Measures of Genetic Distance

1. Measures of Genetic Distance M.B. McEachern, W. Savage, S. Hooper, S. Kanthaswamy

2. Genetic Distance (D) • Quantitative measure of genetic divergence between two sequences, individuals, or taxa • Relative estimate of the time that has past since two populations existed as a single, panmictic population • Units of D depend on the kind of molecular data collected (allozymes, nucleotide sequences, etc.)

3. 3 Most Commonly used Distance Measures • Nei’s genetic distance (Nei, 1972) • Cavalli-Sforza chord measure (Cavalli-Sforza and Edwards, 1967) • Reynolds, Weir, and Cockerham’s genetic distance (1983) • Nei’s assumes that differences arise due to mutation and genetic drift, C-S and RWC assume genetic drift only

4. Nei’s Genetic Distance • D = -ln I where I = Σxiyi / (Σxi2Σyi2)0.5 • For multiple loci, use the arithmetic means across all loci • Interpreted as mean number of codon substitutions per locus

5. Assumptions for Nei’s Distance • IAM • All loci have same rate of neutral mutation • Mutation-genetic drift equilibrium • Stable effective population size

6. Cavalli-Sforza Chord Distance • populations are conceptualised as existing as points in a m-dimensional Euclidean space which are specified by m allele frequencies (i.e. m equals the total number of alleles in both populations). The distance is the angle between these points: • xi and yi are the frequencies of the ith allele in populations x and y • Assumes genetic drift only (no mutation) • Geometric distance b/w points in multi-dimensional space

7. Reynold’s Distance • Assumes IAM • Developed for allozyme data on small populations and assumes genetic drift is only force operating on allelic frequencies (i.e. no mutation) • Based on the coancestry coefficient, θ D = -ln(1-θ)

8. What is Coancestry? • Degree of relationship by descent between two individuals • Probability that a randomly picked allele from one individual is IBD to a randomly picked allele in another individual

9. Testing Significance of Distance Measures • Bootstrap: generation of many new data sets by resampling original data with replacement • For each bootstrap data set, obtain estimates of parameters of interest and their variances • Generates confidences intervals of parameter estimates

10. Phylip • Computes Nei’s, C-S, and Reynold’s genetic distances using GENDIST (we will do this in lab today) • Uses Bootstrap to generate confidence intervals (but we don’t know how to view that output) • Other programs that estimate distance: TFPGA, GDA, Popgene, DISPAN

11. Lots of other Distance Measures! • Euclidean distance • Shared allele distance • Roger’s distance • Goldstein distance (for microsatellites)

12. In Lab Today: • Use Phylip to estimate genetic distance for Bear data • AMOVA using Arlequin