Selection indices for non-linear profit functions

Summary Conventional selection index theory assumes that the total merit or profitability of animals is a linear function of measurable traits. However, in many cases merit may be a non-linear function of these traits. A linear selection index can still be used in this situation but the optimum index depends on the selection intensity to be used and on the number of generation over which the selection response is to be maximized. Nonlinear selection indices have been suggested but these result in a lower selection response than the best linear index. Linear selection indices suggested in the past are shown to correspond to the optimum linear index for either a very small selection response or, in the case of restricted indices, a very large selection response. The economic value of a trait may depend on management decisions taken by the farmer. In this situation the economic values should be calculated assuming that the management decisions taken maximize profit given the present genetic value of the animals.     

通用选择指数原理

本文在对各类种畜评定方法探讨的基础上,提出了通用选择指数概念,对各类评定方法在理论上加以综合,推导出统一的计算公式,并编制出相应的计算程序。为充分利用种畜各种信息,特别是为在多信息来源需作约束、最宜选择时的种畜评定,提供了行之有效的计算方法。避免了在实际应用时对各类评定方法的独立探讨以及因多种计算体系导致应用上的混乱。此外,本文还得出了有关选择理论的三个结论,并改正了文献[2]中的失误之处。     

通用选择指数的通径分析化模型

通过对各种选择指数的通径分析化模型进行系统化的研究,建立了通用选择指数的通径分析化模型,并给出了各种选择指数及其通径分析化的统一表示形式．用该模型可以充分利用各种信息来源,特别是在对各种信息来源需作各种约束时,为选种和评定优种提供了行之有效的计算方法和统一程序,避免了在实际应用中因计算体系不同而导致的混乱．     

Predicted accuracy of and response to genomic selection for new traits in dairy cattle

Genomic selection relaxes the requirement of traditional selection tools to have phenotypic measurements on close relatives of all selection candidates. This opens up possibilities to select for traits that are difficult or expensive to measure. The objectives of this paper were to predict accuracy of and response to genomic selection for a new trait, considering that only a cow reference population of moderate size was available for the new trait, and that selection simultaneously targeted an index and this new trait. Accuracy for and response to selection were deterministically evaluated for three different breeding goals. Single trait selection for the new trait based only on a limited cow reference population of up to 10 000 cows, showed that maximum genetic responses of 0.20 and 0.28 genetic standard deviation (s.d.) per year can be achieved for traits with a heritability of 0.05 and 0.30, respectively. Adding information from the index based on a reference population of 5000 bulls, and assuming a genetic correlation of 0.5, increased genetic response for both heritability levels by up to 0.14 genetic s.d. per year. The scenario with simultaneous selection for the new trait and the index, yielded a substantially lower response for the new trait, especially when the genetic correlation with the index was negative. Despite the lower response for the index, whenever the new trait had considerable economic value, including the cow reference population considerably improved the genetic response for the new trait. For scenarios with a zero or negative genetic correlation with the index and equal economic value for the index and the new trait, a reference population of 2000 cows increased genetic response for the new trait with at least 0.10 and 0.20 genetic s.d. per year, for heritability levels of 0.05 and 0.30, respectively. We conclude that for new traits with a very small or positive genetic correlation with the index, and a high positive economic value, considerable genetic response can already be achieved based on a cow reference population with only 2000 records, even when the reliability of individual genomic breeding values is much lower than currently accepted in dairy cattle breeding programs. New traits may generally have a negative genetic correlation with the index and a small positive economic value. For such new traits, cow reference populations of at least 10 000 cows may be required to achieve acceptable levels of genetic response for the new trait and for the whole breeding goal.     

Phenotypic and genetic correlations for body structure scores (frame) with productive traits and index for CEIP classification in Nellore beef cattle

The present study was carried out to estimate both (co)variance components and genetic parameters for frame scores obtained using two methods (FRAME_GMA and FRAME_BIF) as well as phenotypic and genetic correlations with traits such as weaning weight, weight gain from weaning to yearling, scrotal circumference, muscle score, and an empiric index for animal classification for the Special Certificate of Identification and Production (CEIP). Data on 12,728 animals, raised in Southeastern Brazil, with ages from 490 to 610 days were analyzed. Estimates of heritability for FRAME_GMA and FRAME_BIF in multi-trait analysis were 0.28 and 0.24, respectively. Genetic correlation coefficients between frame scores and the growth trait were of medium magnitude, which indicates that genetic selection for weight resulted in undesirable responses, increasing the animals' frames. Small changes should be expected in the frame of animals that have been submitted to a genetic selection regarding muscle score and scrotal circumference. The low magnitude of phenotypic and genetic correlation between frame scores and the empirical selection index that classifies animals for CEIP, a Brazilian official certificate that recognizes the value of seedstock that is not registered at breeders associations, but is genetically evaluated, does not indicate important responses in giving a CEIP to animals that have been directly or indirectly selected for frame. Other studies must be performed to determine estimates of the genetic parameters for frame scores in other beef cattle populations.     

