Deme Size Research Articles

Effect of population structure on the amount of polymorphism and the fixation probability under overdominant selection

Under overdominant selection, mutants substantially contribute to increase the amount of polymorphism. It is also known that under neutrality as the migration rates among demes decrease in a subdivided population, the amount of polymorphism increases along with the increase of the effective population size, N(e). In this study, under overdominant selection the effect of population subdivision on the amount of polymorphism was investigated using the diffusion approximation and the low migration approximation. It was shown that if selection is medium or strong (e.g., N(T)s > 1, where N(T) is the population size and s is the selective advantage of heterozygotes), the nucleotide diversity, pi, decreases along with the decrease of Nm against the increase of N(e), where N is the size of demes and m is the migration rate per deme. In addition, the ratio of the nucleotide diversity to the evolutionary rate also decreases along with the decrease of Nm. In some cases the ratio becomes smaller than that expected under neutrality as Nm decreases.

The many-demes limit for selection and drift in a subdivided population

A diffusion approximation is obtained for the frequency of a selected allele in a population comprised of many subpopulations or demes. The form of the diffusion is equivalent to that for an unstructured population, except that it occurs on a longer time scale when migration among demes is restricted. This many-demes diffusion limit relies on the collection of demes always being in statistical equilibrium with respect to migration and drift for a given allele frequency in the total population. Selection is assumed to be weak, in inverse proportion to the number of demes, and the results hold for any deme sizes and migration rates greater than zero. The distribution of allele frequencies among demes is also described.

Selection and drift in subdivided populations: a straightforward method for deriving diffusion approximations and applications involving dominance, selfing and local extinctions.

Population structure affects the relative influence of selection and drift on the change in allele frequencies. Several models have been proposed recently, using diffusion approximations to calculate fixation probabilities, fixation times, and equilibrium properties of subdivided populations. We propose here a simple method to construct diffusion approximations in structured populations; it relies on general expressions for the expectation and variance in allele frequency change over one generation, in terms of partial derivatives of a "fitness function" and probabilities of genetic identity evaluated in a neutral model. In the limit of a very large number of demes, these probabilities can be expressed as functions of average allele frequencies in the metapopulation, provided that coalescence occurs on two different timescales, which is the case in the island model. We then use the method to derive expressions for the probability of fixation of new mutations, as a function of their dominance coefficient, the rate of partial selfing, and the rate of deme extinction. We obtain more precise approximations than those derived by recent work, in particular (but not only) when deme sizes are small. Comparisons with simulations show that the method gives good results as long as migration is stronger than selection.

Inclusive fitness for traits affecting metapopulation demography

Defining computable analytical measures of the effects of selection in populations with demographic and environmental stochasticity is a long-standing problem. We derive an analytical measure which takes in account all consequences of the discrete nature of deme size. Expressions of this measure are detailed for infinite island models of population structure. As an illustration we consider the evolution of dispersal in populations made of small demes with environmental and demographic stochasticity. We confirm some results obtained from the analysis of models based on deterministic approximations. In particular, when there is an Allee effect, we show that evolution of the dispersal rate may lead the metapopulation to extinction. Thus, selection on the dispersal rate could restrict the distribution of species subject to Allee effects. This selection-driven extinction is prevented by kin selection when the environmental extinction rate is small.

The two-locus ancestral graph in a subdivided population: convergence as the number of demes grows in the island model.

We study the ancestral recombination graph for a pair of sites in a geographically structured population. In particular, we consider the limiting behavior of the graph, under Wright's island model, as the number of subpopulations, or demes, goes to infinity. After an instantaneous sample-size adjustment, the graph becomes identical to the two-locus graph in an unstructured population, but with a time scale that depends on the migration rate and the deme size. Interestingly, when migration is gametic, this rescaling of time increases the population mutation rate but does not affect the population recombination rate. We compare this to the case of a partially-selfing population, in which both mutation and recombination depend on the selfing rate. Our result for gametic migration holds both for finite-sized demes, and in the limit as the deme size goes to infinity. However, when migration occurs during the diploid phase of the life cycle and demes are finite in size, the population recombination rate does depend on the migration rate, in a way that is reminiscent of partial selfing. Simulations imply that convergence to a rescaled panmictic ancestral recombination graph occurs for any number of sites as the number of demes approaches infinity.

