Selection index updating

Summary When traits become evident at different ages or there are large differences in the costs of measuring various traits, selection by independent culling levels may give a higher aggregate economic return than index selection because not all traits need to be measured on all individuals. The problems with optimum independent culling selection is that general solutions are not possible and numerical integration is needed for specific cases. Recently, Xu and Muir (1991) developed a new independent culling level procedure by use of orthogonal transformation of the original characters. With their procedure, explicit solutions for optimum truncation points are possible without numerical integration. As such, the procedure is proficient for any number of stages, and generalized theoretical comparisons of alternative breeding strategies are possible. However, their procedure was limited to the case where selection is for one character at each stage. In this paper, our previous results are extended to the general case of multi-stage index selection, called selection index updating. This procedure is called selection index updating because as traits become available in latter stages, each subsequent index contains all of the traits available up to that stage.The procedure is to develop sequential indices for each stage such that correlations among indices at different stages are zero. Optimum culling points are obtained for the updating procedure by using Xu and Muir's (1991) iterative equations. Due to the property of orthogonality of the updated indices, aggregate gain can be partitioned into gains due to various stages of selection. Partitioning of aggregate economic gain is useful to breeders who desire to adjust individual trait selection intensity based on facilities available at that stage. Methods are discussed to modify the procedure to obtain maximum aggregate economic return per unit of cost associated with obtaining measures on each trait. An application of multi-stage selection is demonstrated using a set of data for Rhode Island Red layer type chickens. A second example demonstrates the use of multi-stage selection optimized with respect to aggregate economic gain and costs associated with obtaining measurements.Journal Paper No. 12813 of the Purdue University Agricultural Experiment Station     

Optimising two-stage independent culling selection in tree and animal breeding

Summary Theory is given for a simple practical method of predicting gain from two-stage independent culling, where stage 1 of selection is for individual performance and stage 2 is for either progeny performance only, or an index combining individual and progeny performance. Expected gain is determined as a direct function of heritabilities, genetic correlations, selection intensities and progeny-testing capacity. Results show the effect these parameters can have on proportions selected at each stage and, if multiple selection criteria are used, traits selected for first. Methods are discussed in the context of tree and animal breeding, with an example taken from forestry.     

Multistage Selection for Genetic Gain by Orthogonal Transformation

An exact transformed culling method for any number of traits or stages of selection with explicit solution for multistage selection is described in this paper. This procedure does not need numerical integration and is suitable for obtaining either desired genetic gains for a variable proportion selected or optimum aggregate breeding value for a fixed total proportion selected. The procedure has similar properties to multistage selection index and, as such, genetic gains from use of the procedure may exceed ordinary independent culling level selection. The relative efficiencies of transformed to conventional independent culling ranged from 87% to over 300%. These results suggest that for most situations one can chose a multistage selection scheme, either conventional or transformed culling, which will have an efficiency close to that of selection index. After considering cost savings associated with multistage selection, there are many situations in which economic returns from use of independent culling, either conventional or transformed, will exceed that of selection index.     

Evolution of adaptive phenotypic variation patterns by direct selection for evolvability

A basic assumption of the Darwinian theory of evolution is that heritable variation arises randomly. In this context, randomness means that mutations arise irrespective of the current adaptive needs imposed by the environment. It is broadly accepted, however, that phenotypic variation is not uniformly distributed among phenotypic traits, some traits tend to covary, while others vary independently, and again others barely vary at all. Furthermore, it is well established that patterns of trait variation differ among species. Specifically, traits that serve different functions tend to be less correlated, as for instance forelimbs and hind limbs in bats and humans, compared with the limbs of quadrupedal mammals. Recently, a novel class of genetic elements has been identified in mouse gene-mapping studies that modify correlations among quantitative traits. These loci are called relationship loci, or relationship Quantitative Trait Loci (rQTL), and affect trait correlations by changing the expression of the existing genetic variation through gene interaction. Here, we present a population genetic model of how natural selection acts on rQTL. Contrary to the usual neo-Darwinian theory, in this model, new heritable phenotypic variation is produced along the selected dimension in response to directional selection. The results predict that selection on rQTL leads to higher correlations among traits that are simultaneously under directional selection. On the other hand, traits that are not simultaneously under directional selection are predicted to evolve lower correlations. These results and the previously demonstrated existence of rQTL variation, show a mechanism by which natural selection can directly enhance the evolvability of complex organisms along lines of adaptive change.     

