The Branching Bifurcation of Adaptive Dynamics

Rossa, Fabio Della; Dercole, Fabio; Landi, Pietro

doi:10.1142/s0218127415400015

Cited by 21 publications

(14 citation statements)

References 44 publications

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“…A local fitness maximum signals the end of incremental evolution, whereas a local fitness minimum (happening when

σ < {normalσ}_{K}

) begets evolutionary branching . Evolutionary branching allows the resident and mutant to coexist, forming two resident phenotypes diverging under disruptive selection (Della Rossa, Dercole, & Landi, ; Dercole, Della Rossa, & Landi, ; Geritz, Kisdi, Meszéna, & Metz, ). After a branching event, trait evolution continues separately in each lineage, where further branching events are possible (Landi, Dercole, & Rinaldi, ).…”

Section: Methodsmentioning

confidence: 99%

Emergence of weak‐intransitive competition through adaptive diversification and eco‐evolutionary feedbacks

et al. 2018

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Indirect biotic interactions—such as intransitive competition—are increasingly recognized as being important in shaping ecological patterns in natural systems. Over long time‐scales, such indirect interactions may affect the evolution of species phenotypes, which in turn can modify these interactions, thereby begetting eco‐evolutionary feedbacks. If indirect intransitive interactions can emerge in situ during lineage diversification, they could profoundly affect species’ phenotypic diversity, temporal stability, and subsequent diversification rates. We address these questions by investigating the conditions under which indirect intransitive competition can emerge from a lineage diversifying in sympatry. We use an adaptive dynamics model to study the ecological and evolutionary properties of this lineage under different scenarios where competition for resources between phenotypes varies in strength and (a)symmetry. Results show that weak‐intransitive competition can emerge during the sympatric diversification of a single lineage. “Weak‐intransitivity” here refers to situations where species interactions are not perfectly transitive, that is, there is no strict hierarchy in species competitive abilities. The strength of such weak‐intransitivity increases when the competition between phenotypes increases in strength and asymmetry. The strength of intransitivity also correlates with other system properties. We notably found that the strength of intransitivity increases with the number of phenotypes, and that greater intransitivity correlates with the evolution of greater functional trait divergences between phenotypes, greater resistance to invasion by new phenotypes but lower resistance to disturbances as well as slower evolutionary rates. Synthesis. This theoretical exploration of the evolution of intransitive competition provides the first formal bridge between the ecological and evolutionary aspects of intransitive competition. We show that, when competitive interactions are strong enough, weak‐intransitive competition is more likely to emerge through adaptive diversification than from a random community assembly. Intransitive competition is, therefore, not only restricted to between‐species interactions but can also function as a regulator of diversification within species, thereby affecting lineage functional diversity, and ecological and evolutionary stability.

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“…A local fitness maximum signals the end of incremental evolution, whereas a local fitness minimum (happening when

σ < {normalσ}_{K}

Section: Methodsmentioning

confidence: 99%

Emergence of weak‐intransitive competition through adaptive diversification and eco‐evolutionary feedbacks

et al. 2018

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“…This bifurcation is unfolded in detail in [27,28] An example of competitive market dynamics under asymmetric interaction 2 > 1 is shown in Figure 7(left). It illustrates the market dynamics under the influence of trait dependent maximum capacity and interaction function .…”

Section: Coexistence and Divergencementioning

confidence: 99%

Conditions on the Energy Market Diversification from Adaptive Dynamics

Toro-Zapata

Tost

Dercole

2018

Mathematical Problems in Engineering

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We study a mathematical model based on ordinary differential equations to describe the dynamic interaction in the market of two types of energy called standard and innovative. The model consists of an adaptation of the generalized Lotka-Volterra system in which the parameters are assumed to depend on a quantitative and continuous attribute characteristic of energy generation. Using the analysis of the model the fitness function for the innovative energy is determined, from which conditions of invasion can be established in a market dominated by the conventional power. The canonical equation of the adaptive dynamics is studied to know the long-term behavior of the characteristic attribute and its impact on the market. Then we establish conditions under which evolutionary ramifications occur, that is to say, the requirements of coexistence and divergence of the characteristic attributes, whose occurrence leads to the origin of diversity in the energy market.

