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.     

Estimation of long-term genetic improvement for gerbera using the best linear unbiased prediction (BLUP) procedure

Long-term genetic improvement is measured by the selection response predicted from estimates of narrow-sense heritability. Accurate estimates of selection response require partitioning the change of population mean into genetic and environmental components. A selection experiment for cut-flower yield was conducted for 16 generations in the Davis population of gerbera (Gerbera hybrida, Compositae). Breeding values were estimated for individual plants in the population using the best linear unbiased prediction (BLUP) procedure. Genetic change in each generation was calculated from the breeding values of individual plants. The results of this study indicate that long-term selection was successful and necessary for the genetic improvement in cut-flower yield. Genetic improvement in mean breeding value over 16 generations was 33 flowers. Mean breeding values increased monotonically with an S-shape pattern while environmental effects fluctuated from generation to generation. Results predict that cut-flower yield in the Davis population of gerbera will continue to respond to selection.     

Efficiency of early generation selections for yield and related characters in safflower (Carthamus tinctorius L.)

The efficiency of early generation selection for yield and related characters in safflower (Carthamus tinctorius L.) was studied in the F₂, F₃ and F₄ generations. Twenty-five F₂ progenies derived from various crosses were studied. In the F₂ generation, number of capitula per plant (CNSP), number of seeds per capitulum (SPSP), test weight (SWSP), and seed yield (SYSP) were the criteria used for single plant selection. The analysis of variance showed significant differences for all of the characters in the F₂, F₃, and F₄ generations. The analysis of variance in each of the selection classes showed highly significant genotypic differences. A large number of selections in the CNSP and SYSP classes showed greater yield than the check variety. In each class the mean for that particular character showed a positive shift. The observed F₃ and F₄ means for seed yield per plant was higher in SYSP, indicating the effectiveness of single plant selection for yield. Correlated response showed that selection for number of capitula per plant was effective for improvement of yield.     

Progeny selection for agronomic characters in early generations of a potato breeding programme

 Repeatabilities of progeny means, and the univariate cross prediction method were used to study the effectiveness of progeny selection for agronomically important characters in early generations of potato (Solanum tuberosum L.) breeding. The study was based on 90 progenies (72 crosses+18 selfs) evaluated for three successive generations, i.e. seedling, first clonal and second clonal generations. Repeatabilities of progeny means were measured as correlation coefficients between generations. In the univariate cross prediction method, progeny means and within-progeny standard deviations were used to calculate the proportions of clones exceeding the target values, and correlation coefficients between generations for predicted and observed proportions of clones, were calculated. Population means varied from generation to generation. Correlation coefficients between generations for progeny means for most of the characters were significant, but moderate. These were higher than the correlation coefficients between predicted and observed proportions of clones exceeding the target values. The possibility of using progeny means as a selection parameter to reduce the number of genotypes to be examined in later stages by rejecting the poor crosses in seedling generation is discussed. Received: 8 January 1997/Accepted: 28 February 1997     

Impact of genotyping strategy on the accuracy of genomic prediction in simulated populations of purebred swine

Single-step genomic BLUP (ssGBLUP) has been widely used in genomic evaluation due to relatively higher prediction accuracy and simplicity of use. The prediction accuracy from ssGBLUP depends on the amount of information available concerning both genotype and phenotype. This study investigated how information on genotype and phenotype that had been acquired from previous generations influences the prediction accuracy of ssGBLUP, and thus we sought an optimal balance about genotypic and phenotypic information to achieve a cost-effective and computationally efficient genomic evaluation. We generated two genetically correlated traits (h² = 0.35 for trait A, h² = 0.10 for trait B and genetic correlation 0.20) as well as two distinct populations mimicking purebred swine. Phenotypic and genotypic information in different numbers of previous generations and different genotyping rates for each litter were set to generate different datasets. Prediction accuracy was evaluated by correlating genomic estimated breeding values with true breeding values for genotyped animals in the last generation. The results revealed a negligible impact of previous generations that lacked genotyped animals on the prediction accuracy. Phenotypic and genotypic data, including the most recent three to four generations with a genotyping rate of 40% or 50% for each litter, could lead to asymptotic maximum prediction accuracy for genotyped animals in the last generation. Single-step genomic best linear unbiased prediction yielded an optimal balance about genotypic and phenotypic information to ensure a cost-effective and computationally efficient genomic evaluation of populations of polytocous animals such as purebred pigs.     

