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PubMed2007

Direct fitness or inclusive fitness: how shall we model kin selection?

Two standard mathematical formulations of kin-selection models can be found. Inclusive fitness is an actor-centred approach, which calculates the fitness effect on a number of recipients of the behaviour of a single actor. Direct fitness is a recipient-centred approach, which calculates the fitness effect on the recipient of the behaviour of a number of actors. Inclusive fitness offers us a powerful heuristic, of choosing behaviour to maximize fitness, but direct fitness can be mathematically easier to work with and has recently emerged as the preferred approach of theoreticians. In this paper, we explore the fundamental connection between these two approaches in both homogeneous and class-structured populations, and we show that under simple assumptions (mainly fair meiosis and weak selection) they provide equivalent formulations, which correspond to the predictions of Price's equation for allele frequency change. We use a couple of examples to highlight differences in their conception and formulation, and we briefly discuss a two-species example in which we have a class of 'actor' that is never a 'recipient', which the standard direct fitness method can handle but the usual inclusive fitness cannot.

Biological Evolution↗
PubMed2026

Enhancing detection of polygenic adaptation: a comparative study of machine learning and statistical approaches using simulated evolve-and-resequence data.

BACKGROUND: Detecting signals of polygenic adaptation remains a significant challenge in population genomics, as traditional methods often struggle to identify the associated subtle, multi-locus allele-frequency shifts. Here, we introduced and tested several novel approaches combining machine learning techniques with traditional statistical tests to detect polygenic adaptation patterns in time-series of allele frequency changes from whole genome data. We implemented a Naive Bayesian Classifier (NBC) and One-Class Support Vector Machines (OCSVM), and compared their performance against the classical Fisher's Exact Test (FET). Furthermore, we combined machine learning and statistical models (OCSVM-FET and NBC-FET), resulting in 5 competing approaches. The framework is mainly designed and validated for evolve-and-resequence (EaR) experimental designs, where defined selection pressures and temporal sampling are feasible, but might be applicable for certain natural experiments as well. RESULTS: Using a simulated dataset based on empirical C. riparius Pool-Seq data, we evaluated methods across evolutionary scenarios varying in generation, selection strength, and number of loci under selection. Our results demonstrate that the combined OCSVM-FET approach consistently outperformed competing methods, achieving the lowest false positive rate, highest area under the curve, and high accuracy. The performance peak aligned with what we term the 'late dynamic phase' of adaptation - the period after initial selection has occurred but before fixation - highlighting the method's sensitivity to ongoing selective processes. CONCLUSIONS: Furthermore, we emphasize the critical role of parameter tuning, balancing biological assumptions with methodological rigor. While broader applicability remains an important direction for future work, the present benchmarking is intentionally scoped to EaR experimental contexts.

Machine Learning↗
PubMed1999

Two-stage selection strategies utilizing marker-quantitative trait locus information and individual performance.

Short- and long-term response to marker-assisted selection in two stages was studied using a stochastic simulation of a closed nucleus herd for beef production. First-stage selection was carried out within families based on information at a fully additive quantitative trait locus (QTL). Second-stage selection strategies were based on 1) individual phenotype, 2) individual phenotype precorrected for QTL, 3) a selection index incorporating phenotype and QTL information, 4) a standard animal model BLUP, and 5) a selection index incorporating marker-QTL information and standard animal model BLUP on records precorrected for QTL. All strategies were efficient in moving the favorable allele at the QTL to fixation, but they differed in the time to reach fixation. Mass selection was less efficient in changing allele frequencies than BLUP. Discounted accumulated response, accounting for the time response was realized and inflation rate, was proposed to rank strategies and to elude the conflict between short- and long-term response in marker-assisted selection. Discounted accumulated response at a time horizon of 20 yr for alternative two-stage selection strategies was compared with conventional BLUP carried out in second stage only. Within-family selection increased discounted accumulated response by more than 11% using Strategy 4 and by up to 12% using Strategy 5 at an inflation rate of 2%. The percentage increase in response was less for highly heritable traits and when the proportion of additive variance explained by the QTL was small. Strategy 5 gave larger response with reduced inbreeding. This strategy also resulted in the lowest cost-benefit ratio, requiring less genotyping per unit of response. Cost-benefit ratio for discounted genotyping and for discounted in vitro production of embryos for traits with low heritability was two to four times that for traits with high heritability. The use of first-stage selection slightly increased the level of inbreeding for both mass (Strategy 1) and BLUP selection (Strategies 4 and 5).

