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The theory was initially developed by Kingman in 3 papers published in probability theory journals, which outline the foundation of coalescent theory as a suite of probability models.
Recent publications continue to address the mathematical development of the coalescent in mathematical journals e. The 2 important points to take from these facts are that, first, coalescent theory is still an active and exciting topic that continues to be developed in its fundamentals and applications and, second, that any book on coalescent theory is going to be heavy on the mathematics.
The new book by John Wakeley aims to summarize the fundamentals of coalescent theory, and it certainly fits the second expectation. This book provides a walk through the mathematical derivations of major aspects of coalescent theory and some specific applications in population genetics. The text primarily stays in the realm of the theoretical, with only a few points illustrated with specific biological examples. This book offers a challenging, but rewarding, introduction to coalescent theory, and it will remain an indispensable text for some time to come.
Coalescent theory is dependent on tree-based genealogical thinking familiar to systematists Harding Unlike phylogenetic methods, coalescent theory assumes that genealogies are random variables. This follows from an assumption of mutational neutrality; in the basic model no particular ancestor is either more or less fit or likely to produce descendants within the genealogy. Also, phylogenetic trees are measured in terms of substitutions or state changes, without an intrinsic time constraint.
In contrast, coalescent trees are calculated in terms of time, set by a fixed mutation rate, and coalescent analyses therefore assume a molecular clock.
The main parameters that are estimated in coalescence analyses are the coalescence time the number of generations that have passed since samples share an ancestor and theta, the scaled product of the mutation rate and effective population size. Therefore, more diverse populations have longer coalescence times and larger coalescent effective population sizes than less diverse populations assuming the same mutation rate.
The coalescent model can be manipulated to explore other subsidiary questions about population diversity through time, such as changes in population structure and size and the total length of the genealogy further back in time than the MRCA under immediate study.
The models use the starting point of neutrality to simulate and test the magnitude and influences of population-level events such as population fluctuation, migration, recombination, and selection. Any mathematical model, by virtue of its weakness or simplifications, illuminates the unquantified complexities of biological systems. Wakeley's text is organized into 8 chapters, in 2 halves. The first 4 chapters present the basic models or Kingman coalescent.
The second half includes newer work and more complex applications. It explicitly requires a good understanding of calculus and probability theory particularly stochastics , and any potential reader who is not comfortable with those subjects and the mathematical notation involved is advised to keep a probability theory textbook or mathematically inclined colleague close at hand.
Anyone who is comfortable in this realm but has not actively used stochastic models recently is advised to take the time to work through the derivations in order to absorb them fully.
Chapter 1 concerns gene genealogies and the general nature of population-level genetic processes. If you do not know what coalescent theory really is, and you did not read my summary above, you have to wait until Chapter 3.
The chapter includes detailed background of the model assumptions and a review of relevant literature. In particular, the sections focus on background information about genealogical thinking and set up the vocabulary for coalescent theory: mutations and discussion of the fundamental assumption in the basic models that variation in population genetics is selectively neutral.
The third section concerns polymorphisms, which may be the most important piece of coalescent theory background to workers who are interested in genomic data see Rosenberg and Nordborg , and is revisited in more detail in Chapter 8. Chapter 2 is a concise and useful refresher course on probability theory. It begins with familiar examples about tossed coins and dice and moves rapidly into deeper water concerning the properties of random variables in general and further on to basic probability distributions Bernoulli, binomial, geometric, and exponential distributions.
Wakeley clearly finds the subject fascinating and rewarding, and this comes across despite the necessarily rapid-fire distillation. The second part of the chapter focuses in more detail on the Poisson distribution and the calculation of events over continuous time.
In discussing Poisson processes, the subject is constantly and clearly tied to applications within the coalescent but requires dedication and concentration from the reader. The first section of this chapter concerns basic models in classical population genetics: the Wright—Fisher model and the Moran model. Like the mathematical material in Chapter 2, this is definitely intended as a refresher and not as teaching from first principles.
Finally, the second section introduces the derivation of the standard coalescent model, following Kingman and using both the mathematical tools from Chapter 2 and the theoretical ideas introduced earlier in the book.
The following section discusses some specific properties of coalescent theory for investigating the size and structure of gene genealogies. Finally, the material from the chapter is summed up with a case study based on comparing human and Neanderthal sequence data, using a coalescent approach to question whether there was historical interbreeding between the two Nordborg The first half of the book ends with a chapter on neutral variation.
