Selection for uniformity in livestock by exploiting genetic heterogeneity of residual variance

In some situations, it is worthwhile to change not only the mean, but also the variability of traits by selection. Genetic variation in residual variance may be utilised to improve uniformity in livestock populations by selection. The objective was to investigate the effects of genetic parameters, breeding goal, number of progeny per sire and breeding scheme on selection responses in mean and variance when applying index selection. Genetic parameters were obtained from the literature. Economic values for the mean and variance were derived for some standard non-linear profit equations, e.g. for traits with an intermediate optimum. The economic value of variance was in most situations negative, indicating that selection for reduced variance increases profit. Predicted responses in residual variance after one generation of selection were large, in some cases when the number of progeny per sire was at least 50, by more than 10% of the current residual variance. Progeny testing schemes were more efficient than sib-testing schemes in decreasing residual variance. With optimum traits, selection pressure shifts gradually from the mean to the variance when approaching the optimum. Genetic improvement of uniformity is particularly interesting for traits where the current population mean is near an intermediate optimum.     

Impact of genetic selection on management of boar replacement

Boars in an artificial insemination centre have been selected for their superior genetic potential, with 'superior' being defined as having traits the customer wants transmitted to his herd. The ability to meet the customers' needs depends on the heritability of the trait, the geneticist's success in devising a selection scheme for the trait in balance with other economically important traits, and the boar's ability to produce sperm that can fertilise oocytes. Genetic evaluation research over the past 20 years has greatly increased the number of traits for which a boar can be selected: currently in the Canadian national program, these include age at 100 kg, backfat at 100 kg, feed efficiency, lean yield and litter size. In the near future, traits that are very likely to be added to this selection list include piglet survival, marbling, loin eye area and structure traits. In Canada, sires are ranked on two estimated breeding value (EBV) indices; one, focused on development of terminal sire lines, is based on the growth and yield traits and another, primarily focused on maternal line development, de-emphasises these traits and incorporates litter size. Boars that are in Canadian AI centres because of their excellent growth traits are typically in the top 5-10% of the national population for terminal sire line index, but they may be only average or substandard for litter size. Conversely, boars selected to be in the top 5-10% for conveying such reproductive traits as litter size may only be in the top 33% for growth traits. The more offspring from a superior boar in either of these indices, the faster the population average for the trait improves. The original sire gets knocked out of the elite group, is culled and replaced by a higher ranked young boar from the now improved general population. Although genetic superiority should govern an AI centre's selection and culling of boars, decision-making in real life is seldom that simple. Selection criteria may be contradictory as above, or a boar with truly superior traits may be excluded because a newly-developed molecular genetics test determines he carries an undesirable gene such as PSS, RN or others being developed. Selection for terminal sire or maternal line traits can ignore important practical factors that affect an AI centre--boars with superior genetics may not produce good semen because skeletal or penile problems prevent ejaculation, or because sperm production is poor due to a genetic flaw, disease, or some other cause. Interestingly, selection pressure for one trait may inadvertently select for a trait that is linked but whose linkage is unrecognised, and such unintentionally selected genes could benefit, harm, or have no effect on production traits. An AI centre serving a variety of customers must select boars in anticipation of their customers' needs (including new, foreign and niche markets). A centre should also review its genetic evaluation results and progeny records, both to critique its own selection success and to try to detect unexpected linkages. Finally, an AI centre needs to predict its own future, selecting not just for production traits for the swine producer, but also for factors that enhance the centre's efficiency including boar conformation and temperament, and sperm quantity, quality and hardiness. Can we select for efficiency? Our colleagues in dairy cattle AI evaluate bull performance--should the swine industry consider evaluation of male fertility traits?     

Selection indices for non-linear profit functions

Summary Conventional selection index theory assumes that the total merit or profitability of animals is a linear function of measurable traits. However, in many cases merit may be a non-linear function of these traits. A linear selection index can still be used in this situation but the optimum index depends on the selection intensity to be used and on the number of generation over which the selection response is to be maximized. Nonlinear selection indices have been suggested but these result in a lower selection response than the best linear index. Linear selection indices suggested in the past are shown to correspond to the optimum linear index for either a very small selection response or, in the case of restricted indices, a very large selection response. The economic value of a trait may depend on management decisions taken by the farmer. In this situation the economic values should be calculated assuming that the management decisions taken maximize profit given the present genetic value of the animals.     