Phenotypic response to selection for traits with direct and maternal components when generations overlap

Summary Prediction of response to selection for traits with direct and maternal components is described for discrete and overlapping generations. Expected phenotypic response is the sum of direct and maternal contributions, the latter having a genetic and an environmental component. With overlapping generations the selection differentials achieved on these components are added to respective updated vectors containing age-sex distributions with values of previous selection rounds. An example demonstrates that in the early stages, results may be considerably affected by environmental correlations between direct and maternal effects. The method could be helpful in interpreting phenotypic changes in a population selected for traits with maternal effects.     

Gametic models for multitrait selection schemes to study variance of response and drift under adverse genetic correlations

A major issue faced by breeders is how to effectively manage adverse correlations in breeding programs. We present results of a Monte Carlo allele-based simulation of the changes in response and variance of response under adverse genetic correlations by using the examples of two contrasting selection methods: the ‘Smith-Hazel’ selection index (SH) and independent culling (IC). We assumed several gene models, which included linkage and antagonistic pleiotropy as the primary drivers of adverse genetic correlations. The different behaviors of these selection methods allowed us to identify the mechanism behind the generation of uncertainty under antagonistic trait selection: IC had the properties of stabilizing selection, while SH behaved more similar to disruptive selection. Although SH outperformed IC in terms of genetic gain, this advantage happened at the cost of higher variance of response and loss of heterozygosity. Using an optimum selection algorithm (OS) to prevent the loss of heterozygosity through a constraint on inbreeding in SH/OS increased marginally the reliability, remaining still below that of IC under equal conditions. However, SH/OS had lower inbreeding (ΔF) than IC for equivalent levels of genetic gain, so a compromise between high selection reliability, low ΔF, and gain must be made by a breeder under antagonistic trait selection even with the use of optimization tools.     

Reproductive fitness and artificial selection in animal breeding: culling on fitness prevents a decline in reproductive fitness in lines of Drosophila melanogaster selected for increased inebriation time

Summary The maintenance of reproductive fitness in lines subjected to artificial selection is one of the major problems in animal breeding. The decline in reproductive performance has neither been predictable from heritabilities and genetic correlations, nor have conventional selection indices been adequate to avoid the problem. Gowe (1983) has suggested that the heritabilities of reproductive traits are non-linear, with heritabilities being higher on the lower fitness side. Consequently, he has predicted that culling on reproductive fitness in artificial selection lines will be effective in preventing the usual declines in fitness. An experimental evaluation of Gowe's prediction has been carried out by comparing fitnesses of replicated lines of three treatments: selection for increased inebriation time without culling on fitness (HO), selection for inebriation time with culling of 20% (4/20) of selected females on reproductive fitness (HS), and unselected controls (C). Response to selection for inebriation time in the two selection treatments was similar. After 25 generations, the competitive index, a measure of reproductive fitness, was significantly lower in the HO treatment than the HS treatment, while the HS treatment did not differ from the control lines or the base population. These results demonstrate for the first time that culling on reproductive fitness in selection lines can be used to prevent the usual decline in reproductive performance.     

Genetic drift and polygenic inheritance

The interaction of random gene drift and selection was studied by computer simulation for two quantitative traits, which were considered to approximate stature and skin color differences in human populations. The expected effects of gene drift, fixation of alleles and reduction of genotypic and phenotypic variances, were found in the simulation. Stabilizing selection, which seems to be the type of selection operating on these traits, was found to increase the effects of gene drift. Since there seems to be no evidence of reduction in phenotypic and presumably genotypic variability in small human populations, the applicability of these simple genetic models to human traits raises problems for which several possible solutions exist.     

Selection and genetic (co)variance in bighorn sheep

Genetic theory predicts that directional selection should deplete additive genetic variance for traits closely related to fitness, and may favor the maintenance of alleles with antagonistically pleiotropic effects on fitness-related traits. Trait heritability is therefore expected to decline with the degree of association with fitness, and some genetic correlations between selected traits are expected to be negative. Here we demonstrate a negative relationship between trait heritability and association with lifetime reproductive success in a wild population of bighorn sheep (Ovis canadensis) at Ram Mountain, Alberta, Canada. Lower heritability for fitness-related traits, however, was not wholly a consequence of declining genetic variance, because those traits showed high levels of residual variance. Genetic correlations estimated between pairs of traits with significant heritability were positive. Principal component analyses suggest that positive relationships between morphometric traits constitute the main axis of genetic variation. Trade-offs in the form of negative genetic or phenotypic correlations among the traits we have measured do not appear to constrain the potential for evolution in this population.     

