Adaptive Landscape
range of environmental conditions tolerated
. . . can be broken into 2n+1
sub-ranges,
. . . where n = number of genes
or chromosomes.
with p = q:
| n = 1 |
| .25 |
.50 |
.25 |
| AA |
Aa |
aa |
| n = 2 |
| .0625 |
.2500 |
.3750 |
.2500 |
.0625 |
| AAAA |
AAAa |
AAaa |
Aaaa |
aaaa |
| n = 3 |
| .015625 |
.093750 |
.234375 |
.312500 |
.234375 |
.093750 |
.015625 |
| AAAAAA |
AAAAAa |
AAAAaa |
AAAaaa |
AAaaaa |
Aaaaaa |
aaaaaa |
However, if p is not equal to q:
| |
n = 1 |
|
| p |
AA |
Aa |
aa |
q |
| 0.1 |
0.01 |
0.18 |
0.81 |
0.9 |
| 0.2 |
0.04 |
0.32 |
0.64 |
0.8 |
| 0.3 |
0.09 |
0.42 |
0.49 |
0.7 |
| 0.4 |
0.16 |
0.48 |
0.36 |
0.6 |
| 0.5 |
0.25 |
0.50 |
0.25 |
0.5 |
| 0.6 |
0.36 |
0.48 |
0.16 |
0.4 |
| 0.7 |
0.49 |
0.42 |
0.09 |
0.3 |
| 0.8 |
0.64 |
0.32 |
0.04 |
0.2 |
| 0.9 |
0.81 |
0.18 |
0.01 |
0.1 |
assumptions of the Hardy-Weinburg...
. . 1) mating is random,
. . 2) there is no selection,
. . 3) there is no mutation,
. . 4) there is no immigration nor
emmigration, and
. . 5) the population is arbitrarily large
(infinite)
However, in the Real World, these five assumptions
are not met;
. .. so the task becomes estimating which
of the five
. . . has the most influence on the
observed results.
. . 1) if mating is non-random,
. . . -is mathematically complex, or
. . . . requires simulation studies
. . 2) if there is selection,
. . . -multiply the Hardy-Weinburg values by
fitness
. . . . {AA, Aa, aa} =
{wAA*p2,
wAa*2pq,
waa*q2}
. . 3) if there is mutation,
. . . -is mathematically complex, or
. . . . requires simulation studies
. . 4) if there is immigration or
emmigration, and
. . . -is mathematically complex, or
. . . . requires simulation studies
. . 5) if the population is small
(finite)
. . . -requires simulation studies
We do not currently have the mathematics necessary
to solve these problems.
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© 2004 Prof. LaFrance, Ancilla College