An approximate method for optimum independent culling level selection for n stages of selection with explicit solutions

Summary An approximate method with explicit solutions to apply independent culling levels for multiple traits in n-stages of selection was developed. An approximate solution was found for sequentially selected traits. Two assumptions were necessary. The first was to assume that subsequent selection would not appreciably change the mean of traits already selected, and the second was to approximate the variance of a correlated trait in a selected population with an upward biased projection. The procedure was shown to give near optimal results regardless of selection intensity or genetic correlations if phenotypic correlations among traits were low. The procedure gave poor results only for certain sequences of selection when phenotypic correlations were high. However, in those cases good results were obtained using a different sequence of selection. With high correlations, the procedure is recommended only after comparing solutions and expected genetic gain for all sequences of selection. If the expected aggregate gain for the sequence of selection desired is less than that of another order, culling points associated with the optimal ordering must be determined. Genetic gain from use of culling points is independent of order of selection. The procedure is recommended for use with computer programs that attempt to find optimal culling points to reduce computational time and to check results.Journal Paper No. 12448 of the Purdue University Agricultural Experiment Station     

Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data

Background

Arguably, genotypes and phenotypes may be linked in functional forms that are not well addressed by the linear additive models that are standard in quantitative genetics. Therefore, developing statistical learning models for predicting phenotypic values from all available molecular information that are capable of capturing complex genetic network architectures is of great importance. Bayesian kernel ridge regression is a non-parametric prediction model proposed for this purpose. Its essence is to create a spatial distance-based relationship matrix called a kernel. Although the set of all single nucleotide polymorphism genotype configurations on which a model is built is finite, past research has mainly used a Gaussian kernel.

Results

We sought to investigate the performance of a diffusion kernel, which was specifically developed to model discrete marker inputs, using Holstein cattle and wheat data. This kernel can be viewed as a discretization of the Gaussian kernel. The predictive ability of the diffusion kernel was similar to that of non-spatial distance-based additive genomic relationship kernels in the Holstein data, but outperformed the latter in the wheat data. However, the difference in performance between the diffusion and Gaussian kernels was negligible.

Conclusions

It is concluded that the ability of a diffusion kernel to capture the total genetic variance is not better than that of a Gaussian kernel, at least for these data. Although the diffusion kernel as a choice of basis function may have potential for use in whole-genome prediction, our results imply that embedding genetic markers into a non-Euclidean metric space has very small impact on prediction. Our results suggest that use of the black box Gaussian kernel is justified, given its connection to the diffusion kernel and its similar predictive performance.     

Optimum contribution selection in large general tree breeding populations with an application to Scots pine

Development of selection methods that optimises selection differential subject to a constraint on the increase of inbreeding (or coancestry) in a population is an important part of breeding programmes. One such method that has received much attention in animal breeding is the optimum contribution (OC) dynamic selection method. We implemented the OC algorithm and applied it to a diallel progeny trial of Pinus sylvestris L. (Scots pine) focussing on two traits (total tree height and stem diameter). The OC method resulted in a higher increase in genetic gain (8–30%) compared to the genetic gain achieved using standard restricted selection method at the same level of coancestry constraint. Genetic merit obtained at two different levels of restriction on coancestry showed that the benefit of OC was highest when restriction was strict. At the same level of genetic merit, OC decreased coancestry with 56 and 39% for diameter and height, respectively, compared to the level of coancestry obtained using unrestricted truncation selection. Inclusion of a dominance term in the statistical model resulted in changes in contribution rank of trees with 7 and 13% for diameter and height, respectively, compared to results achieved by using a pure additive model. However, the genetic gain was higher for the pure additive model than for the model including dominance for both traits.     

A multivariate method for detecting genetic linkage, with application to a pedigree with an adverse lipoprotein phenotype.

The robust or model-free method for detecting linkage developed by Haseman and Elston for data from sib pairs is extended to incorporate observations of multiple traits on each individual. A method is proposed that estimates the linear function that results in the strongest correlation between the squared pair differences in the trait measurements and identity by descent at a marker locus. The method is illustrated by the study of apolipoprotein and cholesterol levels in individuals from a large family that had many members diagnosed with coronary heart disease.     

