uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Mutual invadability near evolutionarily singular strategies for multivariate traits, with special reference to the strongly convergence stable case
Univ Helsinki, Dept Math & Stat, FIN-00014 Helsinki, Finland..
Leiden Univ, Math Inst, POB 9512, NL-2300 RA Leiden, Netherlands.;Leiden Univ, Inst Biol, POB 9512, NL-2300 RA Leiden, Netherlands.;Naturalis, Netherlands Ctr Biodivers, POB 9517, NL-2300 RA Leiden, Netherlands.;Int Inst Appl Syst Anal, Evolut & Ecol Program, A-2361 Laxenburg, Austria..
Uppsala University, Disciplinary Domain of Science and Technology, Biology, Department of Ecology and Genetics, Animal ecology.
2016 (English)In: Journal of Mathematical Biology, ISSN 0303-6812, E-ISSN 1432-1416, Vol. 72, no 4, 1081-1099 p.Article in journal (Refereed) PublishedText
Abstract [en]

Over the last two decades evolutionary branching has emerged as a possible mathematical paradigm for explaining the origination of phenotypic diversity. Although branching is well understood for one-dimensional trait spaces, a similarly detailed understanding for higher dimensional trait spaces is sadly lacking. This note aims at getting a research program of the ground leading to such an understanding. In particular, we show that, as long as the evolutionary trajectory stays within the reign of the local quadratic approximation of the fitness function, any initial small scale polymorphism around an attracting invadable evolutionarily singular strategy (ess) will evolve towards a dimorphism. That is, provided the trajectory does not pass the boundary of the domain of dimorphic coexistence and falls back to monomorphism (after which it moves again towards the singular strategy and from there on to a small scale polymorphism, etc.). To reach these results we analyze in some detail the behavior of the solutions of the coupled Lande-equations purportedly satisfied by the phenotypic clusters of a quasi-n-morphism, and give a precise characterisation of the local geometry of the set in trait space squared harbouring protected dimorphisms. Intriguingly, in higher dimensional trait spaces an attracting invadable ess needs not connect to . However, for the practically important subset of strongly attracting ess-es (i.e., ess-es that robustly locally attract the monomorphic evolutionary dynamics for all possible non-degenerate mutational or genetic covariance matrices) invadability implies that the ess does connect to , just as in 1-dimensional trait spaces. Another matter is that in principle there exists the possibility that the dimorphic evolutionary trajectory reverts to monomorphism still within the reign of the local quadratic approximation for the invasion fitnesses. Such locally unsustainable branching cannot occur in 1- and 2-dimensional trait spaces, but can do so in higher dimensional ones. For the latter trait spaces we give a condition excluding locally unsustainable branching which is far stricter than the one of strong convergence, yet holds good for a relevant collection of published models. It remains an open problem whether locally unsustainable branching can occur around general strongly attracting invadable ess-es.

Place, publisher, year, edition, pages
2016. Vol. 72, no 4, 1081-1099 p.
Keyword [en]
Adaptive dynamics, Evolutionary branching, Multi-dimensional trait space, Mutual invadability, Strong attractivity, Local dimorphic divergence
National Category
Evolutionary Biology
URN: urn:nbn:se:uu:diva-281483DOI: 10.1007/s00285-015-0944-6ISI: 000370269200012PubMedID: 26615529OAI: oai:DiVA.org:uu-281483DiVA: diva2:915398
Available from: 2016-03-30 Created: 2016-03-24 Last updated: 2016-03-30Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textPubMed

Search in DiVA

By author/editor
Rüffler, Claus
By organisation
Animal ecology
In the same journal
Journal of Mathematical Biology
Evolutionary Biology

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Altmetric score

Total: 10 hits
ReferencesLink to record
Permanent link

Direct link