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.     

Efficiency of one- and two-stage selection indexes for improvement of net economic merit in White Leghorns

Summary Mitochondrial (mt) and chloroplast (ct) DNAs from sugar beet lines carrying normal and introduced sources of male sterile cytoplasms have been characterized and compared on the basis of restriction enzyme analysis. Normal cytoplasm was shown to contain mt and ctDNAs which differed from those of the male sterile cytoplasms examined in the present investigation. On the other hand, four groups of male sterile cytoplasms could be differentiated by their own characteristic mtDNA digest patterns, while two were separated by ctDNA comparisons. In addition, a greater degree of variability of the mitochondrial genome is suggested. Our results also imply strict maternal inheritance of mt and ctDNAs. Thus, the organelle DNA assay provides a positive and alternative means of identifying various male sterile cytoplasms.     

Implications of non-linear economic weights for breeding

Summary Relationships were studied theoretically between phenotypic values of selection candidates (parents) and economic worth of the offspring that would belong to production populations. The candidates could include individuals, crosses or clones, and the offspring could be produced either sexually or vegetatively. Cases considered included: three systems for generating production populations [clonal propagation, pair(full-sib)crosses and half-sib crosses]; three economic-worth (profit) functions for individual offspring (linear, intermediate optimum, acceptable versus cull); and independently varying heritabilities for both parents and offspring. The heritabilities were varied in the model against a background of fixed genetic variance. Parental values were considered in terms of phenotypic standard deviations from the population mean, assuming normality. Lower heritabilities and, to a lesser extent, genetic segregation severely damped down the non-linearities of economic worth in relation to measured parental values, such that the linear weightings for traits in a selection index should usually be a good approximation, provided the profit function for individual offspring is monotonic. The economic advantages of corrective mating within a select population may be minimal if both heritabilities are low and the profit functions apply to individual offspring. The economic advantages accruing from genetic uniformity of clones (or crosses between inbreds) in conjunction with non-linear profit functions are strongly dependent on achieving high broad-sense heritabilites, particularly in the offspring (production population).     

The effect of selection on genealogies

The coalescent process can describe the effects of selection at linked loci only if selection is so strong that genotype frequencies evolve deterministically. Here, we develop methods proposed by Kaplan, Darden, and Hudson to find the effects of weak selection. We show that the overall effect is given by an extension to Price's equation: the change in properties such as moments of coalescence times is equal to the covariance between those properties and the fitness of the sample of genes. The distribution of coalescence times differs substantially between allelic classes, even in the absence of selection. However, the average coalescence time between randomly chosen genes is insensitive to the current allele frequency and is affected significantly by purifying selection only if deleterious mutations are common and selection is strong (i.e., the product of population size and selection coefficient, Ns>3). Balancing selection increases mean coalescence times, but the effect becomes large only when mutation rates between allelic classes are low and when selection is extremely strong. Our analysis supports previous simulations that show that selection has surprisingly little effect on genealogies. Moreover, small fluctuations in allele frequency due to random drift can greatly reduce any such effects. This will make it difficult to detect the action of selection from neutral variation alone.     

The importance of identity-by-state information for the accuracy of genomic selection

Background

It is commonly assumed that prediction of genome-wide breeding values in genomic selection is achieved by capitalizing on linkage disequilibrium between markers and QTL but also on genetic relationships. Here, we investigated the reliability of predicting genome-wide breeding values based on population-wide linkage disequilibrium information, based on identity-by-descent relationships within the known pedigree, and to what extent linkage disequilibrium information improves predictions based on identity-by-descent genomic relationship information.

Methods

The study was performed on milk, fat, and protein yield, using genotype data on 35 706 SNP and deregressed proofs of 1086 Italian Brown Swiss bulls. Genome-wide breeding values were predicted using a genomic identity-by-state relationship matrix and a genomic identity-by-descent relationship matrix (averaged over all marker loci). The identity-by-descent matrix was calculated by linkage analysis using one to five generations of pedigree data.

Results

We showed that genome-wide breeding values prediction based only on identity-by-descent genomic relationships within the known pedigree was as or more reliable than that based on identity-by-state, which implicitly also accounts for genomic relationships that occurred before the known pedigree. Furthermore, combining the two matrices did not improve the prediction compared to using identity-by-descent alone. Including different numbers of generations in the pedigree showed that most of the information in genome-wide breeding values prediction comes from animals with known common ancestors less than four generations back in the pedigree.

