A Note on Response to Selection in Non-Random Mating Populations

The selection theory proposed by Muralidharan and Jain (1992a, b; Biom. J. 34 , 147–152, 633–637) was re-examined. Although they concluded that the theory is appropriate for any system of mating, the author showed that it is not applicable to inbreeding populations, which is the most important type of non-random mating.     

Subset Selection for Exponential Populations: Determination of the Selection Constant

Given are k(≧2) exponential populations differing only in their location parameter. One wishes to choose the best one, that is the population with the largest value of the location parameter. A possible method for solving this problem is to select a subset of the k populations of size at least one which includes the best population with a required confidence P*(k^?1 ≤ P* ≤1). In this paper the required selection constant is determined for different values of k and P*. Also an approximation for the selection constant is derived. A comparison with the exact results is made.     

Impacts of QTL × Environment Interactions on Genetic Response to Marker-Assisted Selection

Genotype × environment (GE) interaction is a common characteristic for quantitative traits, and has been a subject of great concern for breeding programs. Simulation studies were conducted to investigate the effects of GE interaction on genetic response to marker-assisted selection (MAS). In our study we demonstrated that MAS is generally more efficient than phenotypic selection in the presence of GE interaction, and this trend is more pronounced for developing broadly adaptable varieties. The utilization of different QTL information dramatically influences MAS efficiency. When MAS is based on QTLs evaluated in a single environment, the causal QTL × environment (QE) interactions usually reduce general response across environments, and the reduction in the cumulative general response is a function of the proportion of QE interactions for the trait studied. However, MAS using QTL information evaluated in multiple environments not only yields higher general response, but the general response obtained is also reasonably robust to QE interactions. The total response achieved by MAS in a specific environment depends largely on the total heritability of traits and is slightly subject to relative changes between general heritability and GE interaction heritability. Two breeding strategies, breeding experiments conducted in one environment throughout and in two environments alternately, were also examined for the implementation of marker-based selection. It was thus concluded that plant breeders should be cautious to utilize QTL information from only one environment and execute breeding studies in another.     

Response to Selection Under Non-Random Mating II. Prediction

A general expression for response to selection appropriate for both random and non-random mating situations is derived and illustrated with full-sibbing.     

Gene Flow Technique for Response to Selection under Non-Random Mating

The gene flow technique for predicting response to selection in random mating populations with overlapping generations is extended to cover any system of mating and illustrated with full-sibbing.     

Response to Selection and Inbreeding Depression in a Dynamic Population for Amount of Inbreeding

A method for predicting response to selection and inbreeding depression in a dynamic population for amount of inbreeding was derived and illustrated with an example of selection under full-sib mating.     

Individualist and Multi-level Perspectives on Selection in Structured Populations

Recent years have seen a renewed debate over the importance of groupselection, especially as it relates to the evolution of altruism. Onefeature of this debate has been disagreement over which kinds ofprocesses should be described in terms of selection at multiple levels,within and between groups. Adapting some earlier discussions, we presenta mathematical framework that can be used to explore the exactrelationships between evolutionary models that do, and those that donot, explicitly recognize biological groups as fitness-bearing entities.We show a fundamental set of mathematical equivalences between these twokinds of models, one of which applies a form of multi-level selectiontheory and the other being a form of ``individualism.' However, we alsoargue that each type of model can have heuristic advantages over theother. Indeed, it can be positively useful to engage in a kind ofback-and-forth switching between two different perspectives on theevolutionary role of groups. So the position we defend is a``gestalt-switching pluralism.'     

Prediction of Response to Selection and Inbreeding Coefficient under Assortative Mating

A method for predicting response to selection and inbreeding coefficient under the continuous use of assortative mating was derived. Using the method, numerical computation was carried out, and the utility of assortative mating in the selection programmes was evaluated. It was shown that the continuous use of assortative mating could not produce an appreciable additional increase in intermediate- or long-term selection response.     

Further Investigations on the Robustness of the Standardized Selection Difference

The robustness of the standardized selection difference is investigated for the family of central chi-squared-distributions. The results are compared with those for the uniform, a family of triangular distributions and the exponential distribution. Beside these exact results and some simulation results are considered.     

