large diversity of transient neutral gene content. Only sequences that are under strong selection, globally or in individual patches, can be expected to persist. We suggest that genome size is maintained in microorganisms by a quasi-steady state mechanism in which random fluctuations in the effective acquisition and deletion rates result in genome sizes that vary from patch to patch. We assign the genomic identity of a global population to those genes that are required for the participation of patches in the genetic sweeps that maintain the genomic coherence of the population. In contrast, we stress the influence of sequence loss on the isolation and the divergence (speciation) of novel patches from a global population.     

Cultural and biological evolutionary processes, selection for a trait under complex transmission.

We consider the evolution of a trait, which is under both genetic and phenotypic transmission. An individual is always born in one state but can be converted to the other before reaching adulthood. If the conversion takes place by a learning process, the native state is called “unskilled,” and that acquired by learning is called “skilled.” If phenotypic conversion takes place by way of infection, the native state is uninfected, and can be converted to infected. Native and converted phenotypes may be subject to selection; acquiring a skill may lead to selective advantage of skilled versus unskilled, while contracting a disease may involve a selective disadvantage. Conversion probability is a function of the parental phenotypes. In some of our models we assume that only one parent has teaching ability (or transmits the disease) and in others we consider more general situations. The probability of learning (or of taking the disease) may be determined by the individual's genotype. A diallelic locus is considered. The evolution of the genotypes and the phenotypes is studied in a variety of situations. Equilibria, and in a few simple cases the dynamics of the phenotypes and genotypes in the population are given. The usual equilibrium for heterozygote advantage is found to depend, in the present case, on the parameters of the learning process. Oscillatory equilibria and more than one stable equilibrium can exist in certain circumstances. Even in the absence of genotypic differences for the conversion probability gene frequencies may change.     

Evolution of a complex phenotype with biphasic ontogeny: Contribution of development versus function and climatic variation to skull modularity in toads

The theory of morphological integration and modularity predicts that if functional correlations among traits are relevant to mean population fitness, the genetic basis of development will be molded by stabilizing selection to match functional patterns. Yet, how much functional interactions actually shape the fitness landscape is still an open question. We used the anuran skull as a model of a complex phenotype for which we can separate developmental and functional modularity. We hypothesized that functional modularity associated to functional demands of the adult skull would overcome developmental modularity associated to bone origin at the larval phase because metamorphosis would erase the developmental signal. We tested this hypothesis in toad species of the Rhinella granulosa complex using species phenotypic correlation pattern (P‐matrices). Given that the toad species are distributed in very distinct habitats and the skull has important functions related to climatic conditions, we also hypothesized that differences in skull trait covariance pattern are associated to differences in climatic variables among species. Functional and hormonal‐regulated modules are more conspicuous than developmental modules only when size variation is retained on species P‐matrices. Without size variation, there is a clear modularity signal of developmental units, but most species have the functional model as the best supported by empirical data without allometric size variation. Closely related toad species have more similar climatic niches and P‐matrices than distantly related species, suggesting phylogenetic niche conservatism. We infer that the modularity signal due to embryonic origin of bones, which happens early in ontogeny, is blurred by the process of growth that occurs later in ontogeny. We suggest that the species differing in the preferred modularity model have different demands on the orbital functional unit and that species contrasting in climate are subjected to divergent patterns of natural selection associated to neurocranial allometry and T3 hormone regulation.     

Allozyme-Associated Heterosis in Drosophila Melanogaster

Two large experiments designed to detect allozyme-associated heterosis for growth rate in Drosophila melanogaster were performed. Heterosis associated with allozyme genotypes may be explained either by functional overdominance at the allozyme loci, or closely linked loci; or by genotypic correlations between allozyme loci and loci at which deleterious recessive alleles segregate. Such genotypic correlations would be favored by consanguineous mating, small effective population size, population mixing and strong natural or artificial selection. D. melanogaster is outbred, has large effective population size and there is little evidence for genotypic disequilibria. Therefore it would be unlikely to show allozyme heterosis due to genotypic correlations. In the first experiment I estimated the genotypic values of 97 replicated genotypes. In the second experiment, 500 individuals were raised in a fluctuating, stressful environment. In neither experiment was there any consistent evidence for allozyme heterosis in size or development rate, fluctuating asymmetry for size or in tendency to deviate from the population mean. In the first experiment, heterosis explained less than 5.6% of the genetic variance in growth characters. In the second, heterosis explained less than 0.1% of the phenotypic variance in growth characters. Outside of the molluscs, species which show allozyme heterosis have population structures or histories which tend to promote genotypic correlations. There is little evidence that functional overdominance is responsible for observations of allozyme-associated heterosis.     

