Capturing indirect genetic effects on phenotypic variability: Competition meets canalization.

Phenotypic variability of a genotype is relevant both in natural and domestic populations. In the past two decades, variability has been studied as a heritable quantitative genetic trait in its own right, often referred to as inherited variability or environmental canalization. So far, studies on inherited variability have only considered genetic effects of the focal individual, that is, direct genetic effects on inherited variability. Observations from aquaculture populations and some plants, however, suggest that an additional source of genetic variation in inherited variability may be generated through competition. Social interactions, such as competition, are often a source of Indirect Genetic Effects (IGE). An IGE is a heritable effect of an individual on the trait value of another individual. IGEs may substantially affect heritable variation underlying the trait, and the direction and magnitude of response to selection. To understand the contribution of IGEs to evolution of environmental canalization in natural populations, and to exploit such inherited variability in animal and plant breeding, we need statistical models to capture this effect. To our knowledge, it is unknown to what extent the current statistical models commonly used for IGE and inherited variability capture the effect of competition on inherited variability. Here, we investigate the potential of current statistical models for inherited variability and trait values, to capture the direct and indirect genetic effects of competition on variability. Our results show that a direct model of inherited variability almost entirely captures the genetic sensitivity of individuals to competition, whereas an indirect model of inherited variability captures the cooperative genetic effects of individuals on their partners. Models for trait levels, however, capture only a small part of the genetic effects of competition. The estimation of direct and indirect genetic effects of competition, therefore, is possible with models for inherited variability but may require a two-step analysis.

Proportional Cerebellum Size Predicts Fear Habituation in Chickens.

The cerebellum has a highly conserved neural structure across species but varies widely in size. The wide variation in cerebellar size (both absolute and in proportion to the rest of the brain) among species and populations suggests that functional specialization is linked to its size. There is increasing recognition that the cerebellum contributes to cognitive processing and emotional control in addition to its role in motor coordination. However, to what extent cerebellum size reflects variation in these behavioral processes within species remains largely unknown. By using a unique intercross chicken population based on parental lines with high divergence in cerebellum size, we compared the behavior of individuals repeatedly exposed to the same fear test (emergence test) early in life and after sexual maturity (eight trials per age group) with proportional cerebellum size and cerebellum neural density. While proportional cerebellum size did not predict the initial fear response of the individuals (trial 1), it did increasingly predict adult individuals response as the trials progressed. Our results suggest that proportional cerebellum size does not necessarily predict an individual's fear response, but rather the habituation process to a fearful stimulus. Cerebellum neuronal density did not predict fear behavior in the individuals which suggests that these effects do not result from changes in neuronal density but due to other variables linked to proportional cerebellum size which might underlie fear habituation.

Probabilistic inference of the genetic architecture underlying functional enrichment of complex traits.

We develop a Bayesian model (BayesRR-RC) that provides robust SNP-heritability estimation, an alternative to marker discovery, and accurate genomic prediction, taking 22 seconds per iteration to estimate 8.4 million SNP-effects and 78 SNP-heritability parameters in the UK Biobank. We find that only ≤10% of the genetic variation captured for height, body mass index, cardiovascular disease, and type 2 diabetes is attributable to proximal regulatory regions within 10kb upstream of genes, while 12-25% is attributed to coding regions, 32-44% to introns, and 22-28% to distal 10-500kb upstream regions. Up to 24% of all cis and coding regions of each chromosome are associated with each trait, with over 3,100 independent exonic and intronic regions and over 5,400 independent regulatory regions having ≥95% probability of contributing ≥0.001% to the genetic variance of these four traits. Our open-source software (GMRM) provides a scalable alternative to current approaches for biobank data.

Family history of breast cancer is associated with elevated risk of prostate cancer: evidence for shared genetic risks.

