scholarly journals The Branching Bifurcation of Adaptive Dynamics

2015 ◽  
Vol 25 (07) ◽  
pp. 1540001 ◽  
Author(s):  
Fabio Della Rossa ◽  
Fabio Dercole ◽  
Pietro Landi
Keyword(s):  
Adaptive Dynamics ◽  
Stationary Regime ◽  
Joint Effect ◽  
Evolutionary Stability ◽  
Canonical Equation ◽  
Mutant Type ◽  
Invasion Fitness ◽  
Individual Traits ◽  
Classical Setting ◽  
Intermediate Traits

We unfold the bifurcation involving the loss of evolutionary stability of an equilibrium of the canonical equation of Adaptive Dynamics (AD). The equation deterministically describes the expected long-term evolution of inheritable traits — phenotypes or strategies — of coevolving populations, in the limit of rare and small mutations. In the vicinity of a stable equilibrium of the AD canonical equation, a mutant type can invade and coexist with the present — resident — types, whereas the fittest always win far from equilibrium. After coexistence, residents and mutants effectively diversify, according to the enlarged canonical equation, only if natural selection favors outer rather than intermediate traits — the equilibrium being evolutionarily unstable, rather than stable. Though the conditions for evolutionary branching — the joint effect of resident-mutant coexistence and evolutionary instability — have been known for long, the unfolding of the bifurcation has remained a missing tile of AD, the reason being related to the nonsmoothness of the mutant invasion fitness after branching. In this paper, we develop a methodology that allows the approximation of the invasion fitness after branching in terms of the expansion of the (smooth) fitness before branching. We then derive a canonical model for the branching bifurcation and perform its unfolding around the loss of evolutionary stability. We cast our analysis in the simplest (but classical) setting of asexual, unstructured populations living in an isolated, homogeneous, and constant abiotic environment; individual traits are one-dimensional; intra- as well as inter-specific ecological interactions are described in the vicinity of a stationary regime.

scholarly journals Adaptation of Biotrophic Leaf Pathogens to Fertilization-Mediated Changes in Plant Traits: A Comparison of the Optimization Principle to Invasion Fitness

2020 ◽  
Vol 110 (5) ◽  
pp. 1039-1048
Author(s):  
Pierre-Antoine Précigout ◽  
Corinne Robert ◽  
David Claessen
Keyword(s):  
Growth Rate ◽  
Latent Period ◽  
Exponential Growth ◽  
Plant Traits ◽  
Adaptive Dynamics ◽  
Spore Production ◽  
Exponential Growth Rate ◽  
Evolutionarily Stable Strategies ◽  
Invasion Fitness ◽  
Evolutionary Response

One of the conclusions of evolutionary ecology applied to agroecosystem management is that sustainable disease management strategies must be adaptive to overcome the immense adaptive potential of crop pathogens. In this context, knowledge of how pathogens adapt to changes in cultural practices is necessary. In this article we address the issue of the evolutionary response of biotrophic crop pathogens to changes in fertilization practices. For this purpose, we compare predictions of latent period evolution based on three empirical fitness measures (seasonal spore production, within-season exponential growth rate, and area under disease progress curves [AUDPCs]) with predictions based on the concept of invasion fitness from adaptive dynamics. We use pairwise invisibility plots to identify the evolutionarily stable strategies (ESSs) of the pathogen latent period. We find that the ESS latent period is in between the latent periods that maximize the seasonal spore production and the within-season exponential growth rate of the pathogen. The latent periods that maximize the AUDPC are similar to those of the ESS latent periods. The AUDPC may therefore be a critical variable to determine the issue of between-strain competition and shape pathogen evolution.

scholarly journals Trait positions for elevated invasiveness in adaptive ecological networks

2021 ◽  
Author(s):  
Cang Hui ◽  
David M. Richardson ◽  
Pietro Landi ◽  
Henintsoa O. Minoarivelo ◽  
Helen E. Roy ◽  
...  
Keyword(s):  
Native Species ◽  
Evolutionary Dynamics ◽  
Propagule Pressure ◽  
Adaptive Dynamics ◽  
Evolutionary Game ◽  
Ecological Networks ◽  
Positive Interactions ◽  
Ecological Network ◽  
Invasion Fitness ◽  
Ecological Barriers