Genetic gain and cost efficiency of marker-assisted selection of maize for improved resistance to multiple foliar pathogens

Northern corn leaf blight (NCLB) caused by Exserohilum turcicum, gray leaf spot (GLS) caused by Cercospora zeae-maydis and maize streak caused by maize streak Mastrevirus (MSV) are the most destructive foliar diseases limiting maize production in sub-Saharan Africa. Most foliar diseases of maize are managed using quantitative (partial) resistance, and previous studies have reported quantitative trait loci associated with host resistance (rQTL). Our objective was to compare the genetic gain and costs resulting from phenotypic, genotypic, and marker-assisted selection of partially inbred lines derived from many families for resistance to infection by three foliar pathogens. We developed a population of 410 F2:3 families by crossing inbred line CML202 with a breeding line designated VP31. These families were planted in nurseries inoculated separately with each pathogen. We conducted one cycle of early generation pedigree selection using three different procedures, phenotypic, genotypic, and marker/phenotypic index, for improvement of resistance to each pathogen. We used simple sequence repeat (SSR) markers flanking six target rQTL associated with partial resistance. Broad- and narrow-sense heritability estimates were also obtained for the F2:3 families, and selected and non-selected F2:4 families. Genetic gains resulting from the selection procedures were determined. Gene action of the candidate rQTL was determined using orthogonal contrasts. Estimates of costs based on lower boundary values indicated that the cost of marker-based selection was lower than that of phenotypic selection. Our results indicate that molecular markers linked to target rQTL can facilitate pyramiding resistance to multiple diseases during early generation pedigree selection.     

Response to genomic selection: The Bulmer effect and the potential of genomic selection when the number of phenotypic records is limiting

Background

Over the last ten years, genomic selection has developed enormously. Simulations and results on real data suggest that breeding values can be predicted with high accuracy using genetic markers alone. However, to reach high accuracies, large reference populations are needed. In many livestock populations or even species, such populations cannot be established when traits are difficult or expensive to record, or when the population size is small. The value of genomic selection is then questionable.

Methods

In this study, we compare traditional breeding schemes based on own performance or progeny information to genomic selection schemes, for which the number of phenotypic records is limiting. Deterministic simulations were performed using selection index theory. Our focus was on the equilibrium response obtained after a few generations of selection. Therefore, we first investigated the magnitude of the Bulmer effect with genomic selection.

Results

Results showed that the reduction in response due to the Bulmer effect is the same for genomic selection as for selection based on traditional BLUP estimated breeding values, and is independent of the accuracy of selection. The reduction in response with genomic selection is greater than with selection based directly on phenotypes without the use of pedigree information, such as mass selection. To maximize the accuracy of genomic estimated breeding values when the number of phenotypic records is limiting, the same individuals should be phenotyped and genotyped, rather than genotyping parents and phenotyping their progeny. When the generation interval cannot be reduced with genomic selection, large reference populations are required to obtain a similar response to that with selection based on BLUP estimated breeding values based on own performance or progeny information. However, when a genomic selection scheme has a moderate decrease in generation interval, relatively small reference population sizes are needed to obtain a similar response to that with selection on traditional BLUP estimated breeding values.

Conclusions

When the trait of interest cannot be recorded on the selection candidate, genomic selection schemes are very attractive even when the number of phenotypic records is limited, because traditional breeding requires progeny testing schemes with long generation intervals in those cases.     

Fixation probability with multiple alleles and projected average allelic effect on selection

The first-order effect of selection on the probability of fixation of an allele, with respect to an intensity of selection s>0 in a diploid population of fixed finite size N, undergoing discrete, non-overlapping generations, is shown to be given by the sum of the average effects of that allele on the coefficient of selection in the current generation and all future generations, given the population state in the current generation. This projected average allelic effect is a weighted sum of average allelic effects in allozygous and autozygous offspring in the initial generation, with weights given in terms of expected coalescence times, under neutrality, for the lineages of two or three gametes chosen at random in the same generation. This is shown in the framework of multiple alleles at one locus, with genotypic values determining either viability or fertility differences, and with either multinomial or exchangeable reproduction schemes. In the limit of weak selection in a large population such that Ns tends to zero, the initial average allelic effects in allozygous offspring and autozygous offspring have the same weight on the fixation probability only in the domain of application of the Kingman coalescent. With frequency-dependent selection in a linear-game-theoretic context with two phenotypes determined by additive gene action, the first-order effect on the fixation probability is a combination of two effects of frequency-independent selection, one in a haploid population, the other in a diploid population. In the domain of application of the Kingman coalescent as the population size goes to infinity and Ns to zero, the first effect is three times more important than the second effect. This explains the one-third law of evolutionary dynamics in this domain, and shows how this law can be extended beyond this domain.     