Intra-deme molecular diversity in spatially expanding populations.

We report here a simulation study examining the effect of a recent spatial expansion on the pattern of molecular diversity within a deme. We first simulate a range expansion in a virtual world consisting in a two-dimensional array of demes exchanging a given proportion of migrants (m) with their neighbors. The recorded demographic and migration histories are then used under a coalescent approach to generate the genetic diversity in a sample of genes. We find that the shape of the gene genealogies and the overall pattern of diversity within demes depend not only on the age of the expansion but also on the level of gene flow between neighboring demes, as measured by the product Nm, where N is the size of a deme. For small Nm values (< approximately 20 migrants sent outwards per generation), a substantial proportion of coalescent events occur early in the genealogy, whereas with larger levels of gene flow, most coalescent events occur around the time of the onset of the spatial expansion. Gene genealogies are star shaped, and mismatch distributions are unimodal after a range expansion for large Nm values. In contrast, gene genealogies present a mixture of both very short and very long branch lengths, and mismatch distributions are multimodal for small Nm values. It follows that statistics used in tests of selective neutrality like Tajima's D statistic or Fu's F(S) statistic will show very significant negative values after a spatial expansion only in demes with high Nm values. In the context of human evolution, this difference could explain very simply the fact that analyses of samples of mitochondrial DNA sequences reveal multimodal mismatch distributions in hunter-gatherers and unimodal distributions in post-Neolithic populations. Indeed, the current simulations show that a recent increase in deme size (resulting in a larger Nm value) is sufficient to prevent recent coalescent events and thus lead to unimodal mismatch distributions, even if deme sizes (and therefore Nm values) were previously much smaller. The fact that molecular diversity within deme is so dependent on recent levels of gene flow suggests that it should be possible to estimate Nm values from samples drawn from a single deme.

Effect of Group Selection on the Evolution of Altruistic Behavior

By using a Monte Carlo simulation, we studied the effect of group selection on the altruistic trait that is controlled by a single locus. The altruistic trait is disadvantageous to the bearer but advantageous to the others. Group selection is defined as the differential reproductive rate among demes caused by genotypic difference among demes. We found that the simulation reproduced many results of former studies. Additionally, when the mutation rate and the migration rate are small enough, we observed two new phenomena: (1) When the effect of the group selection is as large as that of the individual selection, the gene frequency is quite unstable. We found two local stable states, the A- and the S-state. When the metapopulation is in the A-state, altruists are nearly fixed. When in the S-state, on the contrary, altruists are almost lost. The metapopulation shifted quickly from one state to another. We call this phenomenon as the S–A transition. (2) When the mutation rate and migration rate are small enough we found an extremely strong mechanism to stop the non-altruists from expanding no matter how strong the individual selection coefficient is. This is caused by a phenomenon, which we call SA splitting, in which most demes are fixed either by altruists or non-altruists; thus, the relatedness of the metapopulation becomes nearly equal to one. We show SA splitting plays an important role in S–A transition. We define a parameter d to see the degree of SA splitting. We found that d is roughly proportional to mutation rate and deme size.

The ESS under Spatial Variation with Applications to Sex Allocation

I derive a new approximation which uses the backward Kolmogorov equation to describe evolution when individuals have variable numbers of offspring. This approximation is based on an explicit fixed population size assumption and therefore differs from previous models. I show that for individuals to accept an increase in the variance of offspring number, they must be compensated by an increase in mean offspring number. Based on this model and any given set of feasible alleles, an evolutionary stable strategy (ESS) can be found. Four types of ESS are possible and can be discriminated by graphical methods. These ESS values depend on population size, but population size can be reinterpreted as deme size in a structured population. I adapt this theory to the problem of sex allocation under variable returns to male and female function and derive the ESS sex allocation strategy. I show that allocation to the more variable sexual function should be reduced, but that this effect decreases as population size increases and as variability decreases. These results are compared with results from exact matrix models and computer simulations, all of which show strong congruence.

