Breeding programs aiming to improve the performance of crossbreds may benefit from genomic predic... more Breeding programs aiming to improve the performance of crossbreds may benefit from genomic prediction of crossbred (CB) performance for purebred (PB) selection candidates. In this review, we compared genomic prediction strategies that differed in 1) the genomic prediction model used or 2) the data used in the reference population. We found 27 unique studies, two of which used deterministic simulation, 11 used stochastic simulation, and 14 real data. Differences in accuracy and response to selection between strategies depended on i) the value of the purebred crossbred genetic correlation (rpc), ii) the genetic distance between the parental lines, iii) the size of PB and CB reference populations, and iv) the relatedness of these reference populations to the selection candidates. In studies where a PB reference population was used, the use of a dominance model yielded accuracies that were equal to or higher than those of additive models. When rpc was lower than ~0.8, and was caused mai...
Background Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) ... more Background Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) when combining information sources have been developed based on selection index theory (SIT) and on Fisher information (FI). These two approaches have resulted in slightly different results when considering the combination of pedigree and genomic information. Here, we clarify this apparent contradiction, both for the combination of pedigree and genomic information and for the combination of subpopulations into a joint reference population. Results First, we show that existing expressions for the squared accuracy of GEBV can be understood as a proportion of the variance explained. Next, we show that the apparent discrepancy that has been observed between accuracies based on SIT vs. FI originated from two sources. First, the FI referred to the genetic component that is captured by the marker genotypes, rather than the full genetic component. Second, the common SIT-based derivations did not...
Because of linkage and variation in heterozygosity, individuals differ in the Mendelian sampling ... more Because of linkage and variation in heterozygosity, individuals differ in the Mendelian sampling variance on their gametes. Thus some parents produce genetically more variable offspring than others. With genomic EBV and phased genotypes, these differences can be quantified and potentially used to increase genetic gain. Here we show that genetic gain and the probability of breeding a top-ranking individual can be increased by selecting individuals on an index of their GEBV and the standard deviation on the GEBV of their gametes (SDGEBV). The optimum index was , where is the standardized truncation point belonging to the selected proportion p. Compared to selection on ordinary GEBV, in dairy cattle the probability of breeding a top-ranking individual can be increased by 36%, and response to selection by 3.6% when selection is strong (p = 0.001). Preselection on GEBV facilitates implementation with little loss of gain.
Since 2009, genomic selection (GS) has been widely applied in Holstein Friesian (HF) breeding pro... more Since 2009, genomic selection (GS) has been widely applied in Holstein Friesian (HF) breeding programs. In this study, we evaluated how the introduction of GS in the Dutch-Flemish HF breeding program has affected inbreeding and kinship trends, using both pedigree-based and genomic measures. Rates of inbreeding and kinship for artificial insemination (AI) bulls increased with the introduction of GS, from 0.1-0.7% in 2003-2009 to 1.6-2.5% in 2009-2015. Rates of inbreeding and kinship for cows also increased with GS, although they were lower than for AI-bulls (i.e. 0.79-1.14% in 2009-2017). Levels of identical by state (IBS), which include relatedness due to both recent and distant common ancestors, increased faster than levels of identical by descent (IBD), which include only recent inbreeding and kinship. Accumulation of inbreeding varied substantially across the genome over time, with specific regions showing a striking increase in inbreeding since the introduction of GS. These find...
Objective of this study was to show that an individual’s breeding value for basic reproduction ra... more Objective of this study was to show that an individual’s breeding value for basic reproduction ratio, R0 is a function of its own allele frequencies for susceptibility and infectivity and of population average susceptibility and infectivity. When interacting group mates are unrelated, selection for individual disease status captures heritable variation in susceptibility only, yielding limited response in R0. With related group mates, however, selection also captures heritable variation in infectivity and additional variation in susceptibility, yielding substantial response in R0. This shows that also genetic variation in susceptibility represents an Indirect Genetic Effect. Furthermore, a Generalized Linear Model (GLM) with complementary loglog link function applied to final size from simulated data was developed to estimate relative gene effects for susceptibility and infectivity.
