高通量定序技術已經大幅革新了元基因組學以及癌症演化的研究。當一個野生菌落只存在少數的物種時，我們可以藉由全基因體定序的方式得到該物種的隨機樣本，其中的單核苷酸多型性資訊可以用來推論這些細菌族群過去的演化歷史。隨著基因讀序片段長度增加，未來將有更多資訊可以用來研究野生微生物族群的演化過程。由於全基因體定序所得到的讀序片段之間的關係可以表示為一個譜系網路。了解譜系網路的機率分佈有助於了解演化歷史如何影響定序資料的性質，並且可以用來設計新的分析方法。在這個研究裡面，我們提出一個新的機率模型來描述定序資料的譜系網路。我們的模型可以用兩種隨機過程來描述，第一種方式是譜系樹在基因組不同位置的變化，第二種方式是讀序片段從現在到過去的演化。我們證明這個模型可以視為標準模型的近似，而且複雜度遠低於標準模型，因此可以用來設計較有效率的方法。我們根據這個模型實作的一個模擬軟體 MetaSMC，可以用來模擬任意演化過程下的定序資料。除了古典的 infinite-site model，我們的模擬軟體也支援 Jukes-Cantor, HKY85 以及 generalised time-reversible model 等各種演化模型。我們的模擬軟體可以讓不同族群有不同的突變率，這個功能可以讓我們模擬 mutator phenotype 的效果。

High-throughput sequencing technology has revolutionized the study of metagenomics and cancer evolution. In a relatively simple environment, a metagenomics sequencing data is dominated by a few species. By analyzing the alignment of reads from microbial species, single nucleotide polymorphisms can be discovered and the evolutionary history of the populations can be reconstructed. The ever-increasing read length will allow more detailed analysis about the evolutionary history of microbial or tumor cell population. All reads in the sample from a microbial community or tumor can be related by a sequence of genealogies. Understanding the distribution of genealogies provide insight into how evolutionary process affect the mutation pattern in the reads. In this thesis, we proposed a new model of the genealogies of a set of reads from evolving microbial populations. We proposed a spatial process that generate the sequence of genealogies of a set of reads. Our model ignores unnecessary chromosomal segments and thus is far simpler than standard coalescent when recombination is frequent. We showed that the process behind our spatial process is equivalent to Sequentially Markov Coalescent with an incomplete sample. The accuracy of our model was evaluated by summary statistics and likelihood curves derived from Monte-Carlo integration over large number of random genealogies. Based on our model, we implemented an efficient simulator, MetaSMC. Based on the coalescent theory, our simulator supports all evolutionary scenarios supported by other coalescent simulators. In addition, the simulator supports various substitution models, including Jukes-Cantor, HKY85 and generalised time-reversible (GTR) models. The simulator also supports mutator phenotypes by allowing different mutation rates and substitution models in different subpopulations.

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