Are economic selection indices always superior to a desired gains index?

Conclusions The comparison of different selection indices is justified only if the indices are constrated to achieve the same profit function, even when each index is not optimized with respect to that profit function.When a profit function is known and is non-linear, the desired gains index may be more efficient than the economic index. The optimum desired gains index should be determined by iterative techniques over several generations to compare the genetic progress with the economic index, because gains by the economic index are not linear and the changes observed in the initial generations of selection are not the same rates in future generations, although those changes are linear in the case of the desired gains index.     

The use of constrained selection indexes in breeding for economic merit

Summary Various methods exist for the derivation of restricted and/or desired gains selection indexes, and their use in applied breeding has been advocated. It is shown that there exists a set of implied linear economic weights for all constrained indexes and their derivation is given. Where economic weights are linear and known, a standard selection index is, by definition, optimal and thus a constrained index will usually be suboptimal. It is argued that economic weights can always be estimated and that the effects of uncertain weights can be examined by sensitivity analysis. If economic weights are nonlinear, use of the first order (linear) economic weights or a derived linear index, using previously described methods, will give very close to optimum economic selection responses. Examples from the literature indicate that severe losses of potential economic gain can possibly occur through use of a constrained index. It is concluded that constrained indexes should be avoided for economic genetic selection.     

Multitrait index based on factor analysis and ideotype‐design: proposal and application on elephant grass breeding for bioenergy

This study proposes a new multitrait index based on factor analysis and ideotype‐design (FAI‐BLUP index), and validates its potential on the selection of elephant grass genotypes for energy cogeneration. Factor analysis was carried out, and afterwards, factorial scores of each ideotype were designed according to the desirable and undesirable factors, and the spatial probability was estimated based on genotype‐ideotype distance, enabling genotype ranking. In order to quantify the potential of the FAI‐BLUP index, genetic gains were predicted and compared with the Smith‐Hazel classical index. The FAI‐BLUP index allows ranking the genotypes based on multitrait, free from multicollinearity, and it does not require assigning weights, as in the case of the Smith‐Hazel classical index and its derived indices. Furthermore, the genetic correlation ‐ positive or negative ‐ within each factor was taken into account, preserving their traits relationship, and giving biological meaning to the ideotypes. The FAI‐BLUP index indicated the 15 elephant grass with the highest performance for conversion to bioenergy via combustion, and predicted balanced and desirable genetic gains for all traits. In addition, the FAI‐BLUP index predicted gains of approximately 62% of direct selection, simultaneously for all traits that are desired to be increased, and approximately 33% for traits which are desired to be decreased. The genotypes selected by the FAI‐BLUP index have potential to improve all traits simultaneously, while the Smith‐Hazel classical index predicted gains of 66% for traits that are desired to be increased, and ?32% for traits that are desired to be decreased, and it does not have potential to improve all traits simultaneously. The FAI‐BLUP index provides an undoubtable selection process and can be used in any breeding programme aiming at selection based on multitrait.     

Experimental study of the influence of errors of genetic correlation estimates on unrestricted,optimum, and desired gains selection indices

Summary Effects of errors in estimates of the genetic correlation on the accuracy of unrestricted, optimum, and desired gains selection indices were examined experimentally in Tribolium castaneum. Three lines were selected for three generations for pupal weight at 21 days and adult weight at 31 days, using unrestricted (I9), optimum (O9), and desired gains (G9) index selection methods. The genetic correlation between pupal and adult weights in the base population was 0.95. The optimum index was designed to set the response of pupal weight by a fixed amount, while in the desired gains index the responses of pupal and adult weights were specified as being equal to 31. Three other indices were constructed using a deliberately incorrect genetic correlation (0.25), i.e., unrestricted (I2), optimum (O2), and desired gains (G2). Responses observed in unrestricted index lines (I9 versus I2) and optimum index lines (O9 versus O2) did not differ significantly, even though lines I9 and I2 differed in a practical sense. Responses in desired gains index lines (G9 versus G2) differed significantly. Responses obtained for aggregate genotype (pupal weight + adult weight) and for the component traits were greater in line I9 than those obtained in line I2. Responses obtained in the O9 and O2 lines for pupal and adult weights were similar, while those obtained in the G9 and G2 lines were similar for pupal weight but not (P<0.05) for adult weight. Therefore, underestimation of the genetic correlation seems to affect the efficiency of a desired gains index more than that of unrestricted or optimum indices.     

