The predator-dependent replicator dynamics

2021 ◽  
Author(s):  
Ian Magalhaes Braga ◽  
Lucas Wardil
Keyword(s):  
Time Scales ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Capture Rate ◽  
Evolutionary Game ◽  
Ecological Interactions ◽  
Evolutionary Time ◽  
Predator Prey ◽  
Environmental Interactions ◽  
Selection Of

Abstract Ecological interactions are central to understanding evolution. For example, Darwin noticed that the beautiful colours of the male peacock increase the chance of successful mating. However, the colours can be a threat because of the increased probability of being caught by predators. Eco-evolutionary dynamics takes into account environmental interactions to model the process of evolution. The selection of prey types in the presence of predators may be subjected to pressure on both reproduction and survival. Here, we analyze the evolutionary game dynamics of two types of prey in the presence of predators. We call this model \textit{the predator-dependent replicator dynamics}. If the evolutionary time scales are different, the number of predators can be assumed constant, and the traditional replicator dynamics is recovered. However, if the time scales are the same, we end up with sixteen possible dynamics: the combinations of four reproduction’s games with four predation’s games. We analyze the dynamics and calculate conditions for the coexistence of prey and predator. The main result is that predators can change the equilibrium of the traditional replicator dynamics. For example, the presence of predators can induce polymorphism in prey if one type of prey is more attractive than the other, with the prey ending with a lower capture rate in this new equilibrium. Lastly, we provide two illustrations of the dynamics, which can be seen as rapid feedback responses in a predator-prey evolutionary arm’s race.

scholarly journals Steering eco-evolutionary game dynamics with manifold control

2020 ◽  
Vol 476 (2233) ◽  
pp. 20190643 ◽  
Author(s):  
Xin Wang ◽  
Zhiming Zheng ◽  
Feng Fu
Keyword(s):  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Feedback Loops ◽  
Mathematical Framework ◽  
Stable Manifolds ◽  
Selection Gradient ◽  
Game Dynamics ◽  
Control Approach ◽  
Attraction Basin

Feedback loops between population dynamics of individuals and their ecological environment are ubiquitously found in nature and have shown profound effects on the resulting eco-evolutionary dynamics. By incorporating linear environmental feedback law into the replicator dynamics of two-player games, recent theoretical studies have shed light on understanding the oscillating dynamics of the social dilemma. However, the detailed effects of more general nonlinear feedback loops in multi-player games, which are more common especially in microbial systems, remain unclear. Here, we focus on ecological public goods games with environmental feedbacks driven by a nonlinear selection gradient. Unlike previous models, multiple segments of stable and unstable equilibrium manifolds can emerge from the population dynamical systems. We find that a larger relative asymmetrical feedback speed for group interactions centred on cooperators not only accelerates the convergence of stable manifolds but also increases the attraction basin of these stable manifolds. Furthermore, our work offers an innovative manifold control approach: by designing appropriate switching control laws, we are able to steer the eco-evolutionary dynamics to any desired population state. Our mathematical framework is an important generalization and complement to coevolutionary game dynamics, and also fills the theoretical gap in guiding the widespread problem of population state control in microbial experiments.

Collaborative knowledge management for corporate ecological responsibility

2019 ◽  
Vol 53 (3) ◽  
pp. 304-317
Author(s):  
Weiwei Guo
Keyword(s):  
Knowledge Management ◽  
Simulation Analysis ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Evolutionary Strategy ◽  
Content Type ◽  
Ecological Responsibility ◽  
Collaborative Knowledge Management ◽  
Collaborative Knowledge ◽  
Selection Of