Animals↗
PubMed1993

Detection of quantitative trait loci from frequency changes of marker alleles under selection.

A method was developed to estimate effects of quantitative trait loci (QTL) by maximum likelihood using information from changes of gene frequency at marker loci under selection, assuming an additive model of complete linkage between markers and QTL. The method was applied to data from 16 molecular and coat colour marker loci in mouse lines derived from the F2 of two inbred strains which were divergently selected on 6-week weight for 21 generations. In 4 regions of the genome, marker allele frequencies were more extreme than could be explained by sampling, implying selection at nearby QTL. An effect of about 0.5 standard deviations was located on chromosome 11, and accounted for nearly 10% of the genetic variance in the base population. QTL with effects as small as 0.2 phenotypic standard deviations could be detected. For typing of a given number of individuals, the power of detection of QTL is very high compared to, for example, analysis of an F2 population. The joint effects of linkage and selection were investigated by Monte Carlo simulation. Marker gene frequencies change little as a consequence of selection at a QTL unless the marker and QTL are less than about 20 cM apart.

Alleles↗
PubMed1999

Inbreeding of bottlenecked butterfly populations. Estimation using the likelihood of changes in marker allele frequencies.

Polymorphic enzyme and minisatellite loci were used to estimate the degree of inbreeding in experimentally bottlenecked populations of the butterfly, Bicyclus anynana (Satyridae), three generations after founding events of 2, 6, 20, or 300 individuals, each bottleneck size being replicated at least four times. Heterozygosity fell more than expected, though not significantly so, but this traditional measure of the degree of inbreeding did not make full use of the information from genetic markers. It proved more informative to estimate directly the probability distribution of a measure of inbreeding, sigma2, the variance in the number of descendants left per gene. In all bottlenecked lines, sigma2 was significantly larger than in control lines (300 founders). We demonstrate that this excess inbreeding was brought about both by an increase in the variance of reproductive success of individuals, but also by another process. We argue that in bottlenecked lines linkage disequilibrium generated by the small number of haplotypes passing through the bottleneck resulted in hitchhiking of particular marker alleles with those haplotypes favored by selection. In control lines, linkage disequilibrium was minimal. Our result, indicating more inbreeding than expected from demographic parameters, contrasts with the findings of previous (Drosophila) experiments in which the decline in observed heterozygosity was slower than expected and attributed to associative overdominance. The different outcomes may both be explained as a consequence of linkage disequilibrium under different regimes of inbreeding. The likelihood-based method to estimate inbreeding should be of wide applicability. It was, for example, able to resolve small differences in sigma2 among replicate lines within bottleneck-size treatments, which could be related to the observed variation in reproductive viability.

Alleles↗
PubMed2004

On the distribution of temporal variations in allele frequency: consequences for the estimation of effective population size and the detection of loci undergoing selection.

The effective population size (Ne) is frequently estimated using temporal changes in allele frequencies at neutral markers. Such temporal changes in allele frequencies are usually estimated from the standardized variance in allele frequencies (Fc). We simulate Wright-Fisher populations to generate expected distributions of Fc and of Fc (Fc averaged over several loci). We explore the adjustment of these simulated Fc distributions to a chi-square distribution and evaluate the resulting precision on the estimation of Ne for various scenarios. Next, we outline a procedure to test for the homogeneity of the individual Fc across loci and identify markers exhibiting extreme Fc-values compared to the rest of the genome. Such loci are likely to be in genomic areas undergoing selection, driving Fc to values greater (or smaller) than expected under drift alone. Our procedure assigns a P-value to each locus under the null hypothesis (drift is homogeneous throughout the genome) and simultaneously controls the rate of false positive among loci declared as departing significantly from the null. The procedure is illustrated using two published data sets: (i) an experimental wheat population subject to natural selection and (ii) a maize population undergoing recurrent selection.

Gene Frequency↗
PubMed2006

Selection in a cycling population: differential response among skeletal traits.

