q) [read "delta q"]
in consequence of differences in relative fitness (W)
of phenotypes to which alleles contribute.
If:
variation exists for some
trait, and
a fitness difference is
correlated with that trait, and
trait
is
to some degree heritable
(determined by genetics),
Then:
trait distribution will change
over
the
life
history of organisms within a single generation, and
between generations.
The process of change is called "adaptation".
Or, "Natural
Selection" is a process in which
"adaptation" occurs such that "fitness" increases
[Philosophical discourse
on SVO in English]
Under
certain conditions, this results in Descent
with Modification (evolution)
Three forms [S&R 4.1]: Stabilizing, Disruptive, & Directional selection
Evolution & Natural Selection can be modeled genetically
Natural Selection results in
change of allele frequency (q) [read "delta q"]
in consequence of
differences in relative fitness
(W)
of phenotypes to
which alleles contribute.
Fitness is
a phenotype of individual
organisms (Darwinian fitness)
Fitness
determined
genetically (at least in part).
Fitness
related
to success at Survival AND Reproduction.
Fitness
can be measured & quantified : Analysis
of a survivorship & fecundity schedule
i.e., relative fitness of genotypes can be assigned
numerical values
The consequences of natural
selection depend on the dominance of
fitness:
i.e., whether "fitter" phenotype is due to
dominant or recessive allele
Then, allele frequency change is predicted by General Selection Model:
q
= [pq] [(q)(W2 - W1) + (p)(W1
- W0)] /
where W0, W1, & W2 are the fitness
phenotypes
of AA, AB, & BB genotypes,
respectively [see derivation]
genotype: AA
AB BB
phenotype: W0 = W1 
W2 (AA and AB have
identical phenotypes)
Then
model simplifies to q 
pq2(W2 -
W1)
(since W1 - W0 = 0)
(read as 'is proportional to')
If 'B' phenotype more fit than 'A'
phenotype,
W2 > W1 & q > 0
so q increases
If 'B' phenotype less fit than 'A'
phenotype,
W2 < W1
& q
< 0 so q
decreases
then q 
(W2 - W1) : greater difference
in fitness,
greater
intensity of selection
more rapid change
A numerical
example of Selection:
Tay-Sachs Disease is caused by a series of alleles that
are
rare
(q = 0.001)
recessive (W0
= W1 = 1)
lethal
(W2 = 0)
Then q = pq2(W2
- W1) = -pq2 
-q2 (since if q << p, then p
~ 1)
That
is,
Natural
Selection reduces the frequency of the Tay-Sachs
allele
by ~
one part in a million (1 / 0.0012) per
generation
q' =
0.001000 - 0.000001 = 0.000999
s = 1 - W
Selection Coefficient (s)
= difference in fitness
of
phenotype
relative to 'standard' phenotype with fitness W = 1
Math simpler because only one variable used
(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) [S&R 4.3]
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)
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]
Other
alternatives (Gillespie, 1968) [see S&R Table 4.4]
genotype: AA
AB BB
phenotype: 1
1 - hs 1 - s
1 - s =
fitness difference between the two homozygotes
h scales relative
fitness of heterozygote wrt homozygotes
if h = 1 then (1 - hs)
= (1 - s): fitness of AB same as BB
if h = 0
then (1 - hs) = 1:
fitness of AB same as AA
if h = 0.5 then (1 - hs) = (1 -
(0.5)(s)): fitness of AB intermediate bx AA
& AB
semi-dominance:
each allele contributes equally to heterozygote fitness
HOMEWORK: what if 0 < h < 1 ?
Direction of allele frequency change due to fitness difference of alleles
(whether
effect
of allele on phenotype deleterious or advantageous).
Ultimate
consequences depend on Dominance of Fitness [S&R
04-02]
(whether
allele
dominant,
semi-dominant, or recessive).3
Rate of change an interplay of
both factors (see NatSel Lab),
and if the allele is rare (q < or <<
0.1) at start [S&R 04-03]
AA
AB BB
Consequence of natural selection [
let q = change in f(B) ]
W0
= W1 = W2 No selection
(neither allele has 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 incomplete dominance]:
heterozygote superiority [S&R
04-07]
q 
, where q =
0
Ex.: Balancing selection for Hemoglobin
S & A alleles [NS_07-Box7smc]
HOMEWORK
See National
Public Radio story
on societal aspects of
Sickle-Cell Anemia
Special cases: Alternative
patterns of Dominance of Fitness
Additive selection [NS 07-04]
AKA semi-dominance [S&R_04-02, red
curve]
Genic selection
[NS 07-Box5]
Another special case of incomplete
dominance
Fertility selection
[NS_07-Tab1]
Rh Disease in newborns [S&R_04-02]
"Underdominance"
[SR_04-09]
HOMEWORK [S&R_04-09]
Gametic selection
[SR_04-18]
T alleles in
mice & other
mammals
Frequency-Dependent
selection [S&R_04-13]
Evolutionary Game
Theory: "Hawk
- Dove"
Game [S&R_04-15],
"Prisoner's
Dilemma,"
Natural Selection in natural
populations