scholarly journals Ecological feedback on diffusion dynamics

2019 ◽  
Vol 6 (2) ◽  
pp. 181273 ◽  
Author(s):  
Hye Jin Park ◽  
Chaitanya S. Gokhale
Keyword(s):  
Public Goods ◽  
Spatial Patterns ◽  
Spatial Organization ◽  
Evolutionary Dynamics ◽  
Evolutionary Process ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Public Goods Games ◽  
Diffusion Dynamics ◽  
Spatially Extended

Spatial patterns are ubiquitous across different scales of organization in ecological systems. Animal coat pattern, spatial organization of insect colonies and vegetation in arid areas are prominent examples from such diverse ecologies. Typically, pattern formation has been described by reaction–diffusion equations, which consider individuals dispersing between subpopulations of a global pool. This framework applied to public goods game nicely showed the endurance of populations via diffusion and generation of spatial patterns. However, how the spatial characteristics, such as diffusion, are related to the eco-evolutionary process as well as the nature of the feedback from evolution to ecology and vice versa, has been so far neglected. We present a thorough analysis of the ecologically driven evolutionary dynamics in a spatially extended version of ecological public goods games. Furthermore, we show how these evolutionary dynamics feed back into shaping the ecology, thus together determining the fate of the system.

scholarly journals Ecological feedback on diffusion dynamics

2018 ◽  
Author(s):  
Hye Jin Park ◽  
Chaitanya S. Gokhale
Keyword(s):  
Public Goods ◽  
Spatial Patterns ◽  
Spatial Organization ◽  
Evolutionary Dynamics ◽  
Evolutionary Process ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Public Goods Games ◽  
Diffusion Dynamics ◽  
Spatially Extended

AbstractSpatial patterns are ubiquitous across different scales of organization. Animal coat pattern, spatial organization of insect colonies, and vegetation in arid areas are prominent examples from such diverse ecologies. Typically, pattern formation has been described by reaction-diffusion equations, which considers individuals dispersing between sub-populations of a global pool. This framework applied to public goods game nicely showed the endurance of populations via diffusion and generation of spatial patterns. However, how the spatial characteristics, such as diffusion, are related to the eco-evolutionary process as well as the nature of the feedback from evolution to ecology and vice versa, has been so far neglected. We present a thorough analysis of the ecologically driven evolutionary dynamics in a spatially extended version of ecological public goods games. We show how these evolutionary dynamics feedback into shaping the ecology thus together determining the fate of the system.

scholarly journals Evolutionary dynamics in the public goods games with switching between punishment and exclusion

2018 ◽  
Vol 28 (10) ◽  
pp. 103105 ◽  
Author(s):  
Linjie Liu ◽  
Shengxian Wang ◽  
Xiaojie Chen ◽  
Matjaž Perc
Keyword(s):  
Public Goods ◽  
Evolutionary Dynamics ◽  
The Public ◽  
Public Goods Games

Measuring and characterizing spatial patterns, dynamics and chaos in spatially extended dynamical systems and ecologies

1994 ◽  
Vol 348 (1688) ◽  
pp. 497-514 ◽  
Keyword(s):  
Data Analysis ◽  
Disordered Systems ◽  
Reaction Diffusion ◽  
Space Time ◽  
Reaction Diffusion Equations ◽  
Coupled Map Lattices ◽  
Individual Based Models ◽  
Spatially Extended ◽  
Definition Of

In this paper I discuss space-time chaos in both locally mixing continuum systems (reaction-diffusion equations, coupled map lattices and functional maps) and individual-based models (probabilistic cellular automata and artificial ecologies). I particularly emphasize quantification and data-analysis and attempt to address the characterization of spatial structure and dynamics in such disordered systems. I discuss the relevance of these ideas to ecology, evolution and epidemiology. The artificial ecologies I consider motivate a new definition of space-time chaos for such systems and new data analysis techniques.

