compensatory evolution - senecio7の日記

Poon A & Otto SP 2000 Compensating for our load of mutations: freezing the meltdown of small populations. Evolution 54:1467-1479.

new mutations may restore fitness losses incurred by previous mutations without requiring true reversals
these are known as compensatory, or suppressor, mutations
there is an abundance of experimental evidence
one study in particular (Hartl and Taubes 1998) has derived an analytical estimate for the long-term mean fitness reduction caused by fixed mutations, which we will herein refer to as the "fixed drift load"

compensation by additional mutations in the mutant gene (i.e., intragenic compensation) is often accomplished by restoring the original structural or functional conformation of the gene product
compensation by mutations in other genes (i.e., extragenic or intergenic compensation) is often mediated by the relationship between gene products
compensatory mutations are more common than a reverse mutation
small populations depend more heavily on compensatory mutations for recovering fitness

unlike most classical population genetic models, the genetic context of a mutation defines is effect on fitness in Fisher's model
there are no mutations that are intrinsically and unconditionally deleterious or advantageous

the evolution of a population by the fixation of new mutations is a simple Markovian stochastic process because the probability distribution depends only on the state at the previous time step

mutation lengths were drawn from an exponential distribution with rate parameter λ
any mutation can be completely described by a triangle of vectors regardless of the number of dimensions n
regardless of how many dimensionsn) there are, the process can be summarized in two
to determine the probability distribution of r in the n-dimensional model, we retained the exponential distribution for each axis and build up from these components using a "bottom-up" procedure

for n > 1, equation (15) produces a bell-shaped curve with a mean mutation length equal to n / λ
we will discuss the relative merits of bottom-up and top-down approaches to modeling mutations in the discussion below

one frequent criticism of Fisher's model is that its spherical symmetry is too idealized to apply to real organisms
all of the orthogonal axes are standardized to fit under the same fitness function and mutational distribution
with respect to fitness, we can change the scale for each axis such that the same displacement experiences the same selection intensity
this would alter the mutation probability associated with a displacement along each axis
the spherical geometry of Fisher's model cannot perfectly capture both the fitness effects of mutations and their frequency distribution
the model also assumes that the mutational distribution is symmetrical along each axis, with an equal probability of going toward and away from the optimum
if the number of potentially compensating loci varies among traits, for example, then this assumption would not hold

Hartl and Taubes (1998) used an absolute selection coefficient s = w(z') − w(z)
the probability of fixation for a new mutation is really a function of the relative selection coefficient s = [w(z') − w(z)] / w(z)
their assumption was equivalent to relaxing selection away from the optimum

Hartl and Taubes (1998) used a quadratic fitness curve instead of a linear one (e.g., eq. 7)

we assembled a probability distribution for mutation length, r, from component distributions in a bottom-up fashion
Hartl and Taubes (1998) assumed that the total mutation length in n dimensions was uniformly distributed

we assumed that the distribution for mutation length along each axis is exponential and that the total mutation length is derived from these component effects
a bottom-up derivation
the conventional procedure with respect to Fisher's model is to select a specific shape to the total distribution of mutational length, leaving the component distributions along each axis unspecified
a top-down derivation

it is difficult to derive a probability density function of mutant effects on phenotype that is L-shaped using the bottom-up approach

as the population moves further from the optimum and as n increases, the density of mutations with little effect on fitness increases
an L-shaped distribution of fitness effects may be seen even when the distribution of phenotypic effects is bell-shaped (as in our bottom-up derivation)

very large populations (such as Drosophila populations used to generate the expectation of an L-shaped distribution of mutational effects on fitness) are expected to reside at or close to an optimum
then the observed distribution of fitness effects should be similar in shape to the distribution of total mutation length for populations near an optimum

it seems unlikely that all mutations can be compensated (as in Fisher's model)
previous models of the accumulation of mutations in small populations focus on unconditionally deleterious mutations with a constant fitness effect s occurring at a constant rate μ
similar models draw unconditionally deleterious fitness effects from a continuous distribution (Lande 1994) or both deleterious and advantageous mutations at different rates (Lande 1998)

there may exist, however, a subclass of mutations that cannot be compensated
such mutations cannot be modeled using Fisher's model and will contribute to a mutational meltdown

increasing n within Fisher's model (with n_F = n) will decrease the chance that a new mutation will counteract the effects of a previous mutations
when n is greater than one, then mutations will not always affect all characters simultaneously
the chance that maladapted characters will be little affected by a new mutation increases with n
the delay between deleterious and compensatory mutation events also increases