Longitudinal random effects models for genetic analysis of binary data with application to mastitis in dairy cattle

A Bayesian analysis of longitudinal mastitis records obtained in the course of lactation was undertaken. Data were 3341 test-day binary records from 329 first lactation Holstein cows scored for mastitis at 14 and 30 days of lactation and every 30 days thereafter. First, the conditional probability of a sequence for a given cow was the product of the probabilities at each test-day. The probability of infection at time t for a cow was a normal integral, with its argument being a function of "fixed" and "random" effects and of time. Models for the latent normal variable included effects of: (1) year-month of test + a five-parameter linear regression function ("fixed", within age-season of calving) + genetic value of the cow + environmental effect peculiar to all records of the same cow + residual. (2) As in (1), but with five parameter random genetic regressions for each cow. (3) A hierarchical structure, where each of three parameters of the regression function for each cow followed a mixed effects linear model. Model 1 posterior mean of heritability was 0.05. Model 2 heritabilities were: 0.27, 0.05, 0.03 and 0.07 at days 14, 60, 120 and 305, respectively. Model 3 heritabilities were 0.57, 0.16, 0.06 and 0.18 at days 14, 60, 120 and 305, respectively. Bayes factors were: 0.011 (Model 1/Model 2), 0.017 (Model 1/Model 3) and 1.535 (Model 2/Model 3). The probability of mastitis for an "average" cow, using Model 2, was: 0.06, 0.05, 0.06 and 0.07 at days 14, 60, 120 and 305, respectively. Relaxing the conditional independence assumption via an autoregressive process (Model 2) improved the results slightly.     

Stochastic simulations of a multi-group compartmental model for Johne's disease on US dairy herds with test-based culling intervention

Infection elimination may be an important goal of control programs. Only in stochastic infection models can true infection elimination be observed as a fadeout. The phenomena of fadeout and variable prevalence are important in understanding the transmission dynamics of infectious diseases and these phenomena are essential to evaluate the effectiveness of control measures. To investigate the stochastic dynamics of Mycobacterium avium subsp. paratuberculosis (MAP) infection on US dairy herds with test-based culling intervention, we developed a multi-group stochastic compartmental model (a continuous time Markov chain model) with both horizontal and vertical transmission. The stochastic model predicted fadeout and within-herd prevalence to have a large variance. Although test-based culling intervention generally decreased prevalence over time, it took longer than desired by producers to eliminate the endemic MAP infection from a herd. Uncertainty analysis showed that, using annual culture test and culling of only high shedders or culling of both low and high shedders with a 12-month delay in culling of low shedders, MAP infection persisted in many herds beyond 20 years. While using semi-annual culture test and culling of low and high shedders with a 6-month delay in culling of low shedders, MAP infection in many herds would be extinct within 20 years. Sensitivity analysis of the cumulative density function of fadeout suggested that combining test-based culling intervention and reduction of transmission rates through improved management between susceptible calves and shedding animals may be more effective than either alone in eliminating endemic MAP infection. We also discussed the effects of other factors such as herd size, heifer replacement, and adult cow infection on the probability of fadeout.     

Detection, distribution and probable fate of Escherichia coli O157 from asymptomatic cattle on a dairy farm

The use of commercial anti- Escherichia coli O157-labelled magnetic beads was investigated to improve detection of E. coli O157 by immunomagnetic separation (IMS) from a range of environments on a dairy farm. Immunomagnetic separation proved effective for separation of target cells from laboratory mixtures and during stress in sterile and non-sterile pond water. The IMS procedure was possible with a range of samples (water, faeces, slurry, grass and soil). Non-specific binding of non-target bacterial cells proved problematic in a number of sample types. However, indigenous E. coli O157 cells were detected from samples with a high faecal load, and only with use of IMS. Data on the probable survival and spread of the organism around the farm environment are also discussed.     