Genetic correlation and response to selection in simulated populations

Summary Effects of truncation selection of a primary trait upon genetic correlation with a secondary trait were examined over 30 generations in genetic populations simulated by computer. Populations were 24 males and 24 females mated randomly with replacement; number of offspring was determined by intensity of selection. Each trait was controlled by 48 loci segregating independently, effects were equal at every locus, and gene frequency was arbitrarily set at 0.5 at each locus in the initial generation. All combinations of three genetic correlations, three intensities of selection, and three environmental variances were simulated. Gene action was additive. Genetic correlation was set by number of loci which affected both traits and was measured each generation as the product-moment correlation of genotypic values and estimated by two methods of combining phenotypic covariances between parent and offspring.Genetic correlations in each offspring generation remained consistently near initial correlations for all environmental variances when fraction of offspring saved as parents was as large as one-half. When the fraction of offspring saved was as small as one-fifth, genetic correlations decreased but most rapidly with heritability high and after the 15th generation of selection. Truncation selection caused genetic correlation to decrease in those offspring selected to become parents of the next generation. Amount of reduction depended on heritability of the selected trait rather than on degree of truncation selection. Estimates of genetic correlation from phenotypic covariances between parent and offspring fluctuated markedly from real correlations in the small populations simulated.Michigan Agricultural Experiment Station Journal Article 4836. Part of North Central Regional Project NC-2.     

Simultaneous selection on two fitness-related traits in the butterfly Bicyclus anynana

Abstract. Theory about the role of constraints in evolution is abundant, but few empirical data exist to describe the consequences a bias in phenotypic variation has for micro evolution. Responses to natural selection can be severely hampered by a genetic correlation among a suite of traits. Constraints can be studied using antagonistic selection experiments, that is, two-trait selection in opposition to this correlation. The two traits studied here were development time and wing pattern (eyespot size) in the butterfly Bicyclus anynana , both of which have a clear adaptive significance. Rates of response were higher for eyespot size than for development time, but were independent of the concurrent selection (either in the same direction as the correlation or perpendicular to it). Regimes differed in both traits in all directions after 11 generations of selection. The uncoupling lines had higher relative responses than the synergistic lines in development time and equal relative responses in eyespot size. The patterns for eyespot size (reaction norms) were consistent across different rearing temperatures. Differences in lines selected for fast and slow development time were more pronounced at lower temperatures, irrespective of the direction of joint wing pattern selection. Furthermore, correlated responses in pupal weight and growth rate were observed; lines selected for a slower development had higher pupal weights, especially at lower temperatures. The response of the uncoupling lines was not hampered by a lack of selectable genetic variation, and the relative response in the development time was larger than expected based on response in the coupled direction and quantitative genetic predictions. This suggests that the structure of the genetic architecture does not constrain the short-term, independent evolution of both wing pattern and development time.     

The effects of selection for gain in mice on the direct-maternal genetic correlation

Components of genetic variation for postweaning growth traits were estimated for both control and growth stocks of mice. The effect of phenotypic selection for gain, which genetically combines selection for additive direct and maternal effects, on additive genetic variance components, heritability, and additive genetic correlationsis discussed. Quantitative genetic theory predicts that simultaneous selection for two metric traits in the same direction will cause the genetic correlation between the two traits to become more negative. The results presented in this paper conflict with this theory. The direct-maternal additive genetic correlation was more negative in the control line (with 356 mice) than in the growth-selected line (with 320 mice) for the three traits analyzed (0.310 vs 0.999 for 21-day weight, 0.316 vs 1.000 for 42-day weight, and 0.506 vs 1.000 for gain from 21–42 days). Estimates were obtained by restricted maximum likelihood (REML) computed under a derivative free algorithm (DFREML).     

