The Price equation as a bridge between animal breeding and evolutionary biology.

The genetic response to selection is central to both evolutionary biology and animal and plant breeding. While Price's theorem (PT) is well-known in evolutionary biology, most breeders are unaware of it. Rather than using PT, breeders express response to selection as the product of the intensity of selection (i), the accuracy of selection (ρ) and the additive genetic standard deviation (σA); R = iρσA. In contrast to the univariate 'breeder's equation', this expression holds for multivariate selection on Gaussian traits. Here, I relate R = iρσA to PT, and present a generalized version, R = iwρA,wσA, valid irrespective of the trait distribution. Next, I consider genotype-environment covariance in relation to the breeder's equation and PT, showing that the breeder's equation may remain valid depending on whether the genotype-environment covariance works across generations. Finally, I consider the response to selection in the prevalence of an endemic infectious disease, as an example of an emergent trait. The result shows that disease prevalence has much greater heritable variation than currently believed. The example also illustrates that the indirect genetic effect approach moves elements of response to selection from the second to the first term of PT, so that changes acting via the social environment come within the reach of quantitative genetics. This article is part of the theme issue 'Fifty years of the Price equation'.

A genome-wide association study for susceptibility and infectivity of Holstein Friesian dairy cattle to digital dermatitis.

Selection and breeding can be used to fight transmission of infectious diseases in livestock. The prevalence in a population depends on the susceptibility and infectivity of the animals. Knowledge on the genetic background of those traits would facilitate efficient selection for lower disease prevalence. We investigated the genetic background of host susceptibility and infectivity for digital dermatitis (DD), an endemic infectious claw disease in dairy cattle, with a genome-wide association study (GWAS), using either a simple linear mixed model or a generalized linear mixed model based on epidemiological theory. In total, 1,513 Holstein-Friesian cows of 12 Dutch dairy farms were scored for DD infection status and class (M0 to M4.1) every 2 wk for 11 times; 1,401 of these cows were genotyped with a 75k SNP chip. We performed a GWAS with a linear mixed model on 10 host disease status traits, and with a generalized linear mixed model with a complementary log-log link function (GLMM) on the probability that a cow would get infected between 2 scorings. With the GLMM, we fitted SNP effects for host susceptibility and host infectivity, while taking the variation in exposure of the susceptible cow to infectious herd mates into account. With the linear model we detected 4 suggestive SNP (false discovery rate < 0.20), 2 for the fraction of observations a cow had an active lesion on chromosomes 1 and 14, one for the fraction of observations a cow had an M2 lesion on at least one claw on chromosome 1 (the same SNP as for the fraction of observations with an active lesion), and one for the fraction of observations a cow had an M4.1 lesion on at least one claw on chromosome 10. Heritability estimates ranged from 0.09 to 0.37. With the GLMM we did not detect significant nor suggestive SNP. The SNP effects on disease status analyzed with the linear model had a correlation coefficient of only 0.70 with SNP effects on susceptibility of the GLMM, indicating that both models capture partly different effects. Because the GLMM better accounts for the epidemiological mechanisms determining individual disease status and for the distribution of the y-variable, results of the GLMM may be more reliable, despite the absence of suggestive associations. We expect that with an extended GLMM that better accounts for the full genetic variation in infectivity via the environment, the accuracy of SNP effects may increase.

Value of the Dutch Holstein Friesian germplasm collection to increase genetic variability and improve genetic merit.

