By Ziheng Yang

ISBN-10: 0198567022

ISBN-13: 9780198567028

The sector of molecular evolution has skilled explosive progress in recent times a result of fast accumulation of genetic series information, non-stop advancements to computing device and software program, and the improvement of subtle analytical equipment. The expanding availability of huge genomic info units calls for strong statistical how you can examine and interpret them, producing either computational and conceptual demanding situations for the field.

Computational Molecular Evolution presents an up to date and finished insurance of recent statistical and computational equipment utilized in molecular evolutionary research, similar to greatest probability and Bayesian facts. Yang describes the types, equipment and algorithms which are most beneficial for analysing the ever-increasing provide of molecular series info, for you to furthering our knowing of the evolution of genes and genomes. The booklet emphasizes crucial ideas instead of mathematical proofs. It comprises certain derivations and implementation information, in addition to quite a few 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, facts and desktop technological know-how. Biologists who've used phylogenetic software program courses to research their very own information will locate the booklet really worthwhile, even though it may still entice a person looking an authoritative review of this fascinating zone of computational biology.

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**Extra resources for Computational Molecular Evolution**

**Sample text**

Consistency means that the estimate θˆ converges to the true value θ when the sample size n → ∞. Efﬁciency means that no other estimate can have a smaller variance than the MLE. Furthermore, the MLEs are asymptotically normally distributed. 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 likelihood is given by the multinomial probability with 16 cells, corresponding to the 16 possible site patterns. Let fij (t1 , t2 ) be the probability for the ijth cell, that is, the probability that any site has nucleotide i in sequence 1 and j in sequence 2. Since such a site can result from all four possible nucleotides in the ancestor, we have to average over them fij (t1 , t2 ) = πk pki (t1 )pkj (t2 ). 57) k Let nij be the number of sites in the ijth cell. The log likelihood is then (t1 , t2 , Q) = nij log{fij (t1 , t2 )}.

Evidence for the performance of the distance when different sequences have different base compositions is mixed. The distance appears to have acquired a paranormal status when it was rediscovered or modiﬁed by Lake (1994), Steel (1994b), and Zharkikh (1994), among others. 1 Distance estimation under different substitution models One might expect more complex models to be more realistic and to produce more reliable distance estimates. However, the situation is more complex. At small distances, the different assumptions about the structure of the Q matrix do not make much difference, and simple models such as JC69 and K80 produce very similar estimates to those under more complex models.

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