dorsal/arxiv
View SchemaBreaking records in the evolutionary race
| Authors | Joachim Krug, Kavita Jain |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0409019 |
| URL | https://arxiv.org/abs/q-bio/0409019 |
| DOI | 10.1016/j.physa.2005.06.002 |
| Journal | Physica A 358, 1 (2005) |
Abstract
We explore some aspects of the relationship between biological evolution processes and the mathematical theory of records. For Eigen's quasispecies model with an uncorrelated fitness landscape, we show that the evolutionary trajectories traced out by a population initially localized at a randomly chosen point in sequence space can be described in close analogy to record dynamics, with two complications. First, the increasing number of genotypes that become available with increasing distance from the starting point implies that fitness records are more frequent than for the standard case of independent, identically distributed random variables. Second, fitness records can be bypassed, which strongly reduces the number of genotypes that take part in an evolutionary trajectory. For exponential and Gaussian fitness distributions, this number scales with sequence length $N$ as $\sqrt{N}$, and it is of order unity for distributions with a power law tail. This is in strong contrast to the number of records, which is of order $N$ for any fitness distribution.
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"abstract": "We explore some aspects of the relationship between biological evolution\nprocesses and the mathematical theory of records. For Eigen\u0027s quasispecies\nmodel with an uncorrelated fitness landscape, we show that the evolutionary\ntrajectories traced out by a population initially localized at a randomly\nchosen point in sequence space can be described in close analogy to record\ndynamics, with two complications. First, the increasing number of genotypes\nthat become available with increasing distance from the starting point implies\nthat fitness records are more frequent than for the standard case of\nindependent, identically distributed random variables. Second, fitness records\ncan be bypassed, which strongly reduces the number of genotypes that take part\nin an evolutionary trajectory. For exponential and Gaussian fitness\ndistributions, this number scales with sequence length $N$ as $\\sqrt{N}$, and\nit is of order unity for distributions with a power law tail. This is in strong\ncontrast to the number of records, which is of order $N$ for any fitness\ndistribution.",
"arxiv_id": "q-bio/0409019",
"authors": [
"Joachim Krug",
"Kavita Jain"
],
"categories": [
"q-bio.PE",
"cond-mat.dis-nn"
],
"doi": "10.1016/j.physa.2005.06.002",
"journal_ref": "Physica A 358, 1 (2005)",
"title": "Breaking records in the evolutionary race",
"url": "https://arxiv.org/abs/q-bio/0409019"
},
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