Entropy in the Tangled Nature Model of Evolution

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. We obtain here a qualitative interpretation of the role of entropy in evolving ecological systems. Our interpretation is supported by mathematical arguments using simulation data generated by the Tangled Nature Model (TNM), a stochastic model of evolving ecologies. We define two types of configurational entropy and study their empirical time dependence obtained from the data. 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 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. 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.

[1]  Paolo Sibani,et al.  Tangled nature model of evolutionary dynamics reconsidered: Structural and dynamical effects of trait inheritance. , 2016, Physical review. E.

[2]  S. Gould,et al.  Punctuated equilibria: the tempo and mode of evolution reconsidered , 1977, Paleobiology.

[3]  Paolo Sibani,et al.  Evolution and non-equilibrium physics: A study of the Tangled Nature Model , 2013, 1309.1837.

[4]  S. Cushman Calculating the configurational entropy of a landscape mosaic , 2016, Landscape Ecology.

[5]  Henrik Jeldtoft Jensen,et al.  Network properties, species abundance and evolution in a model of evolutionary ecology. , 2003, Journal of theoretical biology.

[6]  P. T. Landsberg,et al.  Can entropy and order increase together , 1984 .

[7]  Jacques Baudry,et al.  A review on the use of entropy in landscape ecology: heterogeneity, unpredictability, scale dependence and their links with thermodynamics , 2014, Landscape Ecology.

[8]  H. Odum,et al.  TIME'S SPEED REGULATOR: THE OPTIMUM EFFICIENCY FOR MAXIMUM POWER OUTPUT IN PHYSICAL AND BIOLOGICAL SYSTEMS , 2011 .

[9]  Henrik Jeldtoft Jensen,et al.  Time-dependent extinction rate and species abundance in a tangled-nature model of biological evolution. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  J. S. Wicken Evolution, Thermodynamics, and Information: Extending the Darwinian Program , 1987 .

[11]  Henrik Jeldtoft Jensen,et al.  The Tangled Nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource , 2005, q-bio/0510008.

[12]  S. Kauffman,et al.  Coevolution to the edge of chaos: coupled fitness landscapes, poised states, and coevolutionary avalanches. , 1991, Journal of theoretical biology.

[13]  J. Harte Maximum Entropy and Ecology: A Theory of Abundance, Distribution, and Energetics , 2011 .

[14]  Peter Maurer,et al.  Growth And Development Ecosystems Phenomenology , 2016 .

[15]  P. A. Rikvold,et al.  Effects of correlated interactions in a biological coevolution model with individual-based dynamics , 2005, q-bio/0507040.

[16]  K. Barott,et al.  Stable and sporadic symbiotic communities of coral and algal holobionts , 2015, The ISME Journal.

[17]  J. Craik Ecology, the Ascendent Perspective. Robert E. Ulanowicz , 1999 .

[18]  Henrik Jeldtoft Jensen,et al.  Evolution in complex systems , 2004, Complex..

[19]  S. Kauffman,et al.  Towards a general theory of adaptive walks on rugged landscapes. , 1987, Journal of theoretical biology.

[20]  S. Gould,et al.  Punctuated equilibria: an alternative to phyletic gradualism , 1972 .

[21]  David J. Depew,et al.  Entropy, Information and Evolution: New Perspectives on Physical and Biological Evolution , 1988 .

[22]  Henrik Jeldtoft Jensen,et al.  The species-area relationship and evolution. , 2004, Journal of theoretical biology.

[23]  J. S. Wicken,et al.  A thermodynamic theory of evolution. , 1980, Journal of theoretical biology.

[24]  Nobuyasu Ito,et al.  Random walk in genome space: a key ingredient of intermittent dynamics of community assembly on evolutionary time scales. , 2010, Journal of theoretical biology.

[25]  K. Christensen,et al.  Tangled nature: a model of evolutionary ecology. , 2001, Journal of theoretical biology.

[26]  Ethan P. White,et al.  An extensive comparison of species-abundance distribution models , 2015, bioRxiv.