Modelling the rate at which adaptive phenotypes appear in a population is a key to predicting evolutionary processes. Given random mutations, should this rate be modelled by a simple Poisson process, or is a more complex dynamics needed? Here we use analytic calculations and simulations of evolving populations on explicit genotype-phenotype maps to show that the introduction of novel phenotypes can be ‘bursty’ or overdispersed. In other words, a novel phenotype either appears multiple times in quick succession, or not at all for many generations. These bursts are fundamentally caused by statistical fluctuations and other structure in the map from genotypes to phenotypes. Their strength depends on population parameters, being highest for ‘monomorphic’ populations with low mutation rates. They can also be enhanced by additional inhomogeneities in the mapping from genotypes to phenotypes. We mainly investigate the effect of bursts using the well-studied genotype-phenotype map for RNA secondary structure, but find similar behaviour in a lattice protein model and in Richard Dawkins's biomorphs model of morphological development. Bursts can profoundly affect adaptive dynamics. Most notably, they imply that fitness differences play a smaller role in determining which phenotype fixes than would be the case for a Poisson process without bursts.

中文翻译：

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表型变异到来时的非泊松爆发可以强烈影响适应的动态

对种群中适应性表型出现的速率进行建模是预测进化过程的关键。给定随机突变，这个速率应该通过简单的泊松过程建模，还是需要更复杂的动力学？在这里，我们使用显式基因型-表型图谱上进化种群的分析计算和模拟来表明新表型的引入可能是“突发”或过度分散的。换句话说，一种新的表型要么连续快速出现多次，要么在许多代中根本不出现。这些爆发从根本上来说是由统计波动和从基因型到表型的图谱中的其他结构引起的。它们的强度取决于种群参数，对于突变率低的“单态”种群来说是最高的。它们还可以通过从基因型到表型的映射中的额外不均匀性来增强。我们主要使用经过充分研究的 RNA 二级结构基因型-表型图来研究爆发的影响，但在晶格蛋白模型和 Richard Dawkins 的形态发育生物形态模型中发现了类似的行为。爆发可以深刻地影响适应性动态。最值得注意的是，他们暗示，与没有爆发的​​泊松过程相比，适应度差异在确定哪种表型修复方面发挥的作用更小。