偏态子代分布引起的动态抽样偏差和过度离差
Dynamic sampling bias and overdispersion induced by skewed offspring distributions
摘要：
自然种群经常表现出增强的遗传漂变，与其后代数量分布的强烈偏斜一致。出现这种偏差的原因是，家庭规模的可变性要么本身就很强，要么因人口扩张而扩大，导致所谓的“头奖”事件。由此产生的等位基因频率波动很大，因此，挑战标准模型的群体遗传学，假设足够窄的后代分布。虽然中性动力学向后的时间可以很容易地分析使用合并的方法，我们仍然知道很少的影响广泛的后代分布的动态向前的时间，特别是与选择。在这里，我们采用了一个精确的渐近分析与缩放假设相结合，以证明过度分散的频率轨迹出现从传统的力量，如选择或突变的竞争，与新兴的时间依赖性的采样偏差对次要等位基因。抽样偏差来自于每个等位基因类型内最大抽样家庭规模的特征时间依赖性。使用这种见解，我们建立简单的缩放关系的等位基因频率波动，固定概率，灭绝时间，和站点频谱时出现的后代数量分布根据幂律$~n^{-(1+α)}$。为了证明这种粗粒度的模型捕获了各种各样的非平衡动力学，我们验证了我们的结果在行波，其中的现象“基因冲浪”可以产生任何指数$1<α<2$。我们认为，动态抽样偏差的概念是有用的，一般发展的直觉和统计检验的不寻常的动态人口与后代分布偏态，这可能混淆常用的测试选择或人口统计学的历史。
英文摘要：
Natural populations often show enhanced genetic drift consistent with a strong skew in their offspring number distribution. The skew arises because the variability of family sizes is either inherently strong or amplified by population expansions, leading to so-called `jackpot' events. The resulting allele frequency fluctuations are large and, therefore, challenge standard models of population genetics, which assume sufficiently narrow offspring distributions. While the neutral dynamics backward in time can be readily analyzed using coalescent approaches, we still know little about the effect of broad offspring distributions on the dynamics forward in time, especially with selection. Here, we employ an exact asymptotic analysis combined with a scaling hypothesis to demonstrate that over-dispersed frequency trajectories emerge from the competition of conventional forces, such as selection or mutations, with an emerging time-dependent sampling bias against the minor allele. The sampling bias arises from the characteristic time-dependence of the largest sampled family size within each allelic type. Using this insight, we establish simple scaling relations for allele frequency fluctuations, fixation probabilities, extinction times, and the site frequency spectra that arise when offspring numbers are distributed according to a power law $~n^{-(1+α)}$. To demonstrate that this coarse-grained model captures a wide variety of non-equilibrium dynamics, we validate our results in traveling waves, where the phenomenon of 'gene surfing' can produce any exponent $1<α<2$. We argue that the concept of a dynamic sampling bias is useful generally to develop both intuition and statistical tests for the unusual dynamics of populations with skewed offspring distributions, which can confound commonly used tests for selection or demographic history.
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