Population density cycles influence phenotypic evolution through both density-dependent selection during periods of high density and through enhanced genetic drift during periods of low density. We investigated the response of different phenotypic traits to the same density cycles in a population of the yellow-necked mouse, Apodemus flavicollis, from Białowieza National Park in Poland. We examined nonmetric skull traits, skull and mandible size, skull and mandible shape, and transferrin allele frequencies. We found that all of the traits changed significantly over the seven-year study period. The greatest changes in nonmetric traits and mandible size occurred during periods of increasing density, and the magnitude of changes in skull and mandible shape was correlated with the magnitude of density changes. Frequencies of transferrin alleles changed the most when population density was in decline. Changes among the five phenotypic traits were generally uncorrelated with one another, except for skull and mandible shape. Nonmetric traits were selectively neutral when assessed with Q(ST)/F(ST) analysis, whereas mandible size, mandible shape, and skull shape showed evidence of fairly strong selection. Selection on skull size was weak or nonexistent. We discuss how different assumptions about the genetic components of variance affect Q(ST) estimates when phenotypic variances are substituted for genetic ones. We also found that change in mandible size, mandible shape, skull size, and skull shape were greater than expected under a neutral model given reasonable assumptions about heritability and effective population size.

Animals↗
PubMed2001

Somatic mutations in organisms with complex life histories.

A theoretical model is developed of the fate of mutations for organisms with such life-history characteristics as indeterminate growth and clonal reproduction. It focuses on how the fate of a particular mutant depends on whether it arises during mitotic cell division (somatic mutation) or during meiotic cell division (meiotic mutation). At gamete production, individuals carrying somatic mutations will produce some proportion of gametes reflecting the original, zygotic genotype and some proportion reflecting genotypes carrying the somatic mutation. Focusing on allele frequencies at gamete production allows the effects of growth and clonal reproduction to be summarized. The relative strengths of somatic and meiotic mutation can be determined, as well as the conditions under which the change in allele frequency due to one is greater than that due to the other. Examples from a published demographic study of clonal corals are used to compare somatic and meiotic mutation. When there is no selection acting on either type of mutation, only a few cell divisions per time unit on average are needed for the change in allele frequency due to somatic mutation to be greater, given empirically based mutation rates. When somatic selection is added, the most dramatic effect is seen with fairly strong negative selection acting against the somatic mutation within individuals. In this case, selection within organisms can effectively counteract the effects of somatic mutation, and the change in allele frequency due to somatic mutations will not be greater than that due to meiotic mutations for reasonable numbers of within-generation cell divisions. The majority of the mutation load, which would have been due to somatic mutation, is purged by selection within the individual organism.

Animals↗
PubMed1978

The relation between transferrin locus and the breeding quality traits of our country cattle race: lowland black-white and lowland red-white.

The relation between transferrin locus and the breeding quality, especially such traits as--milk quantity, fattening and fertility rate expressed through nine traits, were analyzed. There are presented some results of phenotypes distribution and frequency of alleles of transferrin. Changing of allele frequencies in time in certain direction was observed. The calculated coefficients of regression of frequency on a year in race lrw were: bA = -0.0080; bD = 0.0137; BE = -0.0057 and in race lbw: bA = 0.0134; bD = -0.0034; bE = -0.0089.

Animal Husbandry↗
PubMed1996

A MspI polymorphism in the bovine ornithine decarboxylase gene and its possible association with selection for milk production in Holstein bulls.

A polymerase chain reaction (PCR)-based method for detection of a MspI-restriction fragment length polymorphism (RFLP) in the bovine ornithine decarboxylase gene was developed, and the allele frequencies of the polymorphism in two groups of Holstein bulls representing progeny-tested bulls during the 1950s-1960s and 1980s, respectively, were estimated. The frequencies of the MspI(-) allele ere 0.229 and 0.077 and that of MspI(+) were 0.771 and 0.923 in the progeny-tested bulls of the 1950s-1960s and 1980s, respectively. The difference in allele frequencies between the two groups was statistically significant (P < 0.005). Genetic drift could be responsible for the changes in allele frequencies; however, it could also be possible that selection for milk production was associated with the changes of the allele frequencies in the two bull populations.