Nonequilibrium migration in human history.

A nonequilibrium migration model is proposed and applied to genetic data from humans. The model assumes symmetric migration among all possible pairs of demes and that the number of demes is large. With these assumptions it is straightforward to allow for changes in demography, and here a single abrupt change is considered. Under the model this change is identical to a change in the ancestral effective population size and might be caused by changes in deme size, in the number of demes, or in the migration rate. Expressions for the expected numbers of sites segregating at particular frequencies in a multideme sample are derived. A maximum-likelihood analysis of independent polymorphic restriction sites in humans reveals a decrease in effective size. This is consistent with a change in the rates of migration among human subpopulations from ancient low levels to present high ones.

The case for cloning

With advances in medical research it would now seem possible apply cloning techniques human and C. Richard Seed of Chicago has announced his intention of proceeding with a pilot scheme implant embryos containing the genes of donor adults into the wombs of surrogate mothers. Because human reproduction has in the past involved a constant intergenerational reassortment of genes, public opinion has been encouraged react against voluntary reproduction by means of cloning on the ground that this would produce exact replicas of living individuals. The validity of this and other objections is discussed in this article, and it is pointed out that such objections also constitute an affront against the dignity of identical twins. A more serious consideration involves the possible reduction of necessary diversity in the gene pool of a population, but this is rejected as irrelevant considering the size of most contemporary human breeding populations, compared with the very small size of hominid demes throughout the major part of human evolutionary history. KEY WORDS: Cloning, bioethics, identical twins, birth control, positive eugenics, intelligence. Following the successful British cloning of Dolly, the sheep, and further achievements in that direction, an agreement was signed by a substantial number of member nations of the Council of Europe in January 1998 which prohibited the cloning of human beings. This followed a call from the French President Jacques Chirac for an international ban on such procedures. In order the dignity and identity of all human beings, the protocol legally bound the nineteen signatories ban any intervention seeking create a human being genetically identical another human being, whether living or Daniel Tarschys, the Council's General Secretary, declared that [I]t is important for Europe solemnly declare its determination defend human dignity against the abuse of scientific techniques. The protocol stipulated that the signatory nations must enact laws that would punish those who violate its terms. The 40-member council, established in 1949 to promote democracy, human rights, and the rule of law, is not a constituent institution of the European Union, although most of the Union's members are included amongst its 40 member states. The text of the Convention is produced below: ADDITIONAL PROTOCOL TO THE Convention for the Protection of Human Rights and Dignity of the Human Being with regard the Application of Biology and Medicine, on the Prohibition of Cloning Human Beings The member States of the Council of Europe, the other States and the European Community Signatories this Additional Protocol the Convention for the Protection of Human Rights and Dignity of the Human Being with regard the Application of Biology and Medicine, Noting scientific developments in the field of mammal cloning, particularly through embryo splitting and nuclear transfer; Mindful of the progress that some cloning techniques themselves may bring scientific knowledge and its medical application; Considering that the cloning of human beings may become a technical possibility; Having noted that embryo splitting may occur naturally and sometimes result in the birth of genetically identical twins; Considering however that the instrumentalisation of human beings through the deliberate creation of genetically identical human beings is contrary human dignity and thus constitutes a misuse of biology and medicine; Considering also the serious difficulties of a medical, psychological and social nature that such a deliberate biomedical practice might imply for all the individuals involved; Considering the purpose of the Convention on Human Rights and Biomedicine, in particular the principle mentioned in Article 1 aiming protect the dignity and identity of all human Have agreed as follows: Article 1 1 Any intervention seeking create a human being genetically identical another human being, whether living or dead, is prohibited. …

GENETIC FINGERPRINT-INFERRED POPULATION SUBDIVISION AND SPATIAL GENETIC TESTS FOR ISOLATION BY DISTANCE AND ADAPTATION IN THE COASTAL PLANT LIMONIUM CAROLINIANUM.

