FnR: R package for computing inbreeding and numerator relationship coefficients.

BACKGROUND: Inbreeding and relationship coefficients are essential for conservation and breeding programs. Whether dealing with a small conserved population or a large commercial population, monitoring the inbreeding rate and designing mating plans that minimize the inbreeding rate and maximize the effective population size is important. Free, open-source, and efficient software may greatly contribute to conservation and breeding programs and help students and researchers. Efficient methods exist for calculating inbreeding coefficients. Therefore, an efficient way of calculating the numerator relationship coefficients is via the inbreeding coefficients. i.e., the relationship coefficient between parents is twice the inbreeding coefficient of their progeny. A dummy progeny is introduced where no progeny exists for a pair of individuals. Calculating inbreeding coefficients is very fast, and finding whether a pair of individuals has a progeny and picking one from multiple progenies is computationally more demanding. Therefore, the R package introduces a dummy progeny for any pair of individuals whose relationship coefficient is of interest, whether they have a progeny or not. RESULTS: Runtime and peak memory usage were benchmarked for calculating relationship coefficients between two sets of 250 and 800 animals (200,000 dummy progenies) from a pedigree of 2,721,252 animals. The program performed efficiently (200,000 relationship coefficients, which involved calculating 2,721,252 + 200,000 inbreeding coefficients) within 3:45 (mm:ss). Providing the inbreeding coefficients (for real animals), the runtime was reduced to 1:08. Furthermore, providing the diagonal elements of D in A = TDT ' (d), the runtime was reduced to 54s. All the analyses were performed on a machine with a total memory size of 1 GB. CONCLUSIONS: The R package FnR is free and open-source software with implications in conservation and breeding programs. It proved to be time and memory efficient for large populations and many dummy progenies. Calculation of inbreeding coefficients can be resumed for new animals in the pedigree. Thus, saving the latest inbreeding coefficient estimates is recommended. Calculation of d coefficients (from scratch) was very fast, and there was limited value in storing those for future use.

Use of molecular markers to improve relationship information in the genetic evaluation of beef cattle tick resistance under pedigree-based models.

The selection of genetically superior individuals is conditional upon accurate breeding value predictions which, in turn, are highly depend on how precisely relationship is represented by pedigree. For that purpose, the numerator relationship matrix is essential as a priori information in mixed model equations. The presence of pedigree errors and/or the lack of relationship information affect the genetic gain because it reduces the correlation between the true and estimated breeding values. Thus, this study aimed to evaluate the effects of correcting the pedigree relationships using single-nucleotide polymorphism (SNP) markers on genetic evaluation accuracies for resistance of beef cattle to ticks. Tick count data from Hereford and Braford cattle breeds were used as phenotype. Genotyping was carried out using a high-density panel (BovineHD - Illumina® bead chip with 777 962 SNPs) for sires and the Illumina BovineSNP50 panel (54 609 SNPs) for their progenies. The relationship between the parents and progenies of genotyped animals was evaluated, and mismatches were based on the Mendelian conflicts counts. Variance components and genetic parameters estimates were obtained using a Bayesian approach via Gibbs sampling, and the breeding values were predicted assuming a repeatability model. A total of 460 corrections in relationship definitions were made (Table 1) corresponding to 1018 (9.5%) tick count records. Among these changes, 97.17% (447) were related to the sire's information, and 2.8% (13) were related to the dam's information. We observed 27.2% (236/868) of Mendelian conflicts for sire-progeny genotyped pairs and 14.3% (13/91) for dam-progeny genotyped pairs. We performed 2174 new definitions of half-siblings according to the correlation coefficient between the coancestry and molecular coancestry matrices. It was observed that higher-quality genetic relationships did not result in significant differences of variance components estimates; however, they resulted in more accurate breeding values predictions. Using SNPs to assess conflicts between parents and progenies increases certainty in relationships and consequently the accuracy of breeding value predictions of candidate animals for selection. Thus, higher genetic gains are expected when compared to the traditional non-corrected relationship matrix.

Accounting for genetic differences among unknown parents in microevolutionary studies: how to include genetic groups in quantitative genetic animal models.

