Abstract
Based on the stochastic dynamics of interacting agents which reproduce, mutate, and die, the tangled nature model (TNM) describes key emergent features of biological and cultural ecosystems' evolution. While trait inheritance is not included in many applications, i.e., the interactions of an agent and those of its mutated offspring are taken to be uncorrelated, in the family of TNMs introduced in this work correlations of varying strength are parametrized by a positive integer K. We first show that the interactions generated by our rule are nearly independent of K. Consequently, the structural and dynamical effects of trait inheritance can be studied independently of effects related to the form of the interactions. We then show that changing K strengthens the core structure of the ecology, leads to population abundance distributions better approximated by log-normal probability densities, and increases the probability that a species extant at time t_{w} also survives at t>t_{w}. Finally, survival probabilities of species are shown to decay as powers of the ratio t/t_{w}, a so-called pure aging behavior usually seen in glassy systems of physical origin. We find a quantitative dynamical effect of trait inheritance, namely, that increasing the value of K numerically decreases the decay exponent of the species survival probability.
Highlights
Models of biological [1] and social [2] evolution often involve networks of interacting agents whose dynamics is interpreted in biological or cultural terms [3,4,5]
We describe how trait inheritance affects the dynamics, first qualitatively at the level of the emergent core species structure [13] and more quantitatively, in terms of the species abundance distribution and the time decay of a cohort of species picked at different stages of the system evolution
Core species make up the bulk of the population since the mutualistic interactions which link them together endow them with high reproduction rates
Summary
Models of biological [1] and social [2] evolution often involve networks of interacting agents whose dynamics is interpreted in biological or cultural terms [3,4,5]. The Tangled Nature Model is a relatively recent [6, 7] but already well-studied [3, 8,9,10,11,12,13,14,15] agent based stochastic description of evolutionary dynamics which features punctuated equilibria [16], a key dynamical property of, among others, macro-evolutionary systems The latter go through a series of macroscopically different metastable states, with rapid and dramatic changes, here called quakes, leading from one state to the next. The matrix is averaged locally over neighborhoods in genome space to produce the desired correlations These authors find a stationary fluctuation dynamics, resembling that of a model with uncorrelated interactions. We describe how trait inheritance affects the dynamics, first qualitatively at the level of the emergent core species structure [13] and more quantitatively, in terms of the species abundance distribution and the time decay of a cohort of species picked at different stages of the system evolution
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