3,562 research outputs found
The Expected Fitness Cost of a Mutation Fixation under the One-dimensional Fisher Model
This paper employs Fisher’s model of adaptation to understand the expected fitness
effect of fixing a mutation in a natural population. Fisher’s model in one dimension admits
a closed form solution for this expected fitness effect. A combination of different parameters, including the distribution of mutation lengths, population sizes, and the initial state that the population is in, are examined to see how they affect the expected fitness effect of state transitions. The results show that the expected fitness change due to the fixation of a mutation is always positive, regardless of the distributional shapes of mutation lengths, effective population sizes, and the initial state that the population is in. The further away the initial state of a population is from the optimal state, the slower the population returns to the optimal state. Effective population size (except when very small) has little effect on the expected fitness change due to mutation fixation. The always positive expected fitness change suggests that small populations may not necessarily be doomed due to the runaway process of fixation of deleterious mutations
The inevitability of unconditionally deleterious substitutions during adaptation
Studies on the genetics of adaptation typically neglect the possibility that
a deleterious mutation might fix. Nonetheless, here we show that, in many
regimes, the first substitution is most often deleterious, even when fitness is
expected to increase in the long term. In particular, we prove that this
phenomenon occurs under weak mutation for any house-of-cards model with an
equilibrium distribution. We find that the same qualitative results hold under
Fisher's geometric model. We also provide a simple intuition for the surprising
prevalence of unconditionally deleterious substitutions during early
adaptation. Importantly, the phenomenon we describe occurs on fitness
landscapes without any local maxima and is therefore distinct from
"valley-crossing". Our results imply that the common practice of ignoring
deleterious substitutions leads to qualitatively incorrect predictions in many
regimes. Our results also have implications for the substitution process at
equilibrium and for the response to a sudden decrease in population size.Comment: Corrected typos and minor errors in Supporting Informatio
Compensatory evolution and the origins of innovations
Cryptic genetic sequences have attenuated effects on phenotypes. In the
classic view, relaxed selection allows cryptic genetic diversity to build up
across individuals in a population, providing alleles that may later contribute
to adaptation when co-opted - e.g. following a mutation increasing expression
from a low, attenuated baseline. This view is described, for example, by the
metaphor of the spread of a population across a neutral network in genotype
space. As an alternative view, consider the fact that most phenotypic traits
are affected by multiple sequences, including cryptic ones. Even in a strictly
clonal population, the co-option of cryptic sequences at different loci may
have different phenotypic effects and offer the population multiple adaptive
possibilities. Here, we model the evolution of quantitative phenotypic
characters encoded by cryptic sequences, and compare the relative contributions
of genetic diversity and of variation across sites to the phenotypic potential
of a population. We show that most of the phenotypic variation accessible
through co-option would exist even in populations with no polymorphism. This is
made possible by a history of compensatory evolution, whereby the phenotypic
effect of a cryptic mutation at one site was balanced by mutations elsewhere in
the genome, leading to a diversity of cryptic effect sizes across sites rather
than across individuals. Cryptic sequences might accelerate adaptation and
facilitate large phenotypic changes even in the absence of genetic diversity,
as traditionally defined in terms of alternative alleles
Properties of selected mutations and genotypic landscapes under Fisher's Geometric Model
The fitness landscape - the mapping between genotypes and fitness -
determines properties of the process of adaptation. Several small genetic
fitness landscapes have recently been built by selecting a handful of
beneficial mutations and measuring fitness of all combinations of these
mutations. Here we generate several testable predictions for the properties of
these landscapes under Fisher's geometric model of adaptation (FGMA). When far
from the fitness optimum, we analytically compute the fitness effect of
beneficial mutations and their epistatic interactions. We show that epistasis
may be negative or positive on average depending on the distance of the
ancestral genotype to the optimum and whether mutations were independently
selected or co-selected in an adaptive walk. Using simulations, we show that
genetic landscapes built from FGMA are very close to an additive landscape when
the ancestral strain is far from the optimum. However, when close to the
optimum, a large diversity of landscape with substantial ruggedness and sign
epistasis emerged. Strikingly, landscapes built from different realizations of
stochastic adaptive walks in the same exact conditions were highly variable,