BACKGROUND Perhaps the first question to answer here is: in what way does design and sustainabili... more BACKGROUND Perhaps the first question to answer here is: in what way does design and sustainability in developed countries differ from that in developing countries ? In general, the two problems are the same; getting the maximum possible gain in the breeding goal from the genetic resources available within the technical and environmental constraints that are applied to the breeding program. More specifically, in developing countries breeding goals will often be increasing yields of primary products whilst retaining adaptive fitness, whereas in the developed world it is increasingly about improving health and welfare whilst retaining yields. Schemes in developing and developed countries are both constrained in the genetic resources that can be used either by the need to retain adaptive fitness on the one hand or primary product yields on the other. Again, as a generality, technical capacity will be greater in the developed countries so the challenges will be less about making the fun...
ns= non significant; *p<0.05; **p<0.01; ***p<0.001 Figure 2. Design. Treatment groups A:... more ns= non significant; *p<0.05; **p<0.01; ***p<0.001 Figure 2. Design. Treatment groups A: IGE+ pigs in barren pens; B: IGE+ pigs in straw; C: IGEpigs in barren pens; and D: IGEpigs in straw. Figure 1. IGEs for growth. Pigs with positive IGEs for growth (IGE+) have a positive effect on growth of pen mates while pigs with a negative IGE for growth (IGE-) have a negative effect on growth of pen mates.
Background The genetic correlation between purebred and crossbred performance ( $${r}_{pc}$$ r pc... more Background The genetic correlation between purebred and crossbred performance ( $${r}_{pc}$$ r pc ) is an important parameter in pig and poultry breeding, because response to selection in crossbred performance depends on the value of $${r}_{pc}$$ r pc when selection is based on purebred (PB) performance. The value of $${r}_{pc}$$ r pc can be substantially lower than 1, which is partly due to differences in allele frequencies between parental lines when non-additive genetic effects are present. This relationship between $${r}_{pc}$$ r pc and parental allele frequencies suggests that $${r}_{pc}$$ r pc can be expressed as a function of genetic parameters for the trait in the parental lines. In this study, we derived expressions for $${r}_{pc}$$ r pc based on genetic variances within, and the genetic covariance between parental lines. It is important to note that the variance components used in our expressions are not the components that are typically estimated in empirical data. The ex...
Inbreeding depression has been widely documented for livestock and other animal and plant populat... more Inbreeding depression has been widely documented for livestock and other animal and plant populations. Inbreeding is generally expected to have a stronger unfavorable effect on fitness traits than on other traits. Traditionally, the degree of inbreeding depression in livestock has been estimated as the slope of the linear regression of phenotypic values on pedigree-based inbreeding coefficients. With the increasing availability of SNP-data, pedigree inbreeding can now be replaced by SNP-based measures. We performed a meta-analysis of 154 studies, published from 1990 to 2020 on seven livestock species, and compared the degree of inbreeding depression (1) across different trait groups, and (2) across different pedigree-based and SNP-based measures of inbreeding. Across all studies and traits, a 1% increase in pedigree inbreeding was associated with a median decrease in phenotypic value of 0.13% of a trait’s mean, or 0.59% of a trait’s standard deviation. Inbreeding had an unfavorable ...
Intercropping is both a well-established and yet novel agricultural practice, depending on one’s ... more Intercropping is both a well-established and yet novel agricultural practice, depending on one’s perspective. Such perspectives are principally governed by geographic location and whether monocultural practices predominate. Given the negative environmental effects of monoculture agriculture (loss of biodiversity, reliance on non-renewable inputs, soil degradation, etc.), there has been a renewed interest in cropping systems that can reduce the impact of modern agriculture while maintaining (or even increasing) yields. Intercropping is one of the most promising practices in this regard, yet faces a multitude of challenges if it is to compete with and ultimately replace the prevailing monocultural norm. These challenges include the necessity for more complex agricultural designs in space and time, bespoke machinery, and adapted crop cultivars. Plant breeding for monocultures has focused on maximizing yield in single-species stands, leading to highly productive yet specialized genotype...
Predictions of rates of inbreeding (ΔF), based on the concept of long-term genetic contributions ... more Predictions of rates of inbreeding (ΔF), based on the concept of long-term genetic contributions assuming the infinitesimal model, are developed for populations with discrete or overlapping generations undergoing mass selection. Phenotypes of individuals are assumed to be recorded prior to reproductive age and to remain constant over time. The prediction method accounts for inheritance of selective advantage both within and between age classes and for changing selection intensities with age. Terms corresponding to previous methods that assume constant selection intensity with age are identified. Predictions are accurate (relative errors ≤8%), except for cases with extreme selection intensities in females in combination with high heritability. With overlapping generations ΔF reaches a maximum when parents are equally distributed over age classes, which is mainly due to selection of the same individuals in consecutive years. ΔF/year decreases much more slowly compared to ΔF/generation...
