Two-locus theory in recurrent selection for general combining ability in maize

Summary Two-locus theory for recurrent selection for general combining ability in maize was developed. The theory featured: (a) recombination of the selfed progeny of selected parents; and (b) linkage disequilibrium in the initial gametic array. The theory indicated: (a) that initial linkage disequilibrium exerts a permanent influence upon selection progress; (b) that interposition of one or more generations of random mating before each cycle reduces the permanent effect in ensuing cycles; and (c) that random mating done before initiation of selection is more efficient in removing the influence of linkage disequilibrium on selection progress than random mating done between subsequent cycles.     

A general population genetic framework for antagonistic selection that accounts for demography and recurrent mutation

Antagonistic selection--where alleles at a locus have opposing effects on male and female fitness ("sexual antagonism") or between components of fitness ("antagonistic pleiotropy")--might play an important role in maintaining population genetic variation and in driving phylogenetic and genomic patterns of sexual dimorphism and life-history evolution. While prior theory has thoroughly characterized the conditions necessary for antagonistic balancing selection to operate, we currently know little about the evolutionary interactions between antagonistic selection, recurrent mutation, and genetic drift, which should collectively shape empirical patterns of genetic variation. To fill this void, we developed and analyzed a series of population genetic models that simultaneously incorporate these processes. Our models identify two general properties of antagonistically selected loci. First, antagonistic selection inflates heterozygosity and fitness variance across a broad parameter range--a result that applies to alleles maintained by balancing selection and by recurrent mutation. Second, effective population size and genetic drift profoundly affect the statistical frequency distributions of antagonistically selected alleles. The "efficacy" of antagonistic selection (i.e., its tendency to dominate over genetic drift) is extremely weak relative to classical models, such as directional selection and overdominance. Alleles meeting traditional criteria for strong selection (N(e)s > 1, where N(e) is the effective population size, and s is a selection coefficient for a given sex or fitness component) may nevertheless evolve as if neutral. The effects of mutation and demography may generate population differences in overall levels of antagonistic fitness variation, as well as molecular population genetic signatures of balancing selection.     

Fluctuating selection and its (elusive) evolutionary consequences in a wild rodent population

Temporal fluctuations in the strength and direction of selection are often proposed as a mechanism that slows down evolution, both over geological and contemporary timescales. Both the prevalence of fluctuating selection and its relevance for evolutionary dynamics remain poorly understood however, especially on contemporary timescales: unbiased empirical estimates of variation in selection are scarce, and the question of how much of the variation in selection translates into variation in genetic change has largely been ignored. Using long‐term individual‐based data for a wild rodent population, we quantify the magnitude of fluctuating selection on body size. Subsequently, we estimate the evolutionary dynamics of size and test for a link between fluctuating selection and evolution. We show that, over the past 11 years, phenotypic selection on body size has fluctuated significantly. However, the strength and direction of genetic change have remained largely constant over the study period; that is, the rate of genetic change was similar in years where selection favoured heavier vs. lighter individuals. This result suggests that over shorter timescales, fluctuating selection does not necessarily translate into fluctuating evolution. Importantly however, individual‐based simulations show that the correlation between fluctuating selection and fluctuating evolution can be obscured by the effect of drift, and that substantially more data are required for a precise and accurate estimate of this correlation. We identify new challenges in measuring the coupling between selection and evolution, and provide methods and guidelines to overcome them.     

Genomic selection in a pig population including information from slaughtered full sibs of boars within a sib-testing program