Evolvability and genetic constraint in Dalechampia blossoms: components of variance and measures of evolvability

Many evolutionary arguments are based on the assumption that quantitative characters are highly evolvable entities that can be rapidly moulded by changing selection pressures. The empirical evaluation of this assumption depends on having an operational measure of evolvability that reflects the ability of a trait to respond to a given external selection pressure. We suggest short-term evolvability be measured as expected proportional response in a trait to a unit strength of directional selection, where strength of selection is defined independently of character variation and in units of the strength of selection on fitness itself. We show that the additive genetic variance scaled by the square of the trait mean, IA, is such a measure. The heritability, h2, does not measure evolvability in this sense. Based on a diallel analysis, we use IA to assess the evolvability of floral characters in a population of the neotropical vine Dalechampia scandens (Euphorbiaceae). Although we are able to demonstrate that there is additive genetic variation in a number of floral traits, we also find that most of the traits are not expected to change by more than a fraction of a percent per generation. We provide evidence that the degree of among-population divergence of traits is related to their predicted evolvabilities, but not to their heritabilities.     

Prediction of Selection Response for Threshold Dichotomous Traits

This paper presents a formula to predict expected response to one generation of truncation selection for a dichotomous trait under polygenic additive inheritance. The derivation relies on the threshold liability concept and on the normality assumption of the joint distribution of additive genetic values and their predictors used as selection criteria. This formula accounts for asymmetry of response when both the prevalence of the trait and the selection rate differ from 1/2 via a bivariate normal integral term. The relationship with the classical formula R = iota rho sigma G is explained with a Taylor expansion about a zero value of the correlation factor. Properties are illustrated with an example of sire selection based on progeny test performance which shows a departure from usual predictions up to 15-20% at low (0.05) or high (0.95) selection rates. Univariate approximations and extensions to several paths of genetic change are also discussed.     

ON THE EVOLUTION OF PHENOTYPIC PLASTICITY IN A SPATIALLY HETEROGENEOUS ENVIRONMENT

A genetic model for the dynamics of a quantitative trait is analyzed in terms of gene frequencies, linkage disequilibria, and environmental effects on the trait. In a randomly mating population, at each generation progeny move to niches where they are subject to weak Gaussian selection on the trait, with different fitness levels in the different niches. Initially, the variability of the trait is due to additive loci with heterozygous homeostasis. The evolution of plasticity is then described in terms of the invasion of the population by genetic modifiers that may epistatically affect the trait, its optimum in each niche, the strengths of selection, and other parameters characteristic of the niches. We show that the evolution of trait means within niches depends on the overall evolution in the whole system, and in general, optimum phenotypic values are not attained. The reaction norm and genotype-environment interaction may evolve even if the only effects of the modifier are on individual rates of dispersal, or on fitness effects resulting from the different environments in the different niches; this evolution does not require that the modifier affect parameters that influence the values of the trait. It is conjectured that in the least frequently reached niches with low fitness levels, the deviations from the trait optima should be larger than those in more commonly experienced and less stringent niches. Our analysis makes explicit the different contribution of between- and within-niche effects on the evolutionary dynamics of phenotypic plasticity in heterogeneous environments.     

Economic weights of maternal and direct traits of pigs calculated by applying gene flow methods

Multiple trait selection indexes in pig breeding programmes should take into account the population structure and time delay between parent selection and expressions of traits in all production levels next to the trait impacts on economic efficiency of production systems. Gene flow procedures could be used for the correct evaluation of maternal and direct traits of pig breeds involved in breeding or crossbreeding systems. Therefore, the aim of this study was to expand a previously developed bioeconomic model and computer program to calculate the marginal economic values by including a gene flow procedure to calculate the economic weights for maternal and direct traits in pig breeds. The new program was then applied to the three-way crossbreeding system of the Czech National Programme for Pig Breeding. Using this program, the marginal economic values of traits for dam breeds Czech Large White in the dam position and Czech Landrace in the sire position, and for the sire breed Pietrain were weighted by the number of discounted gene expressions of selected parents of each breed summarised within all links of the crossbreeding system during the 8-year investment period. Economic weights calculated in this way were compared with the approximate economic weights calculated previously without a gene flow procedure. Taking into account the time delay between parent selection and trait expression (using discounting with half-year discount rates of 2% or 5%) and including more than one generation of parent progeny had little impact on the relative economic importance of maternal and direct traits of breeds involved in the evaluated three-way crossbreeding system. These results indicated that this gene-flow method could be foregone when estimating the relative economic weights of traits in pig crossbreeding systems applying artificial insemination at all production levels.     