Purpose Knowledge has become the basis of enhancing the core competitiveness of enterprises in this era of knowledge-driven economies. Collaborative knowledge management not only realizes the real-time exchange and communication of knowledge among different enterprises, but also facilitates the collaboration and integration of knowledge. Collaborative knowledge management has been successfully applied to different fields. To address the poor ecological responsibility of enterprises, the purpose of this paper is to introduce the concept of collaborative knowledge management in this research to determine if the evolution of the decision-making process in collaborative knowledge management is involved in corporate ecological responsibility (CER). Design/methodology/approach This research established an evolutionary game model of collaborative knowledge management for CER. The behavioral, evolutionary law and stable behavioral, evolutionary strategy of the participants was identified according to the replicator dynamics equation. Simulation analysis was conducted using MATLAB software. Findings Research results demonstrated that, first, the strategic selection of firms is influenced by cost and interest coefficients. Second, the strategy, selection of enterprises, is related to the common benefits of enterprise cooperation. Third, during the systematic evolution and stabilization of strategies, enterprises adopt the same knowledge strategies. Originality/value On the basis of the research findings, policy suggestions were proposed to encourage enterprises to implement collaborative knowledge management strategies in ecological responsibility.

scholarly journals Association between shell morphology of micro-land snails (genus Plectostoma) and their predator’s predatory behaviour

2013 ◽  
Author(s):  
Thor-Seng Liew ◽  
Menno Schilthuizen
Keyword(s):  
Land Snails ◽  
Shell Morphology ◽  
Ecological Interactions ◽  
Predatory Behaviour ◽  
Predator Prey ◽  
Resting Behaviour ◽  
Biological Form ◽  
Predation Costs ◽  
Selection Of ◽  
Thickness Shell

Predator-prey interactions are among the main ecological interactions that shape the diversity of biological form. In many cases, the evolution of the mollusc shell form is presumably driven by predation. However, the adaptive significance of several uncommon, yet striking, shell traits of land snails are still poorly known. These include the distorted coiled “tuba” and the protruded radial ribs that can be found in micro-landsnails of the genus Plectostoma. Here, we experimentally tested whether these shell traits may act as defensive adaptations against predators. First, we identified the predators, namely, Atopos slugs and Pteroptyx beetle larvae, and their predatory strategies towards Plectostoma snails. Then, we characterised and quantified the possible anti-predation behaviour and shell traits of Plectostoma snails both in terms of their properties and efficiencies in defending against the Atopos slug predatory strategies, namely, shell-apertural entry and shell-drilling. The results showed that Atopos slugs would first attack the snail by shell-apertural entry, and, should this fail, shift to the energetically more costly shell-drilling strategy. We found that the shell tuba of Plectostoma snails is an effective defensive trait against shell-apertural entry attack. None of the snail traits, such as resting behaviour, shell thickness, shell tuba shape, shell rib density and intensity can protect the snail from the slug’s shell-drilling attack. However, these traits could increase the predation costs to the slug. Further analysis on the shell traits revealed that the lack of effectiveness these anti-predation shell traits may be caused by a functional trade-off between shell traits under selection of two different predatory strategies. Lastly, we discuss our results in the framework of Red Queen predator-prey coevolution and escalation, and propose several key elements for future study.

scholarly journals Extinction rates in tumor public goods games

2017 ◽  
Author(s):  
Philip Gerlee ◽  
Philipp M. Altrock
Keyword(s):  
Population Growth ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Cell Types ◽  
Relative Fitness ◽  
Replicator Equation ◽  
Cellular Interactions ◽  
Cancer Evolution ◽  
Public Goods Games

AbstractCancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumor cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the timescales, in particular in co-evolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell type specific rates have to be accounted for explicitly.

scholarly journals Extinction rates in tumour public goods games

2017 ◽  
Vol 14 (134) ◽  
pp. 20170342 ◽  
Author(s):  
Philip Gerlee ◽  
Philipp M. Altrock
Keyword(s):  
Population Growth ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Cell Types ◽  
Relative Fitness ◽  
Replicator Equation ◽  
Cellular Interactions ◽  
Cancer Evolution ◽  
Public Goods Games

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly.

