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Information about Coalescent Theory

In genetics, coalescent theory is a retrospective model of population genetics that traces all alleles of a gene in a sample from a population to a single ancestral copy shared by all members of the population, known as the most recent common ancestor (MRCA; sometimes also termed the coancestor to emphasize the coalescent relationship[1]). The inheritance relationships between alleles are typically represented as a gene genealogy, similar in form to a phylogenetic tree. This gene genealogy is also known as the coalescent; understanding the statistical properties of the coalescent under different assumptions forms the basis of coalescent theory. In the most simple case, coalescent theory assumes no recombination, no natural selection, and no gene flow or population structure. Advances in coalescent theory, however, allow extension to the basic coalescent, and can include recombination, selection, and virtually any arbitrarily complex evolutionary or demographic model in population genetic analysis. The mathematical theory of the coalescent was originally developed in the early 1980s by John Kingman[2].

Theory

Consider two distinct haploid organisms who differ at a single nucleotide. By tracing the ancestry of these two individuals backwards there will be a point in time when the Most Recent Common Ancestor (MRCA) is encountered and the two lineages will have coalesced.

Probability of fixation

Under conditions of genetic drift alone, every finite set of genes or alleles has a "coalescent point" at which all descendants converge to a single ancestor (i.e. they 'coalesce'). This fact can be used to derive the rate of gene fixation of a neutral allele (that is, one not under any form of selection) for a population of varying size (provided that it is finite and nonzero). Because the effect of natural selection is stipulated to be negligible, the probability at any given time of an allele becoming fixed is just its frequency in the population at that time. For a diploid population of size and (neutral) mutation rate , the initial frequency of a novel mutation is simply and the number of new mutations per generation is . Since the fixation rate is the rate of novel neutral mutation multiplied by their probability of fixation, the overall fixation rate is . Thus the rate of fixation for a mutation not subject to selection is simply the rate of introduction of such mutations.

Time to coalescence

A useful analysis based on coalescence theory seeks to predict the amount of time elapsed between the introduction of a mutation and a particular allele or gene distribution in a population. This time period is equal to how long ago the most recent common ancestor existed.

The probability that two lineages coalesce in the immediately preceding generation is the probability that they share a parent. In a diploid population of constant size with copies of each locus, there are "potential parents" in the previous generation, so the probability that two alleles share a parent is and correspondingly, the probability that they do not coalesce is .

At each successive preceding generation, the probability of coalescence is geometrically distributed - that is, it is the probability of noncoalescence at the preceding generations multiplied by the probability of coalescence at the generation of interest:



For sufficiently large values of , this distribution is well approximated by the continuously defined exponential distribution



The standard exponential distribution has both the expectation value and the standard deviation equal to - therefore, although the expected time to coalescence is , actual coalescence times have a wide range of variation.

Neutral variation

Coalescent theory can also be used to model the amount of variation in DNA sequences expected from genetic drift alone. This value is termed the mean heterozygosity, represented as . Mean heterozygosity is calculated as the probability of a mutation occurring at a given generation divided by the probability of any "event" at that generation (either a mutation or a coalescence). The probability that the event is a mutation is the probability of a mutation in either of the two lineages: . Thus the mean heterozygosity is equal to





For , the vast majority of allele pairs have at least one difference in nucleotide sequence.

Graphical representation

Coalescents can be visualised using dendograms which show the relationship of branches of the population to each other. The point where two branches meet indicates the Most Recent Common Ancestor (MRCA).

Applications

Disease gene mapping

The utility of coalescent theory in the mapping of disease is slowly gaining more appreciation; although the application of the theory is still in its infancy there are a number of researchers who are actively developing algorithms for the analysis of human genetic data that utilise coalescent theory[3][4][5].

History

Coalescent theory is a natural extension the more classical population genetics concept of neutral evolution and is an approximation to the Fisher-Wright (or Wright-Fisher) model for large populations. It was 'discovered' independently by several researchers in the 1980's [6][7][8][9], but the definitive formalisation is attributed to Kingman [6]. Major contributions to the development of coalescent theory have been made by Peter Donnelly[10], Robert Griffiths, Richard R Hudson[11] and Simon Tavaré[10], this has included incorporating variations in population size[12] recombination and selection[13][14].

Software

A large body of software exists for simulating data sets under the coalescent process, and gradually software is emerging that allows the analysis of human genetics data for the mapping of disease susceptibility loci.

References and notes

Articles

Books

  • Hein, J; Schierup, M. H., and Wiuf, C. Gene Genealogies, Variation and Evolution – A Primer in Coalescent Theory. Oxford University Press, 2005. ISBN 0-19-852996-1.
  • Nordborg, M. (2001) Introduction to Coalecsent Theory Chapter 7 in Balding, D., Bishop, M., Cannings, C., editors, Handbook of Statistical Genetics. Wiley ISBN 978-0471860945
  • Wakeley J. (2006) An Introduction to Coalescent Theory Roberts & Co ISBN: 0-9747077-5-9 Accompanying website with sample chapters
  • ^  Rice SH. (2004). Evolutionary Theory: Mathematical and Conceptual Foundations. Sinauer Associates: Sunderland, MA. See esp. ch. 3 for detailed derivations.