AbstractOur ability to predict the outcome of invasion declines rapidly as non-native species progress through intertwined ecological barriers to establish and spread in recipient ecosystems. This is largely due to the lack of systemic knowledge on key processes at play as species establish self-sustaining populations within the invaded range. To address this knowledge gap, we present a mathematical model that captures the eco-evolutionary dynamics of native and non-native species interacting within an ecological network. The model is derived from continuous-trait evolutionary game theory (i.e., Adaptive Dynamics) and its associated concept of invasion fitness which depicts dynamic demographic performance that is both trait mediated and density dependent. Our approach allows us to explore how multiple resident and non-native species coevolve to reshape invasion performance, or more precisely invasiveness, over trait space. The model clarifies the role of specific traits in enabling non-native species to occupy realised opportunistic niches. It also elucidates the direction and speed of both ecological and evolutionary dynamics of residing species (natives or non-natives) in the recipient network under different levels of propagule pressure. The versatility of the model is demonstrated using four examples that correspond to the invasion of (i) a horizontal competitive community; (ii) a bipartite mutualistic network; (iii) a bipartite antagonistic network; and (iv) a multi-trophic food web. We identified a cohesive trait strategy that enables the success and establishment of non-native species to possess high invasiveness. Specifically, we find that a non-native species can achieve high levels of invasiveness by possessing traits that overlap with those of its facilitators (and mutualists), which enhances the benefits accrued from positive interactions, and by possessing traits outside the range of those of antagonists, which mitigates the costs accrued from negative interactions. This ‘central-to-reap, edge-to-elude’ trait strategy therefore describes the strategic trait positions of non-native species to invade an ecological network. This model provides a theoretical platform for exploring invasion strategies in complex adaptive ecological networks.

scholarly journals Fitness and community feedbacks: the two axes that drive long-term invasion impacts

2019 ◽  
Author(s):  
Jean-François Arnoldi ◽  
Matthieu Barbier ◽  
Ruth Kelly ◽  
György Barabás ◽  
Andrew L. Jackson
Keyword(s):  
Regime Shift ◽  
Adaptive Dynamics ◽  
Invasion Success ◽  
Dynamical Models ◽  
Short Term ◽  
Invasion Fitness ◽  
Invasion Impacts ◽  
Invasion Analysis ◽  
Dynamical Features

AbstractMany facets of ecological theory rely on the analysis of invasion processes, and general approaches exist to understand the early stages of an invasion. However, predicting the long-term transformations of communities following an invasion remains a challenging endeavour. We propose an analytical method that uses community structure and invader dynamical features to predict when these impacts can be large, and show it to be applicable across a wide class of dynamical models. Our approach reveals that short-term invasion success and long-term consequences are two distinct axes of variation controlled by different properties of both invader and resident community. Whether a species can invade is controlled by its invasion fitness, which depends on environmental conditions and direct interactions with resident species. But whether this invasion will cause significant transformations, such as extinctions or a regime shift, depends on a specific measure of indirect feedbacks that may involve the entire resident community. Our approach applies to arbitrarily complex communities, from few competing phenotypes in adaptive dynamics to large nonlinear food webs. It hints at new questions to ask as part of any invasion analysis, and suggests that long-term indirect interactions are key determinants of invasion outcomes.

Consumers’ responses to invitations to write online reviews

2019 ◽  
Vol 31 (4) ◽  
pp. 1609-1625 ◽  
Author(s):  
Lu Zhang ◽  
Wan Yang
Keyword(s):  
Behavioral Intention ◽  
Message Framing ◽  
Marketing Research ◽  
Online Reviews ◽  
Joint Effect ◽  
Content Type ◽  
Individual Traits ◽  
Status Seeking ◽  
Sense Of Power ◽  
Practical Implications

PurposeThe main purpose of the current research is to investigate the effectiveness of messages sent out by firms inviting customers to write online reviews. The joint effect of message framing, power and individuals’ need for status (NFS) on consumers’ intentions to write a review was examined.Design/methodology/approachThis study uses a 2 (message framing: self-vs other-focused) × 2 (power state: high vs low) × 2 (NFS: high vs low) factorial design with message framing being manipulated and power and NFS being measured.FindingsThe results show that customers low in power are more likely to be persuaded by a message focused on others (vs self), and customers high in power show similar levels of behavioral intention regardless of message framing. Furthermore, this effect is significant only among those with a high (vs low) NFS.Practical implicationsHospitality practitioners may consider customizing the invitation message based on target consumers’ individual traits. They may either prime consumers’ status seeking intentions and/or sense of power, or gain such insights through outside marketing research companies. Depending on the characteristics of the recipients, companies can choose either a self-focused or an other-focused message to increase its persuasiveness.Originality/valueThis is one of the first studies examining the joint effect of message framing, power and NFS on consumers’ willingness to write online reviews.