Multistage Selection for Genetic Gain by Orthogonal Transformation

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

Genomic selection: prediction of accuracy and maximisation of long term response

Genomic selection refers to the use of dense markers covering the whole genome to estimate the breeding value of selection candidates for a quantitative trait. This paper considers prediction of breeding value based on a linear combination of the markers. In this case the best estimate of each marker’s effect is the expectation of the effect conditional on the data. To calculate this requires a prior distribution of marker effects. If the marker effects are normally distributed with constant variance, BLUP can be used to calculate the estimated effects of the markers and hence the estimated breeding value (EBV). In this case the model is equivalent to a conventional animal model in which the relationship matrix among the animals is estimated from the markers instead of the pedigree. The accuracy of the EBV can approach 1.0 but a very large amount of data is required. An alternative model was investigated in which only some markers have non-zero effects and these effects follow a reflected exponential distribution. In this case the expected effect of a marker is a non-linear function of the data such that apparently small effects are regressed back almost to zero and consequently these markers can be deleted from the model. The accuracy in this case is considerably higher than when marker effects are normally distributed. If genomic selection is practiced for several generations the response declines in a manner that can be predicted from the marker allele frequencies. Genomic selection is likely to lead to a more rapid decline in the selection response than phenotypic selection unless new markers are continually added to the prediction of breeding value. A method to find the optimum index to maximise long term selection response is derived. This index varies the weight given to a marker according to its frequency such that markers where the favourable allele has low frequency receive more weight in the index.     

Index versus tandem selection after repeated generations of selection

Summary A theoretical comparison between two multiple-trait selection methods, index and tandem selection, after several generations of selection was carried out. An infinite number of loci determining the traits, directional and truncation selection, discrete generations and infinite population size were assumed. Under these assumptions, changes in genetic parameters over generations are due to linkage disequilibrium generated by selection. Changes continue for several generations until equilibrium is approached. Algebraic expressions for asymptotic responses from index selection can be derived if index weights are maintained constant across generations. Expressions at equilibrium for genetic parameters and responses are given for the index and its component traits. The loss in response by using initial index weights throughout all generations, instead of updating them to account for changes in genetic parameters, was analyzed. The benefit of using optimum weights was very small ranging from 0% to about 1.5% for all cases studied. Recurrence formulae to predict genetic parameters and responses at each generation of selection are given for both index and tandem selection. A comparison between expected response in the aggregate genotype at equilibrium from index and tandem selection is made considering two traits of economic importance. The results indicate that although index selection is more efficient for improving the aggregate breeding value, its relative efficiency with respect to tandem selection decreases after repeated cycles of selection. The reduction in relative efficiency is highest with the highest selection intensity and heritabilities and with negative correlations between the two traits. The advantage of index over tandem selection might be further reduced if changes in genetic parameters due to gene frequency changes produced by selection, random fluctuations due to the finite size of the population, and errors in estimation of parameters, were also considered.     

Mate selection by selection index theory

Summary Mate selection by selection index prediction of total merit in expected progeny is proposed as a rational basis for making recommendations in the choice of a bull to which a cow may be mated. Growth in USA of service programs recommending bulls to particular cows has motivated the need to rationalize mate selection processes. This paper illustrates that mate selection on the basis of highest index value for expected progeny among potential mates can justify special mate selection programs, when a nonlinear relationship exists between at least one trait in the index and merit.Contribution while on leave to Department Animal Breeding, Agricultural Research Institute of Republic of Ireland and partial support from Senior Fulbright-Hays Research Grant.Approved as Journal Article 180-79 of the Ohio Agricultural Research & Development Center, Wooster 44691     

The evolution of trade-offs under directional and correlational selection

Using quantitative genetic theory, we develop predictions for the evolution of trade-offs in response to directional and correlational selection. We predict that directional selection favoring an increase in one trait in a trade-off will result in change in the intercept but not the slope of the trade-off function, with the mean value of the selected trait increasing and that of the correlated trait decreasing. Natural selection will generally favor an increase in some combination of trait values, which can be represented as directional selection on an index value. Such selection induces both directional and correlational selection on the component traits. Theory predicts that selection on an index value will also change the intercept but not the slope of the trade-off function but because of correlational selection, the direction of change in component traits may be in the same or opposite directions. We test these predictions using artificial selection on the well-established trade-off between fecundity and flight capability in the cricket, Gryllus firmus and compare the empirical results with a priori predictions made using genetic parameters from a separate half-sibling experiment. Our results support the predictions and illustrate the complexity of trade-off evolution when component traits are subject to both directional and correlational selection.     