Effects of random and non-random errors on phenotypic selection in autotetraploids

Summary A theoretical investigation was made to ascertain the effects of random and non-random deviations, called errors, of phenotypic from genotypic values on population means and on the response to phenotypic recurrent selection. The study was motivated as a selection experiment for disease resistance where there was either variability in the inoculation or environment (the random errors) or where the inoculation was above or below the the optimum rate where genetic differences in resistance are maximized (the non-random errors). The study was limited to the genetics at a diallelic locus (alleles B and b) in an autotetraploid population in random mating equilibrium. The response to selection was measured as the covariance of selection and compared to the exact covariance which was the covariance of selection without errors in phenotype. The random errors were modeled by assuming that a given percentage () of the population was uniformly distributed among the five possible genotype classes independent of their true genotypes. This model was analyzed numerically for a theoretical population with the frequency of the B allele (p) ranging from 0.0 to 1.0 and assumed errors of=0.1 and 0.5 for the following six types of genic action of the B allele: additive, monoplex dominance, partial monoplex dominance, duplex dominance, partial duplex dominance, and recessive. The effect of random error was to consistently reduce the response to selection by a percentage independent of the type of genic action at the locus. The effect on the population mean was an upward bias when p was low and a downward bias when p approached unity. In the non-random error model below optimum inoculations altered the phenotypes by systematically including percentage of susceptible genotypes into one or more other genotype classes with more genetic resistance (a positive shift). With above optimum inoculations, some resistant genotypes are classed with the non-resistant genotypes (a negative shift). The effects on the covariance of selection were found by numerical analysis for the same types of genic action and's as investigated for random error. With a negative shift and a low p, the covariance of selection was always reduced, but for an increasing p the covariance approached and exceeded the exact covariance for all types of genic action except additive. With a positive shift and a low p, response to selection was greatly improved for three types of genic action: duplex dominance, partial duplex dominance, and recessive. The effect of a non-random error on population means was to greatly bias the means upwards for a low p and positive shift, but with increasing p the bias decreased. A relatively slight decrease in the mean occurred with a negative shift. This study indicated check varieties commonly used to monitor selection pressures in screening programs are very responsive to positive non-random shifts, but are relatively unresponsive to negative shifts. The interaction of selection pressure, types of genic action, and genotypes in the class shift models was suggested as a partial explanation for the lack of response to increasing selection pressures observed in some breeding programs.Cooperative investigations of the Alfalfa Production Research Unit, United States Department of Agriculture, Agricultural Research Service, and the Nevada Agricultural Experiment Station, Reno, Nevada. Paper No. 404 Scientific Journal Series. Nevada Agricultural Experiment Station     

Effect of Selection on the Failure Rate Function

Effect of selection procedures such as truncation and genotypic selection, are studied using selection differentials. These studies are mainly restricted to the study of mean or percentiles of the characteristics of interest. However, in situations where improvement on longetivity is itself of interest, in addition to studying mean or percentiles, one may study the reliability characteristics such as Failure Rate, Mean Residual Life etc., of the lifetimes of individuals. In this paper, we study the effect of genotypic selection when the distribution function of the lifetime is governed by a single locus with 2 alleles. We compute the difference in the failure rate function from one generation to the next generation for different values of n, the number of generations. We also obtain the limiting values of the failure rate function as n and compute the number of generations required for the failure rate to reach a value close enough to the limiting failure rate function. We also consider an example in a two-loci case and study the effect of selection on the failure rate function.     

性能测定规模对父系猪短期选择效果的影响

利用Monte Carlo模拟,研究了群体大小、公母比例和每窝测定猪头数对父系猪的近交系数、选择反应及其变异系数的影响。设定基础群母猪规模大小为100头到500头共5个规模,公母猪比例为1：10和1：20,每窝测定猪头数为2头和4头,公母猪各半。选择的性状为一般父系猪的选择性状,即断奶后生长速度和达100kg体重时的活体背膘厚,利用多性状BLUP估计性状的育种值,选择指数中后一性状的经济加权系数是前一个的2．5倍,选择共进行了5个世代。结果表明,随着选择群母猪头数的增加,第五世代累积选择反应提高,近交系数上升速度变慢,第五世代累积选择反应的变异系数下降。随每窝测定仔猪头数的增加和公母比例的升高,累积选择反应加快,近交系数上升速度提高,第五世代累积选择反应的变异系数上升。保持公母猪比例不变和每窝测定仔猪头数不变,基础群母猪头数从100头增加到300头,累积选择反应有显著增加,近交系数上升速度显著减慢。母猪头数300头和400头以上的相比,第五世代的累积选择反应增加有限,近交系数下降速度减低。综合评价,对于父系猪的短期选育来说,基础群需要400头母猪以上,每窝测定4头仔猪,公母比例以1：20较好。     

