论文标题
使用融合，与正交多项式扩散和MORAN模型的双重突变漂移模型的种群遗传参数的推断
Inference of population genetic parameters with a biallelic mutation drift model using the coalescent, diffusion with orthogonal polynomials, and the Moran model
论文作者
论文摘要
在种群遗传学中，现有的样本通常用于推断过去的人口遗传力。随着Kingman合并和向后扩散方程，边缘可能性的推断从现存的样本落后进行。在现存的样本上有条件，Moran模型也可以在及时倒退，结果相同，最多可以缩放时间。特别是，所有三种方法 - 融合，向后扩散和Moran模型 - 导致样品的边际可能性相同。如果还可以推断出祖先状态的概率，则如在融合或祖先种群等位基因比例中的离散等位基因颗粒构型，例如在向后扩散中，需要将向后算法与相应的向前算法与前进算法结合使用。通常，求解扩散方程的正交多项式在数值上比其他方法更简单：它们隐含地在许多中间祖先粒子构型上汇总；此外，虽然Moran模型需要迭代矩阵乘法，并具有人口大小平方的尺寸的过渡矩阵，但多项式的扩展仅是样本大小的膨胀。对于离散的样本，远期移动的纯出生育过程类似于多拉或Hoppe-urn模型，以补充向后看起来的合并。因为，样本量是一个随时间转发的随机变量，因此，给定样本的纯生过程不适合模型人群模型。但是，使用正交多项式，不仅可以轻松计算祖先等位基因比例，而且还可以轻松计算祖先粒子构型的概率。假设仅突变和漂移，与替代策略相比，正交多项式的使用在数值上是有利的。
In population genetics, extant samples are usually used for inference of past population genetic forces. With the Kingman coalescent and the backward diffusion equation, inference of the marginal likelihood proceeds from an extant sample backward in time. Conditional on an extant sample, the Moran model can also be used backward in time with identical results, up to a scaling of time. In particular, all three approaches -- the coalescent, the backward diffusion, and the Moran model -- lead to the identical marginal likelihood of the sample. If probabilities of ancestral states are also inferred, either of discrete ancestral allele particle configurations, as in the coalescent, or of ancestral population allele proportions, as in the backward diffusion, the backward algorithm needs to be combined with the corresponding forward algorithm to the forward-backward algorithm. Generally orthogonal polynomials, solving the diffusion equation, are numerically simpler than the other approaches: they implicitly sum over many intermediate ancestral particle configurations; furthermore, while the Moran model requires iterative matrix multiplication with a transition matrix of a dimension of the population size squared, expansion of the polynomials is only necessary up to the sample size. For discrete samples, forward-in-time moving pure birth processes similar to the Polya- or Hoppe-urn models complement the backward-looking coalescent. Because, the sample size is a random variable forward in time, pure-birth processes are unsuited to model population demography given extant samples. With orthogonal polynomials, however, not only ancestral allele proportions but also probabilities of ancestral particle configurations can be calculated easily. Assuming only mutation and drift, the use of orthogonal polynomials is numerically advantageous over alternative strategies.