INTRODUCTION: Although breast and prostate cancers arise in different organs and are more frequent in the opposite sex, multiple studies have reported an association between their family history. Analysis of single nucleotide polymorphism data, based on distant relatives, has revealed a small positive genetic correlation between these cancers explained by common variants. The estimate of genetic correlation based on close relatives reveals the extent to which shared genetic risks are explained by both common and rare variants. This estimate is unknown for breast and prostate cancer. METHOD: We estimated the relative risks, heritability, and genetic correlation of breast cancer and prostate cancer, based on the Minnesota Breast and Prostate Cancer Study, a family study of 141 families ascertained for breast cancer. RESULTS: Heritability of breast cancer was 0.34 (95% credible interval: 0.23-0.49) and 0.65 (95% credible interval: 0.36-0.97) for prostate cancer, and the genetic correlation was 0.23. In terms of odds ratios, these values correspond to a 1.3 times higher odds of breast cancer among probands, given that the brother has prostate cancer. CONCLUSION: This study shows the inherent relation between prostate cancer and breast cancer; an incident of one in a family increases the risk of developing the other. The large difference between estimates of genetic correlation from distant and close relatives, if replicated, suggests that rare variants contribute to the shared genetic risk of breast and prostate cancer. However, the difference could steam from genotype-by-family effects shared between the two types of cancers.

Where do we find missing data in a commercial real-time location system? Evidence from 2 dairy farms.

Real-time indoor positioning using ultra-wideband devices provides an opportunity for modern dairy farms to monitor the behavior of individual cows; however, missing data from these devices hinders reliable continuous monitoring and analysis of animal movement and social behavior. The objective of this study was to examine the data quality, in terms of missing data, in one commercially available ultra-wideband-based real-time location system for dairy cows. The focus was on detecting major obstacles, or sections, inside open freestall barns that resulted in increased levels of missing data. The study was conducted on 2 dairy farms with an existing commercial real-time location system. Position data were recorded for 6 full days from 69 cows on farm 1 and from 59 cows on farm 2. These data were used in subsequent analyses to determine the locations within the dairy barns where position data were missing for individual cows. The proportions of missing data were found to be evenly distributed within the 2 barns after fitting a linear mixed model with spatial smoothing to logit-transformed proportions (mean = 18% vs. 4% missing data for farm 1 and farm 2, respectively), with the exception of larger proportions of missing data along one of the walls on both farms. On farm 1, the variation between individual tags was large (range: 9-49%) compared with farm 2 (range: 12-38%). This greater individual variation of proportions of missing data indicates a potential problem with the individual tag, such as a battery malfunction or tag placement issue. Further research is needed to guide researchers in identifying problems relating to data capture problems in real-time monitoring systems on dairy farms. This is especially important when undertaking detailed analyses of animal movement and social interactions between animals.

Comparison of methods for predicting cow composite somatic cell counts.

One of the most common and reliable ways of monitoring udder health and milk quality in dairy herds is by monthly cow composite somatic cell counts (CMSCC). However, such sampling can be time consuming, and more automated sampling tools entail extra costs. Machine learning methods for prediction have been widely investigated in mastitis detection research, and CMSCC is normally used as a predictor or gold standard in such models. Predicted CMSCC between samplings could supply important information and be used as an input for udder health decision-support tools. To our knowledge, methods to predict CMSCC are lacking. Our aim was to find a method to predict CMSCC by using regularly recorded quarter milk data such as milk flow or conductivity. The milk data were collected at the quarter level for 8 wk when milking 372 Holstein-Friesian cows, resulting in a data set of 30,734 records with information on 87 variables. The cows were milked in an automatic milking rotary and sampled once weekly to obtain CMSCC values. The machine learning methods chosen for evaluation were the generalized additive model (GAM), random forest, and multilayer perceptron (MLP). For each method, 4 models with different predictor variable setups were evaluated: models based on 7-d lagged or 3-d lagged records before the CMSCC sampling and additionally for each setup but removing cow number as a predictor variable (which captures indirect information regarding cows' overall level of CMSCC based on previous samplings). The methods were evaluated by a 5-fold cross validation and predictions on future data using models with the 4 different variable setups. The results indicated that GAM was the superior model, although MLP was equally good when fewer data were used. Information regarding the cows' level of previous CMSCC was shown to be important for prediction, lowering prediction error in both GAM and MLP. We conclude that the use of GAM or MLP for CMSCC prediction is promising.

Investigating Stochastic Differential Equations Modelling for Levodopa Infusion in Patients with Parkinson's Disease.