Genetic changes in a barley population analyzed in terms of some life cycle components of selection

A bulk-hybrid population of barley (CC-XXI) was investigated for changes over a period of six generations, in (1) generation means and variances for three quantitative characters (2) phenotypic and genotypic frequencies at several marker loci and (3) the components of selection at several life cycle stages (germination and seedling survival, fertility, fecundity) for the dominant-recessive phenotypic classes at three of the above loci. The changes in mean and variance for the quantitative characters appeared to be due to both directional and stabilizing types of selection. The estimates of selective values from frequency data suggested heterozygote advantage along with unequal homozygote fitnesses at locuss and heterozygote disadvantage at locibl, r andv, from computations based on higher outcrossing rates in the presence of male-steriles.Of the components studied, fertility and fecundity appeared to account for a larger portion of the total selective differential than the pre-adult stages (germination and seedling establishment). Net selective values based on component analysis approximated the selective values obtained from the frequency data for locusr. For locis, andv, however, the two estimates were often quite different, although they generally agreed in direction. The discrepancies between the two sets of estimates were discussed in terms of the complexity of overall measures of fitness.     

Evolution under Fertility and Viability Selection

Evolution at a single multiallelic locus under arbitrary weak selection on both fertility and viability is investigated. Discrete, nonoverlapping generations are posited for autosomal and X-linked loci in dioecious populations, but monoecious populations are studied in both discrete and continuous time. Mating is random. The results hold after several generations have elapsed. With an error of order s [i.e., O(s)], where s represents the selection intensity, the population evolves in Hardy-Weinberg proportions. Provided the change per generation of the fertilities and viabilities due to their explicit time dependence (if any) is O(s2), the rate of change of the deviation from Hardy-Weinberg proportions is O(s2). If the change per generation of the viabilities and genotypic fertilities is smaller than second order [i.e., o(s2)], then to O(s2) the rate of change of the mean fitness is equal to the genic variance. The mean fitness is the product of the mean fertility and the mean viability; in dioecious populations, the latter is the unweighted geometric mean of the mean viabilities of the two sexes. Hence, as long as there is significant gene frequency change, the mean fitness increases. If it is the fertilities of matings that change slowly [at rate o(s2)], the above conclusions apply to a modified mean fitness, defined as the product of the mean viability and the square root of the mean fertility.     

Modelling gene flow between oilseed rape and wild radish. I. Evolution of chromosome structure

The assessment of gene flow from crop species to weeds has found a new emphasis over the last years because of the marketing of transgenic crops and the possible selective advantage that crop (trans)gene may confer to the weeds. Several studies focused on the F1 interspecific hybrid production but few data are available on the factors affecting the genetic structure of advanced generations. It depends on the genomic structure of the species concerned as well as on the degree of their genome homology that affect the occurrence of intergenomic recombination. Oilseed rape (Brassica napus, AACC, 2n = 38)-wild radish (Raphanus raphanistrum, RrRr, 2n = 18), a distantly related weed, is a good model to address such questions. From seven male sterile oilseed rape lines carrying an herbicide tolerance transgene, F1 interspecific hybrids and four advanced generations were produced under field conditions with wild radish as pollinator. Observation of hybrid chromosome numbers across four generations revealed a high variability, especially in the “BC1” generation. A regression model was fitted in order to describe the relationship between parent and offspring chromosome numbers. The effects of generation, transgenic line and selection pressure on the mean relationship were investigated. The first two factors had an influence on the rate of decrease of chromosome numbers, whereas selection pressure resulted in the presence of an additional chromosome in the herbicide treated plants. The model provided a convenient framework for analysing how chromosome numbers evolve over successive hybridization events and it may prove useful as a basis for simulation-based approaches.     

