dorsal/arxiv
View SchemaEvolutionary trajectories in rugged fitness landscapes
| Authors | Kavita Jain, Joachim Krug |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0501028 |
| URL | https://arxiv.org/abs/q-bio/0501028 |
| DOI | 10.1088/1742-5468/2005/04/P04008 |
| Journal | J. Stat. Mech. (2005) P04008 |
Abstract
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the most populated genotype \textit{jumps} from a local fitness maximum to another and eventually reaches the global maximum. We use a strong selection limit, which reduces the dynamics beyond the first time step to the competition between independent mutant subpopulations, to study the dynamics of this model and of a simpler one-dimensional model which ignores the geometry of the sequence space. We find that the fit genotypes that appear along a trajectory are a subset of suitably defined fitness \textit{records}, and exploit several results from the record theory for non-identically distributed random variables. The genotypes that contribute to the trajectory are those records that are not \textit{bypassed} by superior records arising further away from the initial population. Several conjectures concerning the statistics of bypassing are extracted from numerical simulations. In particular, for the one-dimensional model, we propose a simple relation between the bypassing probability and the dynamic exponent which describes the scaling of the typical evolution time with genome size. The latter can be determined exactly in terms of the extremal properties of the fitness distribution.
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"abstract": "We consider the evolutionary trajectories traced out by an infinite\npopulation undergoing mutation-selection dynamics in static, uncorrelated\nrandom fitness landscapes. Starting from the population that consists of a\nsingle genotype, the most populated genotype \\textit{jumps} from a local\nfitness maximum to another and eventually reaches the global maximum. We use a\nstrong selection limit, which reduces the dynamics beyond the first time step\nto the competition between independent mutant subpopulations, to study the\ndynamics of this model and of a simpler one-dimensional model which ignores the\ngeometry of the sequence space. We find that the fit genotypes that appear\nalong a trajectory are a subset of suitably defined fitness \\textit{records},\nand exploit several results from the record theory for non-identically\ndistributed random variables. The genotypes that contribute to the trajectory\nare those records that are not \\textit{bypassed} by superior records arising\nfurther away from the initial population. Several conjectures concerning the\nstatistics of bypassing are extracted from numerical simulations. In\nparticular, for the one-dimensional model, we propose a simple relation between\nthe bypassing probability and the dynamic exponent which describes the scaling\nof the typical evolution time with genome size. The latter can be determined\nexactly in terms of the extremal properties of the fitness distribution.",
"arxiv_id": "q-bio/0501028",
"authors": [
"Kavita Jain",
"Joachim Krug"
],
"categories": [
"q-bio.PE",
"cond-mat.dis-nn"
],
"doi": "10.1088/1742-5468/2005/04/P04008",
"journal_ref": "J. Stat. Mech. (2005) P04008",
"title": "Evolutionary trajectories in rugged fitness landscapes",
"url": "https://arxiv.org/abs/q-bio/0501028"
},
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