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.     

A method for the dynamic management of genetic variability in dairy cattle

According to the general approach developed in this paper, dynamic management of genetic variability in selected populations of dairy cattle is carried out for three simultaneous purposes: procreation of young bulls to be further progeny-tested, use of service bulls already selected and approval of recently progeny-tested bulls for use. At each step, the objective is to minimize the average pairwise relationship coefficient in the future population born from programmed matings and the existing population. As a common constraint, the average estimated breeding value of the new population, for a selection goal including many important traits, is set to a desired value. For the procreation of young bulls, breeding costs are additionally constrained. Optimization is fully analytical and directly considers matings. Corresponding algorithms are presented in detail. The efficiency of these procedures was tested on the current Norman population. Comparisons between optimized and real matings, clearly showed that optimization would have saved substantial genetic variability without reducing short-term genetic gains.     

Plant breeding: Past achievements and expectations for the future

Plant breeding improvements have been responsible for 50 percent or more of the gains in yield per unit area of major crop plants in the United States over the past 50 yr. Rates of gain attributable to genetic improvements have averaged 1% per year, have generally been linear, and show no sign of slackening. Extrapolations indicate that varieties and hybrids of the year 2000 will yield, on average, 15% more than those of 1985 Improvements in tolerance to environmental stress, in grain-to-straw ratios, and in standability, as well as maintenance of required levels of resistance to disease, insect and nematode pests, have been the major genetic causes of higher achieved yields and will continue to be the foundation for further gains in productivity and stability. Broadened genetic diversity is also an increasingly important goal to promote stability and increase productivity potentials. Proportionately large research inputs are now needed to maintain desired rates of improvement, compared to earlier years. It seems likely that contributions from biotechnology will become increasingly important in years to come if improvement rates are to be maintained.     

A critical analysis of production-associated DNA polymorphisms in the genes of cattle, goat, sheep, and pig

Increasing productivity is one of the main objectives in animal production. Traditional breeding methods have led to increased gains in some traits but gains are not easily attainable in traits with low heritabilities. Exploiting the genetic variations underlying desired phenotypes is the goal of today's animal producers. Such positive genetic variants must, however, be known before possible application. Consequently, candidate genes of traits of interest have been searched for possible relationships with such traits or to explain reported quantitative trait loci (QTL) for such traits. DNA variants or polymorphisms have been identified in many such genes and their relationships with production traits determined. However, only a few genes have been evaluated, given the wealth of information on reported QTL for production traits, and in most cases genes are only partially investigated. This review presents available information on DNA variants for production traits and discusses steps that are required for effective utilization of this information for successful marker-assisted selection programs.     

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.     

Skeletal growth and the changing genetic landscape during childhood and adulthood

