Participation in and Compliance with Public Voluntary Environmental Programs: An Evolutionary Approach

The joint evolution of participating and complying firms in a public VA, along with the evolution of the pollution stock is examined. Replicator dynamics modeling participation and compliance are combined with pollution stock dynamics. Fast-slow selection dynamics are used to capture the fact that decisions to participate in and further comply with the public VA evolve in different time scales. Evolutionary stable (ES) equilibria depend on the structure of the legislation and auditing probability. Partial participation and partial compliance can be ES equilibria, with possible multiplicities, in addition to the monomorphic equilibria of full (non) compliance. Convergence to these equilibria could be monotonic or oscillating. Full participation and compliance can be attained if the regulator is pre-committed to certain legislation and inspection probabilities, or by appropriate choices of the legislatively set emission level and the non-compliance fine.Voluntary agreements, participation, compliance, evolutionary stability, replicator dynamics.

Participation in and Compliance with Public Voluntary Environmental Programs: An Evolutionary Approach

The joint evolution of participating and complying firms in a public VA, along with the evolution of the pollution stock is examined. Replicator dynamics modeling participation and compliance are combined with pollution stock dynamics. Fast-slow selection dynamics are used to capture the fact that decisions to participate in and further comply with the public VA evolve in different time scales. Evolutionary stable (ES) equilibria depend on the structure of the legislation and auditing probability. Partial participation and partial compliance can be ES equilibria, with possible multiplicities, in addition to the monomorphic equilibria of full (non) compliance. Convergence to these equilibria could be monotonic or oscillating. Full participation and compliance can be attained if the regulator is pre-committed to certain legislation and inspection probabilities, or by appropriate choices of the legislatively set emission level and the non-compliance fine.Voluntary agreements, Participation, Compliance, Evolutionary stability, Replicator dynamics

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate $1/f$ fluctuations are observed with noise, while $1/f^{2}$ fluctuations are found for the model without demographic noise

Three-fold way to extinction in populations of cyclically competing species

Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic population model where three species exhibit cyclic competition. The cyclic dynamics reflects the non-equilibrium nature of the species interactions. While previous work focusses on the coarsening process as a mechanism that drives the system to extinction, we found that unexpectedly the dynamics to extinction is much richer. We observed three different types of dynamics. In addition to coarsening, in the evolutionary relevant limit of large times, oscillating traveling waves and heteroclinic orbits play a dominant role. The weight of the different processes depends on the degree of mixing and the system size. By analytical arguments and extensive numerical simulations we provide the full characteristics of scenarios leading to extinction in one of the most surprising models of ecology

A matrix model for density-dependent selection in stage-classified populations, with application to pesticide resistance in Tribolium

The study of eco-evolutionary dynamics is based on the idea that ecological and evolutionary processes may operate on the same, or very similar, time scales, and that interactions of ecological and evolutionary processes may have important consequences. Here we develop a model that combines Mendelian population genetics with nonlinear demography to create a truly eco-evolutionary model. We use the vec-permutation matrix approach, classifying individuals by stage and genotype. The demographic component is female dominant and density-dependent. The genetic component includes random mating by stage and genotype, and arbitrary effects of genotype on the demographic phenotype. Mutation is neglected. The result is a nonlinear matrix population model that projects the stage × genotype distribution. We show that the results can include bifurcations of population dynamics driven by the response to selection. We present analytical criteria that determine whether one allele excludes the other or if they persist in a protected polymorphism. The results are based on local stability analysis of the homozygous boundary equilibria. As an example, we use a density-dependent stage-classified model of the flour beetle Tribolium castaneum. Our model permits arbitrary life-cycle complexity and nonlinearity. Tribolium has developed resistance to the pesticide malathion due to a dominant allele at a single autosomal locus. Using parameters reported from laboratory experiments, we show that the model successfully describes the dynamics of both resistant and susceptible homozygotes, and the outcome of a selection experiment containing both alleles. Stability analysis of the boundary equilibria confirms that the resistant allele excludes the susceptible allele, even in the absence of malathion, agreeing with previously reported results

Evolutionary ecology in-silico: Does mathematical modelling help in understanding the "generic" trends?

Motivated by the results of recent laboratory experiments (Yoshida et al. Nature, 424, 303-306 (2003)) as well as many earlier field observations that evolutionary changes can take place in ecosystems over relatively short ecological time scales, several ``unified'' mathematical models of evolutionary ecology have been developed over the last few years with the aim of describing the statistical properties of data related to the evolution of ecosystems. Moreover, because of the availability of sufficiently fast computers, it has become possible to carry out detailed computer simulations of these models. For the sake of completeness and to put these recent developments in the proper perspective, we begin with a brief summary of some older models of ecological phenomena and evolutionary processes. However, the main aim of this article is to review critically these ``unified'' models, particularly those published in the physics literature, in simple language that makes the new theories accessible to wider audience.Comment: 28 pages, LATEX, 4 eps figure

On the sympatric evolution and evolutionary stability of coexistence by relative nonlinearity of competition

If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as relative nonlinearity of competition, is well understood theoretically, but less is known about its evolutionary properties and its prevalence in real communities. We address this challenge by using adaptive dynamics theory and individual-based simulations to compare community stabilization and evolutionary stability of species that coexist by relative nonlinearity. In our analysis, evolution operates on the species' density-compensation strategies, and we consider a trade-off between population growth rates at high and low resource availability. We confirm previous findings that, irrespective of the particular model of density dependence, there are many combinations of overcompensating and undercompensating density-compensation strategies that allow stable coexistence by relative nonlinearity. However, our analysis also shows that most of these strategy combinations are not evolutionarily stable and will be outcompeted by an intermediate density-compensation strategy. Only very specific trade-offs lead to evolutionarily stable coexistence by relative nonlinearity. As we find no reason why these particular trade-offs should be common in nature, we conclude that the sympatric evolution and evolutionary stability of relative nonlinearity, while possible in principle, seems rather unlikely. We speculate that this may, at least in part, explain why empirical demonstrations of this coexistence mechanism are rare, noting, however, that the difficulty to detect relative nonlinearity in the field [...]Comment: PLOS ONE, in pres

Stability as a natural selection mechanism on interacting networks

Biological networks of interacting agents exhibit similar topological properties for a wide range of scales, from cellular to ecological levels, suggesting the existence of a common evolutionary origin. A general evolutionary mechanism based on global stability has been proposed recently [J I Perotti, O V Billoni, F A Tamarit, D R Chialvo, S A Cannas, Phys. Rev. Lett. 103, 108701 (2009)]. This mechanism is incorporated into a model of a growing network of interacting agents in which each new agent's membership in the network is determined by the agent's effect on the network's global stability. We show that, out of this stability constraint, several topological properties observed in biological networks emerge in a self organized manner. The influence of the stability selection mechanism on the dynamics associated to the resulting network is analyzed as well.Comment: 10 pages, 9 figure