Dr. Szabolcs Bene

Animal breeding

Dr. Ferenc Szabó

Dr. Árpád Bokor

Dr. Péter Polgár J.

Dr. Szabolcs Bene

Animal breeding

by Dr. Ferenc Szabó, Dr. Árpád Bokor, Dr. Péter Polgár J., and Dr. Szabolcs Bene

Publication date 2011

Created by XMLmind XSL-FO Converter.

Animal breeding

Table of Contents

...... 0

1. Basic population and quantitaive genetics ...... 0

1. Basic Mendelian genetics ...... 0

1.1. Mendel's view of inheritance: Single locus...... 0

1.2. Gene effects...... 0

2. Basic population andquantitative genetics...... 0

2.1. Allele and genotyape frequencies...... 0

2.2. Gamete frequencies...... 0

2.3. Contribution of a locus to the phenotypic value of a trait...... 0

2.4. Fisher's decomposition of the genetic value ...... 0

2.5. Average effects and breeding value...... 0

2.6. Genetic variances...... 0

2. Resemblance between relatives...... 0

1. Phenotypic resemblance between relatives...... 0

1.1. Parent-offspring regression...... 0

1.2. Collateral relationships...... 0

1.3. Causes of phenotypic covariance among relatives...... 0

2. The genetic covariance between relatives ...... 0

2.1. Offspring and one parent covariance ...... 0

2.2. Half-sibs covariance...... 0

2.3. Full-sibs covariance...... 0

3. Environmental causes of relationship between relatives...... 0

4. Compex relationships in pedigree...... 0

3. Inbreeding...... 0

1. Inbreeding coefficient (F, or f)...... 0

2. Change of gene frequency under inbreeding...... 0

3. Inbreeding depression coefficient (B)...... 0

4. The effective population size (Ne)...... 0

4.1. Change of variance under inbreeding...... 0

4. Crossbreeding and heterosis...... 0

1. The aim of crossbreeding...... 0

2. Type of crosses...... 0

3. Heterosis: Change in the mean under crossbreeding...... 0

5. Heritability (h2) and repeatability (R)...... 0

1. Heritability (h2)...... 0

1.1. Heritabilities are function of a population ...... 0

1.2. Estimating heritability...... 0

1.2.1. Estimation by results of selection...... 0

1.2.2. Estimation by using regression...... 0

1.2.3. Estimation by correlation...... 0

1.2.4. Esitmation by ANOVA...... 0

2. Heritability values (h2) of some traits (M.B. Willis, 1991)...... 0

3. Repeatability (R) ...... 0

6. Relationship between traits ...... 0

1. Genetic correlation (rg)...... 0

2. Phenotypic correlation (rp)...... 0

3. Environmental correlation (re)...... 0

7. Maternal effects ...... 0

8. Genotype-environment interaction (G x E) ...... 0

1. Importance and feature of G x E interaction...... 0

2. Estimation of genotype and environmet interaction...... 0

9. Breeding value estimation ...... 0

10. Selection...... 0

11. Methods of selection...... 0

1. Sources of information...... 0

2. Aim, direction of selection...... 0

3. Correlation between traits...... 0

4. Number of traits...... 0

12. Effects of selection...... 0

1. The annual selection progress...... 0

2. Factors influencing the effects of selection...... 0

3. Calculating the effects of selection...... 0

4. Exercises...... 0

4.1. 1st exercise...... 0

4.2. 2nd exercise...... 0

4.3. 3rd exercise...... 0

4.4. 4th exercise...... 0

13. Long-term consequences of artificial selection...... 0

14. Marker assisted and genome selection...... 0

1. Marker assisted selection (MAS)...... 0

A. Appendix 1...... 0

Created by XMLmind XSL-FO Converter.

Animal breeding

Lecture notes for students of MSc courses of Nutrition and Feed Safety and Animal Science

All rights reserved. No part of this work may be reproduced, used or transmitted in any form or by any means – graphic, electronic or mechanical, including photocopying, recording, or information storage and retrieval systems - without the written permission of the authors.

Created by XMLmind XSL-FO Converter.

Animal breeding

Authors:

Szabó, Ferenc DSc university professor (University of Pannonia)

Bokor, Árpád PhD associate professor (Kaposvár University)

Bene, Szabolcs PhD assistant professor (University of Pannonia)

Polgár, J. Péter PhD associate professor (University of Pannonia)

Created by XMLmind XSL-FO Converter.

