Maternal environmental effects of competition influence evolutionary potential in rapeseed (<Emphasis Type="Italic">Brassica</Emphasis><Emphasis Type="Italic">rapa</Emphasis>)

Maternal environmental effects reflect the contribution of the maternal environment to the offspring phenotype. Maternal effects are prevalent in plants and animals and may undergo adaptive evolution and affect patterns of natural selection within and across generations. Here, we raise two generations of a rapeseed (Brassica rapa) population derived from a cross between a rapid-cycling and an oilseed genotype in competitive and noncompetitive settings. Maternal environment had little effect on average offspring phenotypes. Maternal genotypes, however, differed in the sensitivity of almost all offspring phenotypes to the maternal environment, demonstrating genetic variation in maternal effects for traits expressed throughout ontogeny. Maternal environment did not significantly affect progeny seed production, and maternal genotypes were not variable for this trait, indicating no evidence for direct maternal effects on offspring fitness. Maternal environment influenced natural selection in the progeny generation; disruptive selection acted on seed mass among seeds matured in the noncompetitive maternal environment versus no significant selection on this trait for seeds matured in the competitive maternal environment. Although maternal effects did not directly increase fitness, they did affect evolutionary potential and selection in the progeny generation. These results suggest that diverse phenotypes of both wild and cultivated B. rapa genotypes will depend on the maternal environment in which the seeds are matured.     

Naturally segregating loci exhibit epistasis for fitness

The extent to which gene interaction or epistasis contributes to fitness variation within populations remains poorly understood, despite its importance to a myriad of evolutionary questions. Here, we report a multi-year field study estimating fitness of Mimulus guttatus genetic lines in which pairs of naturally segregating loci exist in an otherwise uniform background. An allele at QTL x5b—a locus originally mapped for its effect on flower size—positively affects survival if combined with one genotype at quantitative trait locus x10a (aa) but has negative effects when combined with the other genotypes (Aa and AA). The viability differences between genotypes parallel phenotypic differences for the time and node at which a plant flowers. Viability is negatively correlated with fecundity across genotypes, indicating antagonistic pleiotropy for fitness components. This trade-off reduces the genetic variance for total fitness relative to the individual fitness components and thus may serve to maintain variation. Additionally, we find that the effects of each locus and their interaction often vary with the environment.     

Evolution of variance in offspring number: The effects of population size and migration

It was shown by Gillespie [1974. Am. Nat. 108, 145–151], that if two genotypes produce the same average number of offspring on but have a different variance associated within each generation, the genotype with a lower variance will have a higher effective fitness. Specifically, the effective fitness is {ei65-1}, where w is the mean fitness, {ei65-2} is the variance in offspring number, and N is the total population size. The model also predicts that if a strategy has a higher arithmetic mean fitness and a higher variance than the competitor, the outcome of selection will depend on the population size (with larger population sizes favoring the highvariance, high-mean genotype). This suggests that for metapopulation sizes favoring the high-variance, high-mean genotype). This suggests that for metapopulations with large numbers of (relatively) small demes, a strategy with lower variance and lower mean may be favored if the migration rate is low while higher migration rates (consistent with a larger effective population size) favor the opposite strategy. Individual-based simulation confirms that this is indeed the case for an island model of migration, though the effect of migration differs greatly depending on whether migration precedes or follows selection. It is noted in the appendix that while Gillespie [1974. Am. Nat. 108, 145–151] does seem to be heuristically accurate, it is not clear that the definition of effective fitness follows from his derivation.     

Density- and Frequency-Dependent Selection at the Mdh-2 Locus in DROSOPHILA PSEUDOOBSCURA

We have studied differences in the number of Drosophila pseudoobscura produced in a culture when the flies differ with respect to two alleles (F and S) at the Mdh-2 locus, which codes for a malate dehydrogenase enzyme. The studies were done at low and at high density in two- and three-genotype combinations (S/S, F/F and S/F), with one-genotype cultures as controls.——Density affects the fitness of the Mdh-2 genotypes. Different genotypes are differently affected, and the genotype of the competitors also makes a difference on the fitness of a given genotype. When three genotypes are present in a culture, particularly at high density, intergenotypic competition is less intense than intragenotypic competition at several frequency combinations. That is, there is "overcompensation": the three genotypes together exploit the environmental resources better than one genotype alone.—The fitness of the genotypes is frequency dependent in both two-genotype and three-genotype combinations. An inverse relationship between frequency and fitness is observed at high density. This may lead to a stable polymorphism, because the fitness of a genotype increases as its frequency decreases.—Forty independent strains, sampled from a natural population, were used in the experiments. This ensures that more than 95% of the variation present in the genome in the natural population is also present is the experimental cultures. It also ensures that the genetic background of the Mdh-2 alleles is randomized in the same way as it is in nature. However, the possibility remains that Mdh-2 alleles in nature are nonrandomly associated with alleles at closely linked loci. If linkage disequilibrium is present in the experiments because it exists in nature, then the observed effects (such as frequency-dependent selection) would affect the Mdh-2 locus in nature as well.     

