Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

Geritz, Stefan A.H.; Kisdi, Éva; Meszéna, Géza; Metz, J.A.J.

doi:10.1023/a:1006554906681

Cited by 1,601 publications

(2,696 citation statements)

References 50 publications

Supporting

Mentioning

2,661

Contrasting

Unclassified

Order By: Relevance

“…A strategy s * is called a singular strategy (Geritz et al, 1997(Geritz et al, , 1998 if the selection gradient vanishes when that strategy is resident, D 1 (s * ) = 0.…”

Section: First-order Resultsmentioning

confidence: 99%

“…Evolutionary branching is a process in which the trait of an evolving monomorphic population first approaches a so-called singular trait, but then disruptive selection causes the population to become dimorphic, i.e., to contain two different resident traits, and these two traits evolve away from each other (Metz et al, 1992(Metz et al, , 1996Geritz et al, 1997Geritz et al, , 1998. When mutations are so frequent that there is no clear separation between ecological and evolutionary timescales, evolutionary branching means that a unimodal trait distribution first concentrates around the singular strategy, and then the distribution becomes bimodal.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

Parvinen

Ohtsuki

Wakano

2017

Journal of Theoretical Biology

View full text Add to dashboard Cite

By investigating metapopulation fitness, we present analytical expressions for the selection gradient and conditions for convergence stability and evolutionary stability in Wright's island model in terms of fecundity function. Coefficients of each derivative of fecundity function appearing in these conditions have fixed signs. This illustrates which kind of interaction promotes or inhibits evolutionary branching in spatial models. We observe that Taylor's cancellation result holds for any fecundity function: Not only singular strategies but also their convergence stability is identical to that in the corresponding well-mixed model. We show that evolutionary branching never occurs 1 when the dispersal rate is close to zero. Furthermore, for a wide class of fecundity functions (including those determined by any pairwise game), evolutionary branching is impossible for any dispersal rate if branching does not occur in the corresponding well-mixed model. Spatial structure thus often inhibits evolutionary branching, although we can construct a fecundity function for which evolutionary branching only occurs for intermediate dispersal rates.

show abstract

“…A strategy s * is called a singular strategy (Geritz et al, 1997(Geritz et al, , 1998 if the selection gradient vanishes when that strategy is resident, D 1 (s * ) = 0.…”

Section: First-order Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

Parvinen

Ohtsuki

Wakano

2017

Journal of Theoretical Biology

View full text Add to dashboard Cite

show abstract

“…General AD literature (see e.g., Champagnat et al., 2001; Dieckmann & Law, 1996; Geritz et al., 1998) follows the evolution of a quantitative phenotypic trait or set of traits, s , that can change through mutations. In these studies, the probability μ at which mutations appear is considered a possible function of the trait s , but afterwards and further on in the AD literature is usually left as a constant of each model.…”

Section: Adaptive Dynamicsmentioning

confidence: 99%

“…However, this minimal landscape approximation is able to capture the dynamical behaviour of our gene‐related landscape model, mainly with an initial exponential growth followed by saturation around the peak, which can be proven to be an evolutionary stable strategy (Geritz et al., 1998). …”

Section: Evolution Of Instabilitymentioning

confidence: 99%

Adaptive dynamics of unstable cancer populations: The canonical equation

Aguadé-Gorgorió

Solé

2018

Evolutionary Applications

View full text Add to dashboard Cite

In most instances of tumour development, genetic instability plays a role in allowing cancer cell populations to respond to selection barriers, such as physical constraints or immune responses, and rapidly adapt to an always changing environment. Modelling instability is a nontrivial task, since by definition evolving instability leads to changes in the underlying landscape. In this article, we explore mathematically a simple version of unstable tumour progression using the formalism of adaptive dynamics (AD) where selection and mutation are explicitly coupled. Using a set of basic fitness landscapes, the so‐called canonical equation for the evolution of genetic instability on a minimal scenario associated with a population of unstable cells is derived. We obtain explicit expressions for the evolution of mutation probabilities, and the implications of the model on further experimental studies and potential mutagenic therapies are discussed.

show abstract

“…In order to better understand the phenomenon of consumer-resource coevolution and its effects on intervality, the evolution of food webs could be studied using, for example, techniques of adaptive dynamics (Dieckmann and Law, 1996;Geritz et al, 1998). In the adaptive dynamics framework, invasion fitness is derived from the underlying model, removing the need for an externally imposed fitness measure or ad hoc assumptions such as that of focused consumers.…”

Section: Food-web Intervality With Weakly Focused Consumersmentioning

confidence: 99%

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

2010

View full text Add to dashboard Cite

Food webs represent trophic (feeding) interactions in ecosystems. Since the late 1970s, it has been recognized that food-webs have a surprisingly close relationship to interval graphs. One interpretation of food-web intervality is that trophic niche space is low-dimensional, meaning that the trophic character of a species can be expressed by a single or at most a few quantitative traits. In a companion paper we demonstrated, by simulating a minimal food-web model, that food webs are also expected to be interval when niche-space is high-dimensional. Here we characterize the fundamental mechanisms underlying this phenomenon by proving a set of rigorous conditions for food-web intervality in high-dimensional niche spaces. Our results apply to a large class of food-web models, including the special case previously studied numerically.

show abstract

Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree

Cited by 1,601 publications

References 50 publications

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

The effect of fecundity derivatives on the condition of evolutionary branching in spatial models

Adaptive dynamics of unstable cancer populations: The canonical equation

Rigorous conditions for food-web intervality in high-dimensional trophic niche spaces

Contact Info

Product

Resources

About