Unified reduction principle for the evolution of mutation, migration, and recombination
Lee Altenberg a,b,1, Uri Liberman c,1, and Marcus W. Feldman d,1,2
aInformation and Computer Sciences, University of Hawaii at Mānoa, Honolulu, HI 96822;
bKonrad Lorenz Institute for Evolution and Cognition Research, Klosterneuburg, Austria A3400;
cSchool of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;
dDepartment of Biology, Stanford University, Stanford, CA 94305-5020
Contributed by Marcus W. Feldman, January 31, 2017 (sent for review November 29, 2016; reviewed by Reinhard Burger, Yoh Iwasa, and Hamish G. Spencer)
Evolution by Darwinian natural selection can not only shape how organisms survive and reproduce, but also affect transmission of genetic and other information between generations. Modifier-gene models for the evolution of information transmission have revealed a universal tendency for more faithful transmission to evolve in populations at equilibrium where natural selection is balanced by errors in information transmission. This is shown to be a very general property of models that include mutation and migration under selection and recombination under selection on diploids. The breadth of this reduction principle focuses attention on the departures from its mathematical assumptions, which may explain those biological phenomena of information transmission between generations for which the reduction principle fails.
Modifier-gene models for the evolution of genetic information transmission between generations of organisms exhibit the reduction principle: Selection favors reduction in the rate of variation production in populations near equilibrium under a balance of constant viability selection and variation production. Whereas this outcome has been proven for a variety of genetic models, it has not been proven in general for multiallelic genetic models of mutation, migration, and recombination modification with arbitrary linkage between the modifier and major genes under viability selection. We show that the reduction principle holds for all of these cases by developing a unifying mathematical framework that characterizes all of these evolutionary models.
mutation recombination dispersal modifier genes external stability
1L.A., U.L., and M.W.F. contributed equally to this work.
2To whom correspondence should be addressed. Email: firstname.lastname@example.org.
Author contributions: L.A., U.L., and M.W.F. designed research, performed research, analyzed data, and wrote the paper.
Reviewers: R.B., University of Vienna; Y.I., Kyushu University; and H.G.S., University of Otago.
The authors declare no conflict of interest.
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1619655114/-/DCSupplemental.
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