Alleles↗
PubMed2006

An analysis of selection on a colour polymorphism in the northern leopard frog.

In this study, we investigated the role of selection in the maintenance of a dorsal colour polymorphism in natural populations of the northern leopard frog, Rana pipiens. We determined genetic structure both spatially and temporally from a suite of putatively neutral molecular markers and tested whether or not the colour locus exhibited patterns of genetic variation that differed from those of the neutral loci. Spatial genetic structure at the colour locus was indistinguishable from structure at neutral loci [95% confidence intervals of F(ST) (neutral) = (0.07, 0.35), F(ST) (colour locus) = 0.114]. In the temporal analysis, we found that the variance among populations in the change in allele frequency at the colour locus (equal to 0.004) lies within the 95% confidence intervals for the variance among populations in changes in allele frequencies at neutral loci. In light of our inability to show evidence for the selective maintenance of the colour polymorphism, we used computer simulations to infer the power of our spatial and temporal techniques to detect selection. The computer simulations showed that although the strength of selection (s) would need to be relatively strong to have been detected by the temporal approach (s = 0.1-0.4, depending on the model tested), the spatial analysis would have detected all but weak selection (s = 0.01-0.04, depending on the model tested). This study illustrates the importance of using a locus comparison approach to detect evidence for selective maintenance before conducting studies to measure the selective mechanisms maintaining a polymorphism.

Alleles↗
PubMed2005

Kin selection is implicated in partial sib-mating populations with constant viability differences before mating.

The change in the frequency of a rare mutant allele under constant sex-differentiated viability selection in an infinite, partial full-sib mating population is studied. The diplo-diploid and haplo-diploid polygynous models are considered with a Poisson distribution for the number of offspring produced by every mated female. Reproduction is followed by weak selection among the offspring and then mating to form the next generation. It is shown that the rate of change with respect to the frequency of the mutant allele and the intensity of selection can be expressed in terms of costs or benefits of substituting the mutant type for the wild type, which correspond to average excesses in viability in females and males, multiplied by coefficients of relatedness to the individuals affected by such a substitution and reproductive values associated to the sexes of these individuals. This reveals hidden interactions between mated individuals and between males for mating, the former having positive effects on the reproductive success of related individuals and the latter having negative effects. Such interactions are the result of reproductive constraints when a fixed proportion of females must mate with a male sib and all females are fertilized as long as one mate is available. However, they affect the change in allele frequency because there is inbreeding or relatedness between mates and more generally relatedness between interacting individuals. Surprisingly, the effects of these interactions cancel out in a diploid population when the number of offspring is large enough so that the possibility for a female to have no male sib to mate with can be neglected and the viability differences are the same in both sexes.

Algorithms↗
PubMed2004

Selection, subdivision and extinction and recolonization.

In a subdivided population, the interaction between natural selection and stochastic change in allele frequency is affected by the occurrence of local extinction and subsequent recolonization. The relative importance of selection can be diminished by this additional source of stochastic change in allele frequency. Results are presented for subdivided populations with extinction and recolonization where there is more than one founding allele after extinction, where these may tend to come from the same source deme, where the number of founding alleles is variable or the founders make unequal contributions, and where there is dominance for fitness or local frequency dependence. The behavior of a selected allele in a subdivided population is in all these situations approximately the same as that of an allele with different selection parameters in an unstructured population with a different size. The magnitude of the quantity N(e)s(e), which determines fixation probability in the case of genic selection, is always decreased by extinction and recolonization, so that deleterious alleles are more likely to fix and advantageous alleles less likely to do so. The importance of dominance or frequency dependence is also altered by extinction and recolonization. Computer simulations confirm that the theoretical predictions of both fixation probabilities and mean times to fixation are good approximations.

Biological Evolution↗
PubMedDate not supplied

The effects of unidirectional incompatibility on cytonuclear disequilibria in a hybrid zone.

