The use of pedigree for measuring diversity
Utilisation and conservation of farm animal genetic resources 65
Chapter 3. What is genetic diversity?
genetic variation is additive i.e. σ
A 2
= σ
G 2
. Note that in this approach the breed mean is the estimate of the allele frequency for the breed. As an example, if two breeds are
ixed for diferent alleles then no diversity will be observed within breeds and all the diversity will lay between breeds. his is expanded upon below in paragraph 6 and
in chapter 4.
2. he breed means for the frequencies of several alleles, usually from unlinked loci, are combined by some pre-deined function to measure what is called a genetic
distance between the breeds. here are several such distance measures chapter 5 and they oten difer in principle from 1 because no explicit consideration is made
of variance within breeds. his will be expanded upon in chapter 5.
3. Instead of using gene frequency, the frequency of heterozygotes may be measured. A heterozygote has two diferent alleles at a locus, and is function of the allele frequencies
and non-randomness of mating and survival rates. he justiication for this is that in the absence of diversity there will be no heterozygotes in the population. Providing
mating is at random, the heterozygosity increases with the number of alleles found in the population and with decreasing variation among the allele frequencies for the
population. he assumption of random mating is important and is oten assumed to hold within a breed but deviations can be signiicant, particularly if there is relatively
little exchange among breeders. If genotype data is available, the assumption of random mating can be tested by looking at the magnitude and signiicance of
departures from Hardy-Weinberg equilibrium Falconer and Mackay, 1996; Lynch and Walsh, 1998. Nevertheless in the absence of random mating, both the observed
and expected heterozygosity can be informative for studying diversity.
Whatever result is calculated for the heterozygosity it will depend on the sample of loci used, and extension to inferences about the entire genome are diicult.
For example, Toro et al. 2006 describes a remark attributed to Nei, that a irst
approximation to the correlation between the heterozygosity of a sample of r loci and a genome of n loci is rn
12
i.e. for a sample of 20 loci from 20,000 the correlation might be expected to be 0.03. herefore reliable comparisons between breeds must
be made on very dense sets of markers, which may be possible in some species, such as cattle where DNA chips can contain in excess of 50,000 markers.
4. A further simple but limited measure of diversity is counting the number of diferent alleles appearing in the population for a set of loci, with the more alleles the more
diverse. Counting the number of alleles in each breed and the number shared with each other breed ofers an opportunity of examining diferences between breeds.
A variation on this is to count the number of ‘private alleles’, where a ‘private allele’
66 Utilisation and conservation of farm animal genetic resources
John Woolliams and Miguel Toro
is deined as an allele found in one breed but in no other. However the heuristic diversity between breeds will be determined not only by whether or not alleles are
shared between breeds but also by whether those shared are at similar frequencies within each breed. herefore the counting approach to measuring diversity appears
less valuable than measuring the allele frequencies themselves. Nevertheless observations on private alleles can be very useful in other ways, for example in
traceability schemes.
he items 1 to 4 above give some simple ideas about how molecular diversity might be measured. It is a reasonable question to ask what the relationship between molecular
and quantitative measures of variation might be, and whether these tell the same or diferent stories. he answer appears to suggest that the stories are not the same: in a
meta-analysis Reed and Frankham 2001 suggest that the mean correlation between molecular and quantitative estimates of diversity is weak 0.22 ± 0.05, indicating that
molecular measures of diversity only explain 4 of the variation in quantitative traits. his estimate will include studies that pre-date much of the explosion of molecular data,
with the design shortcomings that follow from this limitation. herefore the question remains open and it is very possible that as dense genome information becomes more
available over the next decade, and we gain experience in interpreting it, then our predictions may should improve.