Why measure genetic diversity?

Utilisation and conservation of farm animal genetic resources 109

Chapter 5. Measuring genetic diversity in farm animals

have an efect on the distribution of genetic variation between and within populations, an efect that may not be concluded from the tree presentation. On the other hand, migration between populations is relected as smaller distances. While this leads to errors in the estimated phylogeny, it is nonetheless a good indicator of the closeness of populations. It does not, however, correctly place the shared ancestor. Trees from drit- based genetic distances should not be interpreted as actual phylogeny. Box 5.2. Constructing trees. Example of the construction of a tree using UPGMA. Although NJ, in general, gives better results, UPGMA is more suitable for illustrating the process. Suppose we have four breeds A, B, C and D. he distances between them are given below. B C D A .400 .300 .500 B .200 .100 C .300 We start with the pair of breeds that is closest to one another. he closest pair is B, D. herefore we next calculate the distances between the cluster B,D and A or C as the average of A’s distance to B and D. herefore distance B, D, A = ½.400 +.500=.450 B,D C A .450 .300 B,D .250 Again we ind the smallest distance between B, D and C and recalculate the distance between this cluster and A giving B, D, C, A =.375. he resulting unrooted tree is drawn below. he branches are drawn in such a way the lengths of the branches between two breeds sum up to the distance given above. A B C D 110 Utilisation and conservation of farm animal genetic resources Herwin Eding and Jörn Bennewitz

2.2. F-statistics

Random drit is seen between populations as diferences in allele frequencies and loss of diferent alleles. herefore the efects of drit within and between populations are in opposite direction: Within populations genetic diversity will be lost, while between populations genetic diferentiation will increase. his phenomenon is formulated in the well-known expression of Wright’s F-statistics Wright, 1969: e well-known expression of Wright’s F-statistics ST IS IT F F = F 1 1 1 ¦ on is proportional to 1 – Falconer and population component 1 – and a between population component 1 – ponent estimated by 1 – where F IT is the inbreeding coeicient of an individual relative to the whole set of populations, F IS is the inbreeding coeicient of an individual relative to the sub- populations it belongs to and F ST is the mean inbreeding coeicient of sub-population relative to the entire population. Note that this expression assumes that a set of populations under study are descendant or sub-populations of one population. he inbreeding coeicient F in a population can be computed from the diferences between expected and observed homozygosity: e well-known expression of Wright’s F-statistics 2 p HOM i i exp ¦ on is proportional to 1 – Falconer and ulation component 1 – and a between population component 1 – ponent estimated by 1 – and e well-known expression of Wright’s F-statistics exp 1 Hom F F HOM obs ¦ on is proportional to 1 – Falconer and population component 1 – and a between population component 1 – ponent estimated by 1 – Since the decrease in genetic variance in a population is proportional to 1 – F Falconer and Mackay, 1996, Wrights expression can be used to partition the total genetic variance of populations into a within population component 1 – F IS and a between population component 1 – F ST . Proportions of genetic variation between and within populations are obtained by dividing these by the total variation component estimated by 1 – F IT . Within a population, F IS is usually estimated from the excess of homozygotes or reversely, the deicit of heterozygotes: S obs S IS et H Het et H = F where where S et H i is the mean of expected heterozygosities in populations. Multiple estimates over loci are averaged to obtain a mean estimate. Wright’s F ST statistic is a popular