Spatial genetic structure of northern pike (Esox lucius) in the Baltic Sea

The genetic relationships among 337 northern pike (Esox lucius) collected from the coastal zone of the central Baltic region and the Finnish islands of Aland were analysed using five microsatellite loci. Spatial structure was delineated using both traditional F-statistics and individually based approaches including spatial autocorrelation analysis. Our results indicate that the observed genotypic distribution is incompatible with that of a single, panmictic population. Isolation by distance appears important for shaping the genetic structure of pike in this region resulting in a largely continuous genetic change over the study area. Spatial autocorrelation analysis (Moran's I) of individual pairwise genotypic data show significant positive genetic correlation among pike collected within geographical distances of less than c. 100-150 km (genetic patch size). We suggest that the genetic patch size may be used as a preliminary basis for identifying management units for pike in the Baltic Sea.     

PHENOTYPIC VARIATION AND GENOTYPIC DIVERSITY IN A PLANKTONIC POPULATION OF THE TOXIGENIC MARINE DINOFLAGELLATE ALEXANDRIUM TAMARENSE (DINOPHYCEAE)1

Multiple clonal isolates from a geographic population of Alexandrium tamarense (M. Lebour) Balech from the North Sea exhibited high genotypic and phenotypic variation. Genetic heterogeneity was such that no clonal lineage was repeatedly sampled according to genotypic markers specified by amplified fragment length polymorphism (AFLP) and microsatellites. Subsampling of genotypic data from both markers showed that ordination of individuals by pair‐wise genetic dissimilarity indices was more reliable by AFLP (482 biallelic loci) than by microsatellites (18 loci). However, resulting patterns of pair‐wise genetic similarities from both markers were significantly correlated (Mantel test P < 0.005). The composition of neurotoxins associated with paralytic shellfish poisoning (PSP) was also highly diverse among these isolates and allowed clustering of toxin phenotypes based on prevalence of individual toxins. Correlation analysis of pair‐wise relatedness of individual clones according to PSP‐toxin profiles and both genotypic characters failed to yield close associations. The expression of allelochemical properties against the cryptophyte Rhodomonas salina (Wis?ouch) D. R. A. Hill et Wetherbee and the predatory dinoflagellate Oxyrrhis marina Dujard. manifested population‐wide variation of responses in the target species, from no visible effect to complete lysis of target cells. Whereas the high genotypic variation indicates high potential for adaptability of the population, we interpret the wide phenotypic variation as evidence for lack of strong selective pressure on respective phenotypic traits at the time the population was sampled. Population markers as applied here may elucidate the ecological significance of respective traits when followed under variable environmental conditions, thereby revealing how variation is maintained within populations.     

Population size,habitat fragmentation,and the nature of adaptive variation in a stream fish

Whether and how habitat fragmentation and population size jointly affect adaptive genetic variation and adaptive population differentiation are largely unexplored. Owing to pronounced genetic drift, small, fragmented populations are thought to exhibit reduced adaptive genetic variation relative to large populations. Yet fragmentation is known to increase variability within and among habitats as population size decreases. Such variability might instead favour the maintenance of adaptive polymorphisms and/or generate more variability in adaptive differentiation at smaller population size. We investigated these alternative hypotheses by analysing coding-gene, single-nucleotide polymorphisms associated with different biological functions in fragmented brook trout populations of variable sizes. Putative adaptive differentiation was greater between small and large populations or among small populations than among large populations. These trends were stronger for genetic population size measures than demographic ones and were present despite pronounced drift in small populations. Our results suggest that fragmentation affects natural selection and that the changes elicited in the adaptive genetic composition and differentiation of fragmented populations vary with population size. By generating more variable evolutionary responses, the alteration of selective pressures during habitat fragmentation may affect future population persistence independently of, and perhaps long before, the effects of demographic and genetic stochasticity are manifest.     

Soft sweeps: molecular population genetics of adaptation from standing genetic variation

A population can adapt to a rapid environmental change or habitat expansion in two ways. It may adapt either through new beneficial mutations that subsequently sweep through the population or by using alleles from the standing genetic variation. We use diffusion theory to calculate the probabilities for selective adaptations and find a large increase in the fixation probability for weak substitutions, if alleles originate from the standing genetic variation. We then determine the parameter regions where each scenario-standing variation vs. new mutations-is more likely. Adaptations from the standing genetic variation are favored if either the selective advantage is weak or the selection coefficient and the mutation rate are both high. Finally, we analyze the probability of "soft sweeps," where multiple copies of the selected allele contribute to a substitution, and discuss the consequences for the footprint of selection on linked neutral variation. We find that soft sweeps with weaker selective footprints are likely under both scenarios if the mutation rate and/or the selection coefficient is high.     