Adaptation to slow environmental change, with apparent anticipation of selection

We investigate a genetic model of a large population of sexual organisms in a changing environment. The organisms are subject to stabilising selection on a quantitative trait, with environmental change causing the fitness optimum to move. When the fitness optimum moves slowly, adaptation to the changing environment occurs by means of reasonably well-separated substitutions at the loci controlling the trait. In this way, the trait generally tracks the moving optimum, but in such a case, the population may exhibit periods of time where the mean trait value overshoots the moving optimal trait value, thereby exhibiting an apparent anticipation of selection. The mechanism underlying this phenomenon is determined from consideration of a simpler model that correctly captures the observed dynamical behaviour. We note that very slow rates of changes of traits are seen in the fossil record and the present work may be relevant to this topic.     

The evolution of genetic canalization under fluctuating selection

Abstract.— If the direction of selection changes from generation to generation, the ability to respond to selection is maladaptive: the response to selection in one generation leads to reduced fitness in the next. Because the response is determined by the amount of genetic variance expressed at the phenotypic level, rapidly fluctuating selection should favor modifier genes that reduce the phenotypic effect of alleles segregating at structural loci underlying the trait. Such reduction in phenotypic expression of genetic variation has been named "genetic canalization." I support this argument with a series of two- and multilocus models with alternating linear selection and Gaussian selection with fluctuating optimum. A canalizing modifier gene affects the fitness of its carriers in three ways: (1) it reduces the phenotypic consequences of genetic response to previous selection; (2) it reduces the genetic response to selection, which is manifested as linkage disequilibrium between the modifier and structural loci; and (3) it reduces the phenotypic variance. The first two effects reduce fitness under directional selection sustained for several generations, but improve fitness when the direction of selection has just been reversed. The net effect tends to favor a canalizing modifier under rapidly fluctuating selection regimes (period of eight generations or less). The third effect improves fitness of the modifier allele if the fitness function is convex and reduces it if the function is concave. Under fluctuating Gaussian selection, the population is more likely to experience the concave portion of the fitness function when selection is stronger. Therefore, only weak to moderately strong fluctuating Gaussian selection favors genetic canalization. This paper considerably broadens the conditions that favor genetic canalization, which so far has only been postulated to evolve under long-term stabilizing selection.     

A Population Genetics Model of Marker-Assisted Selection

A deterministic two-loci model was developed to predict genetic response to marker-assisted selection (MAS) in one generation and in multiple generations. Formulas were derived to relate linkage disequilibrium in a population to the proportion of additive genetic variance used by MAS, and in turn to an extra improvement in genetic response over phenotypic selection. Predictions of the response were compared to those predicted by using an infinite-loci model and the factors affecting efficiency of MAS were examined. Theoretical analyses of the present study revealed the nonlinearity between the selection intensity and genetic response in MAS. In addition to the heritability of the trait and the proportion of the marker-associated genetic variance, the frequencies of the selectively favorable alleles at the two loci, one marker and one quantitative trait locus, were found to play an important role in determining both the short- and long-term efficiencies of MAS. The evolution of linkage disequilibrium and thus the genetic response over several generations were predicted theoretically and examined by simulation. MAS dissipated the disequilibrium more quickly than drift alone. In some cases studied, the rate of dissipation was as large as that to be expected in the circumstance where the true recombination fraction was increased by three times and selection was absent.     

Models of sexual selection on a quantitative genetic trait when preference is acquired by sexual imprinting

The evolution of a quantitative genetic trait under stabilizing viability selection and sexual selection is modeled for a polygynous species in which female mating preferences are acquired by sexual imprinting on the parents and by exposure to the surviving population at large. Stabilizing viability selection acts equally on both sexes in the case of a sexually monomorphic trait and on males only in the case of a dimorphic trait. A genetically fixed sensory or perceptual bias defines the origin of the scale on which the trait is measured, and the possibility is incorporated that female preferences may deviate asymmetrically from the familiar-either toward or away from this origin. When viability selection is strong relative to sexual selection, the models predict that the mean trait value will evolve to the viability optimum. With intermediate ratios of the strength of viability to sexual selection, a stable equilibrium can occur on either side of this viability optimum, depending on the direction of asymmetry in female preferences. When viability selection is relatively weak and certain other conditions are also satisfied, runaway selection is predicted.     

Genetic heterogeneity and accelerated responses to directional selection in Drosophila

Summary Strains set up from single inseminated founder females of D. melanogaster from the same population have been previously shown to differ genetically for the incidence of flies with more than four scutellar chaetae (additional chaetae). Therefore the base population is polymorphic for this trait. This was exploited by carrying out directional selection in lines derived from those strains initially having a high mean chaeta number. This led to far more rapid responses to selection than were obtained in lines derived from strains with lower means, such that in one line a continuous accelerated response was observed for the first 12 generations of selection. A correlated response was found for sternopleural chaeta number at generation 19 of selection, showing that at least some genes may affect both traits.     