A method to predict long-term genetic contributions of ancestors to future generations is studied... more A method to predict long-term genetic contributions of ancestors to future generations is studied in detail for a population with overlapping generations under mass or sib index selection. An existing method provides insight into the mechanisms determining the flow of genes through selected populations, and takes account of selection by modeling the long-term genetic contribution as a linear regression on breeding value. Total genetic contributions of age classes are modeled using a modified gene flow approach and long-term predictions are obtained assuming equilibrium genetic parameters. Generation interval was defined as the time in which genetic contributions sum to unity, which is equal to the turnover time of genes. Accurate predictions of long-term genetic contributions of individual animals, as well as total contributions of age classes were obtained. Due to selection, offspring of young parents had an above-average breeding value. Long-term genetic contributions of youngest ...
Here we present the strategy that achieves the lowest possible rate of inbreeding (ΔF) for a popu... more Here we present the strategy that achieves the lowest possible rate of inbreeding (ΔF) for a population with unequal numbers of sires and dams with random mating. This new strategy results in a ΔF as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census number is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertainties about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and...
Infectious diseases have profound effects on life, both in nature and agriculture. However, a qua... more Infectious diseases have profound effects on life, both in nature and agriculture. However, a quantitative genetic theory of the host population for the endemic prevalence of infectious diseases is almost entirely lacking. While several studies have demonstrated the relevance of transmission of infections for heritable variation and response to selection, current quantitative genetics ignores transmission. Thus, we lack concepts of breeding value and heritable variation for endemic prevalence, and poorly understand response of endemic prevalence to selection. Here we integrate quantitative genetics and epidemiology, and propose a quantitative genetic theory for the basic reproduction number R0 and for the endemic prevalence of an infection. We first identify the genetic factors that determine the prevalence. Subsequently we investigate the population level consequences of individual genetic variation, for both R0 and the endemic prevalence. Next, we present expressions for the breed...
Breeding programs aiming to improve the performance of crossbreds may benefit from genomic predic... more Breeding programs aiming to improve the performance of crossbreds may benefit from genomic prediction of crossbred (CB) performance for purebred (PB) selection candidates. In this review, we compared genomic prediction strategies that differed in 1) the genomic prediction model used or 2) the data used in the reference population. We found 27 unique studies, two of which used deterministic simulation, 11 used stochastic simulation, and 14 real data. Differences in accuracy and response to selection between strategies depended on i) the value of the purebred crossbred genetic correlation (rpc), ii) the genetic distance between the parental lines, iii) the size of PB and CB reference populations, and iv) the relatedness of these reference populations to the selection candidates. In studies where a PB reference population was used, the use of a dominance model yielded accuracies that were equal to or higher than those of additive models. When rpc was lower than ~0.8, and was caused mai...
Background Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) ... more Background Deterministic predictions of the accuracy of genomic estimated breeding values (GEBV) when combining information sources have been developed based on selection index theory (SIT) and on Fisher information (FI). These two approaches have resulted in slightly different results when considering the combination of pedigree and genomic information. Here, we clarify this apparent contradiction, both for the combination of pedigree and genomic information and for the combination of subpopulations into a joint reference population. Results First, we show that existing expressions for the squared accuracy of GEBV can be understood as a proportion of the variance explained. Next, we show that the apparent discrepancy that has been observed between accuracies based on SIT vs. FI originated from two sources. First, the FI referred to the genetic component that is captured by the marker genotypes, rather than the full genetic component. Second, the common SIT-based derivations did not...
Because of linkage and variation in heterozygosity, individuals differ in the Mendelian sampling ... more Because of linkage and variation in heterozygosity, individuals differ in the Mendelian sampling variance on their gametes. Thus some parents produce genetically more variable offspring than others. With genomic EBV and phased genotypes, these differences can be quantified and potentially used to increase genetic gain. Here we show that genetic gain and the probability of breeding a top-ranking individual can be increased by selecting individuals on an index of their GEBV and the standard deviation on the GEBV of their gametes (SDGEBV). The optimum index was , where is the standardized truncation point belonging to the selected proportion p. Compared to selection on ordinary GEBV, in dairy cattle the probability of breeding a top-ranking individual can be increased by 36%, and response to selection by 3.6% when selection is strong (p = 0.001). Preselection on GEBV facilitates implementation with little loss of gain.