That is, how the coalescent's basic assumption of neutrality can be used to infer or predict patterns of the occurrence of polymorphisms. Specific sections address measures of sequence polymorphisms and the Ewens sampling formula in itself a substantial field of probability theory, as the author mentions in Chapter 1, p.
Finally, a section covers empirical tests of assumptions of neutrality and then a case study on positive selection in Drosophila. The second half of the text becomes much more mathematically challenging and with less support in terms of the explanation of how major equations are derived. The last 2 sections deal with biological applications to geographic barriers, including a case study that contrasts gene trees and species trees and on testing the influence of strong selective pressures on subsequent generations, again with an excellent illustrative case study from Drosophila literature.
Chapter 6 contrasts the early literature on the coalescent models to very recent developments with Markov processes at 2 timescales. This addresses how to model and infer variation within real biological populations; an uneven ratio of 2 sexes within the population accelerates the coalescent process because the effective population size may be artificially lowered. That is, the effective population size is not equivalent to the total population size.
This can also be influenced by large volume migration, partial selfing, or a large number of subpopulations that do not all completely overlap, as discussed in other sections of this chapter.
The seventh chapter again confronts the earliest basic assumption, selective neutrality, with more rigor than in previous sections. Material here applies the models to cases of selection and recombination with ancestral graphs.
This is followed by a case study from the human genome and actually expands on data used in the first case study Chapter 1. Finally, Chapter 8 presents a focus on computational methods. The preceding parts of the book concentrated entirely on the underlying mathematics of coalescent theory—the objective was to explain the probability theory that underlies the derivation of the coalescent and inferred ancestral processes.
By use of theoretical tools, Wakeley demonstrates the robustness of coalescent theory and its ability to include modifications that can describe significant deviations from the fundamental assumptions.
This final chapter, then, addresses what most working researchers actually interact with: computational models and simulations. Another case study, again from human genetics, introduces the chapter. This section could have been expanded a great deal, and it is left to the interested reader to explore additional literature in a rapidly expanding field.
The only significant flaw with this book is an extraordinary amount of forward referencing. In the same way, the author often assumes too much familiarity in his readers and makes reference to tools and concepts before explaining them in detail later in the book. This means that the book is nearly impossible to read straight through from the beginning and requires jumping back and forth between chapters to follow the progress of some basic ideas such as the definition of coalescent theory, Markov processes, and genetic polymorphisms.
This book has been a long time coming, and sections were available online from late In fact, at the time of this review the publisher still offers early versions of the first 3 chapters available online and an out-of-date table of contents. The early, unpublished version of this book included excellent problem sets at the end of each chapter included in the 3 sample chapters on the publisher's web site and indicated in the draft table of contents.
It is a great mystery why these were excluded from the final publication as problem exercises and solutions would have made the book substantially more accessible and dramatically improved its utility as a teaching aid. It is a little surprising that there are fewer textbooks on the subject of coalescent theory, given the importance of the coalescent for modern population genetics and the huge scope of scientific questions relevant to the field.
Only one other introductory textbook has been published to date Hein et al. The first 2 case studies included in the present book based on Nordborg ; Harris and Hey are also used as illustrative examples in Hein et al. Additional biological case studies would be very welcome there are 7 in the book, in 6 chapters and would probably make the text more accessible to a wider audience of biologists. I hope that Wakeley will be persuaded to update the text in due course, and certainly by that time there will be a much wider base of literature for potential case studies.
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Psychology in Everyday Life
The theory was initially developed by Kingman in 3 papers published in probability theory journals, which outline the foundation of coalescent theory as a suite of probability models. Recent publications continue to address the mathematical development of the coalescent in mathematical journals e. The 2 important points to take from these facts are that, first, coalescent theory is still an active and exciting topic that continues to be developed in its fundamentals and applications and, second, that any book on coalescent theory is going to be heavy on the mathematics. The new book by John Wakeley aims to summarize the fundamentals of coalescent theory, and it certainly fits the second expectation. This book provides a walk through the mathematical derivations of major aspects of coalescent theory and some specific applications in population genetics.
Coalescent Theory: An Introduction
Coalescent theory provides the foundation for molecular population genetics and genomics. It is the conceptual framework for studies of DNA sequence variation within species, and is the source of essential tools for making inferences about mutation, recombination, population structure and natural selection from DNA sequence data. The case studies are a terrific feature I think many biologists will be greatly buoyed by these, and motivated to think deeper about the models and how they can be analyzed. A must for everyone interested in ancestral population genetics. Students and teachers will welcome this accessible treatment. For the first time, Wakeley's book provides a clear and accessible account of this key subject, which takes the reader right up to the frontiers of current research.