Truncation Selection Research Articles

Selection limits and strategies

Strategies are analyzed for maximizing the ultimate limit to truncation selection for a quantitative trait in finite populations. By using a formulation of Kimura and Crow [Kimura, M. & Crow, J. F. (1978) Proc. Natl. Acad. Sci. USA 75, 6168-6171], it is shown that the limit is maximized by truncating at the mode with the highest ordinate of the phenotypic distribution. This implies 50% selection for the normal or any unimodal symmetric distribution and, for skewed distributions, selection of more than one-half if desired phenotypes are in the long tail of the distribution, less than one-half if in the short tail. For dioecious populations, the optimal procedure requires, in addition, equal numbers recorded and selected of each sex. For monoecious populations the limit can be improved by using the best individuals mated to the next-best individuals. Limitations of the results are discussed.

Efficiency of truncation selection

Truncation selection is known to be the most efficient form of directional selection. When this is modified so that the fitness increases linearly over a range of one or two standard deviations of the value of the selected character, the efficiency is reduced, but not greatly. When truncation selection is compared to a system in which fitness is strictly proportional to the character value, the relative efficiency of truncation selection is given by f(c)/sigma, in which f(c) is the ordinate of the frequency distribution at the truncation point and sigma is the standard deviation of the character. It is shown, for mutations affecting viability in Drosophila, that truncation selection or reasonable departures therefrom can reduce the mutation load greatly. This may be one way to reconcile the very high mutation rate of such genes with a small mutation load. The truncation model with directional selection is appropriate for this situation because of the approximate additivity of these mutations. On the other hand, it is doubtful that this simple model can be applied to all genes affecting fitness, for which there are intermediate optima and antagonistic selection among components with negative correlations. Whether nature ranks and truncates, or approximates this behavior, is an empirical question, yet to be answered.

Segregation analysis of chronic childhood spinal muscular atrophy.

A formal segregation analysis for the disease 'chronic childhood spinal muscular atrophy' is presented. This disease is also known as 'Kugelberg-Welander disease', 'arrested Werdnig-Hoffmann disease', and 'chronic proximal or generalised spinal muscular atrophy'. There were 124 index cases occurring in 115 families. Ascertainment of index patients was by incomplete multiple selection. Three types of segregation analysis were performed: Weinberg Proband, an improved Weinberg Proband with a variance corrected formula for differences both in family size and ascertainment probability and a backeting technique assuming the extremes of both single and of truncate selection. All three methods gave similar results. The improved Weinberg Proband method with corrections for differences in ascertainment and in family size gave a segregation ratio of 0.18 and a 95% confidence range of 0.11 to 0.25. The mid-point of the bracketing method assuming extremes of truncate and of single selection was 0.19. The segregation ratio of that group of children with clinical onset before 9 months of age was 0.21, which does not differ significantly from the 0.25 predicted on the basis of autosomal recessivity. Evidence is presented to indicate that 25% of index patients may be due to new dominant mutations, or phenocopies, or both, and that these occur particularly among sporadic cases with clinical onset over 2 years of age. Empirical risk figures for use in genetic counselling are presented, and the literature of the subject is reviewed.

Effect of overall phenotypic selection on genetic change at individual loci.

The selective advantage of an allele Gi (relative to the mean of alleles at this locus) is given by (formula: see text) in which Ai is the average excess of the allele on the character, X; W(X) is the fitness function; F(X) is the frequency function; W is the mean fitness; and the prime denotes differentiation. With truncation selection si = AaF(C)/w in which F(C) is the ordinate at the culling level and w is the proportion saved; this does not depend on any assumption about the distribution of F(X). If the character is normally distributed, si = AiI/sigma2, in which I is the selection differential and sigma2 is the variance of the character distribution. Finally, if the logarithm of the fitness is proportional to the squared deviation from the optimum and the character is distributed normally, si = AiK(Xop--m), in which Xop is the optimum value of the character, m is the mean value, and K is a constant determined by the variances of the fitness function and the frequency function. Truncation is the most efficient form of directional selection in the sense of producing the maximum gene frequency change for a given effect of the gene on the character, but fitness functions can depart considerably from sharp truncation without greatly reducing the efficiency.

A new model for measuring breeding genetic distance. II. Polygenic traits.