This paper examines two wild populations of Limonium carolinianum for population genetic subdivision and spatial patterns of genetic variation in an attempt to simultaneously test for both the action of local adaptation to tidal gradients and isolation by distance (IBD). A VNTR (variable number of tandem repeats) genetic "fingerprinting" marker was used to infer relatedness among mapped plants in two populations. Band sharing within and between populations estimated F'ST , an approximate measure of FST . Regression models were used to analyze the relationship between band sharing and spatial separation in tidal elevation and horizontal distance, as well as the relationship of fecundity differences with band sharing and spatial distance. Populations differed in band size frequency distributions and mean number of bands per profile and, therefore, likely differed in effective population size. F'ST was estimated at 0.0678 and was significantly greater than F'ST among randomly constructed subpopulations. Band sharing decreased 0.13% per meter in one population but showed no significant relation to distance in the other. In the population with significant IBD band sharing increased with increasingly different tidal elevation, contrary to an adaptive hypothesis, possibly due to directional gene flow or drift. Deme sizes were approximately 25 meters and greater than 100 meters, spanning larger areas than the entire environmental gradient. Fecundity differences were not associated with spatial parameters or band sharing. Unequal potential maternal fecundity measured as variance in number of seeds per maternal family was a significant source of genetic sampling variance. The VNTR marker employed is capable of detecting adaptation as identity by descent in ecological time and is an appropriate method for estimating the net evolutionary fate of polygenic traits. The results show that the net balance between selection along an environmental gradient and the effects of IBD and unequal maternal fecundity favor genetic differentiation by random processes in populations of Limonium.

The effects of local selection, balanced polymorphism and background selection on equilibrium patterns of genetic diversity in subdivided populations.

Levels of neutral genetic diversity in populations subdivided into two demes were studied by multilocus stochastic simulations. The model includes deleterious mutations at loci throughout the genome, causing 'background selection', as well as a single locus at which a polymorphism is maintained, either by frequency-dependent selection or by local selective differences. These balanced polymorphisms induce long coalescence times at linked neutral loci, so that sequence diversity at these loci is enhanced at statistical equilibrium. We study how equilibrium neutral diversity levels are affected by the degree of population subdivision, the presence or absence of background selection, and the level of inbreeding of the population. The simulation results are compared with approximate analytical formulae, assuming the infinite sites neutral model. We discuss how balancing selection can be distinguished from local selection, by determining whether peaks of diversity in the region of the polymorphic locus are seen within or between demes. The width of such diversity peaks is shown to depend on the total species population size, rather than local deme sizes. We show that, with population subdivision, local selection enhances between-deme diversity even at neutral sites distant from the polymorphic locus, producing higher FST values than with no selection; very high values can be generated at sites close to a selected locus. Background selection also increases FST, mainly because of decreased diversity within populations, which implies that its effects may be distinguishable from those of local selection. Both effects are stronger in selfing than outcrossing populations. Linkage disequilibrium between neutral sites is generated by both balancing and local selection, especially in selfing populations, because of linkage disequilibrium between the neutral sites and the selectively maintained alleles. We discuss how these theoretical results can be related to data on genetic diversity within and between local populations of a species.

Impact of Migration and Fitness on the Stability of Lethal t-Haplotype Polymorphism in Mus musculus: A Computer Study

The t-haplotype is a chromosomal region in Mus musculus characterized by meiotic drive such that heterozygous males transmit t-bearing chromosomes to roughly 90% of their offspring. Most naturally occurring t-haplotypes express a recessive embryonic lethality, preventing fixation of the t-haplotype. Surprisingly, the t-haplotype occurs in nature as a persistent, low-frequency polymorphism. Early modeling studies led LEWONTIN to hypothesize that this low level polymorphism results from a balance between genetic drift in small demes and interdemic migration. Here, we show that while combination of deme size and migration rate that predict natural t-haplotype frequencies exist, the range of such values is too narrow to be biologically plausible, suggesting that small deme size and interdemic migration alone do not explain the observed t-haplotype frequencies. In response, we tested other factors that might explain the observed t-polymorphism. Two led to biologically plausible models: substantially reduced heterozygous fitness and reduced meiotic drive. This raises the question whether these phenomena occur in nature. Our data suggest an alternative explanation: there is no stable, low-level t-polymorphism. Rather wild populations are in one of two stable states characterized by extinction of the t-haplotype and a high t-haplotype frequency, respectively, or in transition between the two.