Conclusions

Our results show that, in pedigreed breeding populations, the accuracy of genome-wide breeding values obtained by identity-by-descent relationships was not improved by identity-by-state information. Although, in principle, genomic selection based on identity-by-state does not require pedigree data, it does use the available pedigree structure. Our findings may explain why the prediction equations derived for one breed may not predict accurate genome-wide breeding values when applied to other breeds, since family structures differ among breeds.     

The effect of simultaneous selection on the genetic correlation

The theoretical effect of simultaneous selection on the genetic correlations between two traits over 20 generations was examined using simulation. For each generation, a population of 50 male and 50 female diploid gen otypes with 15 loci, each with two alleles, was synthesized. None of the loci exhibited dominance. Five loci affected only trait 1, 5 loci only trait 2 and 5 were pleiotropic (affected both traits). Initial allelic frequencies were equal at each locus. Phenotypes were created by adding a random normal deviation for each trait to the genotype. The size of this deviation for each trait determined its heritability (h²). Index selection with h² combinations of (0.15, 0.15), (0.15,0.45) and (0.45,0.45) and relative economic weights of (1, 1) and (1, 3) for each h² combination was employed. In each generation, the highest ranking 25 genotypes of each sex were used to generate the next generation with single-pair matings, each producing two male and two female offspring. One hundred replicates were run for both negative and positive correlations. With a positive initial value, the genetic correlation tended to decline (toward zero). The rates of change were moderately affected by index weights and h². With a negative initial value, the genetic correlation tended to decrease (towards -1). However, unequal heritabilities and unequal relative economic weights slowed the rate of change with the greatest imbalances tending to hold the correlation constant or move it toward zero. These simulations illustrate that changes in parameters over time can affect the selection practiced. Under some of the conditions simulated, the use of initial genetic parameter values without change could have potentially negative effects on overall genetic gain.     

The effect of parasites on sex differences in selection

The life history strategies of males and females are often divergent, creating the potential for sex differences in selection. Deleterious mutations may be subject to stronger selection in males, owing to sexual selection, which can improve the mean fitness of females and reduce mutation load in sexual populations. However, sex differences in selection might also maintain sexually antagonistic genetic variation, creating a sexual conflict load. The overall impact of separate sexes on fitness is unclear, but the net effect is likely to be positive when there is a large sex difference in selection against deleterious mutations. Parasites can also have sex-specific effects on fitness, and there is evidence that parasites can intensify the fitness consequences of deleterious mutations. Using lines that accumulated mutations for over 60 generations, we studied the effect of the pathogenic bacterium Pseudomonas aeruginosa on sex differences in selection in the fruit fly Drosophila melanogaster. Pseudomonas infection increased the sex difference in selection, but may also have weakened the intersexual correlation for fitness. Our results suggest that parasites may increase the benefits of sexual selection.     

Effects of random and non-random errors on phenotypic selection in autotetraploids

Summary A theoretical investigation was made to ascertain the effects of random and non-random deviations, called errors, of phenotypic from genotypic values on population means and on the response to phenotypic recurrent selection. The study was motivated as a selection experiment for disease resistance where there was either variability in the inoculation or environment (the random errors) or where the inoculation was above or below the the optimum rate where genetic differences in resistance are maximized (the non-random errors). The study was limited to the genetics at a diallelic locus (alleles B and b) in an autotetraploid population in random mating equilibrium. The response to selection was measured as the covariance of selection and compared to the exact covariance which was the covariance of selection without errors in phenotype. The random errors were modeled by assuming that a given percentage () of the population was uniformly distributed among the five possible genotype classes independent of their true genotypes. This model was analyzed numerically for a theoretical population with the frequency of the B allele (p) ranging from 0.0 to 1.0 and assumed errors of=0.1 and 0.5 for the following six types of genic action of the B allele: additive, monoplex dominance, partial monoplex dominance, duplex dominance, partial duplex dominance, and recessive. The effect of random error was to consistently reduce the response to selection by a percentage independent of the type of genic action at the locus. The effect on the population mean was an upward bias when p was low and a downward bias when p approached unity. In the non-random error model below optimum inoculations altered the phenotypes by systematically including percentage of susceptible genotypes into one or more other genotype classes with more genetic resistance (a positive shift). With above optimum inoculations, some resistant genotypes are classed with the non-resistant genotypes (a negative shift). The effects on the covariance of selection were found by numerical analysis for the same types of genic action and's as investigated for random error. With a negative shift and a low p, the covariance of selection was always reduced, but for an increasing p the covariance approached and exceeded the exact covariance for all types of genic action except additive. With a positive shift and a low p, response to selection was greatly improved for three types of genic action: duplex dominance, partial duplex dominance, and recessive. The effect of a non-random error on population means was to greatly bias the means upwards for a low p and positive shift, but with increasing p the bias decreased. A relatively slight decrease in the mean occurred with a negative shift. This study indicated check varieties commonly used to monitor selection pressures in screening programs are very responsive to positive non-random shifts, but are relatively unresponsive to negative shifts. The interaction of selection pressure, types of genic action, and genotypes in the class shift models was suggested as a partial explanation for the lack of response to increasing selection pressures observed in some breeding programs.Cooperative investigations of the Alfalfa Production Research Unit, United States Department of Agriculture, Agricultural Research Service, and the Nevada Agricultural Experiment Station, Reno, Nevada. Paper No. 404 Scientific Journal Series. Nevada Agricultural Experiment Station     