suggesting that several realizations of small genetic landscapes are needed to
gain information about the underlying architecture of the global adaptive
landscape.Comment: 51 pages, 8 figure
Rate of adaptation in sexuals and asexuals: A solvable model of the Fisher-Muller effect
The adaptation of large asexual populations is hampered by the competition
between independently arising beneficial mutations in different individuals,
which is known as clonal interference. Fisher and Muller proposed that
recombination provides an evolutionary advantage in large populations by
alleviating this competition. Based on recent progress in quantifying the speed
of adaptation in asexual populations undergoing clonal interference, we present
a detailed analysis of the Fisher-Muller mechanism for a model genome
consisting of two loci with an infinite number of beneficial alleles each and
multiplicative fitness effects. We solve the infinite population dynamics
exactly and show that, for a particular, natural mutation scheme, the speed of
adaptation in sexuals is twice as large as in asexuals. Guided by the infinite
population result and by previous work on asexual adaptation, we postulate an
expression for the speed of adaptation in finite sexual populations that agrees
with numerical simulations over a wide range of population sizes and
recombination rates. The ratio of the sexual to asexual adaptation speed is a
function of population size that increases in the clonal interference regime
and approaches 2 for extremely large populations. The simulations also show
that the imbalance between the numbers of accumulated mutations at the two loci
is strongly suppressed even by a small amount of recombination. The
generalization of the model to an arbitrary number of loci is briefly
discussed. If each offspring samples the alleles at each locus from the gene
pool of the whole population rather than from two parents, the ratio of the
sexual to asexual adaptation speed is approximately equal to in large
populations. A possible realization of this scenario is the reassortment of
genetic material in RNA viruses with genomic segments.Comment: Title has been changed. Supporting Information (animation) can be
found in the source file. 53 pages. 10 figures. To appear in Genetic
Biological evolution through mutation, selection, and drift: An introductory review
Motivated by present activities in (statistical) physics directed towards
biological evolution, we review the interplay of three evolutionary forces:
mutation, selection, and genetic drift. The review addresses itself to
physicists and intends to bridge the gap between the biological and the
physical literature. We first clarify the terminology and recapitulate the
basic models of population genetics, which describe the evolution of the
composition of a population under the joint action of the various evolutionary
forces. Building on these foundations, we specify the ingredients explicitly,
namely, the various mutation models and fitness landscapes. We then review
recent developments concerning models of mutational degradation. These predict
upper limits for the mutation rate above which mutation can no longer be
controlled by selection, the most important phenomena being error thresholds,
Muller's ratchet, and mutational meltdowns. Error thresholds are deterministic
phenomena, whereas Muller's ratchet requires the stochastic component brought
about by finite population size. Mutational meltdowns additionally rely on an
explicit model of population dynamics, and describe the extinction of
populations. Special emphasis is put on the mutual relationship between these
phenomena. Finally, a few connections with the process of molecular evolution
are established.Comment: 62 pages, 6 figures, many reference
Multidimensional epistasis and the transitory advantage of sex
Identifying and quantifying the benefits of sex and recombination is a long
standing problem in evolutionary theory. In particular, contradictory claims
have been made about the existence of a benefit of recombination on high
dimensional fitness landscapes in the presence of sign epistasis. Here we
present a comparative numerical study of sexual and asexual evolutionary
dynamics of haploids on tunably rugged model landscapes under strong selection,
paying special attention to the temporal development of the evolutionary
advantage of recombination and the link between population diversity and the
rate of adaptation. We show that the adaptive advantage of recombination on
static rugged landscapes is strictly transitory. At early times, an advantage
of recombination arises through the possibility to combine individually
occurring beneficial mutations, but this effect is reversed at longer times by
the much more efficient trapping of recombining populations at local fitness
peaks. These findings are explained by means of well established results for a
setup with only two loci. In accordance with the Red Queen hypothesis the
transitory advantage can be prolonged indefinitely in fluctuating environments,
and it is maximal when the environment fluctuates on the same time scale on
which trapping at local optima typically occurs.Comment: 34 pages, 9 figures and 8 supplementary figures; revised and final
versio
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