Natural selection among Kinnaura of the Himalayan highland: A comparative analysis with other Indian and Himalayan populations

The present investigation on fertility and mortality differential among Kinnaura of the Himalayan highland is based on data collected from 160 post-menopausal women belonging to the middle and high altitude region of Kinnaur district of Himachal Pradesh (Indian Himalayas). Selection potential based on differential fertility and mortality was computed for middle-and high-altitude women. Irrespective of the methodology, the total index of selection was found to be highest among middle-altitude women (0.386) as compared with high-altitude (0.370) women, whereas for the total population it is estimated to be 0.384. It was found that the Kinnaura of the Himalayan highland showing moderate index of total selection and relative contribution of the mortality component (Im) to the index of total selection is higher than the corresponding fertility component (If). The analysis of embryonic and post-natal mortality components shows that the post-natal mortality components are higher in comparison with the embryonic mortality components among highlanders and needs special intervention and health care. The present findings are compared with other Indian tribes as well as non-tribes of the Himalayan region and other parts of the country. It reveals that this index among Kinnaura is moderate than the other population groups; among the Himalayan population, the highest was reported for Galong (It = 1.07) of Arunachal, whereas the lowest was reported from Ahom (It = 0.218) of Manipur. The correlation and regression analysis between total index of selection (It) and fertility (If) and mortality (Im) components for pooled data of populations of the Indian Himalayan states show that If and Im account for 21.6 and 29.1% variability, respectively. In Crow's total index of selection (It) along with strong association, which is significant at the 1% level, this indicates that mortality plays a greater role in natural selection in comparison with fertility among populations of the Indian Himalayas.     

Factor and principal component analyses as alternatives to index selection

Summary Selections from factor and principal component analyses were compared with those from the Smith-Hazel index when selecting for several switchgrass (Panicum virgatum L.) traits. The objective of this study was to examine several alternatives to index selection. Such procedures would potentially eliminate problems of selection associated with Smith-Hazel indices, including errors in genetic parameter estimates and difficulty in assigning relative economic weights to traits. Selection was performed on 1,280 plants that were evaluated over 2 years at 1 location, in a randomized complete block design with 4 replicates. The plants were evaluated for forage yield and several forage quality traits. The comparisons of index selection with principal factor analysis, maximum-likelihood factor analysis and principal component analysis were made for three sets of traits (five traits per set) to estimate repeatability for the comparisons. Multivariate analyses were performed on both simple and genotypic correlation matrices. Comparisons were made by computing Spearman's rank correlations between selection index plant scores and scores computed from multivariate analysis and by determining the number of plants selected in common for the selection methods. Among the three multivariate analysis methods evaluated in this study, principal component analysis had the highest correlation with index selection. The high correlation for principal component analysis of simple correlation matrices indicates the potential for using this statistical method for selection purposes. This would permit the breeder to reduce field costs (e.g., time, labor, equipment) required to obtain the genetic parameter estimates necessary to construct selection indices.     

Index of opportunity for natural selection among the Gowdas of Kodagahalli village,Karnataka, India

BACKGROUND:

In order to understand how selection is operating in the Gowda population, the index of opportunity for selection was calculated and the present findings were compared with some related findings from other South Indian (SI) populations.

MATERIALS AND METHODS:

Crow (1958) and the modified method by Johnston and Kensinger (1971) were used for the present purpose.

RESULTS AND DISCUSSION:

The index of total selection intensity (I) was found to be moderate taking into consideration the range for many Indian populations. Considering certain differences in fertility and mortality heritable, it appears that natural selection play an important role in shaping the genetic constitution of the Gowda population. Analysis of data indicates that the index due to fertility seems to contribute more towards selection than mortality. This trend might be because of better living condition and health-care system among the Gowdas which have a positive impact on the lower contribution of mortality for the evolution mechanism of the Gowda population through natural selection.     

Opportunity for selection in the parish of Tuna, Sweden

This article is part of a series of studies on the opportunity for selection in Swedish populations. The study concerns women who, with some exceptions, were born during the first half of the 19th century. A modified form of Crow's index has been used to estimate the upper limit of natural selection. The average index for the period 1805-1850 was I = 1.136, which value falls within the limits of what has been found for the other Swedish populations that have been studied.     

