© 2012 Massachusetts Institute of Technology Artiicial Life 13: 91–98 Evolutionary Dynamics and Ecosystems Feedback in Two Dimensional Daisyworld Dharani Punithan and RI (Bob) McKay Structural Complexity Laboratory, Department of Computer Science and Engineering, Seoul National University, South Korea. {punithan.dharani,rimsnucse}@gmail.com Abstract We introduce replicator-mutator mechanisms from evolu- tionary dynamics into a two-dimensional daisyworld model, thereby coupling evolutionary changes with daisyworld’s bi- directional feedback between biota and environment. Daisy- world continues to self-regulate in the presence of these evo- lutionary forces. The most interesting behaviours, exhibit- ing a complex and dynamic dance through space and time in species’ abundance, emerges through the introduction of additive spatio-temporal random perturbations in the form of thermal noise. The balance between ecosystem feedback and fluctuations in the ecosystem determines the spatial coexis- tence of domains of dominance between daisy species and their mutants or adaptants. Introduction Evolutionary studies have highlighted the importance of biota-environment feedback in evolutionary dynamics, for example, niche construction (Odling-Smee et al., 2003), extended phenotypes (Dawkins, 1999). Biota-environment feedback is inherent in daisyworld models, so we have cho- sen to extend the basic daisyworld model with evolutionary dynamics based on the replicator-mutator equation (RME) (Hofbauer and Sigmund, 2003). The three fundamental factors in Darwinian evolution are replication (entities reproducing themselves), mutation (pro- ducing small variations in transforming to a new entity) and selection (passing the fitter entities to later generations). These factors determine the population dynamics: changes in population size and evolution of new populations. Pop- ulations are the fundamental basis of evolution; individuals can change over time, but only populations evolve (Nowak, 2006). We focus our attention on population dynamics in daisyworld with evolutionary change. Generally, selection arises as a consequence of compe- tition, commonly due to prey-predator relationships or re- source limits. In the daisyworld of Watson and Lovelock (1983), daisies compete for space and hence for light. Daisy- world also incorporates a feedback mechanism: different daisy species affect the temperature, and the temperature in turn affects daisy survival, and hence selection. Thus the classic daisyworld realises the competition and natural se- lection of an evolutionary framework. What is less studied in classical Darwinian evolution is the global feedback between biota and environment; con- versely, the components that are omitted in the original daisyworld model are mutation and adaptation. In this field, it is common to distinguish between evolution of the daisies in ways which change their effect on the environment (in this case, albedo), which is referred to simply as mutation; and evolution of the daisies in ways which change their re- sponse to the environment (growth curve with temperature), generally referred to as adaptation. Thus a simple evolution- ary daisyworld can incorporate all these factors, through 1) influence of temperature on daisies, 2) influence of daisies on temperature, 3) mutation of daisies and 4) adaptation of daisies to the temperature. A number of researchers have studied evolution in daisy- world. Mutation was introduced into daisyworld by Love- lock (1992) and expanded by Lenton et al. (1998); Lenton and Lovelock (2001). Adaptation in daisyworld was studied by Lenton and Lovelock (2000). For a more detailed survey, please see Wood et al. (2008, section 4). In this paper, we model the population dynamics of daisies using the replicator-mutator equation (RME) of evo- lutionary dynamics, in a diffusively coupled logistic lattice of daisyworld - a model which has not been studied pre- viously. RME has the advantage of expressing replication, mutation and selection mechanisms within a single frame- work; these evolutionary changes can be influenced by ex- ternal environment factors such as temperature or abundance of species. Also, the interaction with the environment affects the survival of daisies and changes their adaptive fitness. We have analysed the population dynamics of our daisyworld model through allowing a range of fluctuations in temper- ature, studying its effects on the evolutionary behaviour of the daisyworld. We did this by introducing ecosystem dis- turbance in the form of additive spatio-temporal Gaussian white noise (Garc´ ıa-Ojalvo and Sancho, 1999). The scale of fluctuation is controlled by the noise level. DOI: http://dx.doi.org/10.7551/978-0-262-31050-5-ch013