Manuscript enclosed: 30 September 2011

Responsible for content: TÁMOP-4.1.2-08/1/A-2009-0059 project consortium

Created by XMLmind XSL-FO Converter.

Responsible for digitalization: Agricultural and Food Science Non-profit Ltd. of Kaposvár University

Created by XMLmind XSL-FO Converter.

Basic population and quantitaive genetics

Chapter1.Basic population and quantitaive genetics

Ferenc Szabó

Mendelian genetics means the rules of gene transmission, population genetics is about how genes behave in populations, and quantitative genetics deals with the rules of transmission of complex traits, those with both a genetic and an environmental basis.

1.Basic Mendelian genetics

1.1.Mendel's view of inheritance: Single locus

Genes are discreate particles, with each parent passing one copy to its offspring. In diploids, each parent carries two alleles for each gene (one from each parent). The genotype can be homozyous dominant (YY), homozigous recessive (gg), and heterozygous (Yg). The phenotype denotes the trait value we observed, while the genotype denotes the (unobserved) genetic state.

1.2.Gene effects

Dominance

An interaction between genes at a single locus such that in heterozygotes one allele has more effect than the other. The allele with the greater effect is dominant over its recessive counterpart. Overdominance is expresion of the heterozygote over homozygote.

Pleitropy

The phenomenon of a single gene affecting more then one trait.

Epistasis

An interaction among genes at different loci such that the expression of genes at one locus depends on the alleles present at one more other loci.

Linkage

The occurance of two or more loci of interest on the same chromosome.

2.Basic population andquantitative genetics

More generally, when we sample a population we are not looking at a single pedigree, but rather a complex collections of pedigrees. What are the rules of transmission (for the population) in this case? What happens to the frequencies of alleles from one generation to the next? What about the frequency of genotypes? The machinery of popoulation genetics provides these answers, extending the Mendelian rules of transmission within a pedigree to rules for the behavior of genes in a population.

2.1.Allele and genotyape frequencies

Hardy-Weinberg equilibrium is a state of constant gene and genotypic frequencies occuring in a population in the absence of forces that charge those frequencies.

The frequency of an allele is p, the frequency of other allelel is q, than

p+ q =1

from which

p= 1 - q, q = 1 - p.

The frequency of allele Ai is just frequency of AiAi homozigotes plus half the frequency of all heterozygotes involving Ai:

pi= freq(Ai) = freq(Ai Ai) + 1/2Σfreq(Ai Aj)

The 1/2 appears since only half of the alleles in heterozygotes are Ai.

The first part of Hardy-Weinberg theorem allows us (assuming random mating) to predict genotypic frequencies from allele frequencies. The second part of Hardy-Weinberg theorem is that allele frequencies remain unchanged from one generation to next, provided: (1) infinite population size (i.e. no genetic drift), (2) no mutation, (3) no selection, (4) no migration.

2.2.Gamete frequencies

Random mating is the same as gametes combining at random. For example, the probability of an AABB offspring is the chance that an AB gamete from the father and an AB from the mother combine. Under random mating,

freq(AABB) = freq(AB/father) x freq(AB/mother)

For heterozygotes, there may be more than one combination of gametes that gives raise to same genotype,

freq(AaBB) = freq(AB/father) x freq(aB/mother) + freq(aB/father) x freq(AB/mother)

If we are working with a single locus, then the gamete frequency is just the allele frequency, and under Hardy-Weinberg conditions, these do not change over the generations. However, when the gametes we consider involve two (or more) loci, recombination can cause gamete frequencies to change over time, even under Hardy-Weinber condition.

2.3.Contribution of a locus to the phenotypic value of a trait

The basic model for quantitative genetics is that the phenotypic value (P) of a trait is the sum of genetic value (G) plus an environmental value (E),

P= G + E

The genetic value (G) represents the average phenotypic value for that particular genotype if we were able to replicate it over the distribution (or universe) of environmental values that the population is expressed to experience. While it is often assumed that the genetic and environmental values are uncorrelated, this not be the case. For example, a genetically higher-yield dairy cow may also be fed more, creating a positive correlation between G and E, and in this case the basic model becomes

P= G + E + Cov(G,E)

2.4.Fisher's decomposition of the genetic value

Fisher developed the analysis of variance (ANOVA). He had two fundamental insights. First, that parents do not pass on their entire genotypic value to their offspring, but rather pass along one of the two possible alleles at each locus. Hence, only part of G is passed on and thus we decompose G into component that can be passed along and those that cannot. Fisher's second great insight was that phenotypic correlations among known relatives can be used to estimate the variances of the components of G.

