of Ne, this distribution is well approximated by the continuously defined exponential distribution 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 DNA elements, such as mitochondrial DNA, however, are only passed on by one sex, and therefore have one quarter the effective size of the equivalent diploid population (Ne/2) Neutral variation Coalescent theory can also be used to model the amount of variation in DNA sequences expected from genetic drift and mutation. 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. Extensions There are numerous extensions to the coalescent model, such as the Λ-coalescent which allows for the possibility of multifurcations. Graphical representation 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 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. A considerable number of human diseases can be attributed to genetics, from simple