Effects of pepper (Capsicum chinense) genotypic diversity on insect herbivores

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Stabilizing selection on sperm number revealed by artificial selection and experimental evolution

Sperm competition is taxonomically widespread in animals and is usually associated with large sperm production, being the number of sperm in the competing pool the prime predictor of fertilization success. Despite the strong postcopulatory selection acting directionally on sperm production, its genetic variance is often very high. This can be explained by trade‐offs between sperm production and traits associated with mate acquisition or survival, that may contribute to generate an overall stabilizing selection. To investigate this hypothesis, we first artificially selected male guppies (Poecilia reticulata) for high and low sperm production for three generations, while simultaneously removing sexual selection. Then, we interrupted artificial selection and restored sexual selection. Sperm production responded to divergent selection in one generation, and when we restored sexual selection, both high and low lines converged back to the mean sperm production of the original population within two generations, indicating that sperm number is subject to strong stabilizing total sexual selection (i.e., selection acting simultaneously on all traits associated with reproductive success). We discuss the possible mechanisms responsible for the maintenance of high genetic variability in sperm production despite strong selection acting on it.     

Selection for divergent emigration rates in laboratory populations ofMusca domestica

High and low emigration rates through a laboratory system were selected for in populations of house flies (Musca domestica L.). Emigration consisted of movement of flies from on plastic box to another by way of a connecting tube. Selection was carried out by first dividing a wild population of flies into two lines and then selecting for movement from the box in one line and against movement from the box in the other line. The selection experiment was performed twice. In both experiments a statistically significant difference between the two strains was obtained in three to four generations of selection. In the second experiment, after 5 genrations the mean number of high emigration rate flies emigrating in 1 hour was 4.37 times the mean number of low emigration rate flies and in 24 hours was 2.81 times the number of low emigration rate flies. The second experiment was terminated after 6 generations, but the first experiment was continued for 35 generations. In this case, divergence ceased in roughly 15 generations. The possible relevance of the findings to laboratory population experiments in which spatial discontinuities are included is discussed.     

POLYGENIC MUTATION IN DROSOPHILA MELANOGASTER: ESTIMATES FROM DIVERGENCE AMONG INBRED STRAINS

A highly inbred line of Drosophila melanogaster was subdivided into 25 replicate sublines, which were independently maintained for 100 generations with 10 pairs of unselected flies per generation. The polygenic mutation rate (V_M) for two quantitative traits, abdominal and sternopleural bristle number, was estimated from divergence among sublines at 10 generation intervals from generations 30-100, and from response of each line to divergent selection after more than 65 generations of mutation accumulation. Estimates of V_M averaged over males and females both from divergence among lines and from response to selection within lines were 3.3 × 10^-3 V_E for abdominal bristles and 1.5 × 10^-3 V_E for sternopleural bristles, where V_E is the environmental variance. The actual rate of production of mutations affecting these traits may be considerably higher if the traits are under stabilizing selection, and if mutations affecting bristle number have deleterious effects on fitness. There was a substantial component of variance for sex × mutant effect interaction and the sublines evolved highly significant mutational variation in sex dimorphism of abdominal bristle number. Pleiotropic effects on sex dimorphism may be a general property of mutations at loci determining bristle number.     

Genetic correlation and response to selection in simulated populations

Summary One of two quantitative traits was selected and correlated response in the other trait was measured in each of 30 generations for models of additive genes and of complete dominance. Each trait was controlled by 48 loci with equal effects, segregating independently from frequencies of 0.5 in the initial generation. Intensity of selection regulated the number of offspring from randomly mating 24 males and 24 females each generation. Three each of genetic correlations between traits, intensities of selection, and amounts of environmental variation were simulated.In the additive model correlated responses of the unselected trait to selection of the primary trait agreed closely with responses expected from theoretical considerations. In the model of complete dominance, responses of genotypic means of the unselected trait to selection of the primary trait in opposite directions were quite symmetrical for the first few generations but became distinctly asymmetrical in later generations. With little selection, response was fairly linear but became distinctly curvilinear as intensity of selection increased and environmental variance decreased. Between 15th and 30th generations some gains in the correlated trait to the 15th generation were lost.Michigan Agricultural Experiment Station Journal Article 4847. Part of North Central Regional Project NC-2.     