BACKGROUND AND OBJECTIVES: Levodopa concentration in patients with Parkinson's disease is frequently modelled with ordinary differential equations (ODEs). Here, we investigate a pharmacokinetic model of plasma levodopa concentration in patients with Parkinson's disease by introducing stochasticity to separate the intra-individual variability into measurement and system noise, and to account for auto-correlated errors. We also investigate whether the induced stochasticity provides a better fit than the ODE approach. METHODS: In this study, a system noise variable is added to the pharmacokinetic model for duodenal levodopa/carbidopa gel (LCIG) infusion described by three ODEs through a standard Wiener process, leading to a stochastic differential equations (SDE) model. The R package population stochastic modelling (PSM) was used for model fitting with data from previous studies for modelling plasma levodopa concentration and parameter estimation. First, the diffusion scale parameter (σw), measurement noise variance, and bioavailability are estimated with the SDE model. Second, σw is fixed to certain values from 0 to 1 and bioavailability is estimated. Cross-validation was performed to compare the average root mean square errors (RMSE) of predicted plasma levodopa concentration. RESULTS: Both the ODE and the SDE models estimated bioavailability to be approximately 75%. The SDE model converged at different values of σw that were significantly different from zero. The average RMSE for the ODE model was 0.313, and the lowest average RMSE for the SDE model was 0.297 when σw was fixed to 0.9, and these two values are significantly different. CONCLUSIONS: The SDE model provided a better fit for LCIG plasma levodopa concentration by approximately 5.5% in terms of mean percentage change of RMSE.

Genomic Prediction Including SNP-Specific Variance Predictors.

The increasing amount of available biological information on the markers can be used to inform the models applied for genomic selection to improve predictions. The objective of this study was to propose a general model for genomic selection using a link function approach within the hierarchical generalized linear model framework (hglm) that can include external information on the markers. These models can be fitted using the well-established hglm package in R. We also present an R package (CodataGS) to fit these models, which is significantly faster than the hglm package. Simulated data were used to validate the proposed model. We tested categorical, continuous and combination models where the external information on the markers was related to 1) the location of the QTL on the genome with varying degree of uncertainty, 2) the relationship of the markers with the QTL calculated as the LD between them, and 3) a combination of both. The proposed models showed improved accuracies from 3.8% up to 23.2% compared to the SNP-BLUP method in a simulated population derived from a base population with 100 individuals. Moreover, the proposed categorical model was tested on a dairy cattle dataset for two traits (Milk Yield and Fat Percentage). These results also showed improved accuracy compared to SNP-BLUP, especially for the Fat% trait. The performance of the proposed models depended on the genetic architecture of the trait, as traits that deviate from the infinitesimal model benefited more from the external information. Also, the gain in accuracy depended on the degree of uncertainty of the external information provided to the model. The usefulness of these type of models is expected to increase with time as more accurate information on the markers becomes available.

Modelling the co-evolution of indirect genetic effects and inherited variability.

When individuals interact, their phenotypes may be affected not only by their own genes but also by genes in their social partners. This phenomenon is known as Indirect Genetic Effects (IGEs). In aquaculture species and some plants, however, competition not only affects trait levels of individuals, but also inflates variability of trait values among individuals. In the field of quantitative genetics, the variability of trait values has been studied as a quantitative trait in itself, and is often referred to as inherited variability. Such studies, however, consider only the genetic effect of the focal individual on trait variability and do not make a connection to competition. Although the observed phenotypic relationship between competition and variability suggests an underlying genetic relationship, the current quantitative genetic models of IGE and inherited variability do not allow for such a relationship. The lack of quantitative genetic models that connect IGEs to inherited variability limits our understanding of the potential of variability to respond to selection, both in nature and agriculture. Models of trait levels, for example, show that IGEs may considerably change heritable variation in trait values. Currently, we lack the tools to investigate whether this result extends to variability of trait values. Here we present a model that integrates IGEs and inherited variability. In this model, the target phenotype, say growth rate, is a function of the genetic and environmental effects of the focal individual and of the difference in trait value between the social partner and the focal individual, multiplied by a regression coefficient. The regression coefficient is a genetic trait, which is a measure of cooperation; a negative value indicates competition, a positive value cooperation, and an increasing value due to selection indicates the evolution of cooperation. In contrast to the existing quantitative genetic models, our model allows for co-evolution of IGEs and variability, as the regression coefficient can respond to selection. Our simulations show that the model results in increased variability of body weight with increasing competition. When competition decreases, i.e., cooperation evolves, variability becomes significantly smaller. Hence, our model facilitates quantitative genetic studies on the relationship between IGEs and inherited variability. Moreover, our findings suggest that we may have been overlooking an entire level of genetic variation in variability, the one due to IGEs.