Growth, development, and decline of the human skeleton are of central importance to physical anthropology. All processes of skeletal growth (longitudinal growth as well as gains and losses of bone mass) are subjected to environmental and genetic influences. These influences, and their relative contributions to the phenotype, can be asserted at any stage of life. We present here the gross phenotypic and genetic landscapes of four skeletal traits, and show how they vary across the life span. Phenotypic sex differences are found in bone diameter and cortical index (a ratio of cortical thickness over bone diameter) at a very early age and continue throughout most of life. Sexual dimorphism in summed cortical thickness and bone length, however, is not evident until shortly after the pubertal growth spurt. Genetic contributions (heritability) to these skeletal phenotypes are generally moderate to high. Bone length and bone diameter (which both scale with body size) tend to have the highest heritability, with heritability of bone length fairly stable across ages (with a notable dip in early childhood) and that of bone diameter peaking in early childhood. The bone traits summed cortical thickness and cortical index that may better reflect bone mass, a more plastic phenomenon, have slightly lower genetic influences, on average. Results from our phenotypic and genetic landscapes serve three key purposes: 1) demonstration of the integrated nature of the genetic and environmental underpinnings of skeletal form, 2) identification of periods of bone's relative sensitivity to genetic and environmental influences, 3) and stimulation of hypotheses predicting the effects of exposure to environmental variables on the skeleton, given variation in the underlying genetic architecture. Am J Phys Anthropol, 2013. © 2012 Wiley Periodicals, Inc.     

Constrained Optimization of Average Arrival Time via a Probabilistic Approach to Transport Reliability

To achieve greater transit-time reduction and improvement in reliability of transport services, there is an increasing need to assist transport planners in understanding the value of punctuality; i.e. the potential improvements, not only to service quality and the consumer but also to the actual profitability of the service. In order for this to be achieved, it is important to understand the network-specific aspects that affect both the ability to decrease transit-time, and the associated cost-benefit of doing so. In this paper, we outline a framework for evaluating the effectiveness of proposed changes to average transit-time, so as to determine the optimal choice of average arrival time subject to desired punctuality levels whilst simultaneously minimizing operational costs. We model the service transit-time variability using a truncated probability density function, and simultaneously compare the trade-off between potential gains and increased service costs, for several commonly employed cost-benefit functions of general form. We formulate this problem as a constrained optimization problem to determine the optimal choice of average transit time, so as to increase the level of service punctuality, whilst simultaneously ensuring a minimum level of cost-benefit to the service operator.     

Genetic modification in the cyclin gene from a Nicotiana interspecific hybrid: role of the GTcyc gene in tumorization process

The organistic constitution of genetic tumors probably causes the constituent cells to undergo genetic change from normal growth to abnormal, a relatively undifferentiated proliferation. We report here that the cyclin GTcyc gene, isolated from genetic tumors yielded notably intense bands while those from the parental DNA were less expressed. In a similar fashion, Northern blot analysis revealed that the genetic tumors expressed high levels of GTcyc relative to non-tumor hybrid tissues. Furthermore, RAPD data showed that the genetic relationships between tumor tissues and their parents did not present a highly corresponding match, suggesting that tumor growth may relate to the genetic modification or hybridization-related genome reorganization. Taken together, the cyclin gene performs a critical role in cell cycle progression, and this particular gene (GTcyc) may be a potential factor in tumor formations, resulting in gene alterations or gains, or changes to specific genomic regions.     

The choice of selection index in kale (Brassica oleracea L.) population improvement

Summary The use of selection indices was explored in a kale (Brassica oleracea L. var. acephala) breeding programme aimed at increasing digestible organicmatter (DOM) yield, and lowering S-methyl cysteine sulphoxide (SMCO) and thiocyanate ion (SCN^–) contents by half-sib family selection. The predicted overall response with the optimum index (1.59) was slightly better than with the base index (1.56) which in turn was superior to the desired gains index (1.41). All three indices were expected to increase height and reduce amino acid content, mainly because of genetical correlations between DOM yield and height (r=0.76) and between SMCO and amino acid contents (r=0.81). Elimination of these correlated responses with the desired gains index would result in virtually no progress, and with the restricted index an undesirable increase in SMCO content would occur.     

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.     

