{
  "id": "1508.04469",
  "version": "v1",
  "published": "2015-08-18T21:58:31.000Z",
  "updated": "2015-08-18T21:58:31.000Z",
  "title": "Lower Bound on the Rate of Adaptation in an Asexual Population",
  "authors": [
    "Michael Kelly"
  ],
  "categories": [
    "math.PR",
    "q-bio.PE"
  ],
  "abstract": "We consider a model of asexually reproducing individuals with random mutations and selection. The rate of mutations is proportional to the population size, $N$. The mutations may be either beneficial or deleterious. In a paper by Yu, Etheridge and Cuthbertson (2009) it was conjectured that the average rate at which the mean fitness increases in this model is $O(\\log N/(\\log\\log N)^2)$. In this paper we show that for any time $t > 0$ there exist values $\\epsilon_N \\rightarrow 0$ and a fixed $c > 0$ such that the maximum fitness of the population is greater than $cs\\log N/(\\log\\log N)^2$ for all times $s \\in [\\epsilon_N,t]$ with probability tending to 1 as $N$ tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-08-18T21:58:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92D15",
      "60J27",
      "60K35",
      "92D10"
    ],
    "keywords": [
      "asexual population",
      "lower bound",
      "adaptation",
      "mean fitness increases",
      "random mutations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150804469K"
    }
  }
}