Index selection for genetic improvement of quantitative characters

A novel selection model based on multivariate methods and arbitrary genetic parameters: a case study on tomato families

BACKGROUND

Selection is one of the essential skills whereby breeders reduce the population size and increase the chance of success. Various selection methods with special applications have been developed. Superior genotypes are assessed according to interesting traits, including univariate, multivariate, phenotypic, genotypic, etc. METHODS: Mathematical calculation of the traits' importance based on the genetic makeup of investigated population (average degree of dominance/additive involved in the action of genes) and arbitrary genetic parameters is functional. In this paper, a general model for multivariate selection has been presented whereby the selection can be made for (a) more than one interesting trait, (b) the trait(s) with complex inheritance, (c) finding superior genotypes from among a large-scale population, (d) finding superior genotypes in segregating generations and (f) finding tolerant genotypes to stresses. This model is developed based on biometric concepts in four steps. MATLAB script is provided for the model, and users can easily apply that to identify the most suitable genotypes after data collection according to the breeding purposes.

RESULTS

The main features of this model are simplicity, precision, repeatability, and speed (improving several traits simultaneously). All the steps and the analysis of the results are explained step by step in a case study.

The statistical theory of linear selection indices from phenotypic to genomic selection

A linear selection index (LSI) can be a linear combination of phenotypic values, marker scores, and genomic estimated breeding values (GEBVs); phenotypic values and marker scores; or phenotypic values and GEBVs jointly. The main objective of the LSI is to predict the net genetic merit (H), which is a linear combination of unobservable individual traits' breeding values, weighted by the trait economic values; thus, the target of LSI is not a parameter but rather the unobserved random H values. The LSI can be single-stage or multi-stage, where the latter are methods for selecting one or more individual traits available at different times or stages of development in both plants and animals. Likewise, LSIs can be either constrained or unconstrained. A constrained LSI imposes predetermined genetic gain on expected genetic gain per trait and includes the unconstrained LSI as particular cases. The main LSI parameters are the selection response, the expected genetic gain per trait, and its correlation with H. When the population mean is zero, the selection response and expected genetic gain per trait are, respectively, the conditional mean of H and the genotypic values, given the LSI values. The application of LSI theory is rapidly diversifying; however, because LSIs are based on the best linear predictor and on the canonical correlation theory, the LSI theory can be explained in a simple form. We provided a review of the statistical theory of the LSI from phenotypic to genomic selection showing their relationships, advantages, and limitations, which should allow breeders to use the LSI theory confidently in breeding programs.

Review: Livestock disease resilience: from individual to herd level

Infectious diseases are a major threat to the sustainable production of high-producing animals. Control efforts, such as vaccination or breeding approaches often target improvements to individual resilience to infections, i.e., they strengthen an animal's ability to cope with infection, rather than preventing infection per se. There is increasing evidence for the contribution of non-clinical carriers (animals that become infected and are infectious but do not develop clinical signs) to the overall health and production of livestock populations for a wide range of infectious diseases. Therefore, we strongly advocate a shift of focus from increasing the disease resilience of individual animals to herd disease resilience as the appropriate target for sustainable disease control in livestock. Herd disease resilience not only captures the direct effects of vaccination or host genetics on the health and production performance of individuals but also the indirect effects on the environmental pathogen load that herd members are exposed to. For diseases primarily caused by infectious pathogens shed by herd members, these indirect effects on herd resilience are mediated both by individual susceptibility to infection and by characteristics (magnitude of infectiousness, duration of infectious period) that influence pathogen shedding from infected individuals. We review what is currently known about how vaccination and selective breeding affect herd disease resilience and its underlying components, and outline the changes required for improvement. To this purpose, we also seek to clarify and harmonise the terminology used in the different animal science disciplines to facilitate future collaborative approaches to infectious disease control in livestock.

Pea Breeding for Intercropping With Cereals: Variation for Competitive Ability and Associated Traits, and Assessment of Phenotypic and Genomic Selection Strategies

