title: The canonical equation of adaptive dynamics for Mendelian diploids and haplo-diploids.
abstract: One of the powerful tools of adaptive dynamics is its so-called canonical equation (CE), a differential equation describing how the prevailing trait vector changes over evolutionary time. The derivation of the CE is based on two simplifying assumptions, separation of population dynamical and mutational time scales and small mutational steps. (It may appear that these two conditions rarely go together. However, for small step sizes the time-scale separation need not be very strict.) The CE was derived in 1996, with mathematical rigour being added in 2003. Both papers consider only well-mixed clonal populations with the simplest possible life histories. In 2008, the CE's reach was heuristically extended to locally well-mixed populations with general life histories. We, again heuristically, extend it further to Mendelian diploids and haplo-diploids. Away from strict time-scale separation the CE does an even better approximation job in the Mendelian than in the clonal case owing to gene substitutions occurring effectively in parallel, which obviates slowing down by clonal interference.
authors: Mathematical Institute , Leiden University , 2333CA Leiden , The Netherlands ; Institute of Biology , Leiden University , 2333CA Leiden , The Netherlands ; Evolution and Ecology Program , International Institute for Applied Systems Analysis , 2361 Laxenburg , Austria ; Naturalis Biodiversity Center , 2333CR Leiden , The Netherlands.
authors: Johan A J
authors: JA
authors: Metz
authors: Department of Medical Genetics , Universitair Medisch Centrum Utrecht , Sectie Complex Genetics, Utrecht , The Netherlands.
authors: Carolien G F
authors: CG
authors: de Kovel
keywords: adaptive dynamics; canonical equation; effective reproductive variance; haplo-diploids; invasion probability; meso-evolution