Stabilizing Selection for Pupa Weight in TRIBOLIUM CASTANEUM

Ninety-five generations of stabilizing selection for pupa weight in Tribolium castaneum resulted in a significant decrease in phenotypic variance, moderate reductions in additive genetic variance, but only slight changes in heritability for the trait. Sterility was significantly lower and the average number of live progeny per fertile mating was significantly higher in populations where stabilizing selection was practiced as compared with random selected populations. The results indicate that more genetic variability is being maintained than would be expected unless a fraction of the genes have a heterozygote advantage on the fitness scale. The reduction in phenotypic variance indicated that the populations with stablizing selection became somewhat more buffered against environmental sources of variation over the course of the experiment.     

Imputation of ungenotyped parental genotypes in dairy and beef cattle from progeny genotypes

The objective of this study was to quantify the accuracy of imputing the genotype of parents using information on the genotype of their progeny and a family-based and population-based imputation algorithm. Two separate data sets were used, one containing both dairy and beef animals (n=3122) with high-density genotypes (735 151 single nucleotide polymorphisms (SNPs)) and the other containing just dairy animals (n=5489) with medium-density genotypes (51 602 SNPs). Imputation accuracy of three different genotype density panels were evaluated representing low (i.e. 6501 SNPs), medium and high density. The full genotypes of sires with genotyped half-sib progeny were masked and subsequently imputed. Genotyped half-sib progeny group sizes were altered from 4 up to 12 and the impact on imputation accuracy was quantified. Up to 157 and 258 sires were used to test the accuracy of imputation in the dairy plus beef data set and the dairy-only data set, respectively. The efficiency and accuracy of imputation was quantified as the proportion of genotypes that could not be imputed, and as both the genotype concordance rate and allele concordance rate. The median proportion of genotypes per animal that could not be imputed in the imputation process decreased as the number of genotyped half-sib progeny increased; values for the medium-density panel ranged from a median of 0.015 with a half-sib progeny group size of 4 to a median of 0.0014 to 0.0015 with a half-sib progeny group size of 8. The accuracy of imputation across different paternal half-sib progeny group sizes was similar in both data sets. Concordance rates increased considerably as the number of genotyped half-sib progeny increased from four (mean animal allele concordance rate of 0.94 in both data sets for the medium-density genotype panel) to five (mean animal allele concordance rate of 0.96 in both data sets for the medium-density genotype panel) after which it was relatively stable up to a half-sib progeny group size of eight. In the data set with dairy-only animals, sufficient sires with paternal half-sib progeny groups up to 12 were available and the within-animal mean genotype concordance rates continued to increase up to this group size. The accuracy of imputation was worst for the low-density genotypes, especially with smaller half-sib progeny group sizes but the difference in imputation accuracy between density panels diminished as progeny group size increased; the difference between high and medium-density genotype panels was relatively small across all half-sib progeny group sizes. Where biological material or genotypes are not available on individual animals, at least five progeny can be genotyped (on either a medium or high-density genotyping platform) and the parental alleles imputed with, on average, ⩾96% accuracy.     

Colony-level selection in the social insects: Single locus additive and nonadditive models

Genetic models of colony-level selection applicable to diploids (termites) and haplodiploids (social Hymenoptera) are analysed. In the Additive model colony fitnesses are just the arithmetic average of the contribution of the worker genotypes. In the Nonadditive model the fitness of the heterogenotypic colonies (those comprised of more than one worker genotype) may be altered due to interaction between the different worker genotypes. This is modelled by multiplying the additive fitness by the variable, e_i. With additive selection the same equilibrium gene frequency occurs in diploids and in haplodiploids with both once and twice mated queens. In haplodiploids if selection is nonadditive and strong, up to three polymorphic equilibria can exist; however, only a maximum of two are possible with weak selection. Multiple mating by queens increases the number of equilibria possible. Worker-produced males alter the conditions for the existence of a polymorphic equilibrium, and shift the male and female equilibrium gene frequencies.     