National gene bank collections for Holstein Friesian (HF) dairy cattle were set up in the 1990s. In this study, we assessed the value of bulls from the Dutch HF germplasm collection, also known as cryobank bulls, to increase genetic variability and improve genetic merit in the current bull population (bulls born in 2010-2015). Genetic variability was defined as 1 minus the mean genomic similarity (SIMSNP) or as 1 minus the mean pedigree-based kinship (fPED). Genetic merit was defined as the mean estimated breeding value for the total merit index or for 1 of 3 subindices (yield, fertility, and udder health). Using optimal contribution selection, we minimized relatedness (maximized variability) or maximized genetic merit at restricted levels of relatedness. We compared breeding schemes with only bulls from 2010 to 2015 with schemes in which cryobank bulls were also included. When we minimized relatedness, inclusion of genotyped cryobank bulls decreased mean SIMSNP by 0.7% and inclusion of both genotyped and nongenotyped cryobank bulls decreased mean fPED by 2.6% (in absolute terms). When we maximized merit at restricted levels of relatedness, inclusion of cryobank bulls provided additional merit at any level of mean SIMSNP or mean fPED except for the total merit index at high levels of mean SIMSNP. Additional merit from cryobank bulls depended on (1) the relative emphasis on genetic variability and (2) the selection criterion. Additional merit was higher when more emphasis was put on genetic variability. For fertility, for example, it was 1.74 SD at a mean SIMSNP restriction of 64.5% and 0.37 SD at a mean SIMSNP restriction of 67.5%. Additional merit was low to nonexistent for the total merit index and higher for the subindices, especially for fertility. At a mean SIMSNP of 64.5%, for example, it was 0.60 SD for the total merit index and 1.74 SD for fertility. In conclusion, Dutch HF cryobank bulls can be used to increase genetic variability and improve genetic merit in the current population, although their value is very limited when selecting for the current total merit index. Anticipating changes in the breeding goal in the future, the germplasm collection is a valuable resource for commercial breeding populations.

The early-life environment of a pig shapes the phenotypes of its social partners in adulthood.

Social interactions among individuals are abundant, both in natural and domestic populations, and may affect phenotypes of individuals. Recent research has demonstrated that the social effect of an individual on the phenotype of its social partners may have a genetic component, known as an indirect genetic effect (IGE). Little is known, however, of nongenetic factors underlying such social effects. Early-life environments often have large effects on phenotypes of the individuals themselves later in life. Offspring development in many mammalian species, for example, depends on interactions with the mother and siblings. In domestic pigs, individuals sharing the same juvenile environment develop similar body weight later in life. We, therefore, hypothesized that offspring originating from the same early-life environment also develop common social skills that generate early-life social effects (ELSEs) that affect the phenotypes of their social partners later in life. We, therefore, quantified IGEs and ELSEs on growth in domestic pigs. Results show that individuals from the same early-life environment express similar social effects on the growth of their social partners, and that such ELSEs shape the growth rate of social partners more than IGEs. Thus, the social skills that individuals develop in early life have a long-lasting impact on the phenotypes of social partners. Early-life and genetic social effects were independent of the corresponding direct effects of offspring on their own growth, indicating that individuals may enhance the growth of their social partners without a personal cost. Our findings also illustrate how research devoted to quantifying IGEs may miss nongenetic and potentially confounded social mechanisms which may bias the estimates of IGEs.

Estimation of total genetic effects for survival time in crossbred laying hens showing cannibalism, using pedigree or genomic information.

Mortality of laying hens due to cannibalism is a major problem in the egg-laying industry. Survival depends on two genetic effects: the direct genetic effect of the individual itself (DGE) and the indirect genetic effects of its group mates (IGE). For hens housed in sire-family groups, DGE and IGE cannot be estimated using pedigree information, but the combined effect of DGE and IGE is estimated in the total breeding value (TBV). Genomic information provides information on actual genetic relationships between individuals and might be a tool to improve TBV accuracy. We investigated whether genomic information of the sire increased TBV accuracy compared with pedigree information, and we estimated genetic parameters for survival time. A sire model with pedigree information (BLUP) and a sire model with genomic information (ssGBLUP) were used. We used survival time records of 7290 crossbred offspring with intact beaks from four crosses. Cross-validation was used to compare the models. Using ssGBLUP did not improve TBV accuracy compared with BLUP which is probably due to the limited number of sires available per cross (~50). Genetic parameter estimates were similar for BLUP and ssGBLUP. For both BLUP and ssGBLUP, total heritable variance (T2 ), expressed as a proportion of phenotypic variance, ranged from 0.03 ± 0.04 to 0.25 ± 0.09. Further research is needed on breeding value estimation for socially affected traits measured on individuals kept in single-family groups.

