Evolution at multiple loci
Model with bialleic loci
Dihybrid cross
F1 Phenotype Smooth yellow x Smooth yellow
Genotype SwYg x SwYg
Gametes SY Sg wY wg x SY Sg wY wg
F2
SY Sg wY Wg
SY SSYY SSYg SwYY SwYg
Sg SSYg SSgg SwYg Swgg
Phenotype ratio 9:3:3:1
wY SwYY SwYg wwYY wwYg
wg SwYg Swgg wwYg wwgg
New combinations of phenotypes (eg. wrinkled and yellow) not found in parental
generations are recombinants
Can place selective advantages of certain alleles
eg. let SS= s; YY=t
SS (1+s) Sw(1+s/2 ww (1)
)
YY SSYY SwYY YYww
(1+t) 1+s+t 1+s/2+t 1+t
Yg SSYg SwYg wwYg
(1+t/2 1+t/2+s 1+(s+t)/2 1+t/2
)
With multiple
gg SSgg Swgg wwgg
loci, many types of gametes possible as there
(1) 1+s 1+/2 1
are combinations of alleles – in absence of
recombination (r=0), each type of gamete can be regarded as an “allele” of one locus
with 4 alleles (simple bialleic loci – 2)
Presence of recombination complicates matters as each gametic type is continually
recreated by recombination even if disfavoured by selection
Influence of recombination on the outcome of selection determined by
recombination fraction and by degree of interaction between loci
When selection acts on phenotype produced by joint effects of multiple loci, there
are 2 general situations:
Changes in allele frequency are driven primarily by selection coefficients and
recombination plays a minor role – weak epistasis, moderate/loose linkage
, Selection and recombination are about equally important in determining outcome –
strong epistasis and tight linkage
Epistasis: gene interaction, any situation in which genetic effects of different loci
contribute to a phenotypic trait are not additive
- Fitness effect of an allele depends on genetic background
- Strong epistasis and tight linkage – complications
With loci and 2 alleles – can be as many as 15 equilibria: most unstable, but
examples are known in which 4 interior equilibria are simultaneously stable
Average fitness not in the population is not necessarily a maximum at equilibrium
- there are cases in which none of the 4 stable equilibria is at a point of
maximum average fitness, natural selection can cause a decrease in average
fitness
Despite this computer simulation and
approximate solutions (Ewens, 1979)
show epistasis is not too strong and
linkage not too tight, then average
fitness in population usually increases
Magnitude Epistasis
Effect is the same bB – the degree to which this change is advantageous is
dependent on the A locus
Will not change the outcome of A locus evolution but may affect the speed – as
selective advantage for A is smaller
Synergistic: mutational effect
increases with the number of
mutations
Antagonistic: mutational effect
decreases with number of mutations
Sign Epistasis: Ab is pulled down lower
than ab
Reciprocal sign epistasis
“fitness value”
- In a large population, it is difficult to change frequencies from ab AB
- Epistasis prevents adaptation
- Stabilise polymorphism
- Can also constrain evolutionary trajectory (path) typically will go from low to
high fitness, but can come across fitness valleys
Antibiotic Resistance
Model with bialleic loci
Dihybrid cross
F1 Phenotype Smooth yellow x Smooth yellow
Genotype SwYg x SwYg
Gametes SY Sg wY wg x SY Sg wY wg
F2
SY Sg wY Wg
SY SSYY SSYg SwYY SwYg
Sg SSYg SSgg SwYg Swgg
Phenotype ratio 9:3:3:1
wY SwYY SwYg wwYY wwYg
wg SwYg Swgg wwYg wwgg
New combinations of phenotypes (eg. wrinkled and yellow) not found in parental
generations are recombinants
Can place selective advantages of certain alleles
eg. let SS= s; YY=t
SS (1+s) Sw(1+s/2 ww (1)
)
YY SSYY SwYY YYww
(1+t) 1+s+t 1+s/2+t 1+t
Yg SSYg SwYg wwYg
(1+t/2 1+t/2+s 1+(s+t)/2 1+t/2
)
With multiple
gg SSgg Swgg wwgg
loci, many types of gametes possible as there
(1) 1+s 1+/2 1
are combinations of alleles – in absence of
recombination (r=0), each type of gamete can be regarded as an “allele” of one locus
with 4 alleles (simple bialleic loci – 2)
Presence of recombination complicates matters as each gametic type is continually
recreated by recombination even if disfavoured by selection
Influence of recombination on the outcome of selection determined by
recombination fraction and by degree of interaction between loci
When selection acts on phenotype produced by joint effects of multiple loci, there
are 2 general situations:
Changes in allele frequency are driven primarily by selection coefficients and
recombination plays a minor role – weak epistasis, moderate/loose linkage
, Selection and recombination are about equally important in determining outcome –
strong epistasis and tight linkage
Epistasis: gene interaction, any situation in which genetic effects of different loci
contribute to a phenotypic trait are not additive
- Fitness effect of an allele depends on genetic background
- Strong epistasis and tight linkage – complications
With loci and 2 alleles – can be as many as 15 equilibria: most unstable, but
examples are known in which 4 interior equilibria are simultaneously stable
Average fitness not in the population is not necessarily a maximum at equilibrium
- there are cases in which none of the 4 stable equilibria is at a point of
maximum average fitness, natural selection can cause a decrease in average
fitness
Despite this computer simulation and
approximate solutions (Ewens, 1979)
show epistasis is not too strong and
linkage not too tight, then average
fitness in population usually increases
Magnitude Epistasis
Effect is the same bB – the degree to which this change is advantageous is
dependent on the A locus
Will not change the outcome of A locus evolution but may affect the speed – as
selective advantage for A is smaller
Synergistic: mutational effect
increases with the number of
mutations
Antagonistic: mutational effect
decreases with number of mutations
Sign Epistasis: Ab is pulled down lower
than ab
Reciprocal sign epistasis
“fitness value”
- In a large population, it is difficult to change frequencies from ab AB
- Epistasis prevents adaptation
- Stabilise polymorphism
- Can also constrain evolutionary trajectory (path) typically will go from low to
high fitness, but can come across fitness valleys
Antibiotic Resistance