DYNAMICS OF ECONOMIC AND TECHNOLOGICAL SEARCH PROCESSES IN COMPLEX ADAPTIVE LANDSCAPES

2001 ◽  
Vol 04 (01) ◽  
pp. 71-88 ◽  
Author(s):  
W. EBELING ◽  
A. SCHARNHORST
Keyword(s):  
Technological Change ◽  
Evolutionary Dynamics ◽  
Fitness Function ◽  
Replicator Dynamics ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Hill Climbing ◽  
Adaptive Landscape ◽  
Apparent Paradox ◽  
Radical Innovations

We investigate the dynamics of economic evolution and technological change as hill-climbing in an adaptive landscape over a continuous characteristics space. A technology/firm is described by a large number of attributes or characteristics representing technology-inherent aspects, financial, organizational and economic features. These parameters span a characteristics space, which is a real Euclidean vector space, in analogy to the phenotype space in biology. Further we define a real-valued multimodal fitness function/functional and a population density over the characteristics space. The evolutionary dynamics including competition and mutations/innovations is modeled by reaction-diffusion equations of Fisher–Eigen or Lotka–Volterra type. We demonstrate the potential of such models, which in certain aspects go beyond the widespread applications of discrete replicator dynamics. Concerning technological change the emergence of technological populations as the result of a search process in an adaptive landscape will be investigated. In particular, the relation between incremental and radical innovations will be considered, especially the apparent paradox of a discrete continuum of technological change. Further, an application of the developed framework to the assessment of firms in the stock market is discussed.

scholarly journals Neighborhood size-effects in nonlinear public goods games

2018 ◽  
Author(s):  
Gregory J. Kimmel ◽  
Philip Gerlee ◽  
Joel S. Brown ◽  
Philipp M. Altrock
Keyword(s):  
Public Goods ◽  
Public Good ◽  
Size Effects ◽  
Evolutionary Dynamics ◽  
Logistic Growth ◽  
Neighborhood Size ◽  
Frequency Dependent ◽  
Frequency Dependent Selection ◽  
The Public ◽  
Public Goods Games

Ecological and evolutionary dynamics can be strongly affected by population assortment and frequency-dependent selection. In growing populations, a particular challenge is to disentangle global ecological effects from local frequency-dependent effects. Here we implement a logistic growth and death model on the global scale, coupled to frequency-dependent growth rates influenced by a public goods game between cooperators and defectors. For each individual, the public good is only effective within a neighborhood of other individuals, and the public good-growth rate relationship can be nonlinear. At low numbers of cooperators, increases of public good accumulate synergistically; at high numbers, increases in public good only provide diminishing returns-the inflection point of this pattern is given by the strength of frequency-dependent selection in relation to the background fitness effect. We observed complex critical behavior in the evolutionary dynamics’ equilibria, determined by the relative magnitude of frequency-dependent to constant (background) growth benefits. We predict neighborhood-size-driven state changes, hysteresis between polymorphic and monomorphic equilibria, and observed that type-dependent differences in neighborhood sizes can destabilize monomorphic cooperative states but increase coexistence of cooperators and defectors. Stochastic neighborhood size fluctuations also led to coexistence and could stabilize the purely cooperative equilibrium. Our results quantify the role of assortment through neighborhood-size effects and nonlinearity of the gains function in eco-evolutionary dynamics, which is relevant for a variety of microbial and cellular public goods games.

scholarly journals Asymptotic limit of a spatially-extended mean-field FitzHugh–Nagumo model

2020 ◽  
Vol 30 (05) ◽  
pp. 957-990
Author(s):  
Joachim Crevat
Keyword(s):  
Field Model ◽  
Mean Field ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Asymptotic Limit ◽  
Mean Field Model ◽  
Interaction Kernel ◽  
Limit System ◽  
Spatially Extended ◽  
Energy Argument

We consider a spatially extended mean-field model of a FitzHugh–Nagumo neural network, with a rescaled interaction kernel. Our main purpose is to prove that its asymptotic limit in the regime of strong local interactions converges toward a system of reaction–diffusion equations taking account for the average quantities of the network. Our approach is based on a modulated energy argument, to compare the macroscopic quantities computed from the solution of the transport equation, and the solution of the limit system. The main difficulty, compared to the literature, lies in the need of regularity in space of the solutions of the limit system and a careful control of an internal nonlocal dissipation.