Converting multi-trait breeding objectives into operative selection indexes to ensure genetic gains in low-input sheep and goat breeding programmes

Small ruminant breeding programmes in low-input production systems are best organised at the community level. Participant farmers have to agree on goal traits and their relative importance. When BLUP breeding values of goal traits are not available in time, appropriate selection indexes can be used to aid visual selection. Taking Ethiopian Abergelle goat and Bonga sheep community-based breeding programmes (CBBPs) as an example, breeding objective functions were defined and selection indexes were constructed and evaluated. Breeding goals for Abergelle goats included early sale weight, survival and milk production. Breeding goals for Bonga included the number of offspring born, sale weight and survival. Economic weights of objective traits can be used in several ways depending on measured traits and the reliability of their genetic parameters. Selection indexes included combinations of objective traits measured on candidates and their dams and situations when Abergelle communities prefer to restrict genetic changes in number of offspring born or adult weight and when Bonga communities prefer to restrict changes in adult weight. Genetic and economic gains were evaluated as well as sensitivity to feed cost assumptions and to repeated dam records. After independent culling on preponderant traits such as coat colour and horn/tail type, sires in Abergelle goat community breeding programmes should be selected on indexes including at least own early live weight and their dams average milk production records. Sires for Bonga sheep programmes should be selected on own early live weight and desirably also on their dam’s number of offspring born. Sensitivity to feed cost assumptions was negligible but repeated measurements of dam records improved index accuracies considerably. Restricting genetic changes in number of offspring born or adult weight is not recommended.     

Correlated responses on growth traits after two-stage selection for ovulation rate and litter size in rabbits

Rabbit commercial maternal lines are usually selected for litter size (LS) and paternal lines for growth rate (GR). Line OR_LS was selected by ovulation rate (OR) and LS to improve LS more efficiently. In this study, growth traits of line OR_LS were evaluated by estimating the correlated response on weaning weight (WW), slaughter weight (SW) and GR during fattening period as well as their variability (DWW, DSW and DGR, respectively). Data were analyzed using Bayesian inference methods. Heritability estimates were low for growth traits (0.09, 0.13 and 0.14 for WW, SW and GR, respectively) and negligible for growth traits variability (0.01, 0.004 and 0.01 for DWW, DSW and DGR, respectively). Moderate common litter effect ratio (c²; 0.35, 0.28 and 0.27) and low maternal effect ratio (m²; 0.11, 0.05 and 0.01) were obtained for WW, SW and GR, respectively. Both c² and m² were lower at slaughter than at weaning. In addition, low common litter effect and negligible maternal effect were observed for growth traits variability. Genetic correlations between LS and both growth traits and their variability were close to zero. Positive genetic correlations were observed between OR and growth traits (0.19, 0.38 and 0.36 for WW, SW and GR, respectively) as well as between OR and growth traits variability (0.35, 0.62 and 0.20 for DWW, DSW and DGR, respectively). Positive correlated responses in both periods were obtained for growth traits, WW, SW and GR (0.037, 0.156 and 0.110 kg, respectively). The correlated response found in growth traits might be due to the positive genetic correlations between OR and these traits. However, selection for OR and LS using independent culling levels did not modify the growth traits variability. Therefore, no negative consequences on growth traits can be expected in current commercial maternal lines.     

Phenotypic and genetic correlations among floral traits in two species of Thalictrum

The evolution of dioecy in plants is expected to be followed by sex-specific selection, leading to sexual dimorphism. The extent of the response to selection depends on the genetic covariance structure between traits both within and between the sexes. Here I describe an investigation to determine phenotypic and genetic correlations between reproductive traits within cryptically dioecious Thalictrum pubescens and within morphologically dioecious T. dioicum. Females of T. pubescens produce flowers having stamens and pistils, appearing hermaphroditic. Genetic correlations were estimated as family-mean correlations among paternal half-sib families. Positive phenotypic and genetic correlations between parts of the same reproductive organs, as the anther and filament of the stamen, indicate developmental associations between these traits in both species. Negative genetic correlations were detected between pistil number and size of reproductive organs in T. dioicum and showed the same direction, but not significance, in T. pubescens. There was a negative phenotypic correlation between the number of stamens and the number of pistils within female flowers of T. pubescens. Within T. pubescens, there was a positive genetic correlation between the number of stamens in males and the number of pistils in females, indicating that floral evolution in males and females may not be independent in this species.     

A comparison of methods to calculate a total merit index using stochastic simulation

Background

Modern dairy cattle breeding goals include several production and more and more functional traits. Estimated breeding values (EBV) that are combined in the total merit index usually come from single-trait models or from multivariate models for groups of traits. In most cases, a multivariate animal model based on phenotypic data for all traits is not feasible and approximate methods based on selection index theory are applied to derive the total merit index. Therefore, the objective of this study was to compare a full multitrait animal model with two approximate multitrait models and a selection index approach based on simulated data.