Selection against demographic stochasticity in age-structured populations

It has been shown that differences in fecundity variance can influence the probability of invasion of a genotype in a population; i.e., a genotype with lower variance in offspring number can be favored in finite populations even if it has a somewhat lower mean fitness than a competitor. In this article, Gillespie's results are extended to population genetic systems with explicit age structure, where the demographic variance (variance in growth rate) calculated in the work of Engen and colleagues is used as a generalization of "variance in offspring number" to predict the interaction between deterministic and random forces driving change in allele frequency. By calculating the variance from the life-history parameters, it is shown that selection against variance in the growth rate will favor a genotypes with lower stochasticity in age-specific survival and fertility rates. A diffusion approximation for selection and drift in a population with two genotypes with different life-history matrices (and therefore different mean growth rates and demographic variances) is derived and shown to be consistent with individual-based simulations. It is also argued that for finite populations, perturbation analyses of both the mean and the variance in growth rate may be necessary to determine the sensitivity of fitness to changes in the life-history parameters.     

Fitness of Allozyme Variants in DROSOPHILA PSEUDOOBSCURA. I. Selection at the PGM-1 and ME-2 Loci

We have studied in Drosophila pseudoobscura the effect of allozyme variation on seven fitness components: female fecundity, egg hatchability, egg-to-adult survival under near-optimal and under competitive conditions, rate of development under near-optimal and under competitive conditions, and mating capacity of males. Three genotypes at each of two loci, Pgm-1 and Me-2, have been studied in various combinations. These two loci are highly polymorphic in natural populations of D. pseudoobscura. Statistically significant differences involving one or more genotypes exist for all components of fitness. No single genotype is best for all fitness components; rather the relative fitnesses of genotypes are reversed when different parameters are considered, or when they are studied in different environmental conditions. Also, the average egg-to-adult survival and rate of development are better when different genotypes are reared together than when they occur in pure culture. Four different modes of selection have been uncovered by our experiments. These forms of selection may account for the persistence of the two allozyme polymorphisms in nature, and for previously observed seasonal fluctuations of the allelic frequencies in natural populations.     

Genic Heterozygosity and Protein Polymorphism among Local Populations of OENOTHERA BIENNIS

Twenty enzyme loci were studied in 44 Illinois populations of Oenothera biennis; four were polymorphic. Most of the variation was distributed between populations. Fifty-nine percent of the populations had one genotype, 27% two genotypes and the remaining 16% from three to five genotypes; the average was 1.50. The proportion of genetic diversity present in single populations is.38 of that present in the state. Members of single populations were uniformly heterozygous for 1 to 4 loci. The mean heterozygosity per population ranged from 0 to 20%. For Illinois populations collectively, heterozygosity averaged 4.5%. There was much gene frequency heterogeneity between populations. The true standardized genetic variance among populations for alleles at polymorphic loci varied from.40 to.78. Populations from Cook County were much more similar inter se than those downstate, had fewer genotypes and polymorphic loci, and had less heterozygosity than downstate populations. The mean normalized genetic identity among Cook County populations was.987 versus.947 for downstate populations. The mean number of genotypes per population in Cook County was 1.06 versus 2.40 in downstate populations. There was only one polymorphic locus in Cook County, VLP. The genetic structure of Oe. biennis suggests that single populations are colonized by one, or at best a few individuals. Cook County populations are judged to be less variable than downstate populations because the mean age of the populations probably is less than that of those downstate.     

Frequency-Dependent Selection at the PGM-1 Locus of DROSOPHILA PSEUDOOBSCURA

Frequency-dependent fitness was studied at the Pgm-1 locus of Drosophila pseudoobscura with respect to two fitness components: rate of development and larva-to-adult survival. The Pgm-1 locus is very polymorphic with only two alleles, Pgm-1¹⁰⁰ and Pgm-1¹⁰⁴, occurring at high frequencies. For each of these two alleles, 20 homozygous strains were obtained from a sample of 1,140 wild-inseminated females. First-instar larvae of the two genotypes were combined in a set of eight different frequencies: 0.0, 0.10, 0.25, 0.40, 0.60, 0.75, 0.90, and 1.0. Frequency-dependent fitness effects were observed for the two survival-related fitness components examined: larvae of the less common genotype develop faster and have a higher probability of survival than larvae of the more common genotype. The rate of survival at intermediate genotypic frequencies is similar to that in pure cultures. If selection acted solely as frequency-dependent effects on survival-related components of fitness, the equilibrium frequency of the Pgm-1¹⁰⁰ allele would be 0.615 for a two-genotype system, which fits an observed frequency range for this allele in nature between 0.55 and 0.71. Experimentally created linkage disequilibrium was excluded from the experiment by using a large number of independent strains. It is nevertheless possible that the frequency-dependent selection may not affect the Pgm-1 locus per se, but may reflect a linkage disequilibrium present in the natural population. Even if this were the case, the frequency-dependent selection could affect the frequency of the Pgm-1 alleles in nature.     