Imperfect Bifurcations and Spatial Structures in Dissipative Systems

1982 ◽  
Vol 37 (1) ◽  
pp. 39-45 ◽  
Author(s):  
V. Hlavacek ◽  
R. Janssen ◽  
P. Van Rompay
Keyword(s):  
Spatial Organization ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Evolution Process ◽  
Dissipative Systems ◽  
Physical Description ◽  
Large Perturbation ◽  
Flux Boundary Conditions ◽  
Imperfect Bifurcations ◽  
Imperfect Bifurcation

Abstract One-dimensional reaction-diffusion equations associated with the trimolecular model of Prigogine and Lefever ("Brusselator") are analyzed. A physical description of possibilities of keeping con-centrations of initial components constant is discussed. It is shown that the problem considering diffusion of initial components gives rise to an imperfect bifurcation problem. The diffusion equa-tions have been solved numerically by a continuation procedure for the fixed and zero flux boundary conditions. The analysis indicates that the models including diffusion of all reacting components do not admit an occurence of trivial solutions. These models, as a result, also exclude the pos-sibility of primary bifurcations. The models which consider diffusion of the initial components suppress the number of possible solutions of governing equations. These models may also predict both symmetric and asymmetric states. Apparently this type of models is more suitable for predic-tion of patterns of spatial organization in growth. Since the number of possible profiles is strongly reduced this principle may lead to a more deterministic way of an evolution process. Symmetric profiles occuring on an isola cannot be reached by an evolution process unless a large perturbation is imposed on the system.

scholarly journals Probabilistic participation in public goods games

2007 ◽  
Vol 274 (1625) ◽  
pp. 2639-2642 ◽  
Author(s):  
Tatsuya Sasaki ◽  
Isamu Okada ◽  
Tatsuo Unemi
Keyword(s):  
Public Goods ◽  
Evolutionary Dynamics ◽  
Voluntary Participation ◽  
Dynamical Regime ◽  
Mixed Strategies ◽  
Public Enterprises ◽  
Interior Equilibrium ◽  
Public Goods Games ◽  
Special Cases ◽  
Pure Strategies

Voluntary participation in public goods games (PGGs) has turned out to be a simple but effective mechanism for promoting cooperation under full anonymity. Voluntary participation allows individuals to adopt a risk-aversion strategy, termed loner. A loner refuses to participate in unpromising public enterprises and instead relies on a small but fixed pay-off. This system leads to a cyclic dominance of three pure strategies, cooperators, defectors and loners, but at the same time, there remain two considerable restrictions: the addition of loners cannot stabilize the dynamics and the time average pay-off for each strategy remains equal to the pay-off of loners. Here, we introduce probabilistic participation in PGGs from the standpoint of diversification of risk, namely simple mixed strategies with loners, and prove the existence of a dynamical regime in which the restrictions no longer hold. Considering two kinds of mixed strategies associated with participants (cooperators or defectors) and non-participants (loners), we can recover all basic evolutionary dynamics of the two strategies: dominance; coexistence; bistability; and neutrality, as special cases depending on pairs of probabilities. Of special interest is that the expected pay-off of each mixed strategy exceeds the pay-off of loners at some interior equilibrium in the coexistence region.

ON PULLBACK ATTRACTORS IN $H^1_0$ FOR NONAUTONOMOUS REACTION–DIFFUSION EQUATIONS

2010 ◽  
Vol 20 (09) ◽  
pp. 2637-2644 ◽  
Author(s):  
G. ŁUKASZEWICZ
Keyword(s):  
Integrability Condition ◽  
Evolutionary Process ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Pullback Attractor ◽  
Estimates Of Solutions ◽  
Kuratowski Measure Of Noncompactness ◽  
Bounded Set ◽  
Right Hand ◽  
The Right

Using a recent method based on the concept of the Kuratowski measure of noncompactness of a bounded set together with some new estimates of solutions, we prove the existence of a unique minimal pullback attractor for the evolutionary process associated with a nonautonomous nonlinear reaction–diffusion system in [Formula: see text] in which the right-hand side satisfies only a certain integrability condition. In particular, we generalize a result obtained recently in [Li & Zhong, 2007] where at most an exponential growth of the right-hand side has been assumed for times going to both plus and minus infinity.

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