Estimation of indirect genetic effects in group-housed mink (Neovison vison) should account for systematic interactions either due to kin or sex.

Social interactions among individuals are abundant, both in wild and in domestic populations. With social interactions, the genes of an individual may affect the trait values of other individuals, a phenomenon known as indirect genetic effects (IGEs). IGEs can be estimated using linear mixed models. Most IGE models assume that individuals interact equally to all group mates irrespective of relatedness. Kin selection theory, however, predicts that an individual will interact differently with family members versus non-family members. Here, we investigate kin- and sex-specific non-genetic social interactions in group-housed mink. Furthermore, we investigated whether systematic non-genetic interactions between kin or individuals of the same sex influence the estimates of genetic parameters. As a second objective, we clarify the relationship between estimates of the traditional IGE model and a family-based IGE model proposed in a previous study. Our results indicate that male siblings in mink show different non-genetic interactions than female siblings in mink and that this may impact the estimation of genetic parameters. Moreover, we have shown how estimates from a family-based IGE model can be translated to the ordinary direct-indirect model and vice versa. We find no evidence for genetic differences in interactions among related versus unrelated mink.

Genome-wide association study reveals novel loci for litter size and its variability in a Large White pig population.

BACKGROUND: In many traits, not only individual trait levels are under genetic control, but also the variation around that level. In other words, genotypes do not only differ in mean, but also in (residual) variation around the genotypic mean. New statistical methods facilitate gaining knowledge on the genetic architecture of complex traits such as phenotypic variability. Here we study litter size (total number born) and its variation in a Large White pig population using a Double Hierarchical Generalized Linear model, and perform a genome-wide association study using a Bayesian method. RESULTS: In total, 10 significant single nucleotide polymorphisms (SNPs) were detected for total number born (TNB) and 9 SNPs for variability of TNB (varTNB). Those SNPs explained 0.83 % of genetic variance in TNB and 1.44 % in varTNB. The most significant SNP for TNB was detected on Sus scrofa chromosome (SSC) 11. A possible candidate gene for TNB is ENOX1, which is involved in cell growth and survival. On SSC7, two possible candidate genes for varTNB are located. The first gene is coding a swine heat shock protein 90 (HSPCB = Hsp90), which is a well-studied gene stabilizing morphological traits in Drosophila and Arabidopsis. The second gene is VEGFA, which is activated in angiogenesis and vasculogenesis in the fetus. Furthermore, the genetic correlation between additive genetic effects on TNB and on its variation was 0.49. This indicates that the current selection to increase TNB will also increase the varTNB. CONCLUSIONS: To the best of our knowledge, this is the first study reporting SNPs associated with variation of a trait in pigs. Detected genomic regions associated with varTNB can be used in genomic selection to decrease varTNB, which is highly desirable to avoid very small or very large litters in pigs. However, the percentage of variance explained by those regions was small. The SNPs detected in this study can be used as indication for regions in the Sus scrofa genome involved in maintaining low variability of litter size, but further studies are needed to identify the causative loci.

Genetic analysis of infectious diseases: estimating gene effects for susceptibility and infectivity.