Since 2009, genomic selection (GS) has been widely applied in Holstein Friesian (HF) breeding pro... more Since 2009, genomic selection (GS) has been widely applied in Holstein Friesian (HF) breeding programs. In this study, we evaluated how the introduction of GS in the Dutch-Flemish HF breeding program has affected inbreeding and kinship trends, using both pedigree-based and genomic measures. Rates of inbreeding and kinship for artificial insemination (AI) bulls increased with the introduction of GS, from 0.1-0.7% in 2003-2009 to 1.6-2.5% in 2009-2015. Rates of inbreeding and kinship for cows also increased with GS, although they were lower than for AI-bulls (i.e. 0.79-1.14% in 2009-2017). Levels of identical by state (IBS), which include relatedness due to both recent and distant common ancestors, increased faster than levels of identical by descent (IBD), which include only recent inbreeding and kinship. Accumulation of inbreeding varied substantially across the genome over time, with specific regions showing a striking increase in inbreeding since the introduction of GS. These find...
Objective of this study was to show that an individual’s breeding value for basic reproduction ra... more Objective of this study was to show that an individual��s breeding value for basic reproduction ratio, R0 is a function of its own allele frequencies for susceptibility and infectivity and of population average susceptibility and infectivity. When interacting group mates are unrelated, selection for individual disease status captures heritable variation in susceptibility only, yielding limited response in R0. With related group mates, however, selection also captures heritable variation in infectivity and additional variation in susceptibility, yielding substantial response in R0. This shows that also genetic variation in susceptibility represents an Indirect Genetic Effect. Furthermore, a Generalized Linear Model (GLM) with complementary loglog link function applied to final size from simulated data was developed to estimate relative gene effects for susceptibility and infectivity.
BACKGROUND Perhaps the first question to answer here is: in what way does design and sustainabili... more BACKGROUND Perhaps the first question to answer here is: in what way does design and sustainability in developed countries differ from that in developing countries ? In general, the two problems are the same; getting the maximum possible gain in the breeding goal from the genetic resources available within the technical and environmental constraints that are applied to the breeding program. More specifically, in developing countries breeding goals will often be increasing yields of primary products whilst retaining adaptive fitness, whereas in the developed world it is increasingly about improving health and welfare whilst retaining yields. Schemes in developing and developed countries are both constrained in the genetic resources that can be used either by the need to retain adaptive fitness on the one hand or primary product yields on the other. Again, as a generality, technical capacity will be greater in the developed countries so the challenges will be less about making the fun...
ns= non significant; *p<0.05; **p<0.01; ***p<0.001 Figure 2. Design. Treatment groups A:... more ns= non significant; *p<0.05; **p<0.01; ***p<0.001 Figure 2. Design. Treatment groups A: IGE+ pigs in barren pens; B: IGE+ pigs in straw; C: IGEpigs in barren pens; and D: IGEpigs in straw. Figure 1. IGEs for growth. Pigs with positive IGEs for growth (IGE+) have a positive effect on growth of pen mates while pigs with a negative IGE for growth (IGE-) have a negative effect on growth of pen mates.
Background The genetic correlation between purebred and crossbred performance ( $${r}_{pc}$$ r pc... more Background The genetic correlation between purebred and crossbred performance ( $${r}_{pc}$$ r pc ) is an important parameter in pig and poultry breeding, because response to selection in crossbred performance depends on the value of $${r}_{pc}$$ r pc when selection is based on purebred (PB) performance. The value of $${r}_{pc}$$ r pc can be substantially lower than 1, which is partly due to differences in allele frequencies between parental lines when non-additive genetic effects are present. This relationship between $${r}_{pc}$$ r pc and parental allele frequencies suggests that $${r}_{pc}$$ r pc can be expressed as a function of genetic parameters for the trait in the parental lines. In this study, we derived expressions for $${r}_{pc}$$ r pc based on genetic variances within, and the genetic covariance between parental lines. It is important to note that the variance components used in our expressions are not the components that are typically estimated in empirical data. The ex...
Inbreeding depression has been widely documented for livestock and other animal and plant populat... more Inbreeding depression has been widely documented for livestock and other animal and plant populations. Inbreeding is generally expected to have a stronger unfavorable effect on fitness traits than on other traits. Traditionally, the degree of inbreeding depression in livestock has been estimated as the slope of the linear regression of phenotypic values on pedigree-based inbreeding coefficients. With the increasing availability of SNP-data, pedigree inbreeding can now be replaced by SNP-based measures. We performed a meta-analysis of 154 studies, published from 1990 to 2020 on seven livestock species, and compared the degree of inbreeding depression (1) across different trait groups, and (2) across different pedigree-based and SNP-based measures of inbreeding. Across all studies and traits, a 1% increase in pedigree inbreeding was associated with a median decrease in phenotypic value of 0.13% of a trait’s mean, or 0.59% of a trait’s standard deviation. Inbreeding had an unfavorable ...