The breeding genetic distance measure of a single locus (Carlson & Welch, 1977) is extended to polygenic traits. For two populations with means -x and approximately x, theta(-x, approximately x) is defined as the size of the largest subpopulation with mean approximately x which can be (artificially) selected from a population with mean -x. The distance is defined as 1--theta(-x, approximately x). It is shown that theta(-x, approximately x) can be calculated from truncation selection and formulas (two loci) and tables (three and four loci) are given. Values for theta(-x, approximately x) based on a normal approximation are seen to be adequate for most cases. The measure is applied to a data example (human skin colour) and to a discussion of the idea of 'genetic inertia'.

SELECTION DIFFERENTIALS AND SELECTION COEFFICIENTS

Proof is offered that s approximately ig for all forms of selection where fitness is a nondecreasing function of a normally distributed phenotype (called fitness potential); s is selection coefficient, i is standard selection differential, and g is standard differential effect of a locus genotype.Evidence is presented that the cost of selection does not limit genic polymorphism; that truncation selection is not necessary for high cost-efficiency; and that opposing directions of selection in a heterogeneous environment do not reduce cost-efficiency critically.

An empirical comparison of selection methods for the improvement of biomass

A single generation of upward truncation selection on families with 20% selected was carried out in each of five replicates using Tribolium castaneum as the test organism. The experiment involved eight lines: N - selected for offspring number; W - selected for pupal weight; B - selected for biomass; Q - quadratic index selected; L21 - linear index selected with relative economic weights of 2∶1 offspring number to pupal weight; L11 - linear index selected with relative economic weights of 1∶1 offspring number to pupal weight; L12 - linear index selected with relative economic weights of 1∶2 offspring number to pupal weight; C - an unselected control.Biomass (weight of offspring per family), offspring number, and pupal weight were measured. No differences in response to selection were found among the linear index lines and the pupal weight line with regard to any trait analysed. Generally, response to selection in the linear index lines and pupal weight line was small for offspring number and high for pupal weight. Selection pressure on offspring number in these lines seemed to be dependent on the correlation between offspring number and pupal weight. As a result, response to selection for biomass was poor in the linear index and pupal weight selected lines. In the case of the linear indices, poor response to selection for biomass appeared to be due to the violation of the assumption of additivity of the traits included in the definition of aggregate genotype.The responses in the quadratic index, biomass, and offspring number selected lines were equal with respect to selection for biomass. The response of the quadratic index selected line was less than the responses of the biomass and offspring number selected lines for offspring number, but the response in the quadratic index line was as large as that of any other line included in the experiment and greater than the biomass and offspring number selected lines where pupal weight was the criterion.Highly significant amounts of variation were found for all traits indicating that more replicates are needed for precise evaluation of selection systems.

Mutation Rates in Globin Genes: The Genetic Load and Haldane's Dilemma

Publisher Summary This chapter discusses the mutation rates for mammalian genomes that have often been computed from rates of amino-acid substitution. The fact that rates differing by manyfold are obtained for different proteins emphasizes that in some proteins, such as the histones, most amino-acid substitutions are sufficiently deleterious to be eliminated during the course of evolution. It reviews that by measuring acceptance rates of silent mutations through direct nucleotide sequence comparisons between species, it can remove one of the most important limitations of previous estimates of the mutation rate, which have been based on amino-acid substitution data. The chapter also discusses that Haldane computed the number of genetic deaths required for a gene substitution to occur according to strict Darwinian principles. With reasonable assumptions about permissive levels of mortality associated with Darwinian evolution, he estimated that there could be about one gene substitution every 300 generations. To account for the observed maintenance of mammalian genomes in the face of Haldane's dilemma, it proposes two solutions—that is, by Truncation selection and Neutral mutations. Truncation selection provides a useful way of explaining accurate maintenance of the repetitive gene clusters and satellite DNAs, but it is difficult to imagine that truncation selection could effectively maintain the accuracy of the single-copy DNA coding for most proteins. It is suggested that only a small fraction of the genome, perhaps less than 2%, is kept accurate as single-copy DNA. Since most mammalian genomes contain large amounts of single-copy DNA, the implication is that most such sequences must be genetically drifting.

Selection in reference to biological groups. V. Analysis of full-sib groups.

Previous studies in this series have dealt with the consequences of truncation selection operating with respect to random groups within which geno-full-sib group structure. The objective is to compare the results of individual and group selection as these methods operate on populations of random versus typic interaction may exist. The present study deal with a non-random, full-sib groups. In almost all comparisons individual selection is found to be qualitatively and quantitatively superior when used in conjunction with full-sib groups. This is due to the fact that the change in gene frequency for full-sib groups is a function of both direct and associate effects, whereas with random groups it is a function of direct effects only. With regard to group selection the efficiency is invariably superior when selection operates on non-random, full-sib rather than random groups.

