q)
[read as "delta q"]
in consequence of differences in the relative fitness (W)
of the phenotypes to which the alleles contribute.
If:
variation exists for some trait, and
a
fitness difference is correlated
with that trait, and
the
trait
is to some degree heritable
(determined by genetics),
Then:
the
trait distribution will change
over
the
life history of organisms in a single generation, and
between
generations.
The process of change is called "adaptation".
Or, "Natural
Selection" describes a process in which
"adaptation" occurs in such a way that "fitness"
increases.
Under
certain
conditions, this results in descent with modification.
Evolution & Natural Selection can be modeled genetically.
Natural Selection results in change
of allele frequency (q)
[read as "delta q"]
in consequence of
differences
in the relative
fitness (W)
of the phenotypes to
which the alleles contribute.
Fitness is a
phenotype
of individual organisms.
Fitness is determined genetically (at least in part).
Fitness is related to success at survival AND reproduction.
Fitness can be measured & quantified (see below).
i.e., the relative fitness of genotypes can be assigned
numerical
values.
The consequences of natural selection
depend
on the dominance of fitness:
e.g., whether the "fit" phenotype is due to a dominant or
recessive
allele.
Then, allele frequency change is predicted by the General Selection Equation:
q
= [pq] [(q)(W2 - W1) + (p)(W1 - W0)]
/
where
W0,
W1,
& W2
are the fitness phenotypes
of
the
AA, AB, & BB genotypes,
respectively
[see derivation]
genotype:
AA AB BB
phenotype:
W0
= W1 
W2 (AA and AB have
identical
phenotypes)
Then the
GSE
simplifies to q
= pq2(W2 - W1)
(since W1 - W0 = 0)
If
'B' phenotype is more fit than 'A' phenotype,
W2 > W1 & q
> 0 so q increases.
If
'B' phenotype is less fit than 'A' phenotype,
W2 < W1 & q
< 0 so q decreases.
then q 
(W2 - W1)
: the greater the difference in fitness,
the
greater
the intensity of selection
and the more rapid the change
A numerical
example
of Selection:
Tay-Sachs Disease is caused by an allele
that
is
rare (q
0.001)
recessive (W0 = W1 = 1)
lethal (W2
= 0)
Then q
= pq2(W2 - W1) = -pq2
-q2
(since p 1)
That
is,
Natural Selection results in a decrease in the
frequency
of
the
Tay-Sachs
allele of about one part in a million (0.0012)
per
generation
s = 1 - W
The
selection coefficient (s)
is the difference in fitness
of
the
phenotype relative to some 'standard' phenotype
that
has
a fitness W = 1
[The
math
is simpler because only one variable is used for fitness.]
(1) Complete dominance
genotype:
AA AB BB
phenotype:
W0 = W1
W2 (AA and AB have
identical
phenotypes)
or
1
=
1 1
- s
if
0
< s < 1 : 'B' is deleterious(at
a
selective
disadvantage)
if
s
< 0 : 'B' is advantageous
then q
= -spq2 / (1 - sq2)
[see derivation]
(2) Incomplete dominance
genotype:
AA AB
BB
phenotype:
W0
W1
W2 (all phenotypes different)
or
1
- s1
1 1
- s2
if 0
<
s1
& s2 < 1 : overdominance
of
fitness (heterozygote advantage)
The
population
has optimal fitness when
both alleles are retained:
q will reach an equilibrium
where q = 0
0
< 
<
1
(read as, "q hat")
then =
(s1) / (s1 + s2)
[see derivation]
Direction
of allele frequency change is due to fitness
difference
of alleles
(whether
the
effect of the allele on phenotype is deleterious or
advantageous).
Ultimate
consequences depend on the dominance of
fitness
(whether
the
allele is dominant, semi-dominant, or recessive).
Rate
of change is an interplay of both of these factors (see Lab
#1)
AA
AB BB Consequence
of
natural
selection [ let q
= change in f(B) ]
W0
= W1 = W2 No
selection (neither allele has a
selective
advantage):
then q
= 0, H-W proportions remain constant
W0
= W1 > W2 deleterious
recessive (advantageous dominant):
then q
< 0, q 
0.00 (loss): how fast? [Does
it get there?]
W0
= W1 < W2 advantageous
recessive (deleterious dominant):
then q
> 0, q
1.00 (fixation): how fast?
W0
< W1 > W2 overdominance
[special case of semi-dominance]:
heterozygote
superiority
q 
, where q = 0