Genomic selection is becoming a common practise in dairy cattle, but only few works have studied its introduction in pig selection programs. Results described for this species are highly dependent on the considered traits and the specific population structure. This paper aims to simulate the impact of genomic selection in a pig population with a training cohort of performance-tested and slaughtered full sibs. This population is selected for performance, carcass and meat quality traits by full-sib testing of boars. Data were simulated using a forward-in-time simulation process that modeled around 60K single nucleotide polymorphisms and several quantitative trait loci distributed across the 18 porcine autosomes. Data were edited to obtain, for each cycle, 200 sires mated with 800 dams to produce 800 litters of 4 piglets each, two males and two females (needed for the sib test), for a total of 3200 newborns. At each cycle, a subset of 200 litters were sib tested, and 60 boars and 160 sows were selected to replace the same number of culled male and female parents. Simulated selection of boars based on performance test data of their full sibs (one castrated brother and two sisters per boar in 200 litters) lasted for 15 cycles. Genotyping and phenotyping of the three tested sibs (training population) and genotyping of the candidate boars (prediction population) were assumed. Breeding values were calculated for traits with two heritability levels (h²=0.40, carcass traits, and h²=0.10, meat quality parameters) on simulated pedigrees, phenotypes and genotypes. Genomic breeding values, estimated by various models (GBLUP from raw phenotype or using breeding values and single-step models), were compared with the classical BLUP Animal Model predictions in terms of predictive ability. Results obtained for traits with moderate heritability (h²=0.40), similar to the heritability of traits commonly measured within a sib-testing program, did not show any benefit from the introduction of genomic selection. None of the considered genomic models provided improvements in prediction ability of pigs with no recorded phenotype. However, a few advantages were found for traits with low heritability (h²=0.10). These heritability levels are characteristic for meat quality traits recorded after slaughtering or for reproduction or health traits, typically recorded on field and not in performance stations. Other scenarios of data recording and genotyping should be evaluated before considering the implementation of genomic selection in a pig-selection scheme based on sib testing of boars.     

A general approach to the concept of varietal ability for synthetic varieties

Summary Genetic effects for varietal value are defined at the level of the population of k-parent synthetic varieties. A simple expression for the total variance among synthetics arises directly from these definitions. A general expression for the covariance among related synthetics is given. Genetic effects are also defined in a completely general way so as to allow for any system of testing and used to derive an expression for the genetic advance in recurrent selection for varietal value. Covariances between relatives evaluated in the system of testing and in varietal combination are introduced, allowing a direct expression of the genetic advance in varietal development when parents are selected either individually or in groups. Some general implications for plant breeding are outlined.Dedicated to Professor F.W. Schnell on the occasion of his 65th birthday     

小麦新品种皖麦17选育的理论与实践

本文对一个高产小麦新品种选育实践进行了剖析。结果表明：在Ｆ１按杂种的综合性状进行指数估算,然后把指数当作一个性状,估算各组合的杂种优势和配合力,并以此评判组合,可以增加对组合认识的预见性。再根据单株表现分别种植,可以在Ｆ３形成系统群。Ｆ２株系间则可表现出遗传差异,结合测产选择单株,并以对照单株综合指数为标准,再把高产组合作为选择（株行或单株）重点,可提高杂种的选择效率。Ｆ３以后一边鉴定株系,一边继续单株选择,可使品系纯化和提高同步深化。Ｆ６以后继续优中选优仍然能使增效基因积累。     

A maximum likelihood approach to the detection of selection from a phylogeny

Summary A large amount of information is contained within the phylogentic relationships between species. In addition to their branching patterns it is also possible to examine other aspects of the biology of the species. The influence that deleterious selection might have is determined here. The likelihood of different phylogenies in the presence of selection is explored to determine the properties of such a likelihood surface. The calculation of likelihoods for a phylogeny in the presence and absence of selection, permits the application of a likelihood ratio test to search for selection. It is shown that even a single selected site can have a strong effect on the likelihood. The method is illustrated with an example fromDrosophila melanogaster and suggests that delerious selection may be acting on transposable elements.     

Relationship among settling,demography and habitat selection: an approach and a case study

Summary We explore the demographic consequences of site selection by animals on their abundance among habitats. We found that pre and post settling survivorship are important links between the behavioral decisions where to settle and the distribution of a population among habitats. This was demonstrated for 10 generations of the desert isopod, Hemilepistus reaumuri, in three habitats in the Negev Desert, Israel. The populations exhibit low survivorship before settling (12%) and high survivorship (55%) after settling. According to our model this implies high site selection. Theoretical considerations and the case study led us to suggest the following relationship among settling, demography and habitat selection: 1) Individuals search for suitable settling sites to inhabit and reproduce. 2) Their decision where and when to settle is a cost benefit decision. They weigh the benefit of searching for a high quality site against mortality due to increased searching time. 3) The individual's decision to settle determines the pre and post settling survivorship pattern. 4) Survivorship pattern dictates density pattern in time and space. 5) Density pattern in a given habitat determines its quality for the individual. 6) Settling selection among habitats and the number of safe sites controls the distribution of densities among habitats.     

