154 Utilisation and conservation of farm animal genetic resources
John Woolliams
1. Unequal mating opportunity e.g. when one sire is allocated many mates but another is allocated very few, perhaps through the unregulated use of AI for some sires, or
when one sire is kept over many breeding seasons but another is culled early in its breeding life.
2. If ofspring have diferential survival due to diferential management of families, or inherited disease or perceived ‘faults’. he latter problem comes from the imposition
of breed standards, usually based on exterior appearance, where ofspring failing to meet standards are excluded from breeding opportunities. he dangers of this are
that there is a reluctance to breed from certain individuals because their ofspring have attained a bad reputation and this problem can be compounded by secrecy in
the results of these examinations. he impact upon the population is to unnecessarily erode the genetic base. A more progressive strategy for both inherited disease and
breed ‘faults’ is to use the test results to identify the degree to which the problem is genetic, and which individuals are more or less likely to carry such genes, and to
develop a breeding scheme to reduce the incidence of the disease or the ‘faults’ in a sustainable way. his is an application of optimum contributions as developed in
chapter 8.
3. Artiicial selection will oten introduce variation in contributions, although selection within families will have no, or only small, impact. Selection may be desirable, e.g.
as mentioned above in 2, and is discussed in more detail later. Many problems are caused by fashion in favouring one sire over another e.g. according to performance
in particular shows in which the animal was judged as ‘best’, and this can result in big demands for matings to these sires, with consequently very unequal contributions.
his is a diicult social problem for many breeds, since their genetic management is shared amongst many private individuals as a hobby. However it is feasible to
develop rules or quotas that retain rewards for owners of individual animals, whilst managing the impact of such activities on the long-term diversity, and these should
be pursued wherever possible. More systematic genetic selection is considered in a later section and its implementation in chapter 8.
3.3. Impact of genomics
Is managing the pedigree the entire answer? In many cases yes, however Wang and Hill 2000 pointed out that efective population sizes could in theory be made ininite if
selection was made actively based upon the alleles that were inherited by the ofspring. his could further reduce the loss of diversity by ensuring that the replacement parents
contain a balanced number of copies of each segment of DNA from each parent, although equality among segments will remain impossible if the mating ratio, d 1. If d
=1 than this would result in no loss of diversity and an ininite efective population size. his ideal is unachievable in practical terms requiring very large families for a genome
Utilisation and conservation of farm animal genetic resources 155
Chapter 7. Genetic contributions and inbreeding
of any size. However with the prospects of dense genome wide SNP typing becoming brighter, there is a realistic prospect of selection within families to minimise the lack of
balance between homologous segments of each parent in the replacement parents i.e. bringing actual contributions closer to their expectations. his concept moves us into
managing diversity through evaluation as well as simply by design.
Genomic technology has developed to where we are expert at obtaining data through high throughput assays, but novices at its interpretation in relation to the range of adaptive
phenotypes. For the next 5 years at least, we will have large-scale individual data based on many anonymous markers with poorly estimated efects on adaptive itness. Additional
beneits from using DNA will come solely from addressing the remaining loss of variation that lies within families: for M=10 males with large
d, utilising ‘best’ management of pedigree alone gives ΔF=1120 from Sanchez
et al., 2003, worse management can lead to ΔF over 5-fold greater. his general perspective on the value of primarily managing
pedigree is supported by the simulations of Fernandez et al. 2004.
4. Selection
In species with large families the management of the pedigree to minimise ΔF can be combined with appropriate selection within families, so that some genetic gain
is made. However in many commercial breeding schemes this rate of gain ΔG will be insuicient and alternative approaches are required that manage diversity in the
presence of some degree of selection between families. In the management of diversity for such schemes, both selection and mating can play a role, however it is useful to
separate these processes since whilst the principles of managing the selection are well understood, those underpinning mating are less advanced.
As stated previously the objective for pure conservation is clear: in each generation every individual should have a long-term contribution equal to those of its contemporaries.
However by deinition any degree of selection between families will give contributions that vary and in efective breeding schemes, this variation will be related to the Mendelian
sampling term denoted a of the individuals. his is evident from the equation for ΔG analogous to Equation 7.1, showing that it is equal to the sum of cross products of long-
term contributions and Mendelian sampling terms Woolliams and hompson, 1994; Woolliams
et al., 1999: ΔG = Σ ra
Eq. 7.2 Why cross products with Mendelian terms and not breeding values denoted A? his
is because the Mendelian terms are the unique contributions of individuals, whereas
156 Utilisation and conservation of farm animal genetic resources
John Woolliams
the breeding value is an aggregation of the individual’s Mendelian term and those of its ancestors, so substituting A for a in Equation 7.2 would result in double counting.
Grundy et al. 1998 predict that as a consequence of Equations 7.1 and 7.2, breeding
schemes optimised to maximise gain for the same rate of inbreeding should allocate long-term contributions of individuals in relation to their estimated Mendelian
sampling term, a prediction conirmed by Avendaño et al. 2004, as described below.
Consequently the target contribution will change over time partly because estimates of genetic merit change, with errors reducing in magnitude as more information becomes
available over time. his is not the only source of uncertainty in desired contribution: even if the breeding value of all individuals is always known with full accuracy, the desired
contribution of an individual parent will change as the genetic values of the ofspring become known, since their contributions cannot be determined independently without
changing the long-term contribution of the parent remember
r
parent
= ½ Σ r
ofspring
.
4.1. Optimum contributions: The problem
his is commonly referenced as Meuwissen 1997, although similar approaches were previously published by other authors see Woolliams
et al. 2002 for a more detailed history. he approach solves the problem of managing diversity in the
course of selection by inding the solution to the following: maximise c
T
g , subject to
ive constraints: ½c
T
Ac ≤ F, c
T
s = ½, c
T
d = ½, h ≤ c and c ≤ m, where c is a vector
of candidate contributions to the next generation, s and d are indicator vectors for
Box 7.1. Mendelian sampling terms. For all autosomal DNA, half the genes come from the sire and half the genes come from the
dam, and moreover the half that passed from each parent to the ofspring are chosen at random. herefore the expected breeding value of the ofspring A
of
is the average of the breeding values of its sire A
sire
and dam A
dam
, i.e. E[A
of
] = ½ A
sire
+ ½ A
dam
, where E[ ] denotes an expectation. Expressing this as a linear regression gives A
of
= ½ A
sire
+ ½ A
dam
+ a, where a is the
deviation of the ofspring from the average of its parents, and is called the Mendelian sampling term, with E[
a] = 0. We can also calculate the variance of a by considering the variance of both sides of the formula for A
of
, with the result that Var[ a] = ½1− ασ
A 2
where α is the deviation from random mating and σ
A 2
is the genetic variance in the base population prior to selection. herefore, for random mating, the Mendelian sampling term makes up ½ the genetic variation in
the base. he Mendelian sampling term arises because the actual alleles passed by each parent will vary from ofspring to ofspring, due to sampling among the two alleles it carries at each locus. he
term is important because it makes each individual unique, not just the average of its parents, and is the source of genetic variance within families, making full-sibs diferent from each other.
