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:
n
ˉ
=
∑
i
=
1
r
n
i
r
,
n
c
=
(
r
n
ˉ
−
∑
i
=
1
r
n
i
2
r
n
ˉ
)
(
r
−
1
)
,
p
lu
˜
=
∑
i
=
1
r
n
i
p
ilu
˜
r
n
ˉ
,
α
il
˜
=
1
−
∑
u
=
1
v
1
p
ilu
2
˜
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
least squares 𝛉 estimator :
θ
L
˜
=
2x
+
y
−
z
±
(
z
−
y
)
2
+
4x
2
2
(
y
−
z
)
tilde{%theta }_{L} = {2x+y-z +- sqrt{( z-y) ^{2}+4x^{2}}} over {2( y-z) }
where:
z
=
∑
l
=
1
m
a
l
2
z= sum ^{m}_{l=1}a_{l}^{2}
,
x
=
∑
l
=
1
m
a
l
b
l
x= sum ^{m}_{l=1}a_{l}b_{l}
and
y
=
∑
l
=
1
m
b
l
2
y= sum ^{m}_{l=1}b_{l}^{2}
.
to check which of the two solutions for ̃𝛉
L provides the minimum, the residual sum of squares, R, should be calculated for each where:
R
=
(
2x
+
y
+
z
)
θ
L
2
˜
−
2
(
x
+
z
)
θ
L
˜
+
z
1
−
2
θ
L
˜
+
2
θ
L
2
˜
R={ ( 2x+y+z ) tilde{%theta }_{L}^{2}-2 ( x+z ) tilde{%theta }_{L}+z} over {1-2 tilde{%theta }_{L}+2 tilde{%theta }_{L}^{2}}