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, R 0 , 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 R 0 . This requires definitions of breeding value and heritable variation for R 0 , and understanding of mechanisms determining response to selection. This is challenging, as R 0 is an emergent trait arising from interactions among individuals in the population. Here we show how to define breeding value and heritable variation for R 0 for genetically heterogeneous host populations. Furthermore, we identify mechanisms determining utilization of heritable variation for R 0 . Using indirect genetic effects, next-generation matrices and a SIR (Susceptible, Infected and Recovered) model, we show that an individual's breeding value for R 0 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 R 0 . 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 R 0 increased substantially when interacting individuals were genetically related. Heredity (2014) 113, 364-374; doi:10.1038/hdy.2014.38; published online 14 May 2014 INTRODUCTIONInfectious diseases are widespread in humans, animals and plants. In natural populations, infectious diseases have a major role in the process of evolution by natural selection (Haldane, 1949;O'Brien and Evermann, 1988). In domestic populations, particularly in livestock, infectious diseases are imposing a worldwide concern owing to their impact on the welfare and productivity of livestock, and in the case of zoonosis, also because of the threat for human health. To contain the threat imposed by infectious diseases, different control strategies such as vaccination, antibiotic treatments and management practices have been implemented widely. However, the evolution of resistance to antibiotics by bacteria, evolution of resistance to vaccines by viruses and undesirable environmental impacts of antibiotic treatment put these strategies under question (Gibson and Bishop, 2005). Thus, there is a need to investigate additional control strategies, so as to extend the repertoire of possible interventions. A greater repertoire is favourable (1) because ...

BackgroundGenetic 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 R0. R0 is an important epidemiological parameter that determines the risk and prevalence of infectious diseases. An individual’s breeding value for R0 is a function of its genes that influence both susceptibility and infectivity. Thus, to estimate the effects of genes on R0, 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 R0, 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.ResultsA 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 R0 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.ConclusionsWe 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.

Implicit assumption of common (co)variance for all loci in multi-trait Genomic Best Linear Unbiased Prediction (GBLUP) results in a genomic relationship matrix (G) that is common to all traits. When this assumption is violated, Bayesian whole genome regression methods may be superior to GBLUP by accounting for unequal (co)variance for all loci or genome regions. This study aimed to develop a strategy to improve the accuracy of GBLUP for multi-trait genomic prediction, using (co)variance estimates of SNP effects from Bayesian whole genome regression methods. Five generations (G1-G5, test populations) of genotype data were available by simulations based on data of 2,200 Danish Holstein cows (G0, reference population). Two correlated traits with heritabilities of 0.1 or 0.4, and a genetic correlation of 0.45 were generated. First, SNP effects and breeding values were estimated using BayesAS method, assuming (co)variance was the same for SNPs within a genome region, and different between regions. Region size was set as one SNP, 100 SNPs, a whole chromosome or whole genome. Second, posterior (co)variances of SNP effects were used to weight SNPs in construction of G matrices. In general, region size of 100 SNPs led to highest prediction accuracies using BayesAS, and wGBLUP outperformed GBLUP at this region size. Our results suggest that when genetic architectures of traits favor Bayesian methods, the accuracy of multi-trait GBLUP can be as high as the Bayesian method if SNPs are weighted by the Bayesian posterior (co)variances.

Key message Heritable variation in phenotypes extracted from multi-spectral images (MSIs) and strong genetic correlations with end-of-season traits indicates the value of MSIs for crop improvement and modeling of plant growth curve. Abstract Vegetation indices (VIs) derived from multi-spectral imaging (MSI) platforms can be used to study properties of crop canopy, providing non-destructive phenotypes that could be used to better understand growth curves throughout the growing season. To investigate the amount of variation present in several VIs and their relationship with important end-of-season traits, genetic and residual (co)variances for VIs, grain yield and moisture were estimated using data collected from maize hybrid trials. The VIs considered were Normalized Difference Vegetation Index (NDVI), Green NDVI, Red Edge NDVI, Soil-Adjusted Vegetation Index, Enhanced Vegetation Index and simple Ratio of Near Infrared to Red (Red) reflectance. Genetic correlations of VIs with grain yield and moisture were used to fit multi-trait models for prediction of end-of-season traits and evaluated using within site/year cross-validation. To explore alternatives to fitting multiple phenotypes from MSI, random regression models with linear splines were fit using data collected in 2016 and 2017. Heritability estimates ranging from (0.10 to 0.82) were observed, indicating that there exists considerable amount of genetic variation in these VIs. Furthermore, strong genetic and residual correlations of the VIs, NDVI and NDRE, with grain yield and moisture were found. Considerable increases in prediction accuracy were observed from the multi-trait model when using NDVI and NDRE as a secondary trait. Finally, random regression with a linear spline function shows potential to be used as an alternative to mixed models to fit VIs from multiple time points.

Vegetation indices (VIs) are produced as a combination of different reflectance bands that are captured by multispectral images (MSIs). These indices, such as normalized difference vegetation index (NDVI), are reported to be proxy indicators of photosynthetic activity, plant canopy biomass, and leaf area index. To determine the utility of using VI derived from MSI to model plant growth, random regression (RR) models with linear splines and different orders of Legendre polynomials were applied to data collected (years 2019 and 2020) as part of the Genome‐to‐Fields initiative. Growth curves of maize (Zea mays L.) hybrids were modeled using both NDVI and cumulative NDVI (cNDVI) phenotypes. Due to the difference in MSI recording dates, and sparse overlap in hybrids between years, all the analyses were nested within a year. Results indicate that RR models using Legendre polynomials provide a robust and scalable method for modeling growth curves using phenotypes extracted from MSI; however, RR models using linear splines showed inconsistent convergence. Growth curves estimated using NDVI and cNDVI showed low‐to‐moderate heritability (0.11–0.44) and a range of genetic correlations (−0.15 to 0.97) with grain yield. This study demonstrates the utility of MSI for modeling genetic growth trends, with the best modeling results obtained when using Legendre polynomials and cNDVI.