BACKGROUND: Genetic selection of livestock against infectious diseases can complement existing interventions to control infectious diseases. Most genetic approaches that aim at reducing disease prevalence assume that individual disease status (infected/not-infected) is solely a function of its susceptibility to a particular pathogen. However, individual infectivity also affects the risk and prevalence of an infection in a population. Variation in susceptibility and infectivity between hosts affects transmission of an infection in the population, which is usually measured by the value of the basic reproduction ratio R 0 . R 0 is an important epidemiological parameter that determines the risk and prevalence of infectious diseases. An individual's breeding value for R 0 is a function of its genes that influence both susceptibility and infectivity. Thus, to estimate the effects of genes on R 0 , we need to estimate the effects of genes on individual susceptibility and infectivity. To that end, we developed a generalized linear model (GLM) to estimate relative effects of genes for susceptibility and infectivity. A simulation was performed to investigate bias and precision of the estimates, the effect of R 0 , the size of the effects of genes for susceptibility and infectivity, and relatedness among group mates on bias and precision. We considered two bi-allelic loci that affect, respectively, the individuals' susceptibility only and individuals' infectivity only. RESULTS: A GLM with complementary log-log link function can be used to estimate the relative effects of genes on the individual's susceptibility and infectivity. The model was developed from an equation that describes the probability of an individual to become infected as a function of its own susceptibility genotype and infectivity genotypes of all its infected group mates. Results show that bias is smaller when R 0 ranges approximately from 1.8 to 3.1 and relatedness among group mates is higher. With larger effects, both absolute and relative standard deviations become clearly smaller, but the relative bias remains the same. CONCLUSIONS: We developed a GLM to estimate the relative effect of genes that affect individual susceptibility and infectivity. This model can be used in genome-wide association studies that aim at identifying genes that influence the prevalence of infectious diseases.

Evaluation of genomic selection for replacement strategies using selection index theory.

Our objective was to investigate the economic effect of prioritizing heifers for replacement at the herd level based on genomic estimated breeding values, and to compute break-even genotyping costs across a wide range of scenarios. Specifically, we aimed to determine the optimal proportion of preselection based on parent average information for all scenarios considered. Considered replacement strategies include a range of different selection intensities by considering different numbers of heifers available for replacement (15-45 in a herd with 100 dairy cows) as well as different replacement rates (15-40%). Use of conventional versus sexed semen was considered, where the latter resulted in having twice as many heifers available for replacement. The baseline scenario relies on prioritization of replacement heifers based on parent average. The first alternative scenario involved genomic selection of heifers, considering that all heifers were genotyped. The benefits of genomic selection in this scenario were computed using a simple formula that only requires the number of lactating animals, the difference in accuracy between parent average and genomic selection (GS), and the selection intensity as input. When all heifers were genotyped, using GS for replacement of heifers was beneficial in most scenarios for current genotyping prices, provided some room exists for selection, in the sense that at least 2 more heifers are available than needed for replacement. In those scenarios, minimum break-even genotyping costs were equal to half the economic value of a standard deviation of the breeding goal. The second alternative scenario involved a preselection based on parent average, followed by GS among all the preselected heifers. It was in almost all cases beneficial to genotype all heifers when conventional semen was used (i.e., to do no preselection). The optimal proportion of preselection based on parent average was at least 0.63 when sexed semen was used. Use of sexed semen increased the potential benefit of using GS, because it increased the room for selection. Critical assumptions that should not be ignored when calculating the benefit of GS are (1) a decrease in replacement rate can only be achieved by increasing productive life in the herd, and (2) accuracies of selection should be used rather than accuracies of estimated breeding values based on the prediction error variance and base-generation genetic variance, because the latter lead to underestimation of the potential of GS.

Comparison of methods to study uniformity of traits: Application to birth weight in pigs.