Mixed stand (MS) cropping of pea with small-grain cereals can produce more productive and environment-friendly grain crops relative to pure stand (PS) crops but may require selection to alleviate the pea competitive disadvantage. This study aimed to assess the pea variation for competitive ability and its associated traits and the efficiency of four phenotypic or genomic selection strategies. A set of 138 semi-leafless, semi-dwarf pea lines belonging to six recombinant inbred line populations and six parent lines were genotyped using genotyping-by-sequencing and grown in PS and in MS simultaneously with one barley and one bread wheat cultivar in two autumn-sown trials in Northern Italy. Cereal companions were selected in a preliminary study that highlighted the paucity of cultivars with sufficient earliness for association. Pea was severely outcompeted in both years albeit with variation for pea proportion ranging from nearly complete suppression (<3%) to values approaching a balanced mixture. Greater pea proportion in MS was associated with greater total yield of the mixture (r ≥ 0.46). The genetic correlation for pea yield across MS and PS conditions slightly exceeded 0.40 in both years. Later onset of flowering and taller plant height at flowering onset displayed a definite correlation with pea yield in MS (r ≥ 0.46) but not in PS, whereas tolerance to ascochyta blight exhibited the opposite pattern. Comparisons of phenotypic selection strategies within or across populations based on predicted or actual yield gains for independent years indicated an efficiency of 52-64% for indirect selection based on pea yield in PS relative to pea yield selection in MS. The efficiency of an indirect selection index including onset of flowering, plant height, and grain yield in PS was comparable to that of pea yield selection in MS. A genome-wide association study based on 5,909 SNP markers revealed the substantial diversity of genomic areas associated with pea yield in MS and PS. Genomic selection for pea yield in MS displayed an efficiency close to that of phenotypic selection for pea yield in MS, and nearly two-fold greater efficiency when also taking into account its shorter selection cycle and smaller evaluation cost.

Purebreeding of Red Maasai and crossbreeding with Dorper sheep in different environments in Kenya

The aim of this article was to study opportunities for improvement of the indigenous and threatened Red Maasai sheep (RM) in Kenya, by comparing purebreeding with crossbreeding with Dorper sheep (D) as a terminal breed, in two different environments (Env. A and a harsher Env. B), assuming different levels of genotype-by-environment interaction (G × E). Breeding goals differed between environments and breeds. Four scenarios of nucleus breeding schemes were stochastically simulated, with the nucleus in Env. A. Overall, results showed an increase in carcass weight produced per ewe by more than 10% over 15 years. Genetic gain in carcass weight was 0.17 genetic SD/year (0.2 kg/year) across scenarios for RM in the less harsh Env. A. For survival and milk yield, the gain was lower (0.04-0.05 genetic SD/year). With stronger G × E, the gain in the commercial tier for RM in the harsher Env. B became increasingly lower. Selection of females also within the commercial tier gave slightly higher genetic gain. The scenario with purebreeding of RM and a subnucleus in Env. B gave the highest total income and quantity of meat. However, quantity of meat in Env. A increased slightly from having crossbreeding with D, whereas that in Env. B decreased. A simple and well-designed nucleus breeding programme would increase the genetic potential of RM. Crossbreeding of RM with D is not recommended for harsh environmental conditions due to the large breed differences expected in that environment.

A Genomic Selection Index Applied to Simulated and Real Data

A genomic selection index (GSI) is a linear combination of genomic estimated breeding values that uses genomic markers to predict the net genetic merit and select parents from a nonphenotyped testing population. Some authors have proposed a GSI; however, they have not used simulated or real data to validate the GSI theory and have not explained how to estimate the GSI selection response and the GSI expected genetic gain per selection cycle for the unobserved traits after the first selection cycle to obtain information about the genetic gains in each subsequent selection cycle. In this paper, we develop the theory of a GSI and apply it to two simulated and four real data sets with four traits. Also, we numerically compare its efficiency with that of the phenotypic selection index (PSI) by using the ratio of the GSI response over the PSI response, and the PSI and GSI expected genetic gain per selection cycle for observed and unobserved traits, respectively. In addition, we used the Technow inequality to compare GSI vs. PSI efficiency. Results from the simulated data were confirmed by the real data, indicating that GSI was more efficient than PSI per unit of time.

Using selection index theory to estimate consistency of multi-locus linkage disequilibrium across populations

BACKGROUND

The potential of combining multiple populations in genomic prediction is depending on the consistency of linkage disequilibrium (LD) between SNPs and QTL across populations. We investigated consistency of multi-locus LD across populations using selection index theory and investigated the relationship between consistency of multi-locus LD and accuracy of genomic prediction across different simulated scenarios. In the selection index, QTL genotypes were considered as breeding goal traits and SNP genotypes as index traits, based on LD among SNPs and between SNPs and QTL. The consistency of multi-locus LD across populations was computed as the accuracy of predicting QTL genotypes in selection candidates using a selection index derived in the reference population. Different scenarios of within and across population genomic prediction were evaluated, using all SNPs or only the four neighboring SNPs of a simulated QTL. Phenotypes were simulated using different numbers of QTL underlying the trait. The relationship between the calculated consistency of multi-locus LD and accuracy of genomic prediction using a GBLUP type of model was investigated.