A CLADISTIC ANALYSIS OF PHEROMONE EVOLUTION IN IPS BARK BEETLES (COLEOPTERA: SCOLYTIDAE).

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A simulation study of microevolutionary inferences by spatial autocorrelation analysis

To explore the extent to which microevolutionary inference can be made using spatial autocorrelation analysis of gene frequency surfaces, we simulated sets of surfaces for nine evolutionary scenarios, and subjected spatially-based summary statistics of these to linear discriminant analysis. Scenarios varied the amounts of dispersion, selection, migration, and deme sizes, and included: panmixia, drift, intrusion, and stepping-stone models with 0-2 migrations, 0-2 selection gradients, and migration plus selection. To discover how weak evolutionary forces could be and still allow discrimination, each scenario had both a strong and a weak configuration. Discriminant rules were calculated using one collection of data (the training set) consisting of 250 sets of 15 surfaces for each of the nine scenarios. Misclassification rates were verified against a second, entirely new set of data (the test set) equal in size. Test set misclassification rates for the 20 best discriminating variables ranged from 39·3% (weak) to 3·6% (strong), far lower than the expected rate of 88·9% absent any discriminating ability. Misclassification was highest when discriminating the number of migrational events or the presence or number of selection events. Discrimination of drift and panmixia from the other scenarios was perfect. A subsequent subjective analysis of a subset of the data by one of us yielded comparable, although somewhat higher, misclassification rates. Judging by these results, spatial autocorrelation variables describing sets of gene frequency surfaces permit some microevolutionary inferences.

A simulation study of microevolutionary inferences by spatial autocorrelation analysis

Abstract To explore the extent to which microevolutionary inference can be made using spatial autocorrelation analysis of gene frequency surfaces, we simulated sets of surfaces for nine evolutionary scenarios, and subjected spatially-based summary statistics of these to linear discriminant analysis. Scenarios varied the amounts of dispersion, selection, migration, and deme sizes, and included: panmixia, drift, intrusion, and stepping-stone models with 0-2 migrations, 0-2 selection gradients, and migration plus selection. To discover how weak evolutionary forces could be and still allow discrimination, each scenario had both a strong and a weak configuration. Discriminant rules were calculated using one collection of data (the training set) consisting of 250 sets of 15 surfaces for each of the nine scenarios. Misclassification rates were verified against a second, entirely new set of data (the test set) equal in size. Test set misclassification rates for the 20 best discriminating variables ranged from 39·3% (weak) to 3·6% (strong), far lower than the expected rate of 88·9% absent any discriminating ability. Misclassification was highest when discriminating the number of migrational events or the presence or number of selection events. Discrimination of drift and panmixia from the other scenarios was perfect. A subsequent subjective analysis of a subset of the data by one of us yielded comparable, although somewhat higher, misclassification rates. Judging by these results, spatial autocorrelation variables describing sets of gene frequency surfaces permit some microevolutionary inferences.

A Stochastic Model for Evolution of Altruistic Genes

We study numerically a stochastic mortel for evolution and maintenance of a population which reproduces asexually under selective pressure and is divided into smaller groups of variable size. An altruistic trait is defined as Iowering the fitness of the carrier, but the sqrvival probability of aII the members of a group with a large enough number of altruists is enhanced. Numerical results show that there is a transition in the average proportion of altruists ~ersus the relative davantage conferred by the presence of altrmsts to aII the members of the group. At the transition the distribution of altruistic frequence in the groups is not trivial, and average deme size reaches a minimum. We found also an error-threshold in mutation rate analogous to the quasi-species mortel of M. Eigen.

POPULATION STRUCTURE AND LEVELS OF GENE FLOW IN THE MEDITERRANEAN LAND SNAIL ALBINARIA CORRUGATA (PULMONATA: CLAUSILIIDAE).