Increasing uniformity of traits is an important objective in livestock production. This study focused on the BWcomparison of a double hierarchical GLM (DHGLM) with the conventional analysis of uniformity, using within-litter variation in birth weight (BW0) in pigs as a case. In pigs, within-litter variation of BW0 is a trait in which uniformity is important in breeding practice. Traditionally, uniformity has been studied by analysis of SD or variances. In DHGLM, differences between animals are studied by analyzing the residual variance of the trait and estimating its variance components. Here we used data on BW0, recorded in 2 sow lines (Large White and Landrace), to compare the estimation of genetic parameters and breeding values for uniformity from DHGLM and traditional analysis of the variance. Comparison of DHGLM with the conventional analysis using the logarithm-transformed variance of BW0 was possible because both methods were on the same scale and the models contained the same random effects. In addition, the genetic CV at the residual SD level (GCV) was proposed as a measure expressing the potential response to selection. Three-fold cross-validation was performed to study predictive ability of both methods. The estimated GCV was highly similar using both methods. Results indicate that the SD of BW0 can be decreased by up to approximately 10% after 1 generation of selection, indicating good prospects for response to selection. The correlation between EBV (0.88 in both sow lines) obtained from both methods indicated high similarity between conventional analysis and DHGLM. Comparison of accuracies of EBV showed that the methods were comparable, with moderate accuracies achieved with approximately 100 piglets per maternal grandsire. Cross-validation also indicated very similar predictive ability in estimating EBV for BW0 variation for both methods. Therefore, it was concluded that conventional analysis and DHGLM produced highly comparable results. Still, the DHGLM potentially has a broader application than conventional analysis to study uniformity of traits, because it also can be used for traits with single observations per animal.

Boar taint in entire male pigs: a genomewide association study for direct and indirect genetic effects on androstenone.

Androstenone is one of the compounds causing boar taint of pork and is highly heritable (approximately 0.6). Recently, indirect genetic effects (IGE; also known as associative effects or social genetic effects) were found for androstenone, meaning that pen mates (boars) affect each other's androstenone level genetically. Similar to estimating variance components with a direct-indirect animal model, direct and indirect genetic SNP effects can be estimated for androstenone. This study aims to detect SNP with significant direct genetic effects and IGE on androstenone. The dataset consisted of 1,282 noncastrated boars (993 boars genotyped) from 184 groups of pen members. After quality control, 46,421 SNP were included in the analysis. One model for single-SNP regression was fitted, where both the direct SNP effect of the individual itself and the indirect SNP effects of its pen mates were included. None of the SNP (direct or indirect) were found genomewide significant. One QTL on SSC6 was chromosome-wide significant for the direct effect. A single SNP on SSC9 and 2 regions and a single SNP on SSC14 were found for the indirect effect. A backwards elimination method and haplotype analysis were used to quantify the variance explained by the SNP. The backwards elimination method identified 4 independent regions affecting androstenone. The QTL on SSC6 explained 2.1 and 2.6% of the phenotypic variance using the backwards elimination method or the haplotype analysis. The QTL on SSC14 explained 3.4 and 2.7% of the phenotypic variance using the backwards elimination method or the haplotype analysis. The single association on SSC9 explained 2.2% of the phenotypic variance. All significant QTL together explained 7 to 8% of phenotypic variance and 40 to 44% of the total genetic variance available for response to selection. Besides the newly discovered QTL and the confirmation of known QTL, this study also presents a methodology to model SNP for IGE.

On the definition and utilization of heritable variation among hosts in reproduction ratio R0 for infectious diseases.

Infectious diseases have a major role in evolution by natural selection and pose a worldwide concern in livestock. Understanding quantitative genetics of infectious diseases, therefore, is essential both for understanding the consequences of natural selection and for designing artificial selection schemes in agriculture. The basic reproduction ratio, R0, is the key parameter determining risk and severity of infectious diseases. Genetic improvement for control of infectious diseases in host populations should therefore aim at reducing R0. This requires definitions of breeding value and heritable variation for R0, and understanding of mechanisms determining response to selection. This is challenging, as R0 is an emergent trait arising from interactions among individuals in the population. Here we show how to define breeding value and heritable variation for R0 for genetically heterogeneous host populations. Furthermore, we identify mechanisms determining utilization of heritable variation for R0. Using indirect genetic effects, next-generation matrices and a SIR (Susceptible, Infected and Recovered) model, we show that an individual's breeding value for R0 is a function of its own allele frequencies for susceptibility and infectivity and of population average susceptibility and infectivity. When interacting individuals are unrelated, selection for individual disease status captures heritable variation in susceptibility only, yielding limited response in R0. With related individuals, however, there is a secondary selection process, which also captures heritable variation in infectivity and additional variation in susceptibility, yielding substantially greater response. This shows that genetic variation in susceptibility represents an indirect genetic effect. As a consequence, response in R0 increased substantially when interacting individuals were genetically related.

