Introduction to Course

Transcription

1 Introduction to Course 1 Aim of the Course The aim of the course is to present linear model methodology for the genetic evaluation of livestock and general analysis of livestock data. 2 Structure of Course The notes are a bare bones outline. Example problems will be presented. Each problem is followed by a possible solution, and associated theory. A method of calculating the solution using R software is given, and the solution will be presented and discussed. Then a set of exercises related to that particular example problem are given. The exercises are designed to expand on different aspects of the problem. 3 The Assumed Genetic Model The Infinitesimal Model (1909) is assumed for most of this course. There are an estimated 30,000 genes in mammals. If each gene has only two alleles (variants), then there are only 3 possible genotypes at each locus. The number of possible genotypes across all loci would be , which is a number greater than the total number of animals in any livestock species. Many genes are likely to have more than two alleles, and hence the number of possibly different genotypes is even greater then Logically, one can assume a genome with essentially an infinite number of loci as being approximately correct for all practical purposes. Infinitesimal Model: An infinite number of loci are assumed, all with an equal and small effect on a quantitative trait. True Breeding Value: The sum of the additive effects of all loci on a quantitative trait is known as the True Breeding Value (TBV). 4 Types of Genetic Effects In this course, only additive genetic effects are of interest. Additive effects are generally the largest of the genetic effects, and the allelic effects are passed directly to offspring while the other genetic effects are not transmitted to progeny, and are generally smaller in magnitude. 1

2 4.1 Additive Effects Assume one locus with three alleles, A 1, A 2, and A 3. Assume also that the effect of the alleles are +3, +1, and -1, respectively. If the genetic effects are entirely additive, then the value of the possible genotypes would be the sum of their respective allele effects, i.e. A 1 A 1 = = +6 A 1 A 2 = = +4 A 1 A 3 = 3 1 = +2 A 2 A 2 = = +2 A 2 A 3 = 1 1 = 0 A 3 A 3 = 1 1 = Dominance Effects Dominance genetic effects are the interactions among alleles at a given locus. This is an effect that is extra to the sum of the additive allelic effects. Each genotype would have its own dominance effect, let these be denoted as δ ij, and each of them are non-zero quantities. Using the previous example, the additive and dominance effects would give A 1 A 1 = δ 11 = +6 + δ 11 A 1 A 2 = δ 12 = +4 + δ 12 A 1 A 3 = δ 13 = +2 + δ 13 A 2 A 2 = δ 22 = +2 + δ 22 A 2 A 3 = δ 23 = 0 + δ 23 A 3 A 3 = δ 33 = 2 + δ Epistatic Genetic Effects Epistatic genetic effects encompass all possible interactions among the m loci (m being approximately 30,000). This includes all two way interactions, three way interactions, etc. As well, epistasis includes interactions between additive effects at different loci, interactions between additive effects at one locus with dominance effects at a second locus, and interactions between dominance effects at different loci. 2

3 5 Necessary Information Genetic improvement of a livestock species requires four pieces of information. 5.1 Pedigrees Animals, their sires, and their dams need to be uniquely identified in the data. Birthdates, breed composition, and genotypes for various markers or QTLs could also be stored. If animals are not uniquely identified, then genetic change of the population may not be possible. In aquaculture species, for example, individual identification may not be feasible, but family identification (sire and dam) may be known. 5.2 Data Traits of economic importance need to be recorded accurately and completely. All animals within a production unit (herd, flock, ranch) should be recorded. Animals should not be selectively recorded. Data includes the dates of events when traits are observed, factors that could influence an animal s performance, and an identification of contemporaries that are raised and observed in the same environment under the same management regime. Observations should be objectively measured, if at all possible. 5.3 Production System A knowledge and understanding of the production system of a livestock species is important for designing optimum selection and mating strategies. The key elements are the gestation length and the age at first breeding. The number of offspring per female per gestation will influence family structure. The use of artificial insemination and/or embryo transfer could be important. Other management practices are also useful to know. All information is used to formulate appropriate linear models for the analysis of the data and accurate estimation of breeding values of animals. 5.4 Prior Information Read the literature. Most likely other researchers have already made analyses of the same species and traits. Their models could be useful starting points for further analyses. Their parameter estimates could predict the kinds of results that might be found. The idea is to avoid the pitfalls and problems that other researchers have already encountered. Be aware of new kinds of analyses of the same data, that may not involve linear models. 3

4 6 Tools for Genetic Evaluation 6.1 Statistical Linear Models A model describes the factors that affect each trait in a linear fashion. That is, a factor has an additive effect on a trait. All models are simple approximations to how factors influence a trait. The goal is to find the best practical model that explains the most variation. Statistical knowledge is required. 6.2 Matrix Algebra Matrix algebra is a notation for describing models and statistical analyses in a simplified manner. Matrix addition, multiplication, inversion, differentiation, and other operations should be mastered at an efficient level of expertise. 6.3 Computing Animal breeders should know how to write programs, or at least to be capable of using software written by others. Available software may not be enough for some analyses, and so new programs may need to be written. The best languages for programming animal breeding work are FORTRAN (77 or 90), C, or C++. For this course, R software will be used to solve the example problems. R is an open source language available on the internet. Go to the CRAN site and download the latest version of R onto your desktop machine or laptop. R is continually being updated with one or two new versions per year. One version should suffice for at least a year. Some of the basics of R will be given in these notes. 4

5 7 EXERCISES 1. Search the literature or internet to fill in the missing values in the following table. Species Age at first breeding Gestation Pairs of Males(days) Females (days) Length (d) Chromosomes Cattle Swine Sheep Goats Horse Elk Deer Llama Rabbit Mink Chicken Turkey Dog Cat Mouse 2. Describe a typical production system for one of the livestock species in the previous table. 3. Take one of the livestock species in the first question and make a file of the different breeds within that species and the number of animals in each breed today in Canada (your country). Include a picture and brief background of each breed. 4. Describe an existing data recording program for a quantitative trait in one species in Canada (your country). 5