The amount of gene flow among local populations partly determines the relative importance of genetic drift and natural selection in the differentiation of such populations. Land snails, because of their limited powers for dispersal, may be particularly likely to show such differentiation. In this study, we directly estimate gene flow in Albinaria corrugata, a sedentary, rock-dwelling gastropod from Crete, by mark-recapture studies. In the same area, 23 samples were taken and studied electrophoretically for six polymorphic enzyme loci. The field studies indicate that the population structure corresponds closely to the stepping-stone model: demes are present on limestone boulders that are a few meters apart, and dispersal takes place mainly between adjacent demes. Average deme size (N) is estimated at 29 breeding individuals and the proportion of migrants per generation at 0.195 (Nm = 5.7). We find no reason to assume long-distance dispersal, apart from dispersal along occasional stretches of suitable habitat. Genetic subdivision of the population, as derived from FST values, corresponds to the direct estimate only at the lowest spatial level (distance between sample sites < 10 m), where values for Nm of 5.4 and 17.6 were obtained. In contrast, at the larger spatial scales, FST values give gene-flow estimates that are incompatible with the expected amount of gene flow at these scales. We explain these discrepancies by arguing that gene flow is in fact extremely limited, making correct estimates of Nm from FST impossible at the larger spatial scales. In view of these low levels of gene flow, it is concluded that both genetic drift and natural selection may play important roles in the genetic differentiation of this species, even at the lowest spatial scales.

THE ROLE OF DEME SIZE, REPRODUCTIVE PATTERNS, AND DISPERSAL IN THE DYNAMICS OF t-LETHAL HAPLOTYPES.

The t-lethal haplotypes (t) found in house mouse (Mus musculus) populations are recessive lethals favored by gametic selection whereby male heterozygotes exhibit a non-Mendelian transmission ratio of about 95% t. The expected equilibrium frequency is 0.385; however, empirical values are lower, averaging close to 0.13. We examined the hypothesis that interdemic selection is the cause of the low empirical values by using a deme-structured simulation model that included overlapping generations, a realistic breeding system, differential deme productivity, and a large total population. We found that under some conditions interdemic selection could lower t frequency below 0.13 in the face of immigration rates up to 5%. Low frequencies were correlated with effective deme size (ne ), regardless of whether ne was changed through changing deme size (n) or through changing the proportion of breeding adults. Earlier workers showed how the first two phases of interdemic selection (random genetic differentiation and mass selection) interacted to reduce the haplotype frequency, but here we show the importance of the third phase (differential productivity of demes) once demes are linked by dispersal. The effect of this phase is not due to the (negative) covariation between deme productivity and haplotype frequency, but occurs when differential deme productivity generates a difference in t frequency between the population of juveniles recruited into their natal deme and the population of juvenile dispersers. This difference was maximized when the average productivity of demes was low, either because few adult females bred at any one time and/or because fecundity was low. Contrary to an earlier prediction, male-biased dispersal also reduced haplotype frequency, and this probably stems from the relative excess of wild-type genotypes among dispersers compared to the deme residents. Another unexpected finding was that the randomly generated excess of heterozygotes (FIS < 0) found in small demes favored t haplotypes; however, the effect was only seen when the more powerful influence of the third phase of interdemic selection was removed. Simulations of neutral polymorphisms showed that a deme structure giving FST ≤ 0.6 is inconsistent with a haplotype frequency below 0.13. Based on current empirical estimates of FST (about 0.2), we concluded that immigration rates in the field are too high for interdemic selection alone to cause the observed deficit of lethal haplotypes. One factor that could combine with population structure effects is the observation that the transmission ratio is lowered to around 0.6 in litters produced from postpartum estrus (PPE). Incorporating this factor, we showed that interdemic selection could be effective in lowering the frequency of t below 0.13 when FST was above 0.43 even when migration rates were up to 10%. These results suggest that if empirical haplotype and FST estimates are accurate, then additional factors such as a lowered fitness of heterozygotes may be involved.

The Role of Deme Size, Reproductive Patterns, and Dispersal in the Dynamics of t-Lethal Haplotypes

The Role of Deme Size, Reproductive Patterns, and Dispersal in the Dynamics of t-Lethal Haplotypes