Modelling of feather pecking behavior in beak-trimmed and non-beak-trimmed crossbred laying hens: variance component and trait-based approach.

Because of a ban on the use of beak trimming in some European countries, feather pecking is becoming a substantial problem in the layer industry, both from animal welfare and economic points of view. The feather condition score (FCS) as a measure of feather damage has been shown to be closely related to feather pecking behavior in laying hens housed in groups. To obtain a better understanding of genetic and other biological mechanisms underlying feather pecking behavior, data on FCS of a population of 2,724 female offspring from crossing 50 male W1 and 907 female WB purebred lines were used. The offspring of 25 sires were beak-trimmed, and the offspring of another 25 sires were non-beak-trimmed. Titers of plasma natural antibody (NAb) isotypes IgM and IgG binding keyhole limpet hemocyanin at 24 wk of age were measured. Feather condition was scored at 53 wk of age. In the first part of the present study, we estimated genetic parameters for FCS with 2 variance components models: a traditional linear animal model and a model combining direct and associative genetic effects. In the second part of the present study, a trait-based analysis for FCS was conducted to investigate whether NAb isotype titers can explain variation in FCS among individuals, by fitting a linear mixed model. Though the estimated associative genetic variance was substantial, associative effects for FCS were not statistically significant in both populations (P = 0.09 in beak-trimmed birds, and P = 0.08 in non-beak-trimmed birds). This suggests an insufficient number of records on FCS. Individual's NAb isotypes titers did not show direct effect for FCS of itself, but individual's IgG titers showed a suggestive effect on the FCS of cage mates (associative effect) in beak-trimmed laying hens, which need further confirmation.

Growth performance and carcass traits in pigs selected for indirect genetic effects on growth rate in two environments.

Production traits such as growth rate may depend on the social interactions between group members. These social interactions may be partly heritable and are referred to as indirect genetic effects (IGE) or social, associative, or competitive genetic effects. Indirect genetic effects may contribute to heritable variation in traits and can therefore be used to increase the response to selection. This, however, has hardly been tested by selection experiments. Our objective was to determine the effects of 1 generation of selection on IGE for growth (IGEg) in pigs on ADG, BW, ADFI, feed efficiency, and postmortem measurements. Sires (n = 24) and dams (n = 64) were selected to create a high vs. low contrast for IGEg in the offspring (n = 480). The IGE difference was 2.8 g ADG per pen mate, corresponding to 14 g higher ADG in high IGEg offspring compared to low IGEg offspring when housed in groups of 6 (i.e., (6 - 1) × 2.8 = 14). Male (barrows) and female (gilts) offspring were housed in groups of 6 of the same IGEg classification, in either barren concrete pens or pens enriched with straw and wood shavings (n = 80 pens). Pigs were followed from birth to slaughter. Data were analyzed in a mixed model with pen as random factor. There was no difference in ADG between high and low IGEg pigs during the finishing period (wk 10 to 23). Opposite to expectations, high IGEg tended to have a 17 g lower ADG from weaning to slaughter (P = 0.08), which was caused by a higher BW of low IGEg pigs in wk 5 (P = 0.008). This led to a 2.3 kg lower carcass weight (P = 0.02) and 2.2 mm less muscle depth for high IGEg pigs (P = 0.03). High IGEg pigs had a higher stomach wall damage score (P = 0.01). Pigs on straw had a 25 g lower ADG during finishing (P = 0.03) and less stomach wall damage (P < 0.001). Fewer interventions against harmful behavior were required in high IGEg pigs. The unexpected results regarding IGEg may be due to several reasons. Despite initial power calculations showing good power, the IGEg contrast between groups may have been too small. Moreover, measures that were taken to limit harmful behavior may have had a substantial role. Harmful behavior such as tail biting may affect ADG and might underlie the effects of selection on IGEg in pigs. Research under commercial circumstances, where harmful behavior is likely to be more profound, may give more accurate insight into the benefits of selecting for IGEg.

