Evolutionary Daisyworld models: A new approach to studying complex adaptive systems

Nuño, Juan Carlos, Javier De Vicente, José Olarrea, Pilar López, and Rafael Lahoz-Beltrá. “Evolutionary Daisyworld models: A new approach to studying complex adaptive systems.” Ecological Informatics 5, no. 4 (2010): 231-240.


This paper presents a model of a population of error-prone self-replicative species (replicators) that interact with its environment. The population evolves by natural selection in an environment whose change is caused by the evolutionary process itself. For simplicity, the environment is described by a single scalar factor, i.e. its temperature. The formal formulation of the model extends two basic models of Ecology and Evolutionary Biology, namely, Daisyworld and Quasispecies models. It is also assumed that the environment can also change due to external perturbations that are summed up as an external noise. Unlike previous models, the population size self-regulates, so no ad hoc population constraints are involved. When species replication is error-free, i.e. without mutation, the system dynamics can be described by an (n + 1)-dimensional system of differential equations, one for each of the species initially present in the system, and another for the evolution of the environment temperature. Analytical results can be obtained straightforwardly in low-dimensional cases. In these examples, we show the stabilizing effect of thermal white noise on the system behavior. The error-prone self-replication, i.e. with mutation, is studied computationally. We assume that species can mutate two independent parameters: its optimal growth temperature and its influence on the environment temperature. For different mutation rates the system exhibits a large variety of behaviors. In particular, we show that a quasispecies distribution with an internal sub-distribution appears, facilitating species adaptation to new environments. Finally, this ecologically inspired evolutionary model is applied to study the origin and evolution of public opinion.

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