even have genetic effects that can easily be misinterpreted as historical changes in population size, or the existence of admixture events, even when no such events occurred. Heterozygosity One of the results of population structure is a reduction in heterozygosity. When populations split, alleles have a higher chance of reaching fixation within subpopulations, especially if the subpopulations are small or have been isolated for long periods. This reduction in heterozygosity can be thought of as an extension of inbreeding, with individuals in subpopulations being more likely to share a recent common ancestor. The scale is important — an individual with both parents born in the United Kingdom is not inbred relative to that country's population, but is more inbred than two humans selected from the entire world. This motivates the derivation of Wright's F-statistics (also called "fixation indices"), which measure inbreeding through observed versus expected heterozygosity. For example, measures the inbreeding coefficient at a single locus for an individual relative to some subpopulation : Here, is the fraction of individuals in subpopulation that are heterozygous. Assuming there are two alleles, that occur at respective frequencies , it is expected that under random mating the subpopulation will have a heterozygosity rate of . Then: Similarly, for the total population , we can define allowing us to compute the expected heterozygosity of subpopulation and the value as: If F is 0, then the allele frequencies between populations are identical, suggesting no structure. The theoretical maximum value of 1 is attained when an allele reaches total fixation, but most observed maximum values are far lower. FST is one of the most common measures of population structure and there are several different formulations depending on the number of populations and the alleles of interest. Although it is sometimes used as a genetic distance between populations, it does not always satisfy the triangle inequality and thus is not a metric. It also depends on within-population diversity, which makes interpretation and comparison difficult. Admixture inference An individual's genotype can be modelled as an admixture between K discrete clusters of populations. Each cluster is defined by the frequencies of its genotypes, and the contribution of a cluster to an individual's genotypes is measured via an estimator. In 2000, Jonathan K. Pritchard introduced the STRUCTURE algorithm to estimate these proportions via Markov chain Monte Carlo, modelling allele frequencies at each locus with a Dirichlet distribution. Since then, algorithms