RESULTS

The accuracy of predicting QTL genotypes, i.e. the measure describing consistency of multi-locus LD, was much lower for across population scenarios compared to within population scenarios, and was lower when QTL had a low MAF compared to QTL randomly selected from the SNPs. Consistency of multi-locus LD was highly correlated with the realized accuracy of genomic prediction across different scenarios and the correlation was higher when QTL were weighted according to their effects in the selection index instead of weighting QTL equally. By only considering neighboring SNPs of QTL, accuracy of predicting QTL genotypes within population decreased, but it substantially increased the accuracy across populations.

CONCLUSIONS

Consistency of multi-locus LD across populations is a characteristic of the properties of the QTL in the investigated populations and can provide more insight in underlying reasons for a low empirical accuracy of across population genomic prediction. By focusing in genomic prediction models only on neighboring SNPs of QTL, multi-locus LD is more consistent across populations since only short-range LD is considered, and accuracy of predicting QTL genotypes of individuals from another population is increased.

Evolutionary constraints in high-dimensional trait sets

Genetic variation for individual traits is typically abundant, but for some multivariate combinations it is very low, suggesting that evolutionary limits might be generated by the geometric distribution of genetic variance. To test this prediction, we artificially selected along all eight genetic eigenvectors of a set of eight quantitative traits in Drosophila serrata. After six generations of 50% truncation selection, at least one replicate population of all treatments responded to selection, allowing us to reject a null genetic subspace as a cause of evolutionary constraint in this system. However, while all three replicate populations of the first five selection treatments displayed a significant response, the remaining three, characterized by low genetic variance in their selection indexes in the base population, displayed inconsistent responses to selection. The observation that only four of the nine replicate populations evolved in response to the direct selection applied to them in these low genetic variance treatments, led us to conclude that a nearly null subspace did limit evolution. Dimensions associated with low genetic variance are often found in multivariate analyses of standing genetic variance in morphological traits, suggesting that the nearly null genetic subspace may be a common mechanism of evolutionary constraint in nature.

How much do genetic covariances alter the rate of adaptation?

Genetically correlated traits do not evolve independently, and the covariances between traits affect the rate at which a population adapts to a specified selection regime. To measure the impact of genetic covariances on the rate of adaptation, we compare the rate fitness increases given the observed G matrix to the expected rate if all the covariances in the G matrix are set to zero. Using data from the literature, we estimate the effect of genetic covariances in real populations. We find no net tendency for covariances to constrain the rate of adaptation, though the quality and heterogeneity of the data limit the certainty of this result. There are some examples in which covariances strongly constrain the rate of adaptation but these are balanced by counter examples in which covariances facilitate the rate of adaptation; in many cases, covariances have little or no effect. We also discuss how our metric can be used to identify traits or suites of traits whose genetic covariances to other traits have a particularly large impact on the rate of adaptation.

An iterative procedure for deriving selection indexes with constant restrictions

The objective of this study was to present an iterative procedure for deriving selection indexes with constant restrictions. Constant restriction means that the genetic responses of the restricted traits are preset to actual amounts for a given selection intensity (ī). Results of this study show that an index with constant restriction alone or in combination with other types of restrictions possesses three distinctive characteristics: 1) the coefficient matrix of the index equations is not symmetric and is nonlinear; 2) the coefficient matrix contains unknown ī, indicating that the index coefficients (b) to be derived depends on the value of ī predetermined before selection; and 3) the coefficient matrix contains unknown b, thus requiring iterative methods to solve the index equations. As a result of these unique characteristics, the index coefficients, genetic responses of the index traits, and overall genetic gain in net merit change nonlinearly with varying levels of ī, which is in sharp contrast to both unrestricted and restricted indexes reported in the literature. The construction of a constant-restricted index requires predetermining the value of ī intended for a selection program to derive the corresponding b. An index with constant restrictions has no meaning unless it is associated with a specific value of ī. Numerical examples are given to illustrate the construction of the index with constant restrictions and to validate the theoretical development proposed. The derived equations have yielded an index that maximized the total merit and fulfilled constant restriction at the same time.

