During a QESS, macroscopic quantities such as the total population fluctuate slightly around fixed plateau values. In all of the above models, each dynamical trajectory is characterized by periods of metastability of increasing duration, referred to as quasi evolutionary stable states (QESSs), which mimic the punctuated equilibria of biological macroevolution. This property makes the TNM highly relevant for a discussion of how order and entropy can evolve together in an ecology. Since these interactions are dynamically selected from a completely unbiased distribution, the degree of order appears to increase over time in our model ecology, precisely as it does in real ecosystems. A key feature of the TNM ecology is a growing network of extant species with increasingly mutualistic, i.e., positive interactions. Introduced more than a decade ago by Christensen, Jensen and collaborators, the TNM has attracted attention ever since, see, e.g., and references therein. The latter aspect is central in a more recent computational model of evolution, the Tangled Nature Model (TNM). Furthermore, the models capture the decelerating rate of evolution and the red queen dynamics seen when interacting species are present, but do not capture that evolving species have a changing environment, a fact which drives much of natural selection. When a better maximum is found, the population rapidly shifts to that maximum, leading to an intermittent coarse-grained dynamics similar to punctuated equilibrium. In practice, at any given time, agents mainly inhabit one local maximum of the landscape and nearby genome space is searched via mutation and drift. A case in point is Kauffman’s NK and NKC models, where agents evolve in a fixed fitness landscape, and where uphill climbs are generated by mutations and by the competitive advantage of fitter individuals. Computational models offer simplified descriptions of biological phenomena that can reveal generic properties of evolving systems through simulations and analyses. Herein we define two types of configurational entropy and investigate their behavior as well as the emergence of structure over time in an evolving in silico ecosystem. As argued by Landsberg long ago, disorder and entropy are not necessarily coupled, and increasing order can emerge along with increasing entropy. That more ordered structures gradually emerge in an evolving ecosystem is clear, but whether its entropy should increase or decrease in time remains an open question. Additionally, statistical entropies have been used in biology to characterize the spatial distribution and structuring of ecologies, as well as to quantify the amount of complexity, organization, and order that emerge from evolutionary processes. Thermodynamic entropy has been used in biology to quantify the efficiency of biological processes. The notions of entropy which have been put forward for use in ecology are based on configurational, topological, and temporal heterogeneity of an ecosystem and/or on the uncertainty linked to its description.
#THE BLUE SPHERES BELOW REPRESENT ATOMS HOW TO#
The TNM serves as an illustrative example of how to calculate and interpret these entropies, which are, however, also relevant to real ecosystems, where they can be used to calculate the number of functional and taxonomic configurations that an ecosystem can realize. We discuss the biological relevance of these entropies to describe niche space and functional space of ecosystems, as well as their use in characterizing the number of taxonomic configurations compatible with different niche partitioning and functionality.
Both entropy measures increase logarithmically with time, while the entropy per individual decreases in time, in parallel with the growth of emergent structures visible from other aspects of the simulation. We define two types of configurational entropy and study their empirical time dependence obtained from the data. Our interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM), a stochastic model of evolving ecologies. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Applications of entropy principles to evolution and ecology are of tantamount importance given the central role spatiotemporal structuring plays in both evolution and ecological succession.
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