Editing Allopatric speciation (section)

=== Mathematical models ===
Developed in the context of the genetic basis of reproductive isolation, mathematical scenarios model both pre[[zygote|zygotic]] and postzygotic isolation with respect to the effects of genetic drift, selection, [[sexual selection]], or various combinations of the three. [[Masatoshi Nei]] and colleagues were the first to develop a [[Neutral theory of molecular evolution|neutral]], [[Stochastic process|stochastic]] model of speciation by genetic drift alone. Both selection and drift can lead to postzygotic isolation, supporting the fact that two geographically separated populations can evolve reproductive isolation<ref name="Speciation"/>{{rp|87}}—sometimes occurring rapidly.<ref>{{Citation |title=A Mechanism for Rapid Allopatric Speciation | author=Christopher J. Wills | journal=The American Naturalist | year=1977 | volume=111 | issue=979 | pages=603–605 | doi= 10.1086/283191| bibcode=1977ANat..111..603W | s2cid=84293637 }}</ref> [[Fisherian runaway|Fisherian sexual selection]] can also lead to reproductive isolation if there are minor variations in selective pressures (such as predation risks or habitat differences) among each population.<ref>{{Citation |title=Runaway ornament diversity caused by Fisherian sexual selection | author=Andrew Pomiankowski and Yoh Iwasa | journal=PNAS | year=1998 | volume=95 | issue=9 | pages=5106–5111 | doi=10.1073/pnas.95.9.5106| pmid=9560236 | pmc=20221 | bibcode=1998PNAS...95.5106P | doi-access=free }}</ref> (See the Further reading section below). Mathematical models concerning reproductive isolation-by distance have shown that populations can experience increasing reproductive isolation that correlates directly with physical, geographical distance.<ref>{{Citation |title=Isolation by distance | author=Sewall Wright | journal=Genetics | year=1943 | volume=28 | issue= 2| pages=114–138| doi=10.1093/genetics/28.2.114 | pmid=17247074 | pmc=1209196 }}</ref><ref>{{Citation |title=Isolation by distance in equilibrium and non-equilibrium populations | author=Montgomery Slatkin | journal=Evolution | year=1993 | volume=47 | issue=1 | pages=264–279 | doi= 10.2307/2410134| pmid=28568097 | jstor=2410134 }}</ref> This has been exemplified in models of [[ring species]];<ref name="Modes and Mechanisms of Speciation" /> however, it has been argued that ring species are a special case, representing reproductive isolation-by distance, and demonstrate parapatric speciation instead<ref name="Speciation"/>{{rp|102}}—as parapatric speciation represents speciation occurring along a [[Cline (biology)|cline]].