Intercropping is both a well-established and yet novel agricultural practice, depending on one’s ... more Intercropping is both a well-established and yet novel agricultural practice, depending on one’s perspective. Such perspectives are principally governed by geographic location and whether monocultural practices predominate. Given the negative environmental effects of monoculture agriculture (loss of biodiversity, reliance on non-renewable inputs, soil degradation, etc.), there has been a renewed interest in cropping systems that can reduce the impact of modern agriculture while maintaining (or even increasing) yields. Intercropping is one of the most promising practices in this regard, yet faces a multitude of challenges if it is to compete with and ultimately replace the prevailing monocultural norm. These challenges include the necessity for more complex agricultural designs in space and time, bespoke machinery, and adapted crop cultivars. Plant breeding for monocultures has focused on maximizing yield in single-species stands, leading to highly productive yet specialized genotype...
Predictions of rates of inbreeding (ΔF), based on the concept of long-term genetic contributions ... more Predictions of rates of inbreeding (ΔF), based on the concept of long-term genetic contributions assuming the infinitesimal model, are developed for populations with discrete or overlapping generations undergoing mass selection. Phenotypes of individuals are assumed to be recorded prior to reproductive age and to remain constant over time. The prediction method accounts for inheritance of selective advantage both within and between age classes and for changing selection intensities with age. Terms corresponding to previous methods that assume constant selection intensity with age are identified. Predictions are accurate (relative errors ≤8%), except for cases with extreme selection intensities in females in combination with high heritability. With overlapping generations ΔF reaches a maximum when parents are equally distributed over age classes, which is mainly due to selection of the same individuals in consecutive years. ΔF/year decreases much more slowly compared to ΔF/generation...
A method to predict long-term genetic contributions of ancestors to future generations is studied... more A method to predict long-term genetic contributions of ancestors to future generations is studied in detail for a population with overlapping generations under mass or sib index selection. An existing method provides insight into the mechanisms determining the flow of genes through selected populations, and takes account of selection by modeling the long-term genetic contribution as a linear regression on breeding value. Total genetic contributions of age classes are modeled using a modified gene flow approach and long-term predictions are obtained assuming equilibrium genetic parameters. Generation interval was defined as the time in which genetic contributions sum to unity, which is equal to the turnover time of genes. Accurate predictions of long-term genetic contributions of individual animals, as well as total contributions of age classes were obtained. Due to selection, offspring of young parents had an above-average breeding value. Long-term genetic contributions of youngest ...
Here we present the strategy that achieves the lowest possible rate of inbreeding (ΔF) for a popu... more Here we present the strategy that achieves the lowest possible rate of inbreeding (ΔF) for a population with unequal numbers of sires and dams with random mating. This new strategy results in a ΔF as much as 10% lower than previously achieved. A simple and efficient approach to reducing inbreeding in small populations with sexes of unequal census number is to impose a breeding structure where parental success is controlled in each generation. This approach led to the development of strategies for selecting replacements each generation that were based upon parentage, e.g., a son replacing its sire. This study extends these strategies to a multigeneration round robin scheme where genetic contributions of ancestors to descendants are managed to remove all uncertainties about breeding roles over generations; i.e., male descendants are distributed as equally as possible among dams. In doing so, the sampling variance of genetic contributions within each breeding category is eliminated and...
Infectious diseases have profound effects on life, both in nature and agriculture. However, a qua... more Infectious diseases have profound effects on life, both in nature and agriculture. However, a quantitative genetic theory of the host population for the endemic prevalence of infectious diseases is almost entirely lacking. While several studies have demonstrated the relevance of transmission of infections for heritable variation and response to selection, current quantitative genetics ignores transmission. Thus, we lack concepts of breeding value and heritable variation for endemic prevalence, and poorly understand response of endemic prevalence to selection. Here we integrate quantitative genetics and epidemiology, and propose a quantitative genetic theory for the basic reproduction number R0 and for the endemic prevalence of an infection. We first identify the genetic factors that determine the prevalence. Subsequently we investigate the population level consequences of individual genetic variation, for both R0 and the endemic prevalence. Next, we present expressions for the breed...
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