Exact and limit distributions of the largest fitness on correlated fitness landscapes

Jain, Kavita; Dasgupta, Abhishek; Das, Gayatri

doi:10.1088/1742-5468/2009/10/l10001

Cited by 3 publications

(8 citation statements)

References 21 publications

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“…It should be noted that the extreme value distribution of correlated fitnesses may change from the corresponding i.i.d. class even if correlations are weak (Jain et al, 2009;Jain, 2011). In the following discussion, we assume that the sequence fitnesses are uncorrelated and deal with the correlated fitnesses in the last subsection of this section.…”

Section: Models and Methodsmentioning

confidence: 99%

Multiple Adaptive Substitutions During Evolution in Novel Environments

Jain

Seetharaman

2011

Genetics

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We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to be high, here we start the adaptation process with a low fitness corresponding to a population in a stressful novel environment. For generic fitness distributions, using an analytic argument we find that the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase. When the fitnesses are exponentially or uniformly distributed, using an evolution equation for the distribution of population fitness, we analytically calculate the fitness distribution of fixed beneficial mutations and the walk length distribution.

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Section: Models and Methodsmentioning

confidence: 99%

Multiple Adaptive Substitutions During Evolution in Novel Environments

Jain

Seetharaman

2011

Genetics

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“…2a for two values of r shifts towards right with increasing r as the average w E = 1 + (55r/36) [29]. Figure 2b shows that the extreme value distribution at fixed r peaks at larger w as δ increases.…”

Section: A Distribution Of the Largest Fitness At Constant Hamming Dmentioning

confidence: 89%

“…II, the largest fitness at a constant Hamming distance from the initial sequence only need to be considered for this purpose. This led us to consider the problem of the extreme statistics of correlated random variables [20,29] which has been much less studied than its uncorrelated counterpart. We found that the extreme value distribution is not of the Gumbel form which is obtained when the random variables are i.i.d.…”

Section: Discussionmentioning

confidence: 99%

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Evolutionary dynamics on strongly correlated fitness landscapes

Seetharaman

Jain²

2010

Phys. Rev. E

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We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables.

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“…In this article, we focus on the extreme value distribution for nonindependent and identically distributed (ni.i.d.) random variables (for some results on nonindependent and nonidentically distributed fitnesses, see [6,23]). Such ni.i.d.…”

Section: Distribution Of the Largest Fitnessmentioning

confidence: 99%

Extreme value distributions for weakly correlated fitnesses in block models

Jain¹

2011

J. Stat. Mech.

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We study the limit distribution of the largest fitness for weakly correlated and identically distributed random fitnesses. A fitness variable is obtained by taking a linear combination of a fixed number of independent random variables drawn from the same parent distribution and two fitnesses are correlated if they have at least one common term in the respective sum. We find that for certain class of parent distributions, the extreme value distribution for correlated random variables can be related either to one of the known limit laws for independent variables or the parent distribution itself. For other cases, new limiting distributions appear. The conditions under which these results hold are identified.

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Exact and limit distributions of the largest fitness on correlated fitness landscapes

Cited by 3 publications

References 21 publications

Multiple Adaptive Substitutions During Evolution in Novel Environments

Multiple Adaptive Substitutions During Evolution in Novel Environments

Evolutionary dynamics on strongly correlated fitness landscapes

Extreme value distributions for weakly correlated fitnesses in block models

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