What is genetic diversity?

68 Utilisation and conservation of farm animal genetic resources John Woolliams and Miguel Toro therefore show patterns of regions of high diversity punctuated by regions of relatively low diversity. his pattern of diversity within the genome is called a selection footprint and may indicate loci important for domestication, or for the characteristics of particular breeds e.g. Wiener et al., 2003, or simply highly-conserved regions for the genus as a whole, whether wild or domesticated. hese regions will be further discussed in more detail in chapter 4. Efective searching for selection footprints is only just beginning in livestock species with the availability of dense, afordable, genome-wide markers such as SNPs. More generally, the expansion in DNA information will allow the diversity of allelic combinations at loci distributed throughout the genome to be studied. his type of diversity within breeds will depend not only on the allele frequencies but also on the extent of linkage disequilibrium LD that is observed. his LD may arise from the breed history of census size and management over time, including bottlenecks or introgression. However this form of diversity, both between and within breeds, may indicate the presence of epistatic interactions afecting performance. In summary, the study of genetic diversity will extend to diferences in genomic patterns between and within breeds.

6. Measuring changes in diversity

So far we have simply considered measuring the amount of diversity present in a population. his will relect events in the history of the population or the breed, oten long ago, and the information on the diversity may illuminate the breed origins. However, sustainable management of genetic resources is concerned with managing the diversity that is present today. It is important to realise that some genetic variation is inevitably lost in each generation due to the inherent randomness in the passing of alleles from parent to ofspring. It is impossible to ensure that every distinct variation at each of ~ 3x10 9 base pairs of a genome can be replicated in the individuals selected as replacements for the current generation. Nevertheless in each generation there is potentially new variation entering the population as a result of mutation, immigration if the population is not closed or the inluence of epistatic interactions uncovering new variations Carlborg et al., 2006 in selected populations. herefore the sustainable management is more concerned with maintaining the expected rate of loss of existing variation to a sustainable level, justiied in more detail by Woolliams et al. 2002. herefore what is required is a means of measuring or predicting the rate of loss. he important concept in measuring the rate of loss is the idea of inbreeding. To measure inbreeding we identify a reference point in the history of a population, called the base generation, when we assume that all the alleles at an assumed neutral locus Utilisation and conservation of farm animal genetic resources 69 Chapter 3. What is genetic diversity? in this generation are identiiably diferent. his is of course unrealistic, but these assumptions provide the necessary conceptual framework to predict the real changes in diversity that we observe with time Every individual born ater the base generation will then have an ‘inbreeding coeicient’ determined by its pedigree, as described in Box 3.6, and these coeicients will directly determine the expected loss of diversity relative to the base generation. he following points are important for considering inbreeding. For a single population derived from a base generation at t=0, and where σ A 2 t, Ht and Ft denote the values of σ A 2 , heterozygosity at time t, and mean inbreeding coeicient at time t: 1. he rate of inbreeding, ΔF = [Ft − Ft-1][1− Ft-1] is a multiplicative deinition, and is constant for a population of constant size and subject to a constant selection regime. Note Ft−Ft-1 is not constant in this case. 2. Equivalently ΔF = [Ht-1−Ht]Ht-1, i.e. the fractional loss of heterozygosity in a generation. 3. It is expected that Ht = [1−Ft] H0 i.e. heterozygosity will decrease if averaged over many lines inbred from the same population. However the process is a random one and heterozygosity may increase or decrease if observed in only a single line. 4. For a trait where σ A 2 0 = σ G 2 0, it is expected that σ A 2 t = [1−Ft] σ A 2 0. However as with item 3 it is an expectation not a rule. 5. Where σ A 2 0 = σ G 2 0, the genetic variance between isolated sub-populations drawn from the same base generation is given by 2Ftσ A 2 0. Since an allele’s frequency is a trait where σ A 2 0 = σ G 2 0, this observation shows that the frequency of a neutral allele will drit away from the initial frequency with accumulated variance 2Ftσ A 2 0, and this variance is called the drit variance. his drit over time of allele frequencies makes it feasible that alleles will either be lost or ixed in a population; in fact over a suiciently long and indeinite period, it is certain that an allele will either become lost or ixed. Items 1 to 5 indicate that changes in some important measures of diversity per unit of time are described by ΔF. It will be explained in chapter 7 that many aspects of sustainable management within breeds will depend on managing ΔF, and so this parameter is very important. Chapter 7 will also explore some predictive formulae appropriate for diferent conditions. ΔF is oten reported as a transformed value called the ‘efective population size’, Ne = [2ΔF] -1 , where ΔF is the rate of inbreeding measured over 1 generation of the population. In general, for most livestock populations the number of parents will greatly exceed the calculated value of Ne, however the justiication for its use is that Ne diploid single-sex individuals would have an identical ΔF if they were subject to random selection and 70 Utilisation and conservation of farm animal genetic resources John Woolliams and Miguel Toro random mating including seling with no limitations on family size. his analogous population is oten called the ‘idealised population’, but it is very misleading to consider other genetic properties of the idealised population as being analogous to the real one herefore efective population size is a useful device for visualising what a rate of Box 3.6. Inbreeding coeicients and examples he inbreeding coeicient is deined with reference to a base generation in which all the individuals are assumed unrelated and that all the alleles in the base generation are considered distinct. hus for a base generation with a total of N parents, there are 2N distinct alleles, since each parent carries 2 alleles. he inbreeding coeicient, F, of an individual is then deined as the probability that for a randomly-chosen neutral locus the two alleles carried by the individual are identical by descent, i.e. copies of the same allele from the base population. here are a number of properties of inbreeding coeicients arising from this deinition: 1. F is a probability and so 0 ≤ F ≤ 1. 2. F = 0 for individuals in the base generation, by deinition 3. For species with no seling, F 0 only when there is a common ancestor in the pedigree of the sire and the pedigree of the dam; equivalently, F 0 when there is a loop in the genealogical tree of the individual’s pedigree. As an example of calculation consider the pedigree below. U V W X Y Z Base generation, t=0 t=1 t=2 F = 0 for ‘U’, ‘V’, ‘W’, ‘X’, ‘Y’. For ‘Z’, ‘V’ is an ancestor common to both sire and dam so F 0, with a loop deined by ‘V’ → ‘X’ → ‘Z’ → ‘Y’ → ‘V’. If ‘Z’ has two copies of the same allele from the base, then three events must all have occurred: a ‘V’ must have passed the same allele to both ‘X’ and ‘Y’, which occurs with probability ½; b this allele must have been passed to ‘Z’ by ‘X’, which occurs with probability ½; and c this allele must have been passed to ‘Z’ by ‘Y’, which occurs with probability ½. herefore the probability that ‘Z’ has two alleles that are identical by descent is ½ x ½ x ½ = 18. he methodology for calculating inbreeding coeicients in complex pedigrees will not be given here and readers are referred to Falconer and Mackay 1996 and literature describing the calculation of the numerator relationship matrix. Inbreeding coeicients steadily increase in a closed population over time, towards 1.