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