Relative changes in genetic variability and correlations in an early-maturing maize population during recurrent selection

Four cycles of S(1) family recurrent selection to improve grain yield and resistance to Striga hermonthica have been completed in TZE-Y Pop STR C(0.) In order to determine whether or not to continue with the recurrent scheme, it was desirable to evaluate the amount of residual genetic variance and associated parameters in the population. The objective of this study was to characterize the relative changes in the levels of the genetic variances, heritability estimates and genetic correlation coefficients, and to predict future gains from selection for grain yield, Striga resistance and other agronomic traits. Fifty S(1) families, derived from each cycle, were evaluated under Striga-infested and Striga-free conditions at Mokwa, Ikenne and Abuja, Nigeria, in 2005 and 2007. Under Striga infestation, genetic variances for grain yield, days to anthesis, plant height and Striga damage generally increased in the advanced cycles of selection. In contrast, the genetic variances for days to silk, anthesis-silking interval, ears per plant, ear aspect and number of emerged Striga plants decreased with selection. The advanced cycles of selection significantly out-yielded the original cycle in both research environments. Heritabilities for grain yield, Striga damage and number of emerged Striga plants were significantly greater than zero. The realized gains from selection for grain yield under Striga infestation (52?kg?ha(-1)?cycle(-1)) and Striga-free conditions (130?kg?ha(-1)?cycle(-1)) were remarkably lower than the predicted gains (350 and 250?kg?ha(-1?)cycle(-1), respectively). Adequate genetic variability exists in cycle 4 of the scheme to ensure future gains from selection.     

Migrant blackbirds,Turdus merula,have higher plasma levels of polyunsaturated fatty acids compared to residents,but not enhanced fatty acid unsaturation index

Birds have been observed to have dietary preferences for unsaturated fatty acids during migration. Polyunsaturated fatty acids (PUFAs) may increase the exercise performance of migrant birds; however, PUFAs are also peroxidation prone and might therefore incur increased costs in terms of enhanced oxidative damage in migratory individuals. To shed light on this potential constraint, we analyzed plasma fatty acid (FA) composition and estimated the unsaturation index as a proxy for susceptibility to lipid peroxidation of migrants and residents of the partially migratory common blackbird (Turdus merula) at a stopover site during autumn migration. As predicted, migrant birds had higher relative and absolute levels of PUFAs compared to resident birds. This included the strictly dietary ω‐3 PUFA α‐linolenic acid, suggesting a dietary and/or storage preference for these FAs in migrants. Interestingly, the FA unsaturation index did not differ between migrants and residents. These findings suggest a mechanism where birds alter their levels of metabolic substrate without simultaneously increasing the susceptibility of the substrate to lipid peroxidation. In summary, our results are in line with the hypothesis that increased exercise performance during migration might be constrained by oxidative stress, which is manifested in changes in the composition of key FAs to retain the unsaturation index constant despite the increased levels of peroxidizable PUFAs.     

Economic weights of somatic cell score in dairy sheep

The economic weights for somatic cell score (SCS) have been calculated using profit functions. Economic data were collected in the Latxa breed. Three aspects have been considered: bulk tank milk payment, veterinary treatments due to high SCS, and culling. All of them are non-linear profit functions. Milk payment is based on the sum of the log-normal distributions of somatic cell count, and veterinary treatments on the probability of subclinical mastitis, which is inferred when individual SCS surpass some threshold. Both functions lead to non-standard distributions. The derivatives of the profit function were computed numerically. Culling was computed by assuming that a conceptual trait culled by mastitis (CBM) is genetically correlated to SCS. The economic weight considers the increase in the breeding value of CBM correlated to an increase in the breeding value of SCS, assuming genetic correlations ranging from 0 to 0.9. The relevance of the economic weights for selection purposes was checked by the estimation of genetic gains for milk yield and SCS under several scenarios of genetic parameters and economic weights. The overall economic weights for SCS range from − 2.6 to − 9.5 € per point of SCS, with an average of − 4 € per point of SCS, depending on the expected average SCS of the flock. The economic weight is higher around the thresholds for payment policies. Economic weights did not change greatly with other assumptions. The estimated genetic gains with economic weights of 0.83 € per l of milk yield and − 4 € per point of SCS, assuming a genetic correlation of − 0.30, were 3.85 l and − 0.031 SCS per year, with an associated increase in profit of 3.32 €. This represents a very small increase in profit (about 1%) relative to selecting only for milk yield. Other situations (increased economic weights, different genetic correlations) produced similar genetic gains and changes in profit. A desired-gains index reduced the increase in profit by 3%, although it could be greater depending on the genetic parameters. It is concluded that the inclusion of SCS in dairy sheep breeding programs is of low economic relevance and recommended only if recording is inexpensive or for animal welfare concerns.     

