Paralog diversity

Following Innan (Genetics 2003 163:803-810), these statistics are specifically designed to compute nucleotide diversity for each paralog in a multigene family ($\pi_w$), as well as between-paralog divergence for all pairs ($\pi_b$). They are availabled from the function stats.paralog_pi().

For a given paralog, we have:

$$\pi_w = \sum_i^L \frac{2}{n_i (n_i-1)}k_i$$

with $L$ the number of sites, $n_i$ the number of exploitable samples for this paralog at site $i$ and $k_i$ the number of pairwise differences at this site.

And for a given pair of paralogs:

$$\pi_b = \sum_i^L \frac{d_i}{n_{ai} n_{bi}}$$

with $d_i$ the number of differences between the two paralogs and $n_{ai}$ and $n_{bi}$ the respective numbers of exploitable samples for the two paralogs at site $i$.