Unidirectional incompatibility selection is examined as an alternate mechanism of natural selection to cytoplasmic male sterility (CMS) for generating cytonuclear disequilibria. Differences in the dynamics and equilibrium behavior of cytonuclear disequilibria between these two cytonuclear selection models may allow for statistical tests of CMS vs. unidirectional incompatibility between mating cytotypes. Unlike CMS without migration, unidirectional incompatibility causes the cytoplasmic allele frequency to change over time rather than remain constant, and the nuclear allele frequencies hitchhike on the cytoplasmic frequencies. The decay of disequilibria is also distinctive in the absence of migration. Furthermore, in comparing both models with migration it is seen that the opportunity for internal equilibrium can be two or three times higher in a unidirectional incompatibility vs. CMS model. An example is presented that shows how unidirectional incompatibility can be statistically eliminated as a possible mechanism of cytonuclear selection.

Alleles↗
PubMed1997

A population genetic study of Borrelia burgdorferi sensu stricto from eastern Long Island, New York, suggested frequency-dependent selection, gene flow and host adaptation.

Eastern Long Island, New York, is one of the major foci of Lyme disease in the United States. As in almost all other parts of North America, Lyme disease in this region is caused by a single genomic species of spirochete, Borrelia burgdorferi sensu stricto. For three consecutive years, natural populations of Lyme Borrelia in this region were sampled and studied for gene flow among different locations, changes in population structure over time, and selective forces. The genetic diversity of Borrelia populations was measured at the outer surface protein A (ospA) locus using Cold Single-Stranded Conformation Polymorphism (Cold SSCP) analysis. The Borrelia populations were found to be highly polymorphic within any of thirteen local populations. Ewens-Watterson tests of neutrality revealed that the high level of genetic diversity within local Borrelia populations is maintained by balancing selection. Frequency-dependent selection for the different strains distinguished by the ospA alleles is likely the mechanism of the balancing selection. Allele frequency distributions of Borrelia populations were homogeneous across the region in any particular year, although different infection rates of local tick (Ixodes scapularis) populations suggested that the Borrelia populations were at least partially isolated. Since the allele frequency distribution changed over time, while remaining homogeneous over space, the nearly uniform allele frequency distribution across the region cannot be explained by recent geographic expansion from a single population. This uniform distribution across the region thus may be maintained by selection, or by a significant amount of migration or both. The genetic structure of B. burgdorferi sensu stricto also differed between spirochetes infecting nymphal ticks and those infecting adult ticks. Since larval and nymphal ticks have distinctly different host feeding preferences, host adaptation of spirochete populations is implied. This distinction and an animal study using chipmunks suggest that ticks infected by Borrelia as larvae may have high mortality in the wild. This study represents a genetic analysis of local populations of a bacterial species.

Alleles↗
PubMed2002

Genetic integrity of ex situ Genebank collections.

The genetic integrity of four accessions of the cross-pollinating species rye (Secale cereale L.) was investigated. Seeds available from the first and most recent regeneration cycles, multiplied 8, 12 (twice) or 14 times were fingerprinted using microsatellite markers. In all four accessions the allele numbers and frequencies changed after regeneration. Alleles present in the original seed sample were not detectable in the regenerated populations, whereas on the other hand, alleles were found in the recent seed sample, which were not observed in the investigated plants of the original one.

Alleles↗
PubMed1973

Apparent selection of enzyme alleles in laboratory populations of Drosophila.

Twelve laboratory populations of recently collected Drosophila willistoni were begun with different frequencies of alleles at three enzyme loci, six populations at 25 degrees and six at 19 degrees . Periodic sampling of the populations allowed monitoring of the frequency changes in allozymes over time.-At Lap-5 (a locus coding for leucine amino peptidase), three alleles converged to the same frequencies in all populations at both temperatures. The apparent equilibrium frequency of the major allele was about.75; this is different from the frequency (.57) found in the natural population from which the experimental populations were begun. Allele frequency changes at the esterase-5 locus (Est-5) were slower but consistent in all cages. It is difficult to determine if an equilibrium has been reached. However, the frequency of the rare allele in all cages is about the same as in wild populations, 5%. Alleles at both Lap-5 and Est-5 are non-randomly associated with inversions in the chromosomes onto which they map. Because of these associations, it is impossible to unambiguously attribute the change in allele frequencies to selection at the loci being observed.-After one year, no significant gene frequency changes were detected at Est-7, the third locus studied.

Alleles↗