Apoptosis-like yeast cell death in response to DNA damage and replication defects

In budding (Saccharomyces cerevisiae) and fission (Schizosaccharomyces pombe) yeast and other unicellular organisms, DNA damage and other stimuli can induce cell death resembling apoptosis in metazoans, including the activation of a recently discovered caspase-like molecule in budding yeast. Induction of apoptotic-like cell death in yeasts requires homologues of cell cycle checkpoint proteins that are often required for apoptosis in metazoan cells. Here, we summarize these findings and our unpublished results which show that an important component of metazoan apoptosis recently detected in budding yeast-reactive oxygen species (ROS)-can also be detected in fission yeast undergoing an apoptotic-like cell death. ROS were detected in fission and budding yeast cells bearing conditional mutations in genes encoding DNA replication initiation proteins and in fission yeast cells with mutations that deregulate cyclin-dependent kinases (CDKs). These mutations may cause DNA damage by permitting entry of cells into S phase with a reduced number of replication forks and/or passage through mitosis with incompletely replicated chromosomes. This may be relevant to the frequent requirement for elevated CDK activity in mammalian apoptosis, and to the recent discovery that the initiation protein Cdc6 is destroyed during apoptosis in mammals and in budding yeast cells exposed to lethal levels of DNA damage. Our data indicate that connections between apoptosis-like cell death and DNA replication or CDK activity are complex. Some apoptosis-like pathways require checkpoint proteins, others are inhibited by them, and others are independent of them. This complexity resembles that of apoptotic pathways in mammalian cells, which are frequently deregulated in cancer. The greater genetic tractability of yeasts should help to delineate these complex pathways and their relationships to cancer and to the effects of apoptosis-inducing drugs that inhibit DNA replication.     

Competition can maintain genetic but not environmental variance in the presence of stabilizing selection

A population in which there is stabilizing selection acting on quantitative traits toward an intermediate optimum becomes monomorphic in the absence of mutation. Further, genotypes that show least environmental variation are also favored, such that selection is likely to reduce both genetic and environmental components of phenotypic variance. In contrast, intraspecific competition for resources is more severe between phenotypically similar individuals, such that those deviating from prevailing phenotypes have a selective advantage. It has been shown previously that polymorphism and phenotypic variance can be maintained if competition between individuals is "effectively" stronger than stabilizing selection. Environmental variance is generally observed in quantitative traits, so mechanisms to explain its maintenance are sought, but the impact of competition on its magnitude has not previously been studied. Here we assume that a quantitative trait is subject to selection for an optimal value and to selection due to competition. Further, we assume that both the mean and variance of the phenotypic value depend on genotype, such that both may be affected by selection. Theoretical analysis and numerical simulations reveal that environmental variance can be maintained only when the genetic variance (in mean phenotypic value) is constrained to a very low level. Environmental variance will be replaced entirely by genotypic variance if a range of genotypes that vary widely in mean phenotype are present or become so by mutation. The distribution of mean phenotypic values is discrete when competition is strong relative to stabilizing selection; but more genotypes segregate and the distribution can approach continuity as competition becomes extremely strong. If the magnitude of the environmental variance is not under genetic control, there is a complementary relationship between the levels of environmental and genetic variance such that the level of phenotypic variance is little affected.     

Climate change: is the dark Soay sheep endangered?

It was recently reported that the proportion of dark-coloured Soay sheep (Ovis aries) in the Hebrides has decreased, despite the fact that dark sheep tend to be larger than lighter sheep, and there exists a selective advantage to large body size. It was concluded that an apparent genetic linkage between loci for the coat colour polymorphism and loci with antagonistic effects on body size explained the decrease. Those results explain why the proportion of dark animals is not increasing, but not why it is decreasing. Between 1985 and 2005 there was a significant increase in mean ambient temperature near the islands. We suggest that, while in the past a dark coat has offset the metabolic costs of thermoregulation by absorbing solar radiation, the selective advantage of a dark coat may be waning as the climate warms in the North Atlantic. In parallel, Bergman''s rule may be operating, reducing the selective advantage of large body size in the cold. Either or both of these mechanisms can explain the decrease in the proportion of dark-coloured larger sheep in this population in which smaller (and light-coloured) sheep should be favoured by their lower gross energy demand. If environmental effects are the cause of the decline, then we can expect the proportion of dark-coloured Soay sheep to decrease further.     

The use of MapPop1.0 for choosing a QTL mapping sample from an advanced backcross population

QTL detection is a good way to assess the genetic basis of quantitative traits such as the plant response to its environment, but requires large mapping populations. Experimental constraints, however, may require a restriction of the population size, risking a decrease in the quality level of QTL mapping. The purpose of this paper was to test if an advanced backcross population sample chosen by MapPop 1.0 could limit the effect of size restriction and improve the QTL detection when compared to random samples. We used the genotypic and phenotypic data obtained for 280 genotypes, considered as the reference population. The “MapPop sample” of 100 genotypes was first compared to the reference population, and genetic maps, genotypic and phenotypic data and QTL results were analysed. Despite the increase in donor allele frequency in the MapPop sample, this did not lead to an increase of the genetic map length or a biased phenotypic distribution. Three QTL among the 10 QTL found in the reference population were also detected in the MapPop sample. Next, the MapPop sample results were compared to those from 500 random samples of the same size. The main conclusion was that the MapPop software avoided the selection of biased samples and the detection of false QTL and appears particularly interesting to select a sample from an unbalanced population.