Population dynamics in variable environments. III. Evolutionary dynamics of r-selection

The boundary dynamics of a genetic model for an age-structured population in a temporally fluctuating environment are analyzed. The condition for invasion by a new allele identifies the logarithmic growth rate a of each life history phenotype as the fitness measure relevant to “r-selection.” An analytical formula is obtained for fitness a when temporal variance in life history characters is small. This formula reveals the major qualitative and quantitative effects of the average life history, fluctuations, and temporal autocorrelation on fitness. A similar approximation is obtained for the log-variance of population number so that the statistical distribution of population size can be estimated.     

Modes of Selection Maintaining an Inversion Polymorphism in DROSOPHILA PAULISTORUM

The possibility that fitness relationships associated with an inversion polymorphism in D. paulistorum were frequency dependent was investigated. Using allozymes of tetrazolium oxidase to mark inversions, the effects of genotype frequency, larval density, and culture conditions on fitness were assessed. The proportions of genotypes among egg-laying females were varied, thus changing the expected proportions of progeny produced in the absence of fecundity or viability selection. The genotypes of progeny were determined by electrophoresis and comparisons of the ratio of the numbers of the different genotypes produced to the expected ratio was used to evaluate fitness relationships. Fitness relationships were dependent on genotype frequency, larval density, and culture conditions. Selection was either absent, directional, frequency dependent (favoring rare types), or heterotic depending on density and culture conditions. It is implied that the adaptive value of genetic variants need not be apparent in all environments, or may change with changing conditions. There is evidence for different criteria for selection in the two sexes. These results add to the evidence supporting the importance of frequency-dependent selection. It is argued that for frequency dependence to be of general importance, selection must act on genes in groups, either as an inversion or as lengths of chromosome with integrity maintained by disequilibrium.     

Natural selection of UDP genotypes in an experimental population of Lolium perenne (Poaceae)

The mating system determines the range of genotypes on which selection will act. Ultimately, the population will contain only those genotypes that can survive in the current environment. This study was conducted to determine the extent to which selection affects genotype at four enzyme loci in Lolium perenne. Starch gel electrophoresis was used to determine genotype at the phosphoglucomutase, 6-phosphogluconate dehydrogenase, phosphoglucose isomerase, and UDP-glucose pyrophosphorylase loci. Genotypes of progeny arrays were used to infer maternal genotype in a field-grown population of plants. A mating system analysis was performed on maternal and progeny plants of the field population and also on a population of plants, from the same seed stock, grown in a greenhouse environment. Allelic frequencies differed among populations at the Udp locus. Results indicate that high mortality in the field strongly favored one allele. Assumptions of the mating system model are examined and used to interpret the observed differentiation among populations.     

The Role of Life Cycle and Migration in Selection for Variance in Offspring Number

For two genotypes that have the same mean number of offspring but differ in the variance in offspring number, naturalselection will favor the genotype with lower variance. In such cases, the average growth rate is not sufficient as a measure of fitness or as a predictor of fixation probability. However, the effect of variance in offspring number on the fixationprobability of mutant strategies has been calculated under several scenarios with the general conclusion that variance in offspring number reduces fitness in proportion to the inverse of the population size [Gillespie, J., Genetics 76:601–606, 1974; Proulx, S.R., Theor. Popul. Biol. 58:33–47, 2000]. This relationship becomes more complicated under a metapopulation scenario where the “effective” population size depends on migration rate, population structure, and lifecycle. It is shown that in a life cycle where reproduction and migration (the birth-migration-regulation life cycle, or BMR)occur prior to density regulation within every deme, the fitness of a strategy depends on migration rate. When migration rates are near zero, the fitness of the strategy is determined by the size of individual demes, so that the strategy favoredin small populations tends to be fixed. As migration rate increases and approaches panmixis between demes, the fitness ofa reproductive strategy approaches what its value would be in a single, panmictic deme with a population size correspondingtothe census size of the metapopulation. Interestingly, when the life cycle is characterized by having density regulation in each deme prior to migration (the BRM life cycle) the fixation probability of a strategy is independent of migration rate. These results are found to be qualitatively consistent with the individual-based simulation results in Shpak [Theor. Biosci.124:65–85, 2005]. An erratum to this article can be found at     

Determining the minimum sample size required to obtain sufficient progeny with a desired genotype at two quantitative trait loci

