Reynold's genetic distance for short-term evolution (1983) [Reynolds, J. 83]
DReynold=−ln(1−θ)DReynold = -ln (1 - %theta)
the following notation is used, for all 𝚹 estimators:
nˉ=∑i=1rnir,nc=(rnˉ−∑i=1rni2rnˉ)(r−1),plu˜=∑i=1rnipilu˜rnˉ,αil˜=1−∑u=1v1pilu2˜bar n = sum _{i=1} ^r {{n_i} over r } , n_c = (r bar n - sum _{i=1} ^r {n^2 _i over {r bar n}}) over (r-1), tilde p _lu = sum _{i=1} ^r {n_i tilde p _ilu} over {r bar n},
tilde %alpha _il = 1 - sum ^{v_1} _{u=1} tilde p _ilu ^2
unweighted average of single-locus ratio estimators, ̃𝛉
U:
θU˜=1m∑l=1mθl˜tilde %theta _U = 1 over m sum from l=1 to m tilde %theta _{l}
, with θl=alal+bl%theta _{l} = {a_l} over {a_l + b_l}. The estimates of the components of variance of interest for the lth locus are within populations, r is the number of populations examined:
bl=2∑i=1rniαil˜r(2nˉ−1)b_l = 2 sum from {i=1} to r {{ n_i tilde %alpha _{il}} over {r(2 bar n - 1)}}
and between populations:
al=[2∑i=1rni∑u=1vl(pilu˜−plu˜)2−(r−1)bl]2(r−1)nca_{l}= {[
2 sum ^{r}_{i=1} n_{i} sum ^{v_{l}}_{u=1} ( tilde{p}_{ilu} - tilde{p}_{lu}) ^{2} - ( r - 1) b_{l}]
} over {2 (r - 1) n_c}
When there are just two populations, r = 2, the usual genetic distance situation obtains, and the most convenient computing formulas for the variance components are (used in Populations)
al=12∑u(p1lu˜−p2lu˜)2−(n1+n2)(n1α1l˜+n2α2l˜)4n1n2(n1+n2−1)a_{l}={1} over {2} sum _{u} ( tilde{p}_{1lu}-tilde{p}_{2lu}) ^{2} - {( n_{1}+n_{2}) ( n_{1} tilde{%alpha }_{1l}+n_{2} tilde{%alpha }_{2l}) } over {4n_{1}n_{2} ( n_{1}+n_{2}-1 ) }
al+bl=12∑u(p1lu˜−p2lu˜)2+(4n1n2−n1−n2)(n1α1l˜+n2α2l˜)4n1n2(n1+n2−1)a_{l}+b_{l} = {1} over {2} sum _{u} ( tilde{p}_{1lu}- tilde{p}_{2lu}) ^{2} + {( 4n_{1}n_{2}-n_{1}-n_{2}) ( n_{1} tilde{%alpha }_{1l}+n_{2} tilde{%alpha }_{2l}) } over {4n_{1}n_{2} ( n_{1}+n_{2}-1) }