By Ziheng Yang

ISBN-10: 0198567022

ISBN-13: 9780198567028

The sector of molecular evolution has skilled explosive progress in recent times as a result of the speedy accumulation of genetic series information, non-stop advancements to laptop and software program, and the improvement of refined analytical tools. The expanding availability of huge genomic information units calls for strong statistical how to study and interpret them, producing either computational and conceptual demanding situations for the field.

Computational Molecular Evolution presents an up to date and entire assurance of contemporary statistical and computational equipment utilized in molecular evolutionary research, reminiscent of greatest chance and Bayesian data. Yang describes the types, tools and algorithms which are most dear for analysing the ever-increasing provide of molecular series information, so as to furthering our figuring out of the evolution of genes and genomes. The ebook emphasizes crucial strategies instead of mathematical proofs. It comprises distinctive derivations and implementation info, in addition to various illustrations, labored examples, and routines. it is going to be of relevance and use to scholars researchers (both empiricists and theoreticians) within the fields of molecular phylogenetics, evolutionary biology, inhabitants genetics, arithmetic, information and laptop technology. Biologists who've used phylogenetic software program courses to research their very own facts will locate the e-book really profitable, even though it should still entice somebody looking an authoritative assessment of this interesting zone of computational biology.

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**Example text**

3). 59) scaled so that the average rate is − i πi qii = 1. 2). 2 The general time-reversible (GTR) model A Markov chain is said to be time-reversible if and only if πi qij = πj qji , for all i = j. 60) Note that πi is the proportion of time the Markov chain spends in state i, and πi qij is the amount of ‘ﬂow’ from states i to j, while πj qji is the ﬂow in the opposite direction. 60) is known as the detailed-balance condition and means that the ﬂow between any two states in the opposite direction is the same.

These properties are known to hold in large samples. How large the sample size has to be for the approximation to be reliable depends on the particular problem. Another important property of MLEs is that they are invariant to transformations of parameters or reparametrizations. The MLE of a function of parameters is the same ˆ ) = h(θˆ ). Thus if the same model can be function of the MLEs of the parameters: h(θ formulated using either parameters θ1 or θ2 , with θ1 and θ2 constituting a one-to-one mapping, use of either parameter leads to the same inference.

Furthermore, the likelihood curve around θˆ provides information about the uncertainty in the point estimate. The theory applies to problems with a single parameter as well as problems involving multiple parameters, in which case θ is a vector. Here we apply the theory to estimation of the distance between two sequences under the JC69 model (Jukes and Cantor 1969). The single parameter is the distance d. The data are two aligned sequences, each n sites long, with x differences. 5), the probability that a site has different nucleotides between two sequences separated by distance d is p = 3p1 = 3 4 − 43 e−4d/3 .

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