Quantifying and predicting microevolutionary responses to environmental change requires unbiased estimation of quantitative genetic parameters in wild populations. 'Animal models', which utilize pedigree data to separate genetic and environmental effects on phenotypes, provide powerful means to estimate key parameters and have revolutionized quantitative genetic analyses of wild populations. However, pedigrees collected in wild populations commonly contain many individuals with unknown parents. When unknown parents are non-randomly associated with genetic values for focal traits, animal model parameter estimates can be severely biased. Yet, such bias has not previously been highlighted and statistical methods designed to minimize such biases have not been implemented in evolutionary ecology. We first illustrate how the occurrence of non-random unknown parents in population pedigrees can substantially bias animal model predictions of breeding values and estimates of additive genetic variance, and create spurious temporal trends in predicted breeding values in the absence of local selection. We then introduce 'genetic group' methods, which were developed in agricultural science, and explain how these methods can minimize bias in quantitative genetic parameter estimates stemming from genetic heterogeneity among individuals with unknown parents. We summarize the conceptual foundations of genetic group animal models and provide extensive, step-by-step tutorials that demonstrate how to fit such models in a variety of software programs. Furthermore, we provide new functions in r that extend current software capabilities and provide a standardized approach across software programs to implement genetic group methods. Beyond simply alleviating bias, genetic group animal models can directly estimate new parameters pertaining to key biological processes. We discuss one such example, where genetic group methods potentially allow the microevolutionary consequences of local selection to be distinguished from effects of immigration and resulting gene flow. We highlight some remaining limitations of genetic group models and discuss opportunities for further development and application in evolutionary ecology. We suggest that genetic group methods should no longer be overlooked by evolutionary ecologists, but should become standard components of the toolkit for animal model analyses of wild population data sets.

Numericware N: Numerator Relationship Matrix Calculator.

We present the generalized numerator relationship matrix (GNRM) algorithm and Numericware N as a software tool for calculating the numerator relationship matrix (NRM). The GNRM algorithm aims to build the NRM based on plant pedigrees. Customary plant pedigrees have a sparse format representing multiple ancestors and offspring. Applying the existing NRM algorithm to plant pedigrees requires transforming the pedigree statements from sparse (multi-founders to offspring) to dense (bi-parents to offspring). The GNRM algorithm enables the computation of the NRM using sparse pedigrees. Because sparse pedigrees can be used, Numericware N produces smaller dimensions of the NRM, thus making computing time much faster. Moreover, Numericware N enables expansion of identical by state (IBS) matrix for scheduled pedigrees, which allows prediction of IBS matrix.

Differences between genomic-based and pedigree-based relationships in a chicken population, as a function of quality control and pedigree links among individuals.

This work studied differences between expected (calculated from pedigree) and realized (genomic, from markers) relationships in a real population, the influence of quality control on these differences, and their fit to current theory. Data included 4940 pure line chickens across five generations genotyped for 57,636 SNP. Pedigrees (5762 animals) were available for the five generations, pedigree starting on the first one. Three levels of quality control were used. With no quality control, mean difference between realized and expected relationships for different type of relationships was ≤ 0.04 with standard deviation ≤ 0.10. With strong quality control (call rate ≥ 0.9, parent-progeny conflicts, minor allele frequency and use of only autosomal chromosomes), these numbers reduced to ≤ 0.02 and ≤ 0.04, respectively. While the maximum difference was 1.02 with the complete data, it was only 0.18 with the latest three generations of genotypes (but including all pedigrees). Variation of expected minus realized relationships agreed with theoretical developments and suggests an effective number of loci of 70 for this population. When the pedigree is complete and as deep as the genotypes, the standard deviation of difference between the expected and realized relationships is around 0.04, all categories confounded. Standard deviation of differences larger than 0.10 suggests bad quality control, mistakes in pedigree recording or genotype labelling, or insufficient depth of pedigree.

Uncertain paternity in primate quantitative genetic studies.

Quantitative genetic studies in primates have generally been based on varying amounts of genealogical information. We consider the case where maternal relationships are known, but paternal relationships are only probabilistic (i.e., a limited number of males can be enumerated as equally likely sires for a given offspring). Using Henderson's [1988] average numerator relationship matrix method, we show for craniometric data from the Cayo Santiago macaque colony that heritability estimates are not greatly affected by the addition of incomplete paternal information. We then show through simulation studies that in order for there to be a substantial increase in power to detect significant heritabilities, the number of possible sires per offspring must be quite small. Given this restriction, we conclude that the current method of ignoring paternal relationships is probably adequate and that considerable effort would have to be expended in performing paternal exclusions before there would be a substantial increase in the precision of heritability estimates. © 1992 Wiley-Liss, Inc.