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Incomplete lineage sorting (ILS) (also referred to as hemiplasy, deep coalescence, retention of ancestral polymorphism, or trans-species polymorphism) is a phenomenon in evolutionary biology and population genetics that results in discordance between species and gene trees. By contrast, complete lineage sorting results in concordant species and gene trees. ILS occurs in the context of a gene in an ancestral species which exists in multiple alleles. If a speciation event occurs in this situation, either complete lineage sorting will occur, and both daughter species will inherit all alleles of the gene in question, or incomplete lineage sorting will occur, when one or both daughter species inherits a subset of alleles present in the parental species. For example, if two alleles of a gene are present and a speciation event occurs, one of the two daughter species might inherit both alleles, but the second daughter species only inherits one of the two alleles. In this case, incomplete lineage sorting has occurred.
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