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.     

Balancing selection response and rate of inbreeding by including genetic relationships in selection decisions

An iterative selection strategy, based on estimated breeding values (EBV) and average relationship among selected individuals, is proposed to optimise the balance between genetic response and inbreeding. Stochastic simulation was used to compare rates of inbreeding and genetic gain with those of other strategies. For a range of heritabilities, population sizes and mating ratios, the iterative strategy, denoted ADJEBV, outperforms other strategies, giving the greatest genetic gain at a given rate of inbreeding and the least breeding at a given genetic gain. Where selection is currently by truncation on the EBV, with a restriction on the number of full-sibs selected, it should be possible to maintain similar levels of genetic gain and inbreeding with a reduction in population size of 10–30%, by changing to the iterative strategy. If performance is measured by the reduction in cumulative inbreeding without losing more than a given amount of genetic gain relative to results obtained under truncation selection on the EBV, then with the EBV based on a family index, the performance of ADJEBV is greater at low heritability, and is generally greater than where EBV are based on individual records. When comparisons of genetic response and inbreeding are made for alternative breeding scheme designs, schemes which give higher genetic gain within acceptable inbreeding levels would usually be favoured. If comparisons are made on this basis, then the selection method used should be ADJEBV, which maximises the genetic gain for a given level of inbreeding. The results indicated that all selection strategies used to reduce inbreeding had very small effects on the variance of gain, and so differences in this respect are unlikely to affect choices among selection strategies. Selection criteria are recommended based on maximising a selection objective which specifies the desired balance between genetic gain and inbreeding.     

An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions

Summary An approximate method with explicit solutions to apply independent culling levels for multiple traits in n-stages of selection was developed. An approximate solution was found for sequentially selected traits. Two assumptions were necessary. The first was to assume that subsequent selection would not appreciably change the mean of traits already selected, and the second was to approximate the variance of a correlated trait in a selected population with an upward biased projection. The procedure was shown to give near optimal results regardless of selection intensity or genetic correlations if phenotypic correlations among traits were low. The procedure gave poor results only for certain sequences of selection when phenotypic correlations were high. However, in those cases good results were obtained using a different sequence of selection. With high correlations, the procedure is recommended only after comparing solutions and expected genetic gain for all sequences of selection. If the expected aggregate gain for the sequence of selection desired is less than that of another order, culling points associated with the optimal ordering must be determined. Genetic gain from use of culling points is independent of order of selection. The procedure is recommended for use with computer programs that attempt to find optimal culling points to reduce computational time and to check results.Journal Paper No. 12448 of the Purdue University Agricultural Experiment Station     

Design of experiments for predictive microbial modeling

Summary Good predictive microbial models can be built with appropriate data from well-designed experiments. Anyone setting up an experiment should consider the sources of variability, possible screening experiments, optimum spacing between points on a continuous scale, and the most appropriate type of design, e.g. factorial, screening, or central composite.     

Quantitative genetic variation and selection of enzyme activities in Drosophila melanogaster

The nature of the genetic variation for the activity of three enzymes (α-GPD, ME, and SOD) was studied by means of analyses of variance among full-sib and half-sib families. The results presented here indicate that the genetic variation of activity of these enzymes consist primarily of non-additive genetic variance. A moderate level of additive genetic variation was found only for α-GPD activity. We also examined the question whether an association exists between enzyme activities and selection for preadult developmental time. Using the method developed by Lande and Arnold (1983), significant directional selection was observed for α-GPD activity.     

Effect of mass selection on the within-family genetic variance in finite populations

Summary The adequacy of an expression for the withinfamily genetic variance under pure random drift in an additive infinitesimal model was tested via simulation in populations undergoing mass selection. Two hundred or one thousand unlinked loci with two alleles at initial frequencies of 1/2 were considered. The size of the population was 100 (50 males and 50 females). Full-sib matings were carried out for 15 generations with only one male and one female chosen as parents each generation, either randomly or on an individual phenotypic value. In the unselected population, results obtained from 200 replicates were in agreement with predictions. With mass selection, within-family genetic variance was overpredicted by theory from the 12th and 4th generations for the 1,000 and 200 loci cases, respectively. Taking into account the observed change in gene frequencies in the algorithm led to a much better agreement with observed values. Results for the distribution of gene frequencies and the withinlocus genetic covariance are presented. It is concluded that the expression for the within-family genetic variance derived for pure random drift holds well for mass selection within the limits of an additive infinitesimal model.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Estimation of genetic parameters for post-weaning traits of Kermani sheep

