There are many excellent computational biology resources now available for learning about methods that have been developed to address specific biological systems, but comparatively little attention has been paid to training aspiring computational biologists to handle new and unanticipated problems. This text is intended to fill that gap by teaching students how to reason about developing formal mathematical models of biological systems that are amenable to computational analysis.
2. This means that the model is extremely unlikely to get to very large k and is certain to eventually reach k 1. It may increase again afterward, but for the purposes of simulating the process, we only need it to get to one lineage once. Once we have an MRCA, we can create its sequence and insert mutations along the lineages forward in time from there.
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(cid:3) (cid:4) kr=2 k 2 199 200 12 Case Study: Molecular Evolution References and Further Study The JukesCantor and Kimura models are standard models for studies of molecular evolution and are covered adequately in a wide variety of sources on these topics. Graur and Li provides a clear coverage of these issues, as well as many others likely to be of interest to readers of this chapter. The best presentation of the coalescent model of which I am aware is found in a review chapter by Nordborg in the Handbook of Statistical Genetics, which was an important source in preparing this chapters discussion of the coalescent and its extensions. For more depth on the general topics covered here, the reader may refer to a more general text on population genetics, such as Hartl and Clark .
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The JukesCantor and Kimura models are, of course, originally due to Jukes and Cantor and Kimura . The coalescent model is due to Kingman . The various extensions of the basic coalescent that were covered here are derived from Nordborg . Many other coalescent extensions are available in the literature, and a current search may therefore prove helpful for those requiring more specialized coalescent variants.
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13 Discrete Event Simulation As we have seen, one way of representing continuous-time Markov models is to repeatedly consider every transition that may happen next, determine the time at which each will happen, and pick the one with minimum time. This representation of CTMMs is a special case of a more general class of models called discrete event models. In a discrete event model, we have a set of discrete states, just as in a Markov model, and move between states in continuous time, as in a CTMM. However, instead of insisting that all transitions have exponential times, we will allow for any possible waiting time distributions.
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