Recombination,selection, and the evolution of tandem gene arrays

Multigene families—immunity genes or sensory receptors, for instance—are often subject to diversifying selection. Allelic diversity may be favored not only through balancing or frequency-dependent selection at individual loci but also by associating different alleles in multicopy gene families. Using a combination of analytical calculations and simulations, we explored a population genetic model of epistatic selection and unequal recombination, where a trade-off exists between the benefit of allelic diversity and the cost of copy abundance. Starting from the neutral case, where we showed that gene copy number is Gamma distributed at equilibrium, we derived also the mean and shape of the limiting distribution under selection. Considering a more general model, which includes variable population size and population substructure, we explored by simulations mean fitness and some summary statistics of the copy number distribution. We determined the relative effects of selection, recombination, and demographic parameters in maintaining allelic diversity and shaping the mean fitness of a population. One way to control the variance of copy number is by lowering the rate of unequal recombination. Indeed, when encoding recombination by a rate modifier locus, we observe exactly this prediction. Finally, we analyzed the empirical copy number distribution of 3 genes in human and estimated recombination and selection parameters of our model.     

Perturbation analysis of a two-locus model with directional selection and recombination

A population genetic two-locus model with additive, directional selection and recombination is considered. It is assumed that recombination is weaker than selection; i.e., the recombination parameter r is smaller than the selection coefficients. This assumption is appropriate for describing the effects of two-locus selection at the molecular level. The model is formulated in terms of ordinary differential equations (ODES) for the gamete frequencies x = (x ₁, x ₂, x ₃, x ₄), defined on the simplex S ₄. The ODEs are analyzed using first a regular pertubation technique. However, this approach yields satisfactory results only if r is very small relative to the selection coefficients and if the initial values x(0) are in the interior part of S ₄. To cope with this problem, a novel two-scale perturbation method is proposed which rests on the theory of averaging of vectorfields. It is demonstrated that the zeroth-order solution of this two-scale approach approximates the numerical solution of the model well, even if recombination rate is on the order of the selection coefficients.     

Selection response and efficiency of doubled-haploid recurrent selection in a cross-fertilized species

Summary Computer simulation was used to compare the simulated response to doubled-haploid (DH) mass selection with the response predicted by mathematical formulae. The efficiency of DH versus diploid mass selection in a cross-fertilized species was also studied by means of theoretical consideration and computer simulation. Simulated gain was in agreement with the predicted gain in the DH population under both additive and complete dominance models. The simulated variance of response to DH mass selection was close to the predicted variance at both the 5% and 25% selection regimes under additive and complete dominance models. The efficiency of DH over diploid mass selection was shown to be dependent upon the allelic frequency, the degree of dominance, and the amount of environmental variance. In theory the efficiency can range from zero to infinity, but in reality it should be greater than one. The efficiency ranges from 2 to 2 in the absence of dominance; it can be greater than two only in the presence of dominance and a small environmental variance. The variance of response to DH mass selection can be smaller than or up to twice as large as the variance of response to diploid mass selection. Computer simulation results agreed with the predicted efficiency of DH mass selection and with the predicted variance-of-response ratio of DH mass selection to diploid mass selection.Joint Contribution from the Charlottetown Research Station, contribution no. 604 and Department of Crop Science, University of Guelph     

Diffusion approximations for one-locus multi-allele kin selection,mutation and random drift in group-structured populations: a unifying approach to selection models in population genetics

Diffusion approximations are ascertained from a two-time-scale argument in the case of a group-structured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multi-allelic locus under recurrent mutation, and applied to the case of random pairwise interactions within groups. The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation, using a coalescent approach. An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I, defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population, given that J is allozygous or autozygous, yields the correct selection drift functions. These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding. They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rank-one matrix for autozygous individuals. In the case of no inbreeding, the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics. Connections are made between dispersal with exact replacement (proportional dispersal), uniform dispersal, and local extinction and recolonization. The timing of dispersal (before or after selection, before or after mating) is shown to have an effect on group competition and the effective population size. In memory of Sam Karlin.     