Gene stacking strategies with doubled haploids derived from biparental crosses: theory and simulations assuming a finite number of loci

Recent progress in genotyping and doubled haploid (DH) techniques has created new opportunities for development of improved selection methods in numerous crops. Assuming a finite number of unlinked loci (ℓ) and a given total number (n) of individuals to be genotyped, we compared, by theory and simulations, three methods of marker-assisted selection (MAS) for gene stacking in DH lines derived from biparental crosses: (1) MAS for high values of the marker score (T, corresponding to the total number of target alleles) in the F₂ generation and subsequently among DH lines derived from the selected F₂ individual (Method 1), (2) MAS for augmented F₂ enrichment and subsequently for T among DH lines from the best carrier F₂ individual (Method 2), and (3) MAS for T among DH lines derived from the F₁ generation (Method 3). Our objectives were to (a) determine the optimum allocation of resources to the F₂ ( n₁^* \, n_{1}^{*} ) and DH generations (n - n₁^* ) (n - n_{1}^{*} ) for Methods 1 and 2 by simulations, (b) compare the efficiency of all three methods for gene stacking by simulations, and (c) develop theory to explain the general effect of selection on the segregation variance and interpret our simulation results. By theory, we proved that for smaller values of ℓ, the segregation variance of T among DH lines derived from F₂ individuals, selected for high values of T, can be much smaller than expected in the absence of selection. This explained our simulation results, showing that for Method 1, it is best to genotype more F₂ individuals than DH lines ($ n_{1}^{*} :n > 0.5 $ n_{1}^{*} :n > 0.5 ), whereas under Method 2, the optimal ratio n₁^* :n n_{1}^{*} :n was close to 0.5. However, for ratios deviating moderately from the optimum, the mean [`(X)] \overline{X} of T in the finally selected DH line ( T<sub>\textDH</sub><sup>*</sup> T_{\text{DH}}^{*} ) was hardly reduced. Method 3 had always the lowest mean [`(X)] \overline{X} of T_\textDH^* T_{\text{DH}}^{*} except for small numbers of loci (ℓ = 4) and is favorable only if a small number of loci are to be stacked in one genotype and/or saving one generation is of crucial importance in cultivar development. Method 2 is under most circumstances the superior method, because it generally showed the highest mean [`(X)] \overline{X} and lowest SD of T_\textDH^* T_{\text{DH}}^{*} for the finally selected DH.     

Genome‐wide analysis of allele frequency change in sunflower crop–wild hybrid populations evolving under natural conditions

Crop‐wild hybridization occurs in numerous plant species and could alter the genetic structure and evolutionary dynamics of wild populations. Studying crop‐derived alleles in wild populations is also relevant to assessing/mitigating the risks associated with transgene escape. To date, crop‐wild hybridization has generally been examined via short‐term studies, typically within a single generation, focusing on few traits or genetic markers. Little is known about patterns of selection on crop‐derived alleles over multiple generations, particularly at a genome‐wide scale. Here, we documented patterns of natural selection in an experimental crop × wild sunflower population that was allowed to evolve under natural conditions for two generations at two locations. Allele frequencies at a genome‐wide collection of SNPs were tracked across generations, and a common garden experiment was conducted to compare trait means between generations. These data allowed us to identify instances of selection on crop‐derived alleles/traits and, in concert with QTL mapping results, test for congruence between our genotypic and phenotypic results. We found that natural selection overwhelmingly favours wild alleles and phenotypes. However, crop alleles in certain genomic regions can be favoured, and these changes often occurred in parallel across locations. We did not, however, consistently observe close agreement between our genotypic and phenotypic results. For example, when a trait evolved towards the wild phenotype, wild QTL alleles associated with that trait did not consistently increase in frequency. We discuss these results in the context of crop allele introgression into wild populations and implications for the management of GM crops.     

Genotypic variation in susceptibility of honey bees (Apis mellifera) to infestation by tracheal mites (Acarapis woodi)

Two-way selection for lines of honey bees (Apis mellifera L.) susceptible and resistant to infestation by tracheal mites (Acarapis woodi Rennie) was conducted for two generations. Individuals of the susceptible line were 1.4 and 2.4 times more likely to become infested by female mites after the first and second generations, respectively. These results demonstrate that genotypic variability exsts within North American populations and that selection for resistance is feasible. The mechanisms of resistance are unknown.     

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.