适应率的渐近行为
Asymptotic behavior of the rate of adaptation
摘要：
我们考虑在大的无性群体中有益和有害突变的积累。适应率受总突变率、有益突变比例和总体规模$N$的影响。我们表明，无论突变率，只要有利的突变的比例是严格积极的，适应率至少是$\mathcal{O}(\log^{1-δ}N)$，其中$δ$可以是任何小的正数，如果总体规模是足够大的。这表明，如果基因组被建模为连续的，自然选择就没有限制，也就是说，适应的速度在$N$中无限增长。
英文摘要：
We consider the accumulation of beneficial and deleterious mutations in large asexual populations. The rate of adaptation is affected by the total mutation rate, proportion of beneficial mutations and population size $N$. We show that regardless of mutation rates, as long as the proportion of beneficial mutations is strictly positive, the adaptation rate is at least $\mathcal{O}(\log^{1-δ}N)$ where $δ$ can be any small positive number, if the population size is sufficiently large. This shows that if the genome is modeled as continuous, there is no limit to natural selection, that is, the rate of adaptation grows in $N$ without bound.
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