Methods

Three production and two functional traits were simulated to mimic the national Austrian Brown Swiss population. The reference method for derivation of the total merit index was a multitrait evaluation based on all phenotypic data. Two of the approximate methods were variations of an approximate multitrait model that used either yield deviations or de-regressed breeding values. The final method was an adaptation of the selection index method that is used in routine evaluations in Austria and Germany. Three scenarios with respect to residual covariances were set up: residual covariances were equal to zero, or half of or equal to the genetic covariances.

Results

Results of both approximate multitrait models were very close to those of the reference method, with rank correlations of 1. Both methods were nearly unbiased. Rank correlations for the selection index method showed good results when residual covariances were zero but correlations with the reference method decreased when residual covariances were large. Furthermore, EBV were biased when residual covariances were high.

Conclusions

We applied an approximate multitrait two-step procedure to yield deviations and de-regressed breeding values, which led to nearly unbiased results. De-regressed breeding values gave even slightly better results. Our results confirmed that ignoring residual covariances when a selection index approach is applied leads to remarkable bias. This could be relevant in terms of selection accuracy. Our findings suggest that the approximate multitrait approach applied to de-regressed breeding values can be used in routine genetic evaluation.     

Simultaneous marker-assisted selection for multiple traits in autogamous crops

A method is presented for the selection of parents with the aim of obtaining improved genotypes in the progeny of a cross. The procedure is designed to select in several unrelated traits simultaneously and is based on the selection of molecular markers that are linked to QTLs. The method was compared with conventional phenotypic selection in simulation experiments for a number of genetic structures underlying the traits and several types of parental populations. Although the method in general provides good results, some of the underlying assumptions may be violated quite easily, thereby reducing the applicability of the procedure in practice. Received: 10 September 1999 / Accepted: 24 August 2000     

Efficiency of direct selection on quantitative trait loci for a two-trait breeding objective

Selection on known loci affecting quantitative traits (DSQ) was compared to phenotypic selection index for a single and a two-trait selection objective. Two situations were simulated; a single known quantitative locus, and ten identified loci accounting for all the additive genetic variance. Selection efficiency of DSQ relative to traitbased selection was higher for two-trait selection, than was selection on a single trait with the same heritability. The advantage of DSQ was greater when the traits were negatively correlated. Relative selection efficiency (RSE) for a single locus responsible for 0.1 of the genetic variance was 1.11 with heritabilities of 0.45 and 0.2 and zero genetic and phenotypic correlations between the traits. RSE of DSQ for ten known loci was 1.5 to 1.8 in the first 3 generations of selection, but declined in each subsequent generation. With DSQ most loci reached fixation after 7 generations. Response to trait-based selection continued through generation 15 and approached the response obtained with DSQ after 10 generations. The cumulative genetic response after 10 generations of DSQ was only 93% to 97% of the economically optimum genotype because the less favorable allele reached fixation for some loci, generally those with effects in opposite directions on the two traits.     

The maintenance of phenotypic and genetic variation in threshold traits by frequency-dependent selection

Many traits are phenotypically dimorphic but determined by the action of many loci, the phenotype being a result of a threshold of sensitivity. Quantitative genetic analysis has shown that generally there is considerable additive genetic variation for the trait, the average heritability being 0.52. In numerous cases threshold traits have been shown, or are assumed, to be under frequency-dependent selection; examples include satellite-territorial behaviour, sex-determination, wing dimorphism and trophic dimorphism. In this paper I investigate the potential for frequency-dependent selection to maintain both phenotypic and additive genetic variation in threshold traits. The qualitative results are robust to the particular form of the frequency-dependent selection function. The equilibrium proportion is more or less independent of population size but the heritability increases with population size, typically approaching its maximal value at a population size of 5000, when the mutation rate is 10^?4. A tenfold decrease in the mutation rate requires an approximate doubling of the population size before an asymptotic value is approached. Thus frequency-dependent selection can account for both the existence of two morphs in a population and the observed levels of heritability. It is also shown, both via simulation and theory, that the quantitative genetic model and a simple phenotypic analysis predict the same equilibrium morph proportion.     

Predicting efficiency of selection on reproductive traits in the medicinal leech Hirudo medicinalis L

A set of selection measures for increasing reproduction efficiency in Hirudo medicinalis has been developed. The optimal values of reproductive traits corresponding to the highest progeny number were determined and recommended. The probability of correlated selection response in traits "number of threads in a cocoon" and "weight of threads" was estimated. Based on earlier results on phenotypic variation and heritability of reproductive traits in medicinal leech, efficiency of different selection modes was predicted.