THE ROLES OF FLUCTUATING SELECTION AND LONG-TERM DIAPAUSE IN MICROEVOLUTION OF DIAPAUSE TIMING IN A FRESHWATER COPEPOD

Direct observations of selection response in natural, unmanipulated populations in the wild are rare. Those that exist have resulted from major changes in environment during an ongoing study. Selection response should be more common and more readily observable in short-lived organisms where the direction of selection changes from year to year. We examined how the interaction of fluctuating selection, and emergence from long-term diapause, caused ongoing microevolutionary change over eight years in an important life-history trait (diapause timing) in the freshwater calanoid copepod Diaptomus sanguineus. Emergence from long-term diapause releases into the population lineages that did not experience the most recent bout of selection, thereby promoting the maintenance of the heritable trait variation that allows continual selection response. A mechanistic selection model was created on the basis of field and laboratory studies to predict how interannual variations in predation intensity generate year-to-year changes in mean diapause timing and in net reproductive success for alternate trait values. The predicted selection response and the estimated effect of emergence from diapause were both significantly correlated with observed changes in trait mean. A linear model combining selection response and emergence from diapause explained 59% of the variance in year-to-year changes in trait mean. According to this model, strong selection occurred in about half of the years studied, and the average annual contributions to changes in trait mean from selection and emergence were roughly equal. Thus, both fluctuating natural selection and emergence from prolonged diapause affect the expression of diapause timing by D. sanguineus. Fluctuating selection is ubiquitous in nature and may provide opportunities in other populations to witness ongoing natural selection without directional trends in mean phenotype.     

Genetic response from marker assisted selection in an outbred population for differing marker bracket sizes and with two identified quantitative trait loci.

Effect of flanking quantitative trait loci (QTL)-marker bracket size on genetic response to marker assisted selection in an outbred population was studied by simulation of a nucleus breeding scheme. In addition, genetic response with marker assisted selection (MAS) from two quantitative trait loci on the same and different chromosome(s) was investigated. QTL that explained either 5% or 10% of phenotypic variance were simulated. A polygenic component was simulated in addition to the quantitative trait loci. In total, 35% of the phenotypic variance was due to genetic factors. The trait was measured on females only. Having smaller marker brackets flanking the QTL increased the genetic response from MAS selection. This was due to the greater ability to trace the QTL transmission from one generation to the next with the smaller flanking QTL-marker bracket, which increased the accuracy of estimation of the QTL allelic effects. Greater negative covariance between effects at both QTL was observed when two QTL were located on the same chromosome compared to different chromosomes. Genetic response with MAS was greater when the QTL were on the same chromosome in the early generations and greater when they were on different chromosomes in the later generations of MAS.     

An experimental test of the efficiency of family selection in chickens

Summary Responses to single trait selection on individual phenotype and sire-family mean phenotype for survivor's egg weight and rate of lay were measured for a single generation in 13 replicates. Each replicate-selection criterion-trait subclass consisted of eight sire families or 72 females measured and was reproduced from the best 25% of the families or individuals. The realized heritability of egg weight was 0.39 and that of rate of lay was 0.31, both of which were significantly greater than zero but not significantly different from the predicted values based on halfsib correlations in the base population.The standardized response to sire-family selection was less than the response to individual selection for both traits and the difference was significant for rate of lay (0.10; 0.31) but not for egg weight (0.22; 0.39). The predicted responses to sire-family selection were less than those for individual selection for both traits, and the observed responses to sire-family selection were not significantly different from the predicted values for either trait.These experimental results do not disagree with the theoretical expectations of the relative efficiencies of individual and sire-family selection.Journal paper no. 7479, Purdue University, Agricultural Experiment Station. This investigation was conducted as a part of the cooperative research of the NC-89 Regional Poultry Breeding Project entitled Nature and Utilization of Genetic Variation in Poultry Improvement     

Efficiency of indirect selection at selection equilibrium

Summary Efficiency of indirect selection compared with that of direct selection to increase the mean value of some trait has been usually studied by considering a single generation of indirect and direct responses to selection only. However, under continued selection, genetic variances and covariances, and therefore expected genetic responses, change each generation due to linkage disequilibrium. With directional and truncation selection, genetic parameters asymptote to limiting values after several generations. The efficiency of indirect selection is examined in this limiting situation. The ratio of correlated response to direct response for the trait to improve in the limit is compared with the ratio after the first generation of selection. For all initial parameter values for which indirect selection is more efficient than direct selection, relative efficiency of indirect selection is smaller in the limit than in the first generation. For some parameter values, indirect selection is more efficient than direct selection in the first generation, but less efficient in the limit. Expressions for minimum values of the initial genetic correlation and heritability of the alternative trait required for indirect selection to be preferred in the limit are derived. These values are higher when limiting responses are used instead of single generation responses. The loss in relative efficiency of indirect selection from changes in genetic parameters due to selection should be taken into account when applications of indirect selection are considered.     