Predicted and realized grain yield responses to full-sib family selection in CIMMYT maize (Zea mays L.) populations

Summary The maize (Zea mays L.) improvement program of the International Maize and Wheat Improvement Center (CIMMYT) develops broad-based maize populations and, until recently, improved all of them through full-sib family selection with international testing. The purpose of this study was to estimate the genetic and genetic × environment variance components for ten of those populations and to measure expected yield improvement from full-sib selection. Mean yield ranged from 3.35–6.81 t ha^–1. For five populations the average yield in the last cycle was higher than in the initial cycles. Several populations showed no improvement or yielded less in the final cycle of selection, either because selection intensity was low or because strong selection pressure was applied simultaneously for several traits. Variation resulting from differences among family means within cycles and from interaction between families and locations within cycles were significant in all populations and cycles. Results indicate that variability among full-sib families was maintained throughout the cycles for all populations. The large _ge ² / _g ² ratio shown by most populations suggests that yield response per cycle could be maximized if the environments in which progenies are tested were subdivided and classified into similar subsets. The proportion of the predicted response realized in improved yield varied for each population.Journal Paper No. 8640, Nebraska Agric. Res. Div. Project No. 12-159. Research was supported in part by USAID/USDA/ CSRS Research Grant No. 86-CRSR-2-2789     

The Effects of Background and Interference Selection on Patterns of Genetic Variation in Subdivided Populations

It is well known that most new mutations that affect fitness exert deleterious effects and that natural populations are often composed of subpopulations (demes) connected by gene flow. To gain a better understanding of the joint effects of purifying selection and population structure, we focus on a scenario where an ancestral population splits into multiple demes and study neutral diversity patterns in regions linked to selected sites. In the background selection regime of strong selection, we first derive analytic equations for pairwise coalescent times and F_ST as a function of time after the ancestral population splits into two demes and then construct a flexible coalescent simulator that can generate samples under complex models such as those involving multiple demes or nonconservative migration. We have carried out extensive forward simulations to show that the new methods can accurately predict diversity patterns both in the nonequilibrium phase following the split of the ancestral population and in the equilibrium between mutation, migration, drift, and selection. In the interference selection regime of many tightly linked selected sites, forward simulations provide evidence that neutral diversity patterns obtained from both the nonequilibrium and equilibrium phases may be virtually indistinguishable for models that have identical variance in fitness, but are nonetheless different with respect to the number of selected sites and the strength of purifying selection. This equivalence in neutral diversity patterns suggests that data collected from subdivided populations may have limited power for differentiating among the selective pressures to which closely linked selected sites are subject.     

Effect of Selection on a Quantitative Characteristic

In this paper we study the effect of selection procedures on certain parameters of the distribution function (d.f.) (such as mean, percentile etc.) of a quantitative characteristic X, in successive generations when the d.f. is governed by a single locus. We study the changes in gene frequencies under the truncation and genotype selection procedures by obtaining approximations to the gene frequencies, since exact expressions are not available. Using these approximations for the gene frequencies, we compute the selection differentials of X for different values of n, the number of generations. We also obtain the limiting distributions as n → ∞ and compute the number of generations required for the above parameter(s) of the d.f. to reach a value close enough to the limiting value.     

