Yet these rules may themselves evolve. A branch of evolutionary theory, called modifier theory, focuses on the evolutionary forces acting on such rules.
(1) A modifier locus is postulated which alters a characteristic of interest.
(2) Alleles at this locus are compared. By examing whether or not new modifier alleles can invade a population, it can be determined which alleles tend to be favored and under what conditions.
(3) Long-term evolution at the modifier locus is used to gain insight into how the characteristic might evolve.
Examples of characteristics examined by modifier models:
)
Neutral modifiers evolve only in response to the genetic associations (linkage disequilibria) between themselves and other loci.
Say that the population is initially fixed on a single chromosome (M1 A1) and that the gene product at this equilibrium is under-produced.
A mutant modifier allele, M2, that alters the transcription rate may experience the following fitness consequences:
Invasion of the M2 allele occurs if it increases the transcription rate.
In this example, the dynamics of the modifier locus are equivalent to a model in which the modifier is actually a viability locus.
Example The "D" (for dilution) gene involved in coat coloration in a number of mammals (see Griffiths et al for more information). This gene modifies the amount of pigment produced by other coat-color genes (dd being less pigmented than DD).
"The pronounced tendency of the mutant gene to be recessive, to the gene of wild type from which it arises, calls for explanation"-- Fisher (1930) The Genetical Theory of Natural Selection
It was to help explain the dominance of wild type alleles that modifier theory was first used (Wright 1929, 1934; Fisher 1928, 1929, 1930).
Now let the M-locus control the degree of dominance experienced at a selectively important locus:
(A2 is assumed deleterious and to be produced by recurrent mutation at rate .)
By performing a local stability analysis on the two-locus dynamics near the equilibrium with M1 fixed, M2 can be found to invade the population if and only if h12 < h11, that is, if the wild type allele (A1) is made more dominant and the mutant gene more recessive!
This led Fisher to argue that dominance of wildtype alleles is an evolved characteristic. Hence, new wild type alleles might not be dominant, but would become so through the action of modifying genes.
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Aside: The leading eigenvalue can be interpretted as a measure of the relative fitness of a an allele while it is rare.
This is because, in the direction of the eigenvector associated with the leading eigenvalue, a perturbation changes according to:
.
This has the same form as the recursion equation obtained when the allele frequency (p) is small and selection is weak: 
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Do modifier alleles that increase the diploid phase of the life cycle invade?
(eg Otto and Goldstein 1992)
When does evolution favor early reproduction (and death) versus delayed reproduction? Can senescence (aging) evolve?
(eg Charlesworth 1980)
When will a modifier allele that increases responsiveness to environmental cues invade?
(eg Bergman and Feldman 1994)
Can a modifier that increases the selfing rate evolve if it increases the fertilization success of pollen but causes inbreeding depression?
(eg Lande and Schemske 1985, Uyenoyama 1991)
Nei (1967) introduced neutral modifiers that alter recombination rates (transmission) without altering survival or reproduction directly.
Let the M-locus modify recombination rates, eg between two selected loci:
Eg, in Drosophila, more than 20 loci are known to alter recombination rates (Baker et al 1976).
Result 1:Invasion of the M2 allele only occurs if there is linkage disequilibrium between loci A and B (when D=0, recombination does not change anything).
Result 2:At a fully polymorphic equilibrium with linkage disequilibrium, M2 invades only if it reduces the recombination rate!!
(eg Nei 1967, 1969; Feldman 1972, 1980)
Reduction Principle
WHY? To maintain a polymorphism, there must be heterozygote advantage at both loci with A1A2-B1B2 most fit.
In models that maintain D at equilibrium, the mean fitness is highest if the population contains only a subset of chromosomes (eg A1B1 and A2B2 only).
Recombination leads to imperfect transmission of these chromosomes (Altenberg and Feldman 1987). This reduces the mean fitness of the population.
Modifier alleles that reduce recombination tend to be more perfectly transmitted with the fittest chromosomes. This genetic association favors modifier alleles that reduce recombination***.
Let the M-locus modify the mutation rate at a selectively important locus (A):
(Examples in Cox 1976).
Result: With arbitrary selection at the primary locus (A), a modifier allele can invade the population only if it reduces mutation rates (
).
(eg Karlin and MacGregor 1974; Holsinger and Feldman 1983)
Reduction Principle also applies to mutations
WHY? Again, as argued by Altenberg and Feldman (1987), more perfect transmission is favored over imperfect transmission. Decreasing the mutation rates makes the reproduction of genotypes more faithful so that the selectively favored alleles are maintained in tact***.
Let the M-locus modify the migration ratebetween two populations:
(Examples in Wiener 1991).
Result: If selection favors allele A1 in one population and allele A2 in the other, only modifiers that reduce the migration rate are able to invade (m12 < m11).
(eg Balkav and Feldman 1973; Wiener 1991)
Reduction Principle again applies
WHY? Migration creates a "mis-match" between the genotype of the migrant and the environment in which it lands. Reduced migration causes more perfect transmission of the genotype AND location of an individual***.
These modifier models suggest that transmission should evolve to be perfect (r=0,
=0, m=0), yet transmission is never perfect. Why?
The assumptions underlying the Reduction Principle include:
Violating any of these assumptions can lead to the failure of the Reduction Principle.
EXAMPLE Evolution of recombination when mutations also occur at selected loci favors increased recombination under certain circumstances.
Does a modifier allele that alters segregation at meiosis invade? Is Mendelian segregation stable?
(eg Feldman and Otto 1989)
If a modifier allele causes females to have stronger mating preferences, when will it invade a population?
(eg Kirkpatrick 1982)
If invading modifier alleles always increased mean fitness while non-invading alleles always decreased mean fitness, then we could simply look at the parameter value which maximized
to see where modifier evolution would eventually take a population (= Optimality approach).
Except for some of the simplest models, mean fitness is not generally maximized
can decrease over time
Knowing what would be "best" for a a population doesn't mean that evolution can lead there. Modifier theory indicates which paths evolution can actually take by following the fate of genetic variants that alter important characteristics of a population.
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