Indirect genetic effects and kin recognition: estimating IGEs when interactions differ between kin and strangers.

Social interactions among individuals are widespread, both in natural and domestic populations. As a result, trait values of individuals may be affected by genes in other individuals, a phenomenon known as indirect genetic effects (IGEs). IGEs can be estimated using linear mixed models. The traditional IGE model assumes that an individual interacts equally with all its partners, whether kin or strangers. There is abundant evidence, however, that individuals behave differently towards kin as compared with strangers, which agrees with predictions from kin-selection theory. With a mix of kin and strangers, therefore, IGEs estimated from a traditional model may be incorrect, and selection based on those estimates will be suboptimal. Here we investigate whether genetic parameters for IGEs are statistically identifiable in group-structured populations when IGEs differ between kin and strangers, and develop models to estimate such parameters. First, we extend the definition of total breeding value and total heritable variance to cases where IGEs depend on relatedness. Next, we show that the full set of genetic parameters is not identifiable when IGEs differ between kin and strangers. Subsequently, we present a reduced model that yields estimates of the total heritable effects on kin, on non-kin and on all social partners of an individual, as well as the total heritable variance for response to selection. Finally we discuss the consequences of analysing data in which IGEs depend on relatedness using a traditional IGE model, and investigate group structures that may allow estimation of the full set of genetic parameters when IGEs depend on kin.

The quantitative genetics of indirect genetic effects: a selective review of modelling issues.

Indirect genetic effects (IGE) occur when the genotype of an individual affects the phenotypic trait value of another conspecific individual. IGEs can have profound effects on both the magnitude and the direction of response to selection. Models of inheritance and response to selection in traits subject to IGEs have been developed within two frameworks; a trait-based framework in which IGEs are specified as a direct consequence of individual trait values, and a variance-component framework in which phenotypic variance is decomposed into a direct and an indirect additive genetic component. This work is a selective review of the quantitative genetics of traits affected by IGEs, with a focus on modelling, estimation and interpretation issues. It includes a discussion on variance-component vs trait-based models of IGEs, a review of issues related to the estimation of IGEs from field data, including the estimation of the interaction coefficient Ψ (psi), and a discussion on the relevance of IGEs for response to selection in cases where the strength of interaction varies among pairs of individuals. An investigation of the trait-based model shows that the interaction coefficient Ψ may deviate considerably from the corresponding regression coefficient when feedback occurs. The increasing research effort devoted to IGEs suggests that they are a widespread phenomenon, probably particularly in natural populations and plants. Further work in this field should considerably broaden our understanding of the quantitative genetics of inheritance and response to selection in relation to the social organisation of populations.

Prediction of heterosis using genome-wide SNP-marker data: application to egg production traits in white Leghorn crosses.

Prediction of heterosis has a long history with mixed success, partly due to low numbers of genetic markers and/or small data sets. We investigated the prediction of heterosis for egg number, egg weight and survival days in domestic white Leghorns, using ∼400 000 individuals from 47 crosses and allele frequencies on ∼53 000 genome-wide single nucleotide polymorphisms (SNPs). When heterosis is due to dominance, and dominance effects are independent of allele frequencies, heterosis is proportional to the squared difference in allele frequency (SDAF) between parental pure lines (not necessarily homozygous). Under these assumptions, a linear model including regression on SDAF partitions crossbred phenotypes into pure-line values and heterosis, even without pure-line phenotypes. We therefore used models where phenotypes of crossbreds were regressed on the SDAF between parental lines. Accuracy of prediction was determined using leave-one-out cross-validation. SDAF predicted heterosis for egg number and weight with an accuracy of ∼0.5, but did not predict heterosis for survival days. Heterosis predictions allowed preselection of pure lines before field-testing, saving ∼50% of field-testing cost with only 4% loss in heterosis. Accuracies from cross-validation were lower than from the model-fit, suggesting that accuracies previously reported in literature are overestimated. Cross-validation also indicated that dominance cannot fully explain heterosis. Nevertheless, the dominance model had considerable accuracy, clearly greater than that of a general/specific combining ability model. This work also showed that heterosis can be modelled even when pure-line phenotypes are unavailable. We concluded that SDAF is a useful predictor of heterosis in commercial layer breeding.