scholarly journals The canonical equation of adaptive dynamics for Mendelian diploids and haplo-diploids

2013 ◽  
Vol 3 (6) ◽  
pp. 20130025 ◽  
Author(s):  
Johan A. J. Metz ◽  
Carolien G. F. de Kovel
Keyword(s):  
Time Scale ◽  
Life Histories ◽  
Adaptive Dynamics ◽  
Canonical Equation ◽  
Small Step ◽  
Evolutionary Time ◽  
Scale Separation ◽  
Slowing Down ◽  
Time Scale Separation ◽  
Simplifying Assumptions

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.

scholarly journals Origin of diversity in spatial social dilemmas

2021 ◽  
Author(s):  
Christoph Hauert ◽  
Michael Doebeli
Keyword(s):  
Spatial Structure ◽  
Adaptive Dynamics ◽  
Social Dilemmas ◽  
Finite Size ◽  
Structured Populations ◽  
Pair Approximation ◽  
Evolutionary Diversification ◽  
Invasion Fitness ◽  
Population Structures ◽  
Mixed Populations

Cooperative investments in social dilemmas can spontaneously diversify into stably co-existing high and low contributors in well-mixed populations. Here we extend the analysis to emerging diversity in (spatially) structured populations. Using pair approximation we derive analytical expressions for the invasion fitness of rare mutants in structured populations, which then yields a spatial adaptive dynamics framework. This allows us to predict changes arising from population structures in terms of existence and location of singular strategies, as well as their convergence and evolutionary stability as compared to well-mixed populations. Based on spatial adaptive dynamics and extensive individual based simulations, we find that spatial structure has significant and varied impacts on evolutionary diversification in continuous social dilemmas. More specifically, spatial adaptive dynamics suggests that spontaneous diversification through evolutionary branching is suppressed, but simulations show that spatial dimensions offer new modes of diversification that are driven by an interplay of finite-size mutations and population structures. Even though spatial adaptive dynamics is unable to capture these new modes, they can still be under-stood based on an invasion analysis. In particular, population structures alter invasion fitness and can open up new regions in trait space where mutants can invade, but that may not be accessible to small mutational steps. Instead, stochastically appearing larger mutations or sequences of smaller mutations in a particular direction are required to bridge regions of unfavourable traits. The net effect is that spatial structure tends to promote diversification, especially when selection is strong.

scholarly journals Evolution and Heterogeneity of Social Preferences

2020 ◽  
Author(s):  
Charles Ayoubi ◽  
Boris Thurm
Keyword(s):  
Social Preferences ◽  
Theoretical Foundation ◽  
Evolutionary Game ◽  
Evolutionary Process ◽  
Evolutionary Stability ◽  
Stable Population ◽  
Assortative Matching ◽  
Classical Setting ◽  
Definition Of ◽  
Evolutionarily Stable

Why do individuals take different decisions when confronted with similar choices? This paper investigates whether the answer lies in an evolutionary process. Our analysis builds on recent work in evolutionary game theory showing the superiority of a given type of preferences, homo moralis, in fitness games with assortative matching. We adapt the classical definition of evolutionary stability to the case where individuals with distinct preferences coexist in a population. This approach allows us to establish the characteristics of an evolutionarily stable population. Then, introducing an assortment matrix for assortatively matched interactions, we prove the existence of a heterogeneous evolutionarily stable population in 2×2 symmetric fitness games under constant assortment, and we identify the conditions for its existence. Conversely to the classical setting, we find that the favored preferences in a heterogeneous evolutionarily stable population are context-dependent. As an illustration, we discuss when and how an evolutionarily stable population made of both selfish and moral individuals exists in a prisoner’s dilemma. These findings offer a theoretical foundation for the empirically observed diversity of preferences among individuals.

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