In this paper we determine the minimum progeny sample size n needed to obtain, with probability , at least m individuals of a desired two-locus genotype affecting quantitative traits. The two quantitative trait loci (QTLs) of interest may be linked or independent, with or without epistatic interaction between them. Parental genotypes may be known or unknown, and gene action at either locus may range from additive to overdominance. To reduce the required sample size, mating patterns that will produce a high proportion of desired progeny are suggested for different progeny genotypes and dominance levels. Based on the assumption of normally distributed quantitative trait expression, individuals can be classified into a genotype or genotypic group according to their phenotypic expressions. This technique is used to select both parents and progeny with unknown genotypes. Choice of parental classification criteria for a given quantitative trait affects classification accuracy, and hence the probability of obtaining progeny of the desired genotype. The complexity of this probability depends on the dominance level at each locus, the recombination fraction, and the awareness of parental genotypes. The procedure can be expanded to deal with more than two loci.BU-1168-MB in the Biometrics Unit Technical Report Series, 337 Warren Hall, Cornell University, Ithaca, NY 14853, USAFormerly known as S.-F. Shyu     

Density dependent selection in parthenogenetic and self-mating populations

The consequences of density dependent selection on genetically heterogeneous, diploid populations reproducing by self-mating or various parthenogenetic mechanisms is investigated. A logistic fitness function that depends upon both the genotype of an individual and the density of the population is used. Such a fitness function simultaneously determines the population size and the genotype frequencies. The equilibrium solutions to a one locus and two locus model are given as well as some generalizations to n loci and nonlogistic fitness functions. Conditions are found that maintain several different genotypes simultaneously in the equilibrium population. The interaction of such selection with the genetic mechanisms which determine mode of reproduction in parthenogenetic populations is also discussed.     

Genome-wide detection of non-additive quantitative trait loci for semen production traits in beef and dairy bulls

Semen production traits are important aspects of bull fertility, because semen quantity leads to direct profits for artificial insemination centres, and semen quality is associated with the probability of achieving a pregnancy. Most genome-wide association studies (GWASs) for semen production traits have assumed that each quantitative trait locus (QTL) has an additive effect. However, GWASs that account for non-additive effects are also important in fitness traits, such as bull fertility. Here, we performed a GWAS using models that accounted for additive and non-additive effects to evaluate the importance of non-additive effects on five semen production traits in beef and dairy bulls. A total of 65 463 records for 615 Japanese Black bulls (JB) and 50 734 records for 873 Holstein bulls (HOL), which were previously genotyped using the Illumina BovineSNP50 BeadChip, were used to estimate genetic parameters and perform GWAS. The heritability estimates were low (ranged from 0.11 to 0.23), and the repeatability estimates were low to moderate (ranged from 0.28 to 0.45) in both breeds. The estimated repeatability was approximately twice as high as the estimated heritability for all traits. In this study, only one significant region with an additive effect was detected in each breed, but multiple significant regions with non-additive effects were detected for each breed. In particular, the region at approximately 64 Mbp on Bos taurus autosome 17 had the highest significant non-additive effect on four semen production traits in HOL. The rs41843851 single nucleotide polymorphism (SNP) in the region had a much lower P-value for the non-additive effect (P-value = 1.1 × 10^?31) than for the additive effect (P-value = 1.1 × 10^?8) in sperm motility. The AA and AB genotypes on the SNP had a higher phenotype than the BB genotype in HOL, and there was no bull with the BB genotype in JB. Our results showed that non-additive QTLs affect semen production traits, and a novel QTL accounting for non-additive effects could be detected by GWAS. This study provides new insights into non-additive QTLs that affect fitness traits, such as semen production traits in beef and dairy bulls.     

Darwinian selection and “altruism”

Models are proposed for evolution at a single locus affecting altruistic behavior in which genotypic fitnesses are Darwinian and frequency (but not density) dependent. The fitnesses are composed, either in a multiplicative or an additive way, of factors which depend on the receipt and donation of altruistic behavior. The factors are determined from the matrices of conditional probabilities which describe the genotypes of relatives. Since selection occurs, these probabilities are in terms of genotype frequencies. The relationship between the risk to helper and benefit to recipient which allows altruism to evolve is shown to depend on the kinship coefficient between helper and helped, the particular fitness function proposed and the degree of dominance of the altruism. The commonly accepted criteria of W. D. Hamilton [J. Theor. Biol.7 (1964), 1–16, 17–52] apply only in the additive case. A second class of models of social cooperation independent of relationship and its evolutionary dynamics are discussed.