Selection in reference to biological groups. VI. Use of extreme forms of nonrandom groups to increase selection efficiency.

The strategy of using non-random groups to increase the efficiency of truncation selection is discussed. The present study, which considers extreme forms of non-rnadom groups, complements a previous study involving full-sib groups. It is shown that of the two kinds of non-randomness, i.e. that due to homozygosity or that due to homogeneity (as represented by cloning), the latter is the most effective. This suggests that with those plant crops in which intense competition among plants exists, use of clonal propagation to produce non-random groups should be investigated.

Predicting Future Type Proofs of Young Holstein Bulls from Pedigree Information

First-available, age adjusted classification scores of 302,921 Holstein cows scored between September, 1967, and June, 1974, were used to compute pedigree evaluations and type proofs for sires in artificial insemination. The intensity of pedigree selection for overall type score was equivalent to that expected from truncation selection on their type performance alone of the upper 15% and 2% of normally distributed populations of males and females. Optimum weights by multiple regression for predicting sons’ type proofs from pedigree information were compared to theoretically expected weights. Empirical weights for sire and maternal grandsire information were less than theoretically expected while those associated with information from the dam were greater than expected. Empirical correlations between sons’ type proofs and pedigree information were 76% or more of their theoretically expected values. The correlation between sons’ type proofs and information from the dam was greater than expected. Selections of young bulls for progeny testing based on their pedigree evaluations for type should be effective preliminary selection although less effective than expected.

Arguments against intermating before selection in a self-fertilising species

The expected benefit from intermating the F 2 population from a cross of two homozygous parents is investigated. It is noted that intermating will only be of benefit for two loci if the alleles are initially in ths repulsion phase, and this result is extended to more than two loci by population simulation. If V n is the population variance after n cycles of intermating followed by repeated selfing, the merit of intermating is measured by the magnitude of V 1/V0. For a character controlled by loci on a short chromosome segment the ratio is invariably greater than 1.0, but as the average recombination value between loci is increased, either by increasing the chromosome length or by situating the loci on different chromosomes, individual values less than 1.0 become possible. If loci are spread over three or more chromosomes then the expected gain from intermating is consistently small. A simulation study shows that truncation selection is usually preferable to intermating as a procedure for increasing the proportion of desirable homozygotes in a population.

Selection in a population with overlapping generations

SUMMARYA theoretical investigation is reported into the effects of overlapping generations on the prediction of genetic gain from repeated within-population truncation selection for a quantitative trait. The gain resulting from the selection process produces genetic differences between the groups of breeding animals of different ages, and between the means of their progeny. These differences are not allowed for in the usual prediction formula. The correct allowances to make for the genetic effects of maternal age are derived for a simple situation. The implications of these allowances on the overall rate of genetic progress, and on the optimum age structure for maximum progress, are shown in a model pig breeding programme. The normal prediction formula underestimates the genetic gain which can be achieved if females are kept for five litters by 10 to 12%, and overestimates the disadvantages of keeping females for more than one or two litters.

Assortative mating and artificial selection.

Theory is developed to assess the consequences of assortative mating immediately following truncation selection. Truncation selection is expected to generate negative correlations between homologous genes and between non-homologous genes in the same and different gametes. Truncation selection is expected to reduce the maximum marital correlation that can be realised by assortative mating based on phenotypic resemblance within a selected population. It is concluded that assortative mating among selected individuals will increase response to selection by a maximum of 10 per cent with high herit-ability and low selection intensity and by no more than 4 or 5 per cent under the conditions met with in most breeding programmes.

Genetic consequences of truncation selection at the phenotypic level in Drosophila melanogaster.