A model for population regulation with density- and frequency-dependent selection

The life-cycle of a species with separate generations is divided into a reproduction phase and a growing-up phase. In the reproduction phase we assume random mating and selection due to genotype differences in fecundity of the parents and viability of the offspring. During the growing-up phase we assume a (deterministic) death process in continuous time with death rates for the genotypes which increase linearly with the genotype population sizes.In the absence of genotype differences the model gives logistic population regulation. With genotype differences the model generalizes the usual separate generations selection patterns. In addition to these we exhibit cases with three polymorphic equilibria or with a stable cycle.     

Host selection behavior of a thistle-feeding fly: choices and consequences

Summary Female Canada thistle seed flies (Orellia ruficauda) preferentially oviposit into seed heads which are a single day from opening. When flies are forced to oviposit into flower heads at other stages of development, offspring typically do slightly poorer: they attain a mature mass of about 15% less than do larvae derived from preferred hosts. Larval mass correlates strongly with reproductive success: heavy larvae develop into adults that produce eggs at a faster rate than do those developing from small larvae. After laying a clutch of eggs, flies circumscribe the rim of the flowerhead with their extended ovipositor and deposit a clear fluid. Flies reject previously-attacked hosts, bearing this apparent marking pheromone, significantly more often than they reject unattacked hosts. Costs of superparasitism in this system are relatively small, inasmuch as there is only a weak relationship between clutch size and larval success at the densities measured in this study. We speculate that flies are highly selective, when the apparent costs of making a mistake are rather low, because the information provided by phenological cues and by the putative marking pheromone is highly reliable, and low fecundity and time costs allow sufficient time to express a high level of discrimination.     

Additive main effect and multiplicative interaction model for a diallel-cross analysis

Diallel mating designs have proved informative in determining the inheritance of quantitative traits of interest to plant breeders. Apart from the well-established analyses of a complete diallel, the two-way factorial data structure of this design lends itself to analysis by the additive-main-effects-and-multiplicative-interaction (AMMI) model. This research article describes the joint application of the AMMI model and Griffing’s method 1, model I, to gain insight into the breeding value of inbred lines in a self-pollinated crop such as disomic, hexaploid bread wheat. Data from a multi-environment trial of a complete diallel cross between eight lines adapted to the East African highlands were analyzed to provide an example of this joint analysis. This combined approach identified not only the direction of a cross, i.e. which parent should be male or female, but also which crosses produce offspring showing F₁ heterosis. Received: 10 June 2000 / Accepted: 31 July 2000     

A general model of the relation between phenotypic selection and genetic response

The phenotypic view of selection assumes that genetic responses can be predicted from selective forces and heritability — or in the classical quantitative genetic equation: R = h²S. However, data on selection in bird populations show that often no selection responses is found, despite consistent selective forces on phenotypes and significant heritable variation. Such discrepancies may arise due to the assumption that selection only acts on observed phenotypes. We derive a general selection equation that takes into account the possibility that some relevant (internal or external) traits are not measured. This equation shows that the classic equation applies if selection directly acts on the measured, phenotypic traits. This is not the case when, for instance, there are unknown internal genetic trade-offs, or unknown common environmental factors affecting both trait and fitness. In such cases, any relationship between phenotypic selection and genetic response is possible. Fortunately, the classical model can be tested by comparing phenotypic and genetic covariances between traits and fitness; an indication that important internal or external traits are missing can thus be obtained. Such an analysis was indeed found in the literature; for selection on fledging weight in Great Tits it yielded valuable extra information.     

A general framework for the analysis of animal resource selection from telemetry data

Summary .   We propose a general framework for the analysis of animal telemetry data through the use of weighted distributions. It is shown that several interpretations of resource selection functions arise when constructed from the ratio of a use and availability distribution. Through the proposed general framework, several popular resource selection models are shown to be special cases of the general model by making assumptions about animal movement and behavior. The weighted distribution framework is shown to be easily extended to readily account for telemetry data that are highly autocorrelated; as is typical with use of new technology such as global positioning systems animal relocations. An analysis of simulated data using several models constructed within the proposed framework is also presented to illustrate the possible gains from the flexible modeling framework. The proposed model is applied to a brown bear data set from southeast Alaska.