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“…To this end, the canonical equation of AD has been used to describe the evolution of traits under directional selection through the continuous invasion of rare mutants into resident populations . The most interesting feature of AD is its capacity to formally describe the condition of evolutionary branching: At an evolutionarily singular strategy, where directional selection ceases (ie, equilibrium of the canonical equation where the selection gradient vanishes), the fitness landscape can be found to locate at either its maxima or minima, determined by the second‐order derivatives of the mutant fitness at the singular strategy. In the latter case, if the resident and the initially resembling mutant can further competitively coexist (known as protected dimorphism), the disruptive selection posed by the fitness minima could then give rise to an evolutionary branching, a typical phenomenon of adaptive diversification.…”

Section: Adaptive Dynamicsmentioning

confidence: 99%

“…The singularity

x_{i}^{*}

represents a fitness minimum, an indication of disruptive selection, if the curvature of fitness landscape at the trait

x_{i}^{*}

is greater than zero,

{\frac{\partial^{2} f ((),, X, x^{true'})}{\partial {x^{true'}}^{2}}|}_{\begin{array}{l} x^{'} = x_{i}^{*} \\ X = X^{*} \end{array}} > 0,

which allows traits other than the singularity to invade; intuitively, the curvature is also a measure of the strength of disruptive selection. To have an evolutionary branching, not only the singularity needs to be a fitness minimum and under disruptive selection but also the 2 morphs emerged from the evolutionary branching need to be protected; that is, the two morphs ( x ′ and x ″ ) can coexist and invade each other:

{((), \frac{\partial^{2} f ((),, x^{true'}, x^{true″})}{\partial {x^{true'}}^{2}} + \frac{\partial^{2} f ((),, x^{true'}, x^{true″})}{\partial {x^{true″}}^{2}})|}_{x^{'} = x^{″} = x_{i}^{*}} > 0 .

…”

Section: Resource Competitionmentioning

confidence: 99%

Modelling coevolution in ecological networks with adaptive dynamics

Hui

Minoarivelo

Landi

2017

Math Methods in App Sciences

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MOS Classification: 92D40; 47J35; 91A22 Communicator: R. Anguelov Coevolution can impose density-dependent selection through reciprocal biotic interactions on the fitness of involved species, driving directional and disruptive trait evolution and rich evolutionary possibilities. Coevolution has since Darwin been considered a potential path leading to adaptive diversification that could explain the emergence of ecological networks of biotic interactions that harbour multiple interacting species (eg, pollination networks and food webs). Here, we present adaptive dynamics, a powerful tool of evolutionary invasion analysis that explores how quantitative traits undergo incremental evolution, to exploring the emergence of multi-species networks through coevolution. Specifically, we exemplify the feasibility of using adaptive dynamics to investigate trait evolution in 4 ecological networks, driven, respectively, by resource competition, trophic interactions, as well as bipartite mutualistic and antagonistic interactions. We use a set of ordinary differential equations to describe, at different paces, the population dynamics and trait dynamics of involved species assemblages. Through computing ecological equilibrium, invasion fitness, selection gradient and evolutionary singularity, and testing for evolutionary stability and the coexistence criterion of mutual invasibility, we illustrate the typical evolutionary dynamics and the criteria of evolutionary stability and branching in these ecological networks. Results highlight the importance of the form of trait-mediated interaction kernel (ie, interaction strength as a function of trait difference) to adaptive diversification in these coevolutionary systems. We conclude by advocating that biotic interactions between two species can indeed lead to diffuse and even escape-and-radiate coevolution, making the emerged ecological networks an ideal model for studying complex adaptive systems. KEYWORDSadaptive dynamics, complex adaptive networks, ecological networks, evolutionary branching, evolutionary invasion analysis, evolutionary stability

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The Branching Bifurcation of Adaptive Dynamics

Cited by 21 publications

References 44 publications

Emergence of weak‐intransitive competition through adaptive diversification and eco‐evolutionary feedbacks

Emergence of weak‐intransitive competition through adaptive diversification and eco‐evolutionary feedbacks

Conditions on the Energy Market Diversification from Adaptive Dynamics

Modelling coevolution in ecological networks with adaptive dynamics

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