Parental effects in Lychnis flos-cuculi. II: Selection on time of emergence and seedling performance in the field

Selection on the timing of seedling emergence was investigated in an experimental population of Lychnis flos-cuculi, a perennial hay-meadow species. Seeds obtained from a full diallel cross of 8 genotypes from a field population were sown along an environment gradient that included the parental site. Significant directional selection for early emergence was found and the intensity of selection varied among sites. Emergence time varied significantly among progeny families of different maternal and paternal genotypes. These differences could be attributed to parental effects whereas narrow-sense heritabilities were close to zero. Survivorship until autumn differed among progeny of paternal families. Survivorship of maternal progeny varied among sites. Whereas differences in survival and plant size among individuals from different emergence cohorts persisted over the winter, the significance of these differences among progeny from different parental genotypes disappeared. It is suggested that a response to selection on emergence time might be low since (1) the narrow sense heritability was low, (2) parental genotypes differed in their effect on offspring emergence time when used as female parent or as pollen donor and (3) there was a family x site interaction for survival. Families with relatively early emerging seedlings also had a significantly higher seed weight, emergence percentage, and plant weight although the strength of these among-family correlations varied among sites. It is therefore not likely that simultaneous selection on emergence time and either of these traits would retard a response to selection on emergence time.     

Adaptation of experimental yeast populations to stressful conditions in relation to population size

The purpose of this experiment was to find out how a population becomes adapted to extremely stressful conditions as its environment deteriorates. We created a deteriorating environment for experimental selection lines of yeast by a stepwise increase in the concentration of salt in the growth medium. After each step, we tested the ability of the lines to grow at a high concentration of salt near the lethal limit for the ancestral strain. We found that mutations enhancing growth in this highly stressful environment began to spread at intermediate salt concentrations. The degree of enhancement was related to effective population size by a power law with a small exponent. The effect size of these mutations also increased with the population size in a similar fashion. From these results, we interpret adaptation to lethal stress as an indirect response to selection for resistance to previous lower levels of stress in a deteriorating environment. This suggests that the pattern of genetic correlation between successively higher levels of stress is an important factor in facilitating evolutionary rescue.     

Effect of selection on genetic parameters of correlated traits

Summary Changes in genetic parameters of correlated traits due to the buildup of linkage (gametic phase) disequilibrium from repeated truncation selection on a single trait are studied. After several generations of selection, an equilibrium is approached where there are no further changes in genetic parameters and limiting values are reached. Formulae are derived under an infinitesimal model for these limiting values of genetic variances and covariances, heritabilities, and genetic correlations between traits directly and indirectly selected. Changes from generation zero to the limit in all these parameters become greater as heritability of the trait under direct selection increases and, to a lesser extent, as intensity of selection increases. Change in heritability of a trait under indirect selection also increases as the absolute value of the correlation between the trait under indirect and the trait under direct selection increases. The change is maximum when the initial value of heritability is close to 0.5 and insignificant when the initital value is close to zero or one. Change in the genetic correlation between the trait under direct selection and the trait under indirect selection is maximum when its initial value is close to ±0.6 and insignificant when its initial value is close to zero or ±1. Heritability of the trait indirectly selected and genetic correlation between that trait and the trait directly selected always decrease in absolute value, whereas genetic correlation between two traits indirectly selected can either decrease or increase in absolute value. It is suggested that use be made of formulae at selection equilibrium in the prediction of correlated responses after several generations of selection.     

Seedling-selection effects on morphological traits of mature plants in red clover

Knowledge of the correlation between juvenileand mature-plant traits is critical in determining the opportunities for early stage selection. The effects of early stage selection on mature-plant performance have rarely been quantified. This study was conducted to identify seedling traints in red clover (Trifolium pratense L.) that correlate to mature-plant traits and to evaluate the effect of seedling selection on forage yields and other mature-plant traits. The results showed that relationships between most seedlingand mature-plant traits were weak (r ranged from 0.170 to 0.239). Nevertheless, selecting the top 10% seedlings for petiole length, days from emergence to full expansion of the 4th leaf (D4LE), or leaves per seedling, produced a mature-plant population with higher individual plant dry weight (IPDW1) and higher annual yield in 1993 (Y93). Selection for leaves per seedling increased IPDW1 by 23.2%. Selection for petiole length and the smallest D4LE increased Y93 by 15.7% and 13.8%, respectively. Furthermore, substantial expected genetic gains were obtained for IPDW1 and Y93 when selecting for some seedling traits. We conclude that plants and families with low potential yield can be eliminated at the seedling stage in red clover. This will allow breeders to increase the number of superior plants to be field tested or to conduct a more rigorous evaluation of the selected plants. Among the five selection schemes tested for direct selection of mature-plant traits, mass selection produced the largest genetic gain.