Fisher suggested that genotypic value (Gij) associated with an individual carrying a (QiQj) genotype can be written in terms of the average effects (α) for each allele and dominace deviation (δ) giving the deviation of the actual value for this genotype from the value predicted by the average contribution of each of single alleles,

Gij = μG + αi + αj +δij

The predicted value is

Ĝij = μG + αi + αj amiből Gij - Ĝij = δij:

Here μG is simply the average genotypic value

μG = Σ Gij x (QiQj )gyakorisága.

Since we assumed the environmental values have mean zero, μG = μP.

2.5.Average effects and breeding value

The αi value is the average effect of allele Q1 . Note that α and δ are function of allelel frequencies and that these change as the allele frequencies change. Breeders are concerned with the breeding values (BV) of individuals, which are related to average effects. The BV assiciated with genotype (Gij) is just

BV (Gij) = αi + αj

Likewise, for n loci underlining the trait, the BV is just

BV (Gij) = Σ(αi(k) + αk(k)

The average value of the offsping thus becomes

μO = μG = (αx + αy)/2 =BV(sire)/2

Thus one (simple) estimate of the sire's BV is just twice the deviation from its offspring and overall population mean

BV(sire) =2(μO - μG)

Similarly, the expected breeding value of the offspring given the breeding value of both parents just their average,

μO - μG = BV(sire)/2 + BV(dam)/2

2.6.Genetic variances

The genetic value is expressed as

Gij = μg + αi + αj +δij

The term μg +( αj + αj) corresponds to the regression estimate of G, while δ corresponds to a residual.

Assuming linkage equilibrium, we can sum over loci,

σ2(G) = Σσ2(αik + αjk) + Σσ2(δijk)

This is usually written more compactly as

σ2G = σ2A + σ2D

where:

σ2G total genetic variance,

σ2A additive genetic variance represents the variance in breeding values in the population,

σ2D dominance genetic variance.

Bibliography

Bourdon M. R.Understanding animal breeding, Prentice Hall, Inc, 1997.

Bruce W.Notes for a short course taught June 2006 at University of Aarhus

Created by XMLmind XSL-FO Converter.

Resemblance between relatives

Chapter2.Resemblance between relatives

Ferenc Szabó

The resemblance between relatives is important source of information for prediction breeding values of individuals.

The heritability of a trait, a central concept in quantitative genetics, is the proportion of variation among individuals in a population that is due to variation in additive genetic (i.e. breeding) value of individuals.

h2=VA / VP

where:

VA = Variance of breedigng values (additive)

VP = Phenotypic variance

Since an individual's phenotype can be directly scored, the phenotypic variance (Vp) can be estimated from measurements made directly on the random breeding population. In contrast, an individual's breeding value cannot be observed directly, but rather must be inferred from mean value of its offspring (or more generally using the phenotypic values of other known relatives).

Thus estimates of VA require known collections relatives. The most common situations (which we focus on here) are comparisons between parentes and their offspring or comparisons among sibs.

We can classify relatives as

•ancestral (parent, grandparent and offspring),

•collateral (full sibs, half sibs).

In ancestral relationships we measure phenotypes of one or both parents and k offspring of each. In collateral relationships we measure k offspring in each family, but not the parents.

The amount of phenotypic resemblance among relatives for the trait provides an indication of the amount of genetic variation for the trait. Further, if trait variation has significant genetic basis, the closer the relatives, the more similar their apperiance.

1.Phenotypic resemblance between relatives

Statistically resemblance appears by regression, covariance and correlation.

1.1.Parent-offspring regression

Ther are three types of this regression

•Sire (Pf) - offspring (k) regression

•Dam (Pm) - offspring (k) regression

•parental mean (Pf + Pm)/2) - offspring (k) regression.

1.2.Collateral relationships

With collateral relatives, the above formule for sample covariance is not appropriate, for two reasons. First, there are usually more than two collateral relatives per family. Second, even if families consist of only two relatives, the order of the two is arbitrary. Another way of stating the second point is that collateral relatives belong to the same class or category. In contrast, parents and offspring belong to different calasses. The covariance between parents and offfspring is an interclass (between-class) covariance, while the covariance between collateral relatives is an intraclass (within-class) covariance.

