Accounting for spatial heterogeneity of parameters in the sequentially Markov coalescent process

序列马尔可夫合并（SMC）是一个近似的合并过程与重组，使其应用于全基因组数据集。SMC模型不同于标准聚结，因为它在空间上沿着比对沿着而不是按时间顺序对一组序列的谱系进行建模。此外，系谱变化的过程沿着基因组是马尔可夫的，允许使用隐马尔可夫模型推断群体基因组参数。虽然SMC在空间上对聚结进行建模，但目前的模型假定沿着基因组的参数具有同质性。这种假设显然与我们对基因组生物学的了解不一致，因为突变率、重组率和有效群体大小是高度异质的。SMC模型也专门应用于高等真核生物，主要是灵长类。这些物种具有非常大的基因组，因此参数异质性相当稀释。随着下一代测序数据变得越来越便宜，正在为具有更小，更紧凑基因组的物种生成群体基因组数据集。对于这些数据集，参数异质性可能比灵长类动物基因组极端得多。这些物种包括经济上重要的真菌病原体，这些病原体不能用当前过于简单的模型进行分析。在这个项目中，我们提出了一个扩展目前的SMC模型，占随机过程沿着基因组。空间异质性建模为马尔可夫过程，当与SMC的固有马尔可夫属性相结合时，结果在马尔可夫调制的顺序马尔可夫模型。该项目将建立这种马尔可夫调制SMC（MSMC）的分析和使用模拟程序的正式属性。生物应用提出了灵长类动物和真菌的数据集。

The sequentially Markov coalescent (SMC) is an approximation of the coalescent process with recombination enabling its application to whole genome data sets. The SMC model differs from the standard coalescent as it models the genealogy of a set of sequences spatially along the alignment rather than chronologically. In addition, the process of genealogy change along the genome is Markovian, allowing the use of hidden Markov models for inference of population genomic parameters. While the SMC models the coalescent in space, current models so far assume homogeneity of parameters along the genome. This assumption is clearly at odds with our knowledge of the biology of genomes, as mutation rate, recombination rate and effective population size are highly heterogeneous. SMC models have also been exclusively applied to higher eukaryotic species, essentially Primates. These species have very large genomes, for which the parameter heterogeneity is rather diluted. With next-generation sequencing data becoming increasingly affordable, population genomic data sets are being generated for species with smaller, more compact genomes. For these data sets, parameter heterogeneity can be much more extreme than for primate genomes. Such species include economically important fungal pathogens, which cannot be analyzed with current, over-simplistic models. In this project we propose an extension of current SMC models to account for stochastic processes along the genome. The spatial heterogeneity is modeled as a Markov process, which, when combined with the intrinsic Markov property of the SMC, results in a Markov-modulated sequentially Markov model. The project will establish the formal properties of such Markov-modulated SMC (MMSMC) analytically and using simulation procedures. Biological applications are proposed for both primate and fungal data sets.