The effect of neural adaptation on population coding accuracy

Most neurons in the primary visual cortex initially respond vigorously when a preferred stimulus is presented, but adapt as stimulation continues. The functional consequences of adaptation are unclear. Typically a reduction of firing rate would reduce single neuron accuracy as less spikes are available for decoding, but it has been suggested that on the population level, adaptation increases coding accuracy. This question requires careful analysis as adaptation not only changes the firing rates of neurons, but also the neural variability and correlations between neurons, which affect coding accuracy as well. We calculate the coding accuracy using a computational model that implements two forms of adaptation: spike frequency adaptation and synaptic adaptation in the form of short-term synaptic plasticity. We find that the net effect of adaptation is subtle and heterogeneous. Depending on adaptation mechanism and test stimulus, adaptation can either increase or decrease coding accuracy. We discuss the neurophysiological and psychophysical implications of the findings and relate it to published experimental data.     

The effects of selection for different combinations of weights at two ages on the growth curve of mice

Summary The weights of mice in lines selected for different combinations of high and low body weights at 5 and at 10 weeks of age were recorded from 3 to 21 weeks of age. The average growth curve for each line was computed using the Gompertz function. The growth curves of lines selected for high or low weight at a single age (ST lines) showed large differences in estimates of mature size and small differences in estimates of maturing rate, i.e. of the relative rate of growth to maturity. The growth curves of lines selected by independent culling for divergent combinations of deviations of opposite sign in 5- and 10-week weights (ICL lines) showed little difference in estimates of mature size and a large difference in estimates of maturing rate. The growth curves of lines selected by index for divergence in 5-week weight with no change in 10-week-weight or for divergence in 10-week-weight with no change in 5-week weight showed large differences in estimates of mature size and large differences in estimates of the maturing rate. The relationship between mature size and maturing rate was affected in different ways by the three types of selection.     

Experimental assessment of the accuracy of genomic selection in sugarcane

Sugarcane cultivars are interspecific hybrids with an aneuploid, highly heterozygous polyploid genome. The complexity of the sugarcane genome is the main obstacle to the use of marker-assisted selection in sugarcane breeding. Given the promising results of recent studies of plant genomic selection, we explored the feasibility of genomic selection in this complex polyploid crop. Genetic values were predicted in two independent panels, each composed of 167 accessions representing sugarcane genetic diversity worldwide. Accessions were genotyped with 1,499 DArT markers. One panel was phenotyped in Reunion Island and the other in Guadeloupe. Ten traits concerning sugar and bagasse contents, digestibility and composition of the bagasse, plant morphology, and disease resistance were used. We used four statistical predictive models: bayesian LASSO, ridge regression, reproducing kernel Hilbert space, and partial least square regression. The accuracy of the predictions was assessed through the correlation between observed and predicted genetic values by cross validation within each panel and between the two panels. We observed equivalent accuracy among the four predictive models for a given trait, and marked differences were observed among traits. Depending on the trait concerned, within-panel cross validation yielded median correlations ranging from 0.29 to 0.62 in the Reunion Island panel and from 0.11 to 0.5 in the Guadeloupe panel. Cross validation between panels yielded correlations ranging from 0.13 for smut resistance to 0.55 for brix. This level of correlations is promising for future implementations. Our results provide the first validation of genomic selection in sugarcane.     