Artificial Selection Response due to Polygenic Adaptation from a Multilocus, Multiallelic Genetic Architecture.

The ability of a population to adapt to changes in their living conditions, whether in nature or captivity, often depends on polymorphisms in multiple genes across the genome. In-depth studies of such polygenic adaptations are difficult in natural populations, but can be approached using the resources provided by artificial selection experiments. Here, we dissect the genetic mechanisms involved in long-term selection responses of the Virginia chicken lines, populations that after 40 generations of divergent selection for 56-day body weight display a 9-fold difference in the selected trait. In the F15 generation of an intercross between the divergent lines, 20 loci explained >60% of the additive genetic variance for the selected trait. We focused particularly on fine-mapping seven major QTL that replicated in this population and found that only two fine-mapped to single, bi-allelic loci; the other five contained linked loci, multiple alleles or were epistatic. This detailed dissection of the polygenic adaptations in the Virginia lines provides a deeper understanding of the range of different genome-wide mechanisms that have been involved in these long-term selection responses. The results illustrate that the genetic architecture of a highly polygenic trait can involve a broad range of genetic mechanisms, and that this can be the case even in a small population bred from founders with limited genetic diversity.

Genetics of Interactive Behavior in Silver Foxes (Vulpes vulpes).

Individuals involved in a social interaction exhibit different behavioral traits that, in combination, form the individual's behavioral responses. Selectively bred strains of silver foxes (Vulpes vulpes) demonstrate markedly different behaviors in their response to humans. To identify the genetic basis of these behavioral differences we constructed a large F2 population including 537 individuals by cross-breeding tame and aggressive fox strains. 98 fox behavioral traits were recorded during social interaction with a human experimenter in a standard four-step test. Patterns of fox behaviors during the test were evaluated using principal component (PC) analysis. Genetic mapping identified eight unique significant and suggestive QTL. Mapping results for the PC phenotypes from different test steps showed little overlap suggesting that different QTL are involved in regulation of behaviors exhibited in different behavioral contexts. Many individual behavioral traits mapped to the same genomic regions as PC phenotypes. This provides additional information about specific behaviors regulated by these loci. Further, three pairs of epistatic loci were also identified for PC phenotypes suggesting more complex genetic architecture of the behavioral differences between the two strains than what has previously been observed.

Increasing the power of genome wide association studies in natural populations using repeated measures - evaluation and implementation.

Genomewide association studies (GWAS) enable detailed dissections of the genetic basis for organisms' ability to adapt to a changing environment. In long-term studies of natural populations, individuals are often marked at one point in their life and then repeatedly recaptured. It is therefore essential that a method for GWAS includes the process of repeated sampling. In a GWAS, the effects of thousands of single-nucleotide polymorphisms (SNPs) need to be fitted and any model development is constrained by the computational requirements. A method is therefore required that can fit a highly hierarchical model and at the same time is computationally fast enough to be useful.Our method fits fixed SNP effects in a linear mixed model that can include both random polygenic effects and permanent environmental effects. In this way, the model can correct for population structure and model repeated measures. The covariance structure of the linear mixed model is first estimated and subsequently used in a generalized least squares setting to fit the SNP effects. The method was evaluated in a simulation study based on observed genotypes from a long-term study of collared flycatchers in Sweden.The method we present here was successful in estimating permanent environmental effects from simulated repeated measures data. Additionally, we found that especially for variable phenotypes having large variation between years, the repeated measurements model has a substantial increase in power compared to a model using average phenotypes as a response.The method is available in the r package RepeatABEL. It increases the power in GWAS having repeated measures, especially for long-term studies of natural populations, and the R implementation is expected to facilitate modelling of longitudinal data for studies of both animal and human populations.

