Evolutionary stability: One concept, several meanings

Lessard, Sabin

doi:10.1016/0040-5809(90)90033-r

Cited by 67 publications

(53 citation statements)

References 35 publications

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“…This condition is a summary and generalisation of previous work on stability criteria (e.g. Lessard, 1990;Abrams et al, 1993;Matessi and Di Pasquale, 1996). Depending on the kind of adaptive dynamics one studies, there are of course a great number of stability issues and dynamical phenomena to consider, and this field is now quite advanced (Hofbauer and Sigmund, 1998).…”

Section: Discussionmentioning

confidence: 99%

Evolutionary Change and Darwinian Demons

Leimar¹

2002

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Models of adaptive evolution often have the property that change is guided by, but not fully determined by fitness. In a given situation many different mutant phenotypes may have a fitness advantage over the residents, and are thus potential invaders, implying that the mutational process plays an important role in deciding which particular invasion will take place. By introducing an imaginary 'Darwinian demon' in charge of mutations, one can examine the maximal role that mutation could play in determining evolutionary change. Taking into account pleiotropic mutations and shifting fitness landscapes, it seems likely that a Darwinian demon could exert considerable influence and most likely would be able to produce any viable form of organism. This kind of perspective can be helpful in clarifying concepts of evolutionary stability.

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Section: Discussionmentioning

confidence: 99%

Evolutionary Change and Darwinian Demons

Leimar¹

2002

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“…It is in this context that Maynard Smith and Price [32] introduced the concept of an evolutionarily stable strategy (ESS) -a strategy that, when common, has higher fitness than any other strategy and thereby resists invasion and displacement. However, this immunity to invasion once established does not insure that an ESS will actually become established during the course of evolution [33,34]. An ESS will become established only if it is convergence stable, such that types closer to the ESS can always invade populations dominated by types farther than the ESS, thereby making the ESS essentially an evolutionary attractor [35,36].…”

Section: Theoretical Approaches To Trait Evolutionmentioning

confidence: 99%

The emergence of diversity in plant communities

Levin

Muller‐Landau

2000

Comptes Rendus de l'Académie des Sciences - Series III - Scienc

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“…14 An NIS is also known as a good invader (Kisdi and Meszéna, 1995) and as satisfying (multi-dimensional) m * −stability (Lessard, 1990). For a one-dimensional trait space, Eshel and Sansone (2003) proved the NIS condition is necessary for asymptotic stability of δ 0 .…”

Section: Dynamic Stability Local Superiority and Nismentioning

confidence: 99%

“…We then have the following theorem. ) (see also Lessard, 1990) that the multi-dimensional CSS concept is equivalent to the one-dimensional CSS conditions for each line through the origin.…”

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confidence: 99%

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

Cressman

Hofbauer

Riedel

2006

Journal of Theoretical Biology

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract. The replicator equation model for the evolution of individual behaviors in a single-species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability measures. Stability of monomorphisms in this model using the weak topology is compared to more traditional methods of adaptive dynamics. For quadratic fitness functions and initial normal trait distributions, it is shown that the multi-dimensional CSS (Continuously Stable Strategy) of adaptive dynamics is often relevant for predicting stability of the measure-theoretic model but may be too strong in general. For general fitness functions and trait distributions, the CSS is related to dominance solvability which can be used to characterize local stability for a large class of trait distributions that have no gaps in their supports whereas the stronger NIS (Neighborhood Invader Strategy) concept is needed if the supports are arbitrary. Terms of use: Documents in

show abstract

Evolutionary stability: One concept, several meanings

Cited by 67 publications

References 35 publications

Evolutionary Change and Darwinian Demons

Evolutionary Change and Darwinian Demons

The emergence of diversity in plant communities

Stability of the replicator equation for a single species with a multi-dimensional continuous trait space

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