Integration of genomic information into sport horse breeding programs for optimization of accuracy of selection

Reliable selection criteria are required for young riding horses to increase genetic gain by increasing accuracy of selection and decreasing generation intervals. In this study, selection strategies incorporating genomic breeding values (GEBVs) were evaluated. Relevant stages of selection in sport horse breeding programs were analyzed by applying selection index theory. Results in terms of accuracies of indices (r_TI) and relative selection response indicated that information on single nucleotide polymorphism (SNP) genotypes considerably increases the accuracy of breeding values estimated for young horses without own or progeny performance. In a first scenario, the correlation between the breeding value estimated from the SNP genotype and the true breeding value (= accuracy of GEBV) was fixed to a relatively low value of r_mg = 0.5. For a low heritability trait (h² = 0.15), and an index for a young horse based only on information from both parents, additional genomic information doubles r_TI from 0.27 to 0.54. Including the conventional information source ‘own performance’ into the before mentioned index, additional SNP information increases r_TI by 40%. Thus, particularly with regard to traits of low heritability, genomic information can provide a tool for well-founded selection decisions early in life. In a further approach, different sources of breeding values (e.g. GEBV and estimated breeding values (EBVs) from different countries) were combined into an overall index when altering accuracies of EBVs and correlations between traits. In summary, we showed that genomic selection strategies have the potential to contribute to a substantial reduction in generation intervals in horse breeding programs.     

Fertility and mortality differentials among selected tribal population groups of north-western and eastern India

Selection potential based on differential fertility and mortality has been computed for six tribal groups inhabiting different geo-climatic conditions, namely: Sahariya, Mina and Bhil of the State of Rajasthan, north-western India, and Munda, Santal and Lodha of the State of West Bengal, eastern India. Irrespective of the methodology, the total index of selection was found to be highest among Lodhas (0.668), followed by Sahariyas (0.524), Santals (0.462), Bhils (0.386), Mundas (0.353) and Minas (0.334). Incidentally, Lodha and Sahariya are two of the seventy-four notified primitive tribal groups of India, and these two study populations show the highest index of total selection, mainly because of a higher embryonic and postnatal mortality. The relative contribution of the fertility component to the index of total selection is higher than the corresponding mortality component in all tribal groups. The analysis of postnatal mortality components indicates that childhood mortality constitutes the bulk of postnatal mortality, suggesting that children under 5 years need better health care in these tribal groups.     

Response of fluctuating and directional asymmetry to selection on wing shape in Drosophila melanogaster

We tested whether directional selection on an index-based wing character in Drosophila melanogaster affected developmental stability and patterns of directional asymmetry. We selected for both an increase (up selection) and a decrease (down selection) of the index value on the left wing and compared patterns of fluctuating and directional asymmetry in the selection index and other wing traits across selection lines. Changes in fluctuating asymmetry across selection lines were predominantly small, but we observed a tendency for fluctuating asymmetry to decrease in the up-selected lines in both replicates. Because changes in fluctuating asymmetry depended on the direction of selection, and were not related to changes in trait size, these results fail to support existing hypotheses linking directional selection and developmental stability. Selection also produced a pattern of directional asymmetry that was similar in all selected lines whatever the direction of selection. This result may be interpreted as a release of genetic variance in directional asymmetry under selection.     

The evolutionary psychology of physical attractiveness: Sexual selection and human morphology

Psychological evidence suggests that sex differences in morphology have been modified by sexual selection so as to attract mates (intersexual selection) or intimidate rivals (intrasexual selection). Women compete with each other for high quality husbands by advertising reproductive value in terms of the distribution of fat reserves and by exaggerating morphological indicators of youthfulness such as a small nose and small feet and pale, hairless skin. Men's physical appearance tends to communicate social dominance, which has the combined effects of intimidating reproductive rivals and attracting mates. In addition to their attractiveness and intimidatory effects, human secondary sexual characters also provide cues to hormonal status and phenotypic quality consistent with the good genes model of sexual selection (which includes parasite resistance). Low waist-hip ratio is sexually attractive in women and indicates a high estrogen/testosterone ratio (which favors reproductive function). Facial attractiveness provides honest cues to health and mate value. The permanently enlarged female breast appears to have evolved under the influence of both the good genes and the runaway selection mechanisms. The male beard is not obviously related to phenotypic quality and may have evolved through a process of runaway intersexual selection.     

长期指数选择的遗传效果分析—计算机模拟研究

本文利用Monte Carlo模拟技术研究比较了普通选择指数、实际选择指数、约束指数和单性状选择四种方法的长期选择效果及对群体遗传结构的影响。50世代的结果表明:群体大小和遗传参数能明显影响长期指数选择的反应;实际指数选择是有效的,其总体效果好于普通指数;约束选择的早期反应虽低于普通指数,但后期效果好,而且对群体遗传结构影响较小。同时,指数选择使性状加性遗传方差和遗传力衰减变化,而遗传相关依指数公式的系数呈定向改变。建议多性状长期选择时应用实际指数法或约束指数法。