L567, Evolution, Indiana University
Prepared by C. Lively
1
TAYLOR AND FRANKS MODEL FOR KIN SELECTION
Let
y
be the phenotype of our focal (or target) individual
Let
z
be the mean phenotype in the population.
Keep in mind that a
change in
y
might also change
z
.
Also keep in mind that individual
fitness is affected by the mean phenotype in the population,
z
.
Thus,
individual fitness could be a function of both
y
and
z
.
W
i
=
f
(
y
,
z
)
.
Now let
x
be the genic value or breeding value underlying the
phenotype,
y
, of our focal individual.
We want to know how individual fitness (
W
i
) is affected by changing
x
.
In other words we want to know
dW
i
dx
’
which is the change in fitness with respect to the change in
x
.
(Note
we have the total derivative here.)
By the chain rule, we get
dW
i
dx
=
!
W
i
!
y
dy
dx
+
!
W
i
!
z
dz
dx
Have a close look at the righthand side of the equation.
The red part
(
dy
/
dx
) takes into account how the phenotype,
y
, changes with the
genotype,
x
.
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 Fall '10
 Curtis
 Derivative, Evolution, Ratio, WI, Kin selection, Pun

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