Contents 1 Theory 1.1 Time to coalescence 1.2 Neutral variation 2 Graphical representation 3 Applications 3.1 Disease gene mapping 3.2 The genomic distribution of heterozygosity 4 History 5 Software 6 Sources 6.1 Articles 6.2 Books 7 External links Theory[edit]
Time to coalescence[edit]
Consider a single gene locus sampled from two haploid individuals in a
population. The ancestry of this sample is traced backwards in time to
the point where these two lineages coalesce in their most recent
common ancestor (MRCA).
P c ( t ) = ( 1 − 1 2 N e ) t − 1 ( 1 2 N e ) . displaystyle P_ c (t)=left(1- frac 1 2N_ e right)^ t-1 left( frac 1 2N_ e right). For sufficiently large values of Ne, this distribution is well approximated by the continuously defined exponential distribution P c ( t ) = 1 2 N e e − t − 1 2 N e . displaystyle P_ c (t)= frac 1 2N_ e e^ - frac t-1 2N_ e . This is mathematically convenient, as the standard exponential
distribution has both the expected value and the standard deviation
equal to 2Ne. Therefore, although the expected time to coalescence is
2Ne, actual coalescence times have a wide range of variation. Note
that coalescent time is the number of preceding generations where the
coalescence took place and not calendar time, though an estimation of
the latter can be made multiplying 2Ne with the average time between
generations. The above calculations apply equally to a diploid
population of effective size Ne (in other words, for a non-recombining
segment of DNA, each chromosome can be treated as equivalent to an
independent haploid individual; in the absence of inbreeding, sister
chromosomes in a single individual are no more closely related than
two chromosomes randomly sampled from the population). Some
effectively haploid
H ¯ displaystyle bar H . 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: 2 μ displaystyle 2mu . Thus the mean heterozygosity is equal to H ¯ = 2 μ 2 μ + 1 2 N e = 4 N e μ 1 + 4 N e μ = θ 1 + θ displaystyle begin aligned bar H &= frac 2mu 2mu + frac 1 2N_ e \[3pt]&= frac 4N_ e mu 1+4N_ e mu \[3pt]&= frac theta 1+theta end aligned For 4 N e μ ≫ 1 displaystyle 4N_ e mu gg 1 , the vast majority of allele pairs have at least one difference in
nucleotide sequence.
Graphical representation[edit]
Coalescents can be visualised using dendrograms which show the
relationship of branches of the population to each other. The point
where two branches meet indicates a coalescent event.
Applications[edit]
Disease gene mapping[edit]
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.[6][7][8]
A considerable number of human diseases can be attributed to genetics,
from simple Mendelian diseases like sickle-cell anemia and cystic
fibrosis, to more complicated maladies like cancers and mental
illnesses. The latter are polygenic diseases, controlled by multiple
genes that may occur on different chromosomes, but diseases that are
precipitated by a single abnormality are relatively simple to pinpoint
and trace – although not so simple that this has been achieved for
all diseases. It is immensely useful in understanding these diseases
and their processes to know where they are located on chromosomes, and
how they have been inherited through generations of a family, as can
be accomplished through coalescent analysis[1].
Genetic diseases are passed from one generation to another just like
other genes. While any gene may be shuffled from one chromosome to
another during homologous recombination, it is unlikely that one gene
alone will be shifted. Thus, other genes that are close enough to the
disease gene to be linked to it can be used to trace it[1].
Polygenic diseases have a genetic basis even though they don’t
follow
BEAST –
Sources[edit] Articles[edit] ^ Arenas, M. and Posada, D. (2014) Simulation of Genome-Wide Evolution
under Heterogeneous Substitution Models and Complex Multispecies
Coalescent Histories. Molecular Biology and
Books[edit] Hein, J; Schierup, M. H., and Wiuf, C. Gene Genealogies, Variation and
External links[edit] EvoMath 3: Genetic Drift and Coalescence, Briefly — overview, with probability equations for genetic drift, and simulation graphs v t e Population genetics Key concepts Hardy-Weinberg law Genetic linkage Identity by descent Linkage disequilibrium Fisher's fundamental theorem Neutral theory Shifting balance theory Price equation Coefficient of relationship Fitness Heritability Selection Natural Sexual Artificial Ecological Effects of selection on genomic variation Genetic hitchhiking Background selection Genetic drift Small population size Population bottleneck Founder effect Coalescence Balding–Nichols model Founders R. A. Fisher J. B. S. Haldane Sewall Wright Related topics Evolution Microevolution Evolutionary game theory Fitness landscape Genetic genealogy Quantitative genetics Index of evolutionary biology articles ^ a b c Morris, A., Whittaker, J., & Balding, D. (2002). Fine-Scale Mapping of Disease Loci via Shattered Coalescent Modeling of Genealogies. The American Journal of Human Genetics, 70(3), 686-707. doi:10.1086/339271 ^ a b c Rannala, B. (2001). Finding genes influencing susceptibility to complex diseases in the post-genome era. American journal of pharmacogenomi |