I F selection operates independently on each locus, its action on the large amounts of genic variability discovered in many populations (e.g., LEWONTIN and HUBBY 1966) would cause excessive genetic loads compared with the actual situation. In order to accommodate selection for many genes, threshold or truncationselection models have been proposed assuming heterozygote superiority ( SVED, REED and BODMER 1967; KING 1967; MILKMAN 1967; WILLS, CRENSHAW and VITALE 1970). As a typical form, MILKMAN and WILLS et al. assumed that the individuals having the largest number of heterozygous loci are selected to produce the next generation. Selection acts at the phenotypic level, the phenotype being the result of genotypic and environmental (including chance) effects. Thus. for any trait including fitness. large phenotypic values do not always follow from large genotypic values. We have attempted to examine the genetic consequences of the typical phenotypic truncation selection on the basis of the genetic parameters for viability obtained in D. melanogaster. If this truncation-selection occurs, it is probably operating mainly in the period from egg to adult. We have estimated the genotypic and environmental variances, and the heritability (broad sense) of egg-adult viability. Two experiments were conducted, one to estimate the variability in relative viability and the other to estimate mean viability. Employed were second chromosomes from 691 extracted by the marked inversion technique from a population in a state park near Raleigh, North Carolina. This population is probably near equilibrium (MUKAI et al. 1971 ) . To estimate variability, the relative viabilities of 688 random heterozygotes were estimated using the Cy method (cf. WALLACE 1956). Crosses were made between five Cy/+i females and five CY/+^+^ males (between successively numbered lines where the subscript indicates line number), and Cy is SMI ( C y ) . Four days after the crosses were made, all flies were transferred to the second vial for another four days and then discarded. The numbers of C y and of wild-type flies of each pair of vials were pooled, and the relative viability of heterozygous wild-

Comparison of Expected and Observed Genetic Gain in Rice Selection Experiments

Truncation selection in F4 and F5 Iines derived from F2 population of rice plant was conducted to cornpare the expected with observed genetic gains. The expected and observed direct responses to selection were substantially large in all traits measured. Correlated responses obtained in all traits measured were smaller than direct responses. There was comparatively good agreement between the expected and observed responses. It is estirnated that an expected genetic gain is available to develop an effective selection method in the rice breeding programme.

Optimum Allocation of Selection Intensity in Two Stages of Truncation Selection

This paper discusses the problem of estimating gain when sequential truncation selection is followed, and develops its solution in terms of bivariate truncation. Gain is maximized in terms of the selection differential (e.g., truncation points) required to balance the costs of operations. The solution depends on the correlation between the measurements of the two stages and the cost iratio for testing in the two stages. Tabular solutions are presented for a wide range in both parameters and show how first-stage selection intensity should increase with higher initial heritabilities and with higher progeny-testing costs. In forest tree breeding, it will often occur that progeny testiing cannot be justified solely in terms of gain per unit cost, though other utilities of the testing may provide juistification.

Genetic correlation and response to selection in simulated populations

Effects of truncation selection of a primary trait upon genetic correlation between the primary trait and an unselected secondary trait were observed during 30 generations. Populations were 24 male and 24 female parents per generation randomly mated with replacement, the number of offspring set by intensity of selection. Each trait was controlled by genes with equal effects and complete dominance segregating independently from starting frequencies of 0.5 at each of 48 loci. Three levels each of genetic correlation, selection, and environmental variation were simulated.Genetic correlation decreased faster under more intense selection by lower than by upper truncation but behaved similarly in both by remaining near initial level when as many as one-half of the offspring were saved for parents. Truncation selection decreased genetic correlation in the offspring selected to be parents whether selection was by upper or lower truncation. Estimates of genetic correlation from covariances between phenotypes of parent and offspring were erratic for both directions of selection.

Correlated Truncation Selection for Yield in Soybeans1

Random genetically heterogeneous, F2‐derived maternal lines and genetically homogeneous, F5‐derived daughter lines of two soybean crosses were evaluated for nine characters in three environments in the F0‐F7 generations.Heritability was relatively consistent across environments for all traits except seed yield. For yield, heritability was greatest under favorable growth conditions and least when moisture stress was alleviated by irrigation. Variability over environments in correlations of all traits with yield was related largely to the degree of moisture stress in each environment. Crosses revealed similar magnitudes of correlation with yield for all traits except chemical composition. This was related to the chemical composition of parents used in these crosses. Correlations of early lodging with yield in genetically homogeneous lines were generally greater than for genetically heterogeneous lines. This was related to the relative uniformity of the plant canopy in these populations.Because of the inconsistency in character associations, predictions of yield advance from selection in any environment were inaccurate estimates of actual advance evaluated over environments. Selection of yield invariably resulted in maximum actual yield advance. Chemical composition was generally the best yield predictor for heterogeneous lines, while early lodging was the most effective trait for correlated yield selection in genetically homogeneous lines.

Genetic correlation and response to selection in simulated populations

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.