Under the simplest ANOVA framework, we can consider the total variance of a trait to consist of two components: a between-group (also colled among-group) component (for example, differences in the mean value of different families) and a within group component (the variation in trait value within each family). The total variance (T) variance is the sum of the between (B) and within (W) group variances .

Var (T) = Var(B) + Var(W)

The key feature of ANOVA is that the betwen-group variance equals the within-group covariance (Var(B) = Cov(W). Thus, the larger the covariance between members of a family, the larger the fraction of total variation that attributed to differences between family means.

1.3.Causes of phenotypic covariance among relatives

Relatives resemble each other for quantitive traits more than they do unrelated members of the population for two potential reasons:

•relatives share genes (the closer the relationship, the higher the proportion of shared genes),

•relatives may share similar environment

2.The genetic covariance between relatives

The genetic covariance (Cov(Gx,Gy) = covariance of the genotypic values (Gx,Gy)of individuals x and y. Genetic covariance arise because two related individuals are more likely to share alleles than are two unrelated individuals. Sharing alleles means having alleles that are identical by descent (IBD): namely that both copies of an allele can be traced back to a single copy in a recent common ancestor. Alleles can also be identical in state but not identical by descent.

2.1.Offspring and one parent covariance

What is the covariance of genotypic values an offspring (GO) and its parent (GP)? Denoting the two parental alleles at a given locus by A1A2, since a parent and its offspring share exactly one allele. One allale (A1) came from the parent, while the other offspring allele (A2) came from the other parent. To consider the genetic contribution from a parent to its offspring, write the genotypic value of the parent GP = A + D. We can further decompose this by considering the contribution from each parental allele to the overall breeding value, with A = α1 + α2, and we can write the the genotypic value of the parent as GP= α1 + α2 + δ12, where δ12 denotes the dominace deviation an A1A2.

2.2.Half-sibs covariance

In case of halb-sibs, one parent is shared, the other is drown at random from the population. The genetic covariance between half-sibs is the covariance of the genetic values between o1 and o2 progeny. To compute this, consider a single locus. First note that o1 and o2 share either one allele IBD from the father or no alleles IBD, and no maternal allele IBD. The probability that o1 and o2 both receive the same allele from the male is one-half, 50%. In this case, the two offspring have one allele IBD, and the contribution to the genetic covariance when this occurs is Cov(α1,α1) =Var(A)2. When o1 and o2 share no alleles IBD, they have no genetic covariance..

2.3.Full-sibs covariance

In case of full-sibs both parents are in common. As illustrated previously, three cases are possible when considering pairs of full sibs: they can share either 0, 1, or 2 alleles IBD. Applying the same approach as for half sibs, if we can compute: 1) the probability of each case, and 2) the contribution the genetic variance for each case.

Each full sib receives one parental and one maternal allele. The probability that each sib receives the same paternal allalel is 50% , which is also the probability each receives the same maternal allele. The results: Cov(Go1,Go1) =Var(A)/2 + Var(D)/2

3.Environmental causes of relationship between relatives

Shared environmental effects (such as common maternal effect) also contribute to the covariance between relatives, and care must be taken to distinguish these environmental covariances.

If members of a family are reared together they share common environmental value, (Ec). If the common environmental circumstance are different for each family, the variance due to common environmental effects (VEc), causes greater similarity among members of a family, and greater differences among families, than would be expected from the proportion of genes they share.

Just as we decomposed the total genotypic value into common components, some shared, others not transmitted between relatives, we can do the same for environmental effects. In particular, the total environmental effect (E) is the sum of common environmental effect (Ec), general environmental effect (Eg) and specific environmental effect (Es) , that is E = Ec + Eg + Es. Partitioning the environmental variance as

VE= VEc + VEg + VEs

4.Compex relationships in pedigree

Much of the analysis in animal breeding occurs with pedigree data, where relationships can be increasingly complex (i.e, inbred relative).

Suppose that single alleles are drown randomly from individuals x and y. The probability that these two alleles are identical by descent (IBD) is called coefficient of coancestry (Θx,y). The probability that two genes at a locus in individual z offspring is inbreeding coefficient (fz).

Thus, an individual's inbreeding coefficient is equivalent to its parents' coefficient of coancestry,

fz = Θxy.

The above results for the contribution when relatives share one or two alleles IBD suggests the general expression for covariance between non inbred relatives. The genetic correlation (rxy) involves the probability that relatives share one and the probability they share two alleles.