The effect of fast created inbreeding on litter size and body weights in mice

This study was designed to reveal any differences in effects of fast created versus total inbreeding on reproduction and body weights in mice. A line selected for large litter size for 124 generations (H) and a control line (K) maintained without selection for the same number of generations were crossed (HK) and used as a basis for the experiment. Within the HK cross, full sib, cousin or random mating were practised for two generations in order to create new inbreeding (IB_F) at a fast rate. In the first generation of systematic mating, old inbreeding was regenerated in addition to creation of new inbreeding from the mating design giving total inbreeding (IB_T). The number of pups born alive (NBA) and body weights of the animals were then analysed by a model including both IB_T and IB_F. The IB_T of the dam was in the present study found to reduce the mean NBA with -0.48 (± 0.22) (p < 0.05) pups per 10% increase in the inbreeding coefficient, while the additional effect of IB_F was -0.42 (± 0.27). For the trait NBA per female mated, the effect of IB_T was estimated to be -0.45 (± 0.29) per 10% increase in the inbreeding coefficient and the effect of IB_F was -0.90 (± 0.37) (p < 0.05) pups. In the present study, only small or non-significant effects of IB_F of the dam could be found on sex-ratio and body weights at three and six weeks of age in a population already adjusted for IB_T.     

The effect of genotyping errors on the robustness of composite linkage disequilibrium measures

We conclude that composite linkage disequilibrium (LD) measures be adopted in population-based LD mapping or association mapping studies since it is unaffected by Hardy-Weinberg disequilibrium. Although some properties of composite LD measures have been recently studied, the effects of genotyping errors on composite LD measures have not been examined. In this report, we derived deterministic formulas to evaluate the impact of genotyping errors on the composite LD measures Δ'AB and rAB, and compared the robustness of Δ'AB and rAB in the presence of genotyping errors. The results showed that Δ'AB and rAB depend on the allele frequencies and the assumed error model, and show varying degrees of robustness in the presence of errors. In general, whether there is HWD or not, rAB is more robust than Δ'AB except some special cases and the difference of robustness between Δ'AB and rAB becomes less severe as the difference between the frequencies of two SNP alleles A and B becomes smaller.     

The effect of replication errors on the mismatch analysis of PCR-amplified DNA.

The mismatch analysis of PCR-amplified DNA has generally assumed the absence of artificially introduced base substitutions in a significant proportion of the amplification product. This technique, however, differs from the direct sequencing of amplified DNA in that non-specific substitutions will render a molecule useless in analysis. The expected signal-to-noise ratio is heavily influenced by several parameters viz. initial template copy number, number of replication cycles, eventual product yield and the type of experimental system adopted. Mathematical modelling can be used to optimize fragment length with respect to the method applied and suggests as yet undescribed improvements such as partial modification or cleavage to optimize signal detection.     

Prediction of effects of beef selection indexes on greenhouse gas emissions

Genetic improvement in production efficiency traits can also drive reduction in greenhouse gas emissions. This study used international ‘best-practice’ methodology to quantify the improvements in system-wide CO₂ equivalent emissions per unit of genetic progress in the Irish Maternal Replacement (MR) and Terminal (T) beef cattle indexes. Effects of each index trait on system gross emissions (GE) and system emissions intensity (EI) were modelled by estimating effects of trait changes on per-animal feed consumption and associated methane production, per-animal meat production and numbers of animals in the system. Trait responses to index selection were predicted from linear regression of individual bull estimated breeding values for each index trait on their MR or T index value, and the resulting regression coefficients were used to calculate trait-wise responses in GE and EI from index selection. Summed over all trait responses, the MR index was predicted to reduce system GE by 0.810 kg CO₂e/breeding cow per year per € index and system EI by 0.009 kg CO₂e/kg meat per breeding cow per year per € index. These reductions were mainly driven by improvements in cow survival, reduced mature cow maintenance feed requirements, shorter calving interval and reduced offspring mortality. The T index was predicted to reduce system EI by 0.021 kg CO₂e/kg meat per breeding cow per year per € index, driven by increased meat production from improvements in carcass weight, conformation and fat. Implications for incorporating an EI reduction index to the current production indexes and long-term projections for national breeding programs are discussed.