Genetic selection strategies: computer modeling

There are four primary factors to consider in genetic selection strategies: 1) accuracy of selection, 2) selection intensity, 3) effective population size, and 4) mating system. Current theory indicates that optimum response to selection is achieved by maximizing the first three factors and using a mating systems that allows optimization of reproductive characteristics in dam lines and production characteristics in sire lines. However, with limited resources, compromises among the first three factors are needed. Simulations are useful for examining those compromises. Unrealistic simplifying assumptions are necessary for analytic theoretical results and thus do not address real world breeding problems. Using simulations, the relationship between selection accuracy, which is increased by use of family selection indices or Best Linear Unbiased Prediction (BLUP), and response to selection was examined. Results show that those procedures place a great restriction on effective population size, which offsets most of their advantage, i.e., there is too little emphasis on effective population size. A revision of the methodology and a reappraisal of the results of selection theory for optimization of genetic response is required. Another relationship that is of fundamental importance in breeding programs is that between selection intensity and effective population size. Analytical results for the additive case have been developed but have never been extended to heterotic traits. A gene level simulation program was developed to examine that relationship. Results show that the optimal selection strategy depends on the trait being selected. For additive traits and in the short term (20 generations), one should maximize selection intensity. For heterotic traits, an intermediate proportion (25% of each sex) gives optimal response. In all breeding strategies, primary attention must be given to the rate of inbreeding, which is increased by increasing either accuracy of selection or selection intensity. Inbreeding reduces response to selection in two ways. First, for both additive and nonadditive traits, inbreeding is a measure of the amount of random genetic drift that has occurred. Genetic drift causes loss of favorable alleles. Once lost, those alleles can never be recovered and thus genetic drift lowers the selection limit. Second, for heterotic traits, inbreeding results in a depression of the mean caused by directional dominance.

Comparison of index selection and best linear unbiased prediction for simulated layer poultry data

The advantage of using best linear unbiased prediction (BLUP) of breeding value over different selection indexes was examined for a sex-limited trait in a simulated layer poultry population. The base breeding population consisted of 30 males and 300 females that were unrelated to each other. Heritability for different analyses was assumed to be either .1, .2, or .5. Each generation was reproduced from two hatches each year, with a hatch variance of 3.165% of the phenotypic variance, except for one simulation, in which it was assumed to be 40% to test the effect of a large fixed effect. Parents were selected on 1) BLUP of breeding value, 2) optimum selection index (individual, full-, and half-sibs), 3) classical selection index (as for optimum, but index weight constant across generations), 4) reduced selection index (individual and full-sibs only), or 5) combination of classical and BLUP. The relative selection response with the selection indices compared to the BLUP estimates (except for the reduced selection index) were from 94.5 to 99.4% of BLUP. Inbreeding was higher in the BLUP selected populations, which could offset any advantage of BLUP if the populations were structured so that inbreeding could rise too rapidly.

Genetics of Brassica rapa (syn. campestris). 2. Multiple disease resistance to three fungal pathogens: Peronospora parasitica, Albugo candida and Leptosphaeria maculans

Although the genetic basis of multiple disease resistance (MDR) is poorly understood, it is of great value for understanding the evolution of disease resistance in natural plant populations and for increasing crop yields in agriculture. In Brassica rapa, we studied genetic correlations among levels of disease resistance to three fungal pathogens: Peronospora parasitica, Albugo candida and Leptosphaeria maculans. A large, replicated quantitative genetics experiment used artificial selection on resistance to individual pathogens, and examined correlated responses to selection for resistance to other, unselected pathogens. Data from 9518 plants, each measured simultaneously for resistance to three fungal pathogens, showed heritable genetic variation for resistance to each pathogen and a positive genetic correlation between resistance to P. parasitica and L. maculans. This indicates that some resistance genes provide defence against fundamental characteristics common to two taxonomic orders of fungal pathogens. Conceivably, such MDR could contribute to a durable defence that might not be easily circumvented by rapidly evolving fungal pathogens.

Linkage between loci of quantitative traits and marker loci: multi-trait analysis with a single marker

An efficient approach to increase the resolution power of linkage analysis between a quantitative trait locus (QTL) and a marker is described in this paper. It is based on a counting of the correlations between the QTs of interest. Such correlations may be caused by the segregation of other genes, environmental effects and physiological limitations. Let a QT locus A/a affect two correlated traits, x and y. Then, within the framework of mixture models, the accuracy of the parameter estimates may be seriously increased, if bivariate densities f aa(x, y), f Aa(x, y) and f AA(x, y) rather than the marginals are considered as the basis for mixture decomposition. The efficiency of the proposed method was demonstrated employing Monte-Carlo simulations. Several types of progeny were considered, including backcross, F2 and recombinant inbred lines. It was shown that provided the correlation between the traits involved was high enough, a good resolution to the problem is possible even if the QTL groups are strongly overlapping for their marginal densities.