Spatial modeling of data with excessive zeros applied to reindeer pellet-group counts.

We analyze a real data set pertaining to reindeer fecal pellet-group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi-Poisson hierarchical generalized linear model (HGLM), zero-inflated Poisson (ZIP), and hurdle models. The quasi-Poisson HGLM allows for both under- and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi-Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi-Poisson HGLM with spatial random effects.

Genome-wide association mapping in a wild avian population identifies a link between genetic and phenotypic variation in a life-history trait.

Understanding the genetic basis of traits involved in adaptation is a major challenge in evolutionary biology but remains poorly understood. Here, we use genome-wide association mapping using a custom 50 k single nucleotide polymorphism (SNP) array in a natural population of collared flycatchers to examine the genetic basis of clutch size, an important life-history trait in many animal species. We found evidence for an association on chromosome 18 where one SNP significant at the genome-wide level explained 3.9% of the phenotypic variance. We also detected two suggestive quantitative trait loci (QTLs) on chromosomes 9 and 26. Fitness differences among genotypes were generally weak and not significant, although there was some indication of a sex-by-genotype interaction for lifetime reproductive success at the suggestive QTL on chromosome 26. This implies that sexual antagonism may play a role in maintaining genetic variation at this QTL. Our findings provide candidate regions for a classic avian life-history trait that will be useful for future studies examining the molecular and cellular function of, as well as evolutionary mechanisms operating at, these loci.

High female mortality resulting in herd collapse in free-ranging domesticated reindeer (Rangifer tarandus tarandus) in Sweden.

Reindeer herding in Sweden is a form of pastoralism practised by the indigenous Sámi population. The economy is mainly based on meat production. Herd size is generally regulated by harvest in order not to overuse grazing ranges and keep a productive herd. Nonetheless, herd growth and room for harvest is currently small in many areas. Negative herd growth and low harvest rate were observed in one of two herds in a reindeer herding community in Central Sweden. The herds (A and B) used the same ranges from April until the autumn gathering in October-December, but were separated on different ranges over winter. Analyses of capture-recapture for 723 adult female reindeer over five years (2007-2012) revealed high annual losses (7.1% and 18.4%, for herd A and B respectively). A continuing decline in the total reindeer number in herd B demonstrated an inability to maintain the herd size in spite of a very small harvest. An estimated breakpoint for when herd size cannot be kept stable confirmed that the observed female mortality rate in herd B represented a state of herd collapse. Lower calving success in herd B compared to A indicated differences in winter foraging conditions. However, we found only minor differences in animal body condition between the herds in autumn. We found no evidence that a lower autumn body mass generally increased the risk for a female of dying from one autumn to the next. We conclude that the prime driver of the on-going collapse of herd B is not high animal density or poor body condition. Accidents or disease seem unlikely as major causes of mortality. Predation, primarily by lynx and wolverine, appears to be the most plausible reason for the high female mortality and state of collapse in the studied reindeer herding community.

MAPfastR: quantitative trait loci mapping in outbred line crosses.

MAPfastR is a software package developed to analyze quantitative trait loci data from inbred and outbred line-crosses. The package includes a number of modules for fast and accurate quantitative trait loci analyses. It has been developed in the R language for fast and comprehensive analyses of large datasets. MAPfastR is freely available at: http://www.computationalgenetics.se/?page_id=7.

Genetic heterogeneity of within-family variance of body weight in Atlantic salmon (Salmo salar).