Bayesian estimation of multivariate normal mixtures with covariate‐dependent mixing weights,with an application in antimicrobial resistance monitoring

Bacteria with a reduced susceptibility against antimicrobials pose a major threat to public health. Therefore, large programs have been set up to collect minimum inhibition concentration (MIC) values. These values can be used to monitor the distribution of the nonsusceptible isolates in the general population. Data are collected within several countries and over a number of years. In addition, the sampled bacterial isolates were not tested for susceptibility against one antimicrobial, but rather against an entire range of substances. Interest is therefore in the analysis of the joint distribution of MIC data on two or more antimicrobials, while accounting for a possible effect of covariates. In this regard, we present a Bayesian semiparametric density estimation routine, based on multivariate Gaussian mixtures. The mixing weights are allowed to depend on certain covariates, thereby allowing the user to detect certain changes over, for example, time. The new approach was applied to data collected in Europe in 2010, 2012, and 2013. We investigated the susceptibility of Escherichia coli isolates against ampicillin and trimethoprim, where we found that there seems to be a significant increase in the proportion of nonsusceptible isolates. In addition, a simulation study was carried out, showing the promising behavior of the proposed method in the field of antimicrobial resistance.     

Correcting the estimated level of differential expression for gene selection bias: application to a microarray study

The level of differential gene expression may be defined as a fold change, a frequency of upregulation, or some other measure of the degree or extent of a difference in expression across groups of interest. On the basis of expression data for hundreds or thousands of genes, inferring which genes are differentially expressed or ranking genes in order of priority introduces a bias in estimates of their differential expression levels. A previous correction of this feature selection bias suffers from a lack of generality in the method of ranking genes, from requiring many biological replicates, and from unnecessarily overcompensating for the bias. For any method of ranking genes on the basis of gene expression measured for as few as three biological replicates, a simple leave-one-out algorithm corrects, with less overcompensation, the bias in estimates of the level of differential gene expression. In a microarray data set, the bias correction reduces estimates of the probability of upregulation or downregulation from 100% to as low as 60%, even for genes with estimated local false discovery rates close to 0. A simulation study quantifies both the advantage of smoothing estimates of bias before correction and the degree of overcompensation.     

Step down procedure for comparing several treatments with a control based on multivariate normal response

In this study we consider a multiple comparison of several treatments with a control based on multivariate normal response in clinical trials. Specifically we construct a step down procedure by referring to Dunnett and Tamhane (1991). Furthermore we formulate the all-pairs power by using the recursive formula derived by Hayter and Tamhane (1991) and Dunnett, Horn and Vollandt (2001). Finally we compare the step down procedure with the single step procedure proposed by Nakamura and Imada (2005) in terms of some numerical examples regarding the power of the test.     

A codon-based model of host-specific selection in parasites,with an application to the influenza A virus

Parasites sometimes expand their host range by acquiring a new host species. After a host change event, the selective regime acting on a given parasite gene may change as a result of host-specific adaptive alterations of protein functionality or host-specific immune-mediated selection. We present a codon-based model that attempts to include these effects by allowing the position-specific substitution process to change in conjunction with a host change event. Following maximum-likelihood parameter estimation, we employ an empirical Bayesian procedure to identify candidate sites potentially involved in host-specific adaptation. We discuss the applicability of the model to the more general problem of ascertaining whether the selective regime differs in two groups of related organisms. The utility of the model is illustrated on a data set of nucleoprotein sequences from the influenza A virus obtained from avian and human hosts.     

Application of absorbing Markov chains to sib mating populations with selection for a pair of independent diallelic loci

In this paper we consider a sib mating population with a pair of independent diallelic loci. The average, variance, and third order moment about the mean have been calculated for the distribution representing the number of generations needed to reach an absorbing state beginning in any one of the trnsient states. Four cases are analysed: the no selection one and those cases arising from the combination of favorable selective values for the homozygous and heterozygous genotypes for both genes. The different cases are considered separately and compared, but only some typical starting cases have been reported so as to save space. No selective differences were assumed between the two sexes. The formalism of absorbing Markov chains have been used for the calculations.     