Stabilizing Selection,Purifying Selection,and Mutational Bias in Finite Populations

Genomic traits such as codon usage and the lengths of noncoding sequences may be subject to stabilizing selection rather than purifying selection. Mutations affecting these traits are often biased in one direction. To investigate the potential role of stabilizing selection on genomic traits, the effects of mutational bias on the equilibrium value of a trait under stabilizing selection in a finite population were investigated, using two different mutational models. Numerical results were generated using a matrix method for calculating the probability distribution of variant frequencies at sites affecting the trait, as well as by Monte Carlo simulations. Analytical approximations were also derived, which provided useful insights into the numerical results. A novel conclusion is that the scaled intensity of selection acting on individual variants is nearly independent of the effective population size over a wide range of parameter space and is strongly determined by the logarithm of the mutational bias parameter. This is true even when there is a very small departure of the mean from the optimum, as is usually the case. This implies that studies of the frequency spectra of DNA sequence variants may be unable to distinguish between stabilizing and purifying selection. A similar investigation of purifying selection against deleterious mutations was also carried out. Contrary to previous suggestions, the scaled intensity of purifying selection with synergistic fitness effects is sensitive to population size, which is inconsistent with the general lack of sensitivity of codon usage to effective population size.     

Evolution in a changing environment: a case study with great tit fledging mass

Heritable phenotypic traits under significant and consistent directional selection often fail to show the expected evolutionary response. A potential explanation for this contradiction is that because environmental conditions change constantly, environmental change can mask an evolutionary response to selection. We combined an "animal model" analysis with 36 years of data from a long-term study of great tits (Parus major) to explore selection on and evolution of a morphological trait: body mass at fledging. We found significant heritability of this trait, but despite consistent positive directional selection on both the phenotypic and the additive genetic component of body mass, the population mean phenotypic value declined rather than increased over time. However, the mean breeding value for body mass at fledging increased over time, presumably in response to selection. We show that the divergence between the response to selection observed at the levels of genotype and phenotype can be explained by a change in environmental conditions over time, that is, related both to increased spring temperature before breeding and elevated population density. Our results support the suggestion that measuring phenotypes may not always give a reliable impression of evolutionary trajectories and that understanding patterns of phenotypic evolution in nature requires an understanding of how the environment has itself changed.     

A finite locus effect diffusion model for the evolution of a quantitative trait

A diffusion model is constructed for the joint distribution of absolute locus effect sizes and allele frequencies for loci contributing to an additive quantitative trait under selection in a haploid, panmictic population. The model is designed to approximate a discrete model exactly in the limit as both population size and the number of loci affecting the trait tend to infinity. For the case when all loci have the same absolute effect size, formal multiple-timescale asymptotics are used to predict the long-time response of the population trait mean to selection. For the case where loci can take on either of two distinct effect sizes, not necessarily with equal probability, numerical solutions of the system indicate that response to selection of a quantitative trait is insensitive to the variability of the distribution of effect sizes when mutation is negligible.     

The levels of artificial insemination and missing sire information make genomic selection not always beneficial in meat sheep

Numerous meat sheep breeding programs in developed and developing countries are characterized by incomplete sire information and a predominant use of natural matings. These two parameters potentially affect the benefit of genomic selection (GS), especially for the selection of a late-in-life trait. Using stochastic simulations, the genetic gains obtained using genomic and conventional strategies for a maternal trait were evaluated in meat sheep population. Natural mating and artificial insemination (AI)-based designs, inspired by the current diversity of designs used for French meat sheep breeds, were modeled and three genomic strategies were tested and compared with a conventional selection strategy: parentage assignment, GS based on a male or a male and female reference population. Genomic selection based on a male reference population did not always outperform conventional selection. Its benefit depended on the design, the level of missing information on dam sires, and the level of AI. Genomic selection based on a male and female reference population always outperformed the conventional selection strategy, even if only 25 % of the females in the nucleus were genotyped.