The objective of the present study was to estimate genetic parameters for post-weaning traits in Kermani sheep. Traits were included 6-month weight (6MW), 9-month weight (9MW), yearling weight (YW), greasy fleece weight at first shearing (GFW) and greasy fleece weights at various shearings (RFW). Data and pedigree information used in this research were collected at Breeding Station of Kermani sheep during 1993–2004. Genetic parameters were estimated with single- and multi-traits analysis using restricted maximum likelihood (REML) procedures, under animal models. Log likelihood ratio test indicated the most appropriate model for 6MW and 9MW should included direct additive genetic effects as well as maternal permanent environmental effects. However the most appropriate model for YW and GFW had only the direct additive genetic effects. The effects of sex, age of dam and year of birth were significant on body weight traits (P < 0.01). GFW was influenced significantly by sex and year of birth (P < 0.01) but was not affected by age of dam (P > 0.05). Type of birth was no significant effect on studied traits (P > 0.05). Also, the age of lamb at weighing time was a significant influence on 6MW, 9MW and YW. Direct heritability estimates for 6MW, 9MW, YW and GFW were 0.32, 0.03, 0.15 and 0.15, respectively. Maternal permanent environmental estimates of 0.09 were obtained for 6MW and 9MW. Genetic correlation estimates between mentioned traits ranged from 0.51 to 0.99. Phenotypic correlations were generally lower than those of genetic correlation and varied from 0.05 to 0.79 for various traits. The environmental correlations estimates between GFW with growth traits were low, but between other traits were positive and high, ranged from 0.54 to 0.72. The value of repeatability estimated for greasy fleece weight was 0.22.     

Effect of assortative mating on genetic change due to selection

Summary Two mathematical models (A and B) were used to study joint effects of selection and assortative mating on genetic change. Computer simulation was used to verify and extend the results. In each model, the genotype was additive with equal effects at each of N loci and the environmental distribution was N(0, ²). In Model A, each locus had two alleles; in Model B, allelic effects at each locus followed a normal distribution. Using Model A, genetic change with assortative or random mating of selected parents was evaluated for combinations of number of loci (N = 1, 2, 3), heritability in base population (H^[0] = 0.2, 0.5, 0.8), allelic frequency in base population (p = 0.1, 0.5), and proportion selected ( = 0.20, 0.85). Using Model B, genetic change with or without assortative mating was calculated for combinations of N (1, 2, 3, 5, 10, 100, H^[0] (0.2, 0.5, 0.8) and (0.20, 0.85). Response to selection under both mating systems in a finite population was estimated using Model A from 200 replications of a computer simulation; this was done for all combinations of N (1,2, 3, 5, 10) and (0.20, 0.85), with H^[0] = 0.5 and p = 0.1. Results obtained with both models indicate that the effect of assortative mating on genetic change increases with H^[0] and , and decreases with p. With Model A, the relationship between N and the effect of assortative mating on genetic change was not clear; with Model B, however, the advantage of assortative over random mating increased with N, as expected. Simulation results were in agreement with theory of Model A. This study indicates that selection with assortative mating can have a sizable (10 to 20%) long-term advantage over selection with random mating of parents when H^[0] is high, p is low and is large.     

Estimates of genetic parameters and genetic trends for live weight and fleece traits in Menz sheep

Menz sheep are indigenous to the highlands of Ethiopia, and highly valued for their meat and wool production. The area is characterized as a low input mixed barley-sheep production system. In 1998, a selection experiment was set up to evaluate the response of Menz sheep to selection for yearling live weight (WT12) and greasy fleece weight (GFW) combined in an economic index. In this paper, we report the results of this breeding program obtained between 1998 and 2003. Average annual genetic selection responses for WT12 and GFW were 1.506 and 0.043 kg in the selected flock and 0.392 and −0.008 kg in the control flock. Annual genetic trends in the selected flock, estimated by regressing BLUP estimated breeding values on year of birth, were 0.495 ± 0.053 kg for WT12, 0.012 ± 0.002 kg for GFW, and Birr 5.53 ± 0.55 for the aggregate breeding value (1 Ethiopian Birr = 0.115 USD). Corresponding values for the control flock were 0.276 ± 0.065 kg, 0.003 ± 0.002 kg and Birr 2.93 ± 0.69. Correlated responses in birth weight (WT0), weaning weight (WT3), 6-month weight (WT6) and staple length (STPL) in the selected flock were 0.038 ± 0.005 kg, 0.271 ± 0.03 kg, 0.388 ± 0.039 kg and 0.011 ± 0.017 cm, respectively. Heritabilities, estimated by fitting a multitrait individual animal model were 0.464 ± 0.014, 0.477 ± 0.016, 0.514 ± 0.017, 0.559 ± 0.019, 0.393 ± 0.016 and 0.339 ± 0.014 for WT0, WT3, WT6, WT12, GFW and staple length (STPL), respectively. Phenotypic and genetic correlations between all traits were positive, except for STPL and WT12. Estimates of genetic parameters and observed genetic trends confirm that selective breeding can lead to significant genetic improvement in Menz sheep.     