Index versus tandem selection after repeated generations of selection

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.

Selection index: economic weights for maximum simultaneous genetic gain

Selection indices that maximize the correlation between an individual organism's index score and its breeding value frequently require a priori known "economic" weights before the optimum phenotypic weights can be estimated. The long generation intervals and economic uncertainty that surround forest tree breeding can make the choice of weights arbitrary. In this paper an algorithm is introduced for finding "economic" weights that will ensure maximum simultaneous progress in all index traits. At the outset the traits are assumed to be of equal preference. The solutions are functions of the eigenvalues and eigenvectors of a quadratic form of the additive genetic and phenotypic covariance matrices. Examples of applications in tree breeding emphasize the practical aspects of the method.

Genetic and economic responses to breeding programs that consider mastitis

Eight breeding programs were evaluated with a simulation study using discounted gene flow. Discounted economic responses and annual genetic changes were calculated. The evaluation was over 25 periods of 13 mo and the population modeled was DHI cows served by AI sires in the US. A breeding program without regard for mastitis gave annual genetic increases of 53.5 kg milk, 2.24 kg fat, .020 cases of mastitis, and an economic response of $98.24. Including SCC or mastitis in selection indexes that maximize economic gain reduced the rate of improvement in yield traits by 1 to 2% but did not reduce clinical mastitis. Instead these indexes slowed the rate of increase in clinical mastitis by 20 to 25% and increased response in economic merit by less than 1%. Restricted selection, which permitted no genetic change in mastitis, reduced the rates of improvement by up to 27% for yield and 17% for economic response. Direct selection against mastitis is unrealistic due to lack of field data on clinical mastitis. Indirect selection would be less efficient than predicted here, due in part to incomplete enrollment in SCC testing program. Simultaneous improvement of both yield and mastitis apparently is not economically desirable due to the antagonistic genetic correlation between yield and mastitis and to the relatively greater economic value and higher heritability of yield.

Selection strategies and artificial evolution

Artificial selection results in biolgical changes, creating artificial evolution. When using selection indexes, the artificial evolution depends on the relative economic (or other) weight of traits in the breeding objective, and on the phenotypic and genetic variances and covariances among these traits and the traits recorded in the selection index. As shown here, the selection strategy (in this case, individual selection versus progeny test selection) can also have marked effects on the kind of artificial evolution produced. Thus, where economic weights are uncertain, choice between alternative selection strategies might take into account the different types of animal or plant resulting.

Factor and principal component analyses as alternatives to index selection

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.

An alternative approach to multivariate selection in plant breeding where genotypes are evaluated at many locations

A new approach to genotypic selection in a plant breeding programme where the genotypes under assessment are grown in a number of environments is examined. It is assumed that these environments are a random sub-set of all possible environments where the genotypes are likely to be grown. It involves estimating the probability that each genotype will, if grown at any location, exceed predefined target values for one or more characters. The multi-normal probabilities are estimated from the genotype means and environmental variance of each variate. Where more than a single variate is to be considered, the correlation coefficients between variates are also used in the estimation. It was found that the coefficient obtain by correlating the predicted proportion of locations that genotypes would exceed the set target values, with the observed proportion of locations in a different year, were consistently higher than similar coefficients between observed proportions in different seasons. The latter were high enough to conclude that the approach would be of use in practise. Such a method may therefore be used to identify genotypes which have a high probability of being suitable over a range of locations.

The influence of composite traits on genotype by environment relations

In breeding for multiple trait value functions, the existence of genotype-by-environment interaction effects can vastly complicate the designation of optimum sets of genotype-environment pairings into Target Populations of Environments. In this paper it is shown that even in the absence of any changes in genotypic ranking over environments on a trait-by-trait basis, it is possible to generate changes in genotypic ranking in value in different environments. This is shown to be true even for linear value functions in a case example in pine breeding.

Association of heifer fertility with cow fertility and yield in dairy cattle

Genetic correlations of heifer fertility and first-parity yield usually were negative and opposite in sign from genetic correlations of first-parity fertility and yield. Most estimates of genetic correlation between heifer and first-parity fertility were not significantly different from zero. Increasing yield may improve genetic potential for fertility, but stress of increased yield may overcome genetic potential for improved fertility. Days open and 305-day yield for first parity were considered with index selection; sires were evaluated on daughter performance. Days open had a small influence on the selection index; genetic gains in days open for first parity were largely offset by correlated losses in service period for heifers. Restricted index selection, holding days open constant, required considerable economic importance of days open.