Effects of competition on means,variances and covariances in quantitative genetics with an application to general combining ability selection

Summary General expressions are established for means, variances and covariances, taking into account the effect of interactions between individuals. For simplicity, only groups of size two are considered so that interactions are restricted to pairs of individuals; genetic effects are reduced to additivity and to additive × additive interaction between the direct effect of an allele and the associate effect of another. The effect of family structure is studied, and some consequences of interest to plant breeding are discussed by an application to general combining ability selection. From a population genetic point of view, this approach reveals a new application of coefficients of kinship.     

Relationship between resource selection, distribution, and abundance: a test with implications to theory and conservation

Much of applied and theoretical ecology is concerned with the interactions of habitat quality, animal distribution, and population abundance. We tested a technique that uses resource selection functions (RSF) to scale animal density to the relative probability of selecting a patch of habitat. Following an accurate survey of a reference block, the habitat-based density estimator can be used to predict population abundance for other areas with no or unreliable survey data. We parameterized and tested the technique using multiple years of radiotelemetry locations and survey data collected for woodland caribou across four landscape-level survey blocks. The habitat-based density estimator performed poorly. Predictions were no better than those of a simple area estimator and in some cases deviated from the observed by a factor of 10. We developed a simulation model to investigate factors that might influence prediction success. We experimentally manipulated population density, caribou distribution, ability of animals to track carrying capacity, and precision of the estimation equation. Our simulations suggested that interactions between population density, the size of the reference block, and the pattern of distribution can lead to large discrepancies between observed and predicted population numbers. Over- or undermatching patch carrying capacity and precision of the estimator can influence predictions, but the effect is much less extreme. Although there is some empirical and theoretical evidence to support a relationship between animal abundance and resource selection, our study suggests that a number of factors can seriously confound these relationships. Habitat-based density estimators might be effective where a stable, isolated population at equilibrium is used to generate predictions for areas with similar population parameters and ecological conditions.     

Development of a novel stall design for dairy cattle: Part I. The effect of an increased slope on lying behavior,rumination, cleanliness,and preference

The longitudinal slope of a stall is important for positioning cows in the stall and maintaining cleanliness of the stall surface. The objectives of this study were to determine the short-term effect of increasing free-stall slope from 4.5% to 9.3% on dairy cow lying behavior, rumination, milk production, cleanliness, and preference. In experiment 1, 60 multiparous Holstein cows were divided randomly into two groups and exposed to a 4.5% stall slope (standard in the research facility) and a 9.3% stall slope in a replicated crossover design with four 7-day periods. Each group of cows were housed in a pen with 30 free-stalls and switched between treatments weekly. Lying behavior and rumination were recorded continuously, milk yields were recorded twice per day, and cleanliness scores were collected on the last day of each week. Experiment 2 consisted of an 8-day preference test conducted with 14 cows from experiment 1 in an experimental pen with 32 stalls (16 stalls with a 4.5% slope and 16 stalls with a 9.3% slope). Continuous video monitoring was used to record time spent lying, standing, and perching in each treatment during the last 5 days, and lying time was used to assess preference. In experiment 1, cows spent 12 min/day less time lying down (12.8 vs 12.6 ± 0.28 h/d) and had 0.6 more bouts/day (9.5 vs 10.1 ± 0.38 no./d) with a shorter duration by 6 min/day (1.4 vs 1.3 ± 0.03 h/bout) in stalls with a 9.3% slope. Rumination was 5.5 min less per day in stalls with a 9.3% slope (578.4 vs 572.9 ± 16.56 min/d) and milk yield did not differ between treatments (33.6 vs 33.4 ± 0.78 kg/d). Stall slope did not affect cow cleanliness (1.6 vs 1.6 ± 0.05 points on a 1–5 scale). In experiment 2, cows showed no clear preference for lying, standing, or perching in either stall slope (4.5% and 9.3%) when given a choice. These results indicate that increasing stall slope from 4.5% to 9.3% marginally altered lying behavior, but did not interfere with stall use or influence cow preferences.