Multilevel selection with kin and non-kin groups, experimental results with Japanese quail (Coturnix japonica).

An experiment was conducted comparing multilevel selection in Japanese quail for 43 days weight and survival with birds housed in either kin (K) or random (R) groups. Multilevel selection significantly reduced mortality (6.6% K vs. 8.5% R) and increased weight (1.30 g/MG K vs. 0.13 g/MG R) resulting in response an order of magnitude greater with Kin than Random. Thus, multilevel selection was effective in reducing detrimental social interactions, which contributed to improved weight gain. The observed rates of response did not differ significantly from expected, demonstrating that current theory is adequate to explain multilevel selection response. Based on estimated genetic parameters, group selection would always be superior to any other combination of multilevel selection. Further, near optimal results could be attained using multilevel selection if 20% of the weight was on the group component regardless of group composition. Thus, in nature the conditions for multilevel selection to be effective in bringing about social change maybe common. In terms of a sustainability of breeding programs, multilevel selection is easy to implement and is expected to give near optimal responses with reduced rates of inbreeding as compared to group selection, the only requirement is that animals be housed in kin groups.

Effect of gestating sow body condition, feed refusals, and group housing on growth and feed intake in grower-finishing pigs.

The main focus of this study was to identify sow gestation features that affect growth rate (GR) and feed intake (FI) of their offspring during grower-finishing stage. Because the sow provides a specific environment to her offspring during gestation, certain features (e.g., BW of the sow), feed refusals or gestation group, may affect her ability to deliver and feed a healthy litter. Data on 17,743 grower-finishing pigs, coming from 604 sires and 681 crossbred sows, were obtained from the Institute for Pigs Genetics. Sow gestation features were collected during multiple gestations and divided into 3 clusters describing i) sow body condition (i.e., BW, backfat, and gestation length), ii) sow feed refusals (FR), the difference between offered and eaten feed during 3 periods of gestation: 1 to 28, 25 to 50, 45 to 80 d, and iii) sow group features (i.e., number of sows, and average parity). Sow gestation features were added to the base model 1 at a time to study their effect on GR and FI. Significant gestation features (P < 0.1) were fitted simultaneously in animal model to investigate whether they could explain common litter and permanent sow effects. Gestation length had effect on GR [1.4 (g/d)/d; P = 0.04] and FI [6.8 (g/d)/d; P = 0.007]. Body weights of the sow at insemination [0.07 (g/d)/kg; P = 0.08], at farrowing [0.14 (g/d)/kg; P < 0.0001], and after lactation [0.1 (g/d)/kg; P = 0.003] had effect on GR. Sow parturition-lactation loss in backfat thickness and weight were not significant for GR and FI. Days with FR during 25 to 50 and 45 to 80 d of gestation and average FR during 45 to 80 d of gestation had negative effect on GR and when substantially increased had also a positive effect on FI. Sow FR from 1 to 28 d of gestation were not significant. Number of sows in gestation group had effect on FI [-9 (g/d)/group member; P = 0.04] and day sow entered group had an effect on GR [-0.9 (g/d)/day; P = 0.04]. Sow gestation features explained 1 to 3% of the total variance in grower-finishing pigs. Gestation features did explain phenotypic variance due to permanent sow and part of phenotypic variance due to common litter effects for FI but not for GR.