Department of Scientific Computing, Florida State University, Tallahassee, FL 32306
Department of Scientific Computing, Florida State University, Tallahassee, FL 32306.
Proc Natl Acad Sci U S A. 2019 Mar 26;116(13):6244-6249. doi: 10.1073/pnas.1810239116. Epub 2019 Mar 13.
An approach to the coalescent, the fractional coalescent (f-coalescent), is introduced. The derivation is based on the discrete-time Cannings population model in which the variance of the number of offspring depends on the parameter α. This additional parameter α affects the variability of the patterns of the waiting times; values of [Formula: see text] lead to an increase of short time intervals, but occasionally allow for very long time intervals. When [Formula: see text], the f-coalescent and the Kingman's n-coalescent are equivalent. The distribution of the time to the most recent common ancestor and the probability that n genes descend from m ancestral genes in a time interval of length T for the f-coalescent are derived. The f-coalescent has been implemented in the population genetic model inference software Migrate Simulation studies suggest that it is possible to accurately estimate α values from data that were generated with known α values and that the f-coalescent can detect potential environmental heterogeneity within a population. Bayes factor comparisons of simulated data with [Formula: see text] and real data (H1N1 influenza and malaria parasites) showed an improved model fit of the f-coalescent over the n-coalescent. The development of the f-coalescent and its inclusion into the inference program Migrate facilitates testing for deviations from the n-coalescent.
引入了一种合并方法，即分数合并（f-coalescent）。这种推导基于离散时间 Cannings 种群模型，其中后代数量的方差取决于参数α。这个附加的参数α影响等待时间模式的可变性；值为[Formula: see text]导致短时间间隔的增加，但偶尔也允许非常长时间间隔。当[Formula: see text]时，f-coalescent 和 Kingman 的 n-coalescent 是等效的。推导了 f-coalescent 中最近共同祖先的时间分布和在长度为 T 的时间间隔内 n 个基因从 m 个祖先基因遗传的概率。f-coalescent 已在种群遗传模型推断软件 Migrate 中实现。模拟研究表明，从具有已知α值的数据中准确估计α值是可能的，并且 f-coalescent 可以检测种群内潜在的环境异质性。模拟数据与[Formula: see text]和真实数据（H1N1 流感和疟原虫）的贝叶斯因子比较表明，f-coalescent 比 n-coalescent 更能拟合模型。f-coalescent 的发展及其纳入推断程序 Migrate 有助于测试与 n-coalescent 的偏差。
