If:
variation exists for some
trait, and
fitness difference is
correlated with that trait, and
trait is to some degree heritable
(determined by genetics),
Then:
trait distribution will change
over
life
history within single generation, and
between generations.
Process of change called "adaptation"
Or, "Natural
Selection" is a process in which
"adaptation" occurs such that "fitness" increases
[Discourse on SVO structure
of English language: 'adaptation' as noun & verb]
Under
certain conditions, this results in Descent
with Modification (evolution)
& The
Origin of Species
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 survivorship
& fecundity schedule
relative fitness of phenotypes (genotypes) assigned numerical
values
Consequences of natural selection
depend on dominance of fitness:
Are "fitter" phenotypes due to
dominant or recessive allele ?
Then, allele frequency change over time predicted by General Selection Model [see derivation]
q = [pq] [(q)(W2 - W1) + (p)(W1 - W0)] /
where W0, W1, & W2 are measure of fitness phenotypes
of AA, AB, & BB genotypes,
respectively,
read as "W
bar" = Mean fitness
genotype: AA
AB BB
phenotype: W0 = W1
W2
(AA & AB phenotypes identical)
Model
simplifies to q pq2(W2 - W1)
(since W1 - W0 = 0)
(read as '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 frequency of Tay-Sachs allele
~ one
part in a million (1 / 0.0012) per generation
q' =
0.001000 - 0.000001 = 0.000999
General cases of Directional Selection
Dependence on Dominance
model [SR2019 4.3]
Rate of vs q [SR2019 4.2]
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)
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
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 SR2019
Table 4.4]
genotype: AA
AB BB
phenotype: 1
1 - hs 1 - s
1 - s =
fitness difference between homozygotes
h scales relative
fitness of heterozygote wrt homozygotes
if h = 1
then (1 - hs) = (1 - s)
fitness of AB =
BB
if h = 0
then (1 - hs) = 1
fitness of AB = AA
if h = 0.5 then (1 - hs) = (1 -
(0.5)(s)) fitness of AB intermediate
bx AA & BB
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 [SR2019 4.2]
(whether
allele
dominant,
semi-dominant, or recessive).
Rate of change: interplay of
both factors (see MATLAB exercise),
q0 at start, if q <
or << 0.1) at start [SR2019 4.3]
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
heterozygote superiority
[special case of incomplete dominance]:
AKA "overdominance"
[SR2019
4.7, 4.6]
q , where q =
0
Ex.: Balancing selection for Hemoglobin
S & A alleles [NS_07-Box7
smc] HOMEWORK
See National
Public Radio story
on societal aspects of
Sickle-Cell Anemia
See
National
Public Radio story
on use of CRISPR to
treat Sickle-Cell Anemia
Stabilizing, Disruptive, & Directional selection [SR2019 4.1 modified]
Alternative
models of
Natural
Selection
Natural Selection in natural
populations