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Dynamical role of the degree of intraspecific cooperation: A simple model for prebiotic replicators and ecosystems

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  • Fontich, Ernest
  • Sardanyés, Josep

Abstract

We present a simple mean field model to analyze the dynamics of competition between two populations of replicators in terms of the degree of intraspecific cooperation (i.e., autocatalysis) in one of these populations. The first population can only replicate with