Evolutionary community ecology

2019 ◽  
pp. 307-333
Author(s):  
Gary G. Mittelbach ◽  
Brian J. McGill
Keyword(s):  
Population Dynamics ◽  
Community Ecology ◽  
Species Interactions ◽  
Evolutionary Dynamics ◽  
Ecological Interactions ◽  
Predator Prey ◽  
Evolutionary Rescue ◽  
Species Pools ◽  
Laboratory Populations ◽  
Long Time

Ecology and evolution go hand in hand. However, since evolution occurs over relatively long time scales, ecologists had long thought it unlikely that evolutionary events could affect population dynamics or species interactions in ecological time. This view is changing. Today, there are multiple areas of research examining how evolutionary processes feedback directly on ecology. For example, eco-evolutionary dynamics focus on the cyclical interaction between ecology and adaptive evolution, such that changes in ecological interactions drive selection on organismal traits that, in turn, alter the outcome of ecological interactions. Striking examples of eco-evolutionary feedbacks are found in predator–prey interactions of laboratory populations. However, less is known about eco-evolutionary feedbacks in nature. Evolutionary rescue describes a process whereby rapid adaptation may prevent extinction in a changing environment. Other topics covered in this chapter are community phylogenetics and the evolution of regional species pools.

scholarly journals Analyses of evolutionary dynamics in viruses are hindered by a time-dependent bias in rate estimates

2014 ◽  
Vol 281 (1786) ◽  
pp. 20140732 ◽  
Author(s):  
Sebastián Duchêne ◽  
Edward C. Holmes ◽  
Simon Y. W. Ho
Keyword(s):  
Time Scales ◽  
Evolutionary Dynamics ◽  
Nucleotide Substitution ◽  
Viral Evolution ◽  
Negative Relationship ◽  
Purifying Selection ◽  
Time Dependent ◽  
Rate Variation ◽  
Nucleotide Substitution Rate ◽  
Evolutionary Time

Time-scales of viral evolution and emergence have been studied widely, but are often poorly understood. Molecular analyses of viral evolutionary time-scales generally rely on estimates of rates of nucleotide substitution, which vary by several orders of magnitude depending on the timeframe of measurement. We analysed data from all major groups of viruses and found a strong negative relationship between estimates of nucleotide substitution rate and evolutionary timescale. Strikingly, this relationship was upheld both within and among diverse groups of viruses. A detailed case study of primate lentiviruses revealed that the combined effects of sequence saturation and purifying selection can explain this time-dependent pattern of rate variation. Therefore, our analyses show that studies of evolutionary time-scales in viruses require a reconsideration of substitution rates as a dynamic, rather than as a static, feature of molecular evolution. Improved modelling of viral evolutionary rates has the potential to change our understanding of virus origins.

scholarly journals Steering ecological-evolutionary dynamics during artificial selection of microbial communities

2018 ◽  
Author(s):  
Li Xie ◽  
Wenying Shou
Keyword(s):  
Microbial Communities ◽  
Artificial Selection ◽  
Evolutionary Dynamics ◽  
Ecological Interactions ◽  
Evolutionary Trajectory ◽  
Community Function ◽  
Selection Strategies ◽  
Effective Selection ◽  
Orthogonal Components ◽  
Selection Of

AbstractMicrobial communities often perform important functions that arise from interactions among member species. Community functions can be improved via artificial selection: Many communities are repeatedly grown, mutations arise, and communities with the highest desired function are chosen to reproduce where each is partitioned into multiple offspring communities for the next cycle. Since selection efficacy is often unimpressive in published experiments and since multiple experimental parameters need to be tuned, we sought to use computer simulations to learn how to design effective selection strategies. We simulated community selection to improve a community function that requires two species and imposes a fitness cost on one of the species. This simplified case allowed us to distill community function down to two fundamental and orthogonal components: a heritable determinant and a nonheritable determinant. We then visualize a “community function landscape” relating community function to these two determinants, and demonstrate that the evolutionary trajectory on the landscape is restricted along a path designated by ecological interactions. This path can prevent the attainment of maximal community function, and trap communities in landscape locations where community function has low heritability. Exploiting these observations, we devise a species spiking approach to shift the path to improve community function heritability and consequently selection efficacy. We show that our approach is applicable to communities with complex and unknown function landscapes.