Genetic steady-state under BLUP selection for an infinite and homogeneous population with discrete generations

A matrix derivation is proposed to analytically calculate the asymptotic genetic variance-covariance matrix under BLUP selection according to the initial genetic parameters in a large population with discrete generations. The asymptotic genetic evolution of a homogeneous population with discrete generations is calculated for a selection operating on an index including all information (pedigree and records) from a non-inbred and unselected base population (BLUP selection) or on an index restricted to records of a few ancestral generations. Under the first hypothesis, the prediction error variance of the selection index is independent of selection and is calculated from the genetic parameters of the base population. Under the second hypothesis, the prediction error variance depends on selection. Furthermore, records of several generations of ancestors of the candidates for selection must be used to maintain a constant prediction error variance over time. The number of ancestral generations needed depends on the population structure and on the occurrence of fixed effects. Without fixed effects to estimate, accounting for two generations of ancestors is sufficient to estimate the asymptotic prediction error variance. The amassing of information from an unselected base population proves to be important in order not to overestimate the asymptotic genetic gains and not to underestimate the asymptotic genetic variances.     

Bias and efficiency in family-based gene-characterization studies: conditional, prospective, retrospective, and joint likelihoods

We revisit the usual conditional likelihood for stratum-matched case-control studies and consider three alternatives that may be more appropriate for family-based gene-characterization studies: First, the prospective likelihood, that is, Pr(D/G,A second, the retrospective likelihood, Pr(G/D); and third, the ascertainment-corrected joint likelihood, Pr(D,G/A). These likelihoods provide unbiased estimators of genetic relative risk parameters, as well as population allele frequencies and baseline risks. The parameter estimates based on the retrospective likelihood remain unbiased even when the ascertainment scheme cannot be modeled, as long as ascertainment only depends on families' phenotypes. Despite the need to estimate additional parameters, the prospective, retrospective, and joint likelihoods can lead to considerable gains in efficiency, relative to the conditional likelihood, when estimating genetic relative risk. This is true if baseline risks and allele frequencies can be assumed to be homogeneous. In the presence of heterogeneity, however, the parameter estimates assuming homogeneity can be seriously biased. We discuss the extent of this problem and present a mixed models approach for providing consistent parameter estimates when baseline risks and allele frequencies are heterogeneous. The efficiency gains of the mixed-model prospective, retrospective, and joint likelihoods relative to the efficiency of conditional likelihood are small in the situations presented here.     

Management of subdivided populations in conservation programs: development of a novel dynamic system

Within the context of a conservation program the management of subdivided populations implies a compromise between the control of the global genetic diversity, the avoidance of high inbreeding levels, and, sometimes, the maintenance of a certain degree of differentiation between subpopulations. We present a dynamic and flexible methodology, based on genealogical information, for the maximization of the genetic diversity (measured through the global population coancestry) in captive subdivided populations while controlling/restricting the levels of inbreeding. The method is able to implement specific restrictions on the desired relative levels of coancestry between and within subpopulations. By accounting for the particular genetic population structure, the method determines the optimal contributions (i.e., number of offspring) of each individual, the number of migrants, and the particular subpopulations involved in the exchange of individuals. Computer simulations are used to illustrate the procedure and its performance in a range of reasonable scenarios. The method performs well in most situations and is shown to be more efficient than the commonly accepted one-migrant-per-generation strategy.