1 Theta (\( \theta \))
Population genetics, under neutral Wright-Fisher Model (neutral Wright-Fisher model), a scale parameter
\ (\ Theta = 4N \ mu \)
For each mutation average twice the number of generations. Wherein, \ (N \) is the effective population size (effective population size), \ ( \ mu \) for each individual mutations generation rate ( Klein et Al. 1999 ).
2 Watterson's estimator
Watterson GA (1975) Theoretical Population Biology 7:256-276
Carlson CS, et al. (2005) Genome Res 15: 1553-1565
\( \theta = \frac{S}{ \sum_{i=1}^{n-1} \frac{1}{n} } \)
Wherein, (S \) is the number of separate sites (segregating site) \, \ (n \) is the number of individuals.
2.1 computing
vcftools --vcf geno.vcf --SNPdensity 100000
\( \theta_w = \frac{SNP\_COUNT}{\sum \frac{1}{1} + \frac{1}{2} + ... + \frac{1}{n-1}} \)
3 Nucleotide diversity
Nei M, Li WH (1979) PNAS 76: 5269-5273
Carlson CS, et al. (2005) Genome Res 15: 1553-1565
\( \pi = \sum_{ij} x_i x_j \pi_{ij} \)
Wherein, \ (x_i \) for the first \ (I \) frequency sequence, \ (π_ {ij} \) for the first \ (I \) sequence and \ (J \) differences between nucleotide sequences number (the number of nucleotide differences).
3.1 computing
vcftools --vcf geno.vcf --site-pi vcftools --vcf geno.vcf --window-pi 100000 --window-pi-step 25000