BACKGROUND: Canalization is defined as the stability of a genotype against minor variations in both environment and genetics. Genetic variation in degree of canalization causes heterogeneity of within-family variance. The aims of this study are twofold: (1) quantify genetic heterogeneity of (within-family) residual variance in Atlantic salmon and (2) test whether the observed heterogeneity of (within-family) residual variance can be explained by simple scaling effects. RESULTS: Analysis of body weight in Atlantic salmon using a double hierarchical generalized linear model (DHGLM) revealed substantial heterogeneity of within-family variance. The 95% prediction interval for within-family variance ranged from ~0.4 to 1.2 kg2, implying that the within-family variance of the most extreme high families is expected to be approximately three times larger than the extreme low families. For cross-sectional data, DHGLM with an animal mean sub-model resulted in severe bias, while a corresponding sire-dam model was appropriate. Heterogeneity of variance was not sensitive to Box-Cox transformations of phenotypes, which implies that heterogeneity of variance exists beyond what would be expected from simple scaling effects. CONCLUSIONS: Substantial heterogeneity of within-family variance was found for body weight in Atlantic salmon. A tendency towards higher variance with higher means (scaling effects) was observed, but heterogeneity of within-family variance existed beyond what could be explained by simple scaling effects. For cross-sectional data, using the animal mean sub-model in the DHGLM resulted in biased estimates of variance components, which differed substantially both from a standard linear mean animal model and a sire-dam DHGLM model. Although genetic differences in canalization were observed, selection for increased canalization is difficult, because there is limited individual information for the variance sub-model, especially when based on cross-sectional data. Furthermore, potential macro-environmental changes (diet, climatic region, etc.) may make genetic heterogeneity of variance a less stable trait over time and space.

Estimation of genetic variance for macro- and micro-environmental sensitivity using double hierarchical generalized linear models.

BACKGROUND: Genetic variation for environmental sensitivity indicates that animals are genetically different in their response to environmental factors. Environmental factors are either identifiable (e.g. temperature) and called macro-environmental or unknown and called micro-environmental. The objectives of this study were to develop a statistical method to estimate genetic parameters for macro- and micro-environmental sensitivities simultaneously, to investigate bias and precision of resulting estimates of genetic parameters and to develop and evaluate use of Akaike's information criterion using h-likelihood to select the best fitting model. METHODS: We assumed that genetic variation in macro- and micro-environmental sensitivities is expressed as genetic variance in the slope of a linear reaction norm and environmental variance, respectively. A reaction norm model to estimate genetic variance for macro-environmental sensitivity was combined with a structural model for residual variance to estimate genetic variance for micro-environmental sensitivity using a double hierarchical generalized linear model in ASReml. Akaike's information criterion was constructed as model selection criterion using approximated h-likelihood. Populations of sires with large half-sib offspring groups were simulated to investigate bias and precision of estimated genetic parameters. RESULTS: Designs with 100 sires, each with at least 100 offspring, are required to have standard deviations of estimated variances lower than 50% of the true value. When the number of offspring increased, standard deviations of estimates across replicates decreased substantially, especially for genetic variances of macro- and micro-environmental sensitivities. Standard deviations of estimated genetic correlations across replicates were quite large (between 0.1 and 0.4), especially when sires had few offspring. Practically, no bias was observed for estimates of any of the parameters. Using Akaike's information criterion the true genetic model was selected as the best statistical model in at least 90% of 100 replicates when the number of offspring per sire was 100. Application of the model to lactation milk yield in dairy cattle showed that genetic variance for micro- and macro-environmental sensitivities existed. CONCLUSION: The algorithm and model selection criterion presented here can contribute to better understand genetic control of macro- and micro-environmental sensitivities. Designs or datasets should have at least 100 sires each with 100 offspring.

A novel generalized ridge regression method for quantitative genetics.

As the molecular marker density grows, there is a strong need in both genome-wide association studies and genomic selection to fit models with a large number of parameters. Here we present a computationally efficient generalized ridge regression (RR) algorithm for situations in which the number of parameters largely exceeds the number of observations. The computationally demanding parts of the method depend mainly on the number of observations and not the number of parameters. The algorithm was implemented in the R package bigRR based on the previously developed package hglm. Using such an approach, a heteroscedastic effects model (HEM) was also developed, implemented, and tested. The efficiency for different data sizes were evaluated via simulation. The method was tested for a bacteria-hypersensitive trait in a publicly available Arabidopsis data set including 84 inbred lines and 216,130 SNPs. The computation of all the SNP effects required <10 sec using a single 2.7-GHz core. The advantage in run time makes permutation test feasible for such a whole-genome model, so that a genome-wide significance threshold can be obtained. HEM was found to be more robust than ordinary RR (a.k.a. SNP-best linear unbiased prediction) in terms of QTL mapping, because SNP-specific shrinkage was applied instead of a common shrinkage. The proposed algorithm was also assessed for genomic evaluation and was shown to give better predictions than ordinary RR.