The effect of repeated cycles of selection on genetic variance,heritability, and response

Summary The genetic variance of a quantitative trait decreases under directional selection due to generation of linkage disequilibrium. After a few cycles of selection on individual phenotype, a limit is reached where there is no further reduction in the genetic variance. Bulmer's model is extended to an animal breeding situation where selection is on information on relatives rather than on the individual's own performance. Algebraic expressions are derived to predict the decrease in genetic variance and associated reductions in heritability and response in the limit. Consequences of the results are discussed in the context of breeding strategies.     

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).     

Bias in genetic variance estimates due to spatial autocorrelation

Summary A central problem in the analysis of genetic field trials is the dichotomy of genetic and environmental effects because one cannot be defined without the other. Results from 768,000 simulated family trials in complete randomized block designs demonstrated a serious upward bias in estimates of family variance components from multi-unit plot designs when the phenotypic observations were compatible with a first-order autoregressive (AR1) process. The inflation of family variances and, thus, additive genetic variance and narrow sense individual heritabilities progressed exponentially with an increase in the nearest neighbor correlation () in the AR1 process. Significant differences in inflation rates persisted among various plot configurations. At = 0.2 the inflation of family variances reached 48–73%. Inflation rates were independent of the level of heritability. Modified Papadakis nearest neighbor (NN) adjustment procedures were tested for their ability to remove the bias in family variances. A NN-adjustment based on Mead's coefficient of interplant interaction and one derived from Bartlett's simultaneous autoregressive scheme removed up to 97% of the bias introduced by the phenotypic correlations. NN-adjusted estimates had slightly (5–8%) higher relative errors than did unadjusted estimates.     

Probabilities of negative estimates of genetic variances

Summary The probability of negative analysis of variance estimates of genetic variance components due to sampling error (Ps) was investigated. The objectives were to evaluate the magnitude of Ps, to compare Ps for estimates of _A ² and _D ² , and to compare Ps for genetic variance component estimates from the nested and factorial mating designs. Ps was defined in terms of ratios of mean squares and the F distribution was used to calculate probabilities of the negative estimates. The results indicated that Ps is often greater than 0.20 for _D ² . It is generally lower for _A ² than for _D ² , and lower for the factorial mating design than the nested mating design.Technical Contribution No. 2589 from the South Carolina Agricultural Experiment Station, Clemson University     

Design and analysis of multiple-choice feeding-preference experiments

Summary A serious omission in ecological methodology is the absence of a rigorous statistical procedure to analyse multiple-choice feeding-preference experiments. A sample of 21 studies in the littoral marine context shows that results from such experiments are used to study a variety of conceptual issues, ranging from nutritional biology to ecosystem dynamics. A majority of such studies have been incorrectly analysed. The analytical problem has two facets: (1) lack of independence in the simultaneous offer of food types and (2) the existence of autogenic changes particular to each food type. Problem (2) requires the use of control arenas without the consumer. A recent advance allows the rigorous analysis of experiments with two food types offered simultaneously. Here I propose a method for the multiple-choice case. For the first problem I suggest the use of multivariate statistical analysis, providing both a parametric and a nonparametric procedure. The second problem is solved using basic statistical theory. I analyse data from an experiment with the sea urchin Tetrapygus niger feeding on three species of algae: Ulva nematoidea, Gymnogongrus furcellatus, and Macrocystis pyrifera. The parametric and nonparametric procedures yielded similar results, and showed that when offered the three species of algae T. niger does not feed at random but shows a preference for U. nematoidea. The method requires that the number of replicates in the treatment and control arenas be the same, and greater than the number of food types. The method is useful for other kinds of multiple-choice experiments.     

Optimum spacing of genetic markers for determining linkage between marker loci and quantitative trait loci

The cost of experiments aimed at determining linkage between marker loci and quantitative trait loci (QTL) was investigated as a function of marker spacing and number of individuals scored. It was found that for a variety of experimental designs, fairly wide marker spacings (ca. 50 cM) are optimum or close to optimum for initial studies of marker-QTL linkage, in the sense of minimizing overall cost of the experiment. Thus, even when large numbers of more or less evenly spaced markers are available, it will not always be cost effective to make full utilization of this capacity. This is particularly true when costs of rearing and trait evaluation per individual scored are low, as when marker data are obtained on individuals raised and evaluated for quantitative traits as part of existing programs. When costs of rearing and trait evaluation per individual scored are high, however, as in human family data collection carried out primarily for subsequent marker — QTL analyses, or when plants or animals are raised specifically for purposes of marker — QTL linkage experiments, optimum spacing may be rather narrow. It is noteworthy that when marginal costs of additional markers or individuals are constant, total resources allocated to a given experiment will determine total number of individuals sampled, but not the optimal marker spacing.