Utilisation and conservation of farm animal genetic resources 71
Chapter 3. What is genetic diversity?
inbreeding may mean in an approachable way. Beware, do not accept any other deinition for Ne other than Ne = [2ΔF]
-1
, even if stated in a scientiic publication or text book − they are wrong and potentially very misleading See Box 3.7 for a description of issues
surrounding the use of Ne.
7. Relating diversity measures to F and ΔF
If we re-examine the measures of diversity described in paragraph 4, we may use the inbreeding framework of paragraph 6 to inform our inferences in a number of ways:
1. Heterozygosity at an initial point will be completely determined by the allele frequencies at the chosen loci and prior breed history, but the change in heterozygosity
is related to ΔF and the number of generations over which the change is measured. he observed heterozygosity and change in heterozygosity as measured by markers is
Box 3.7. Pitfalls in efective population sizes. 1. A common unit of time in considering livestock populations is the year, since for many species
and for many farmers it constitutes the length of the husbandry or economic cycle. However the populations are renewed at diferent rates called the generation interval Falconer and
Mackay, 1996, and for common livestock species this may be much longer e.g. ~3 years for sheep, ~6 years for cattle, ~10 years for horses. Data over time will oten appear in units of
years, and consequently when estimating ΔF the parameter will then appear as scaled per year, say ΔFy. It would be tempting, but dangerous to calculate Ney = 1[2ΔFy]. It is
more appropriate to calculate Neg = 1[2ΔFg] where 2ΔFg is the rate of inbreeding per generation, since this more truly relects the expected loss of diversity incurred in replacing
a generation. For a generation of L years ΔFg ≈ L ΔFy, and Neg = 1[2LΔFy]. he impact of this can be seen by considering a horse population where L = 10 years and ΔFy
= 0.0025, and a pig population where L = 1 year and ΔFy = 0.01. For these, Ney = 200 and 50 for horse and pigs respectively, whereas Neg = 20 and 50 respectively. Comparison
of Ney suggests the population at greater genetic risk is the pigs, yet comparison of Neg makes it clear that the population subject to greatest genetic risk is the horse population. See
chapters 7 and 8 for further discussion of generation interval.
2. It is common and erroneous to give an unqualiied deinition of Ne = 4MF[M+F] where M
and F are the numbers of male and female parents. From the correct deinition of Ne this is equivalent to stating ΔF = [8M]
-1
+ [8F]
-1
, a predictive formula derived by Wright 1969 that is
only appropriate where there is random selection and mating among the 2 sexes with unrestricted family sizes. Such a situation rarely applies and very frequently such an estimate
will be a gross underestimate of ΔF.
72 Utilisation and conservation of farm animal genetic resources
John Woolliams and Miguel Toro
subject to considerable sampling error and, consequently, the change in inbreeding coeicient may be low. Hence changes in heterozygosity are not particularly robust
for measuring efective population size, although studies such as Daetwyler et al.
2006 show that observed heterozygosity in ield populations has the expected relationship with Ft as stated in paragraph 6.3.
2. he diversity in allelic frequency between and within breeds can be related to inbreeding providing we assume that at some time in the past the group of breeds
that are being studied are all derived from the same base population, and that all the alleles were present in the base population, and are assumed to be neutral in all
populations involved. his second assumption is strong. An allele may be present in one group of breeds but absent in another group because 1 the allele was
present in the base but has been lost in some breeds see paragraph 6 item5. 2 an allele appeared as a mutation in a breed that contributed to the development of
one group of breeds but not to the other group, or 3 a mutation occurred several times in diferent breeds. he likelihood of these diferent options will depend on
how far back to the common base, and what type of marker, since some marker types, such as microsatellites Box 3.3, may be subject to faster mutation rates than
others making it more likely that some alleles will have appeared in recent times. In livestock, hitch-hiking associated with selection Maynard-Smith and Haigh, 1974
may raise questions on the extent of neutrality over anonymous DNA markers over long periods of time.
However, if these assumptions are made, we can relate the observed σ
B 2
for allele frequencies to the value of 2Ftσ
A 2
0 see paragraph 6 item5, where σ
A 2
0 is an estimated genetic variance for allele frequency in the presumed base generation,
and Ft is the estimated inbreeding of the populations relative to a base from which the breeds are assumed to be distinct sub-lines. his concept leads ater
further development to the measure of breed relationships called F
ST
developed in chapter 5, which decomposes the estimated inbreeding of two individuals from
two breeds into that part of the inbreeding process shared by two breeds, and the remainders.
3. In Box 3.2 the concept of variation between breeds in performance traits was explored. his estimate of breed variation is based upon the observed variation
present now and tells us how much performance may be improved or reduced from breed substitution. However McKay and Latta 2002 review Q
ST
, a measure of breed relationship developed by treating the observed genetic variation between and within
breeds for quantitative traits as if it were derived by drit from a base population, i.e. analogous to the development of F
ST
for the variation in allele frequency. he