scholarly journals Evolutionary Game Theory: Darwinian Dynamics and the G Function Approach

Games ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 72
Author(s):  
Anuraag Bukkuri ◽  
Joel S. Brown
Keyword(s):  
Game Theory ◽  
Drug Resistance ◽  
Population Dynamics ◽  
Evolutionary Game Theory ◽  
Evolutionary Dynamics ◽  
Evolutionary Game ◽  
Function Model ◽  
Predator Prey ◽  
Evolutionary Stable Strategies ◽  
Over Time

Classical evolutionary game theory allows one to analyze the population dynamics of interacting individuals playing different strategies (broadly defined) in a population. To expand the scope of this framework to allow us to examine the evolution of these individuals’ strategies over time, we present the idea of a fitness-generating (G) function. Under this model, we can simultaneously consider population (ecological) and strategy (evolutionary) dynamics. In this paper, we briefly outline the differences between game theory and classical evolutionary game theory. We then introduce the G function framework, deriving the model from fundamental biological principles. We introduce the concept of a G-function species, explain the process of modeling with G functions, and define the conditions for evolutionary stable strategies (ESS). We conclude by presenting expository examples of G function model construction and simulations in the context of predator–prey dynamics and the evolution of drug resistance in cancer.

Growth–defense trade-offs shape population genetic composition in an iconic forest tree species

2021 ◽  
Vol 118 (37) ◽  
pp. e2103162118 ◽  
Author(s):  
Olivia L. Cope ◽  
Ken Keefover-Ring ◽  
Eric L. Kruger ◽  
Richard L. Lindroth
Keyword(s):  
Evolutionary Dynamics ◽  
Evolutionary Ecology ◽  
Functional Trait ◽  
Forest Tree ◽  
Ecological Interactions ◽  
Trait Variation ◽  
Trade Offs ◽  
Spatiotemporal Scales ◽  
Evolutionary Consequences ◽  
Selection Of

All organisms experience fundamental conflicts between divergent metabolic processes. In plants, a pivotal conflict occurs between allocation to growth, which accelerates resource acquisition, and to defense, which protects existing tissue against herbivory. Trade-offs between growth and defense traits are not universally observed, and a central prediction of plant evolutionary ecology is that context-dependence of these trade-offs contributes to the maintenance of intraspecific variation in defense [Züst and Agrawal, Annu. Rev. Plant Biol., 68, 513–534 (2017)]. This prediction has rarely been tested, however, and the evolutionary consequences of growth–defense trade-offs in different environments are poorly understood, especially in long-lived species [Cipollini et al., Annual Plant Reviews (Wiley, 2014), pp. 263–307]. Here we show that intraspecific trait trade-offs, even when fixed across divergent environments, interact with competition to drive natural selection of tree genotypes corresponding to their growth–defense phenotypes. Our results show that a functional trait trade-off, when coupled with environmental variation, causes real-time divergence in the genetic architecture of tree populations in an experimental setting. Specifically, competitive selection for faster growth resulted in dominance by fast-growing tree genotypes that were poorly defended against natural enemies. This outcome is a signature example of eco-evolutionary dynamics: Competitive interactions affected microevolutionary trajectories on a timescale relevant to subsequent ecological interactions [Brunner et al., Funct. Ecol. 33, 7–12 (2019)]. Eco-evolutionary drivers of tree growth and defense are thus critical to stand-level trait variation, which structures communities and ecosystems over expansive spatiotemporal scales.

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