External links

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Topics in population genetics
Key conceptsHardy-Weinberg law • genetic linkage • linkage disequilibrium • Fisher's fundamental theorem • neutral theory
Selectionnatural • sexual • artificial • ecological
Effects of selection on genomic variationgenetic hitchhiking • background selection
Genetic driftsmall population size • population bottleneck • founder effect • coalescence
FoundersR.A. Fisher • J. B. S. Haldane • Sewall Wright
Related topicsevolution • microevolution • evolutionary game theory • fitness landscape • genetic genealogy
List of evolutionary biology topics
Genetics is the science of heredity and variation in living organisms.[1][2] Knowledge of the inheritance of characteristics has been implicitly used since prehistoric times for improving crop plants and animals through selective breeding.
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For the hard rock band, see .
An allele (Pronounced: /əˈlil/) is a viable DNA (deoxyribonucleic acid) coding that occupies a given locus (position) on a chromosome.
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For a non-technical introduction to the topic, see .
A gene is a locatable region of genomic sequence, corresponding to a unit of inheritance, which is associated with regulatory regions, transcribed regions and/or other functional sequence regions.
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The most recent common ancestor (MRCA) of any set of organisms is the most recent individual from which all organisms in the group are directly descended. The term is most frequently used of humans.
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A phylogenetic tree, also called an evolutionary tree, is a tree showing the evolutionary relationships among various biological species or other entities that are believed to have a common ancestor.
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Genetic recombination is the process by which a strand of DNA is broken and then joined to the end of a different DNA molecule. In eukaryotes recombination commonly occurs during meiosis as chromosomal crossover between paired chromosomes.
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Natural selection is the process by which favorable traits that are heritable become more common in successive generations of a population of reproducing organisms, and unfavorable traits that are heritable become less
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In population genetics, gene flow (also known as gene migration) is the transfer of alleles of genes from one population to another.
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Sir John Frank Charles Kingman, a mathematician, was born on 28 August 1939 in Beckenham, Kent1. Since 2001, he has been N. M. Rothschild and Sons Professor of Mathematical Science and Director of the Isaac Newton Institute at the University of Cambridge1,2,3.
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Plantae
  • Chromalveolata
  • Heterokontophyta
  • Haptophyta
  • Cryptophyta
  • Alveolata

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    • A nucleotide is a chemical compound that consists of 3 portions: a heterocyclic base, a sugar, and one or more phosphate groups. In the most common nucleotides the base is a derivative of purine or pyrimidine, and the sugar is the pentose (five-carbon sugar) deoxyribose or ribose.
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    In population genetics, fixation occurs when every individual within a population has the same allele at a particular locus. The allele, such as a single point mutation or whole gene, will be initially rare (e.g.
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    Probability is the likelihood that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of
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    mutations are changes to the base pair sequence of the genetic material of an organism. Mutations can be caused by copying errors in the genetic material during cell division, by exposure to ultraviolet or ionizing radiation, chemical mutagens, or viruses, or can occur deliberately
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    mutations are changes to the base pair sequence of the genetic material of an organism. Mutations can be caused by copying errors in the genetic material during cell division, by exposure to ultraviolet or ionizing radiation, chemical mutagens, or viruses, or can occur deliberately
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    Lineage may refer to:

    In science:
    • Lineage (anthropology), descent group that can demonstrate their common descent from an apical ancestor
    • Lineage (evolution), group composed of species, taxa, or individuals related by descent from a common ancestor

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    geometric distribution is either of two discrete probability distributions:
    • the probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set , or
    • the probability distribution of the number Y

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    exponential distributions are a class of continuous probability distribution. They are often used to model the time between independent events that happen at a constant average rate.
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    expected value (or mathematical expectation, or mean) of a discrete random variable is the sum of the probability of each possible outcome of the experiment multiplied by the outcome value (or payoff).
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    In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma).
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    Zygosity refers to the genetic condition of a zygote. In genetics, zygosity describes the similarity or dissimilarity of DNA between homologous chromosomes at a specific allelic position or gene.

    Every gene in a diploid organism has two alleles at the gene's locus.
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    A nucleotide is a chemical compound that consists of 3 portions: a heterocyclic base, a sugar, and one or more phosphate groups. In the most common nucleotides the base is a derivative of purine or pyrimidine, and the sugar is the pentose (five-carbon sugar) deoxyribose or ribose.
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    Population genetics is the study of the allele frequency distribution and change under the influence of the four evolutionary forces: natural selection, genetic drift, mutation and gene flow. It also takes account of population subdivision and population structure in space.
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    19th century - 20th century - 21st century
    1950s  1960s  1970s  - 1980s -  1990s  2000s  2010s
    1977 1978 1979 - 1980 - 1981 1982 1983

    Year 1980 (MCMLXXX
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    Peter Donnelly, FRS is an Australian mathematician and Professor of Statistical Science at the University of Oxford. He is a specialist in applied probability and has made important mathematical contributions to coalescent theory.
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    Robert C. Griffiths is an Australian mathematician and statistician. He is Professor of Mathematical Genetics in the University of Oxford.
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    Bayesian refers to methods in probability and statistics named after the Reverend Thomas Bayes (ca. 1702–1761), in particular methods related to:
    • the degree-of-belief interpretation of probability, as opposed to frequency or proportion or propensity

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    MCMC may refer to:
    • Malaysian Communications and Multimedia Commission
    • Markov chain Monte Carlo

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    Linkage disequilibrium is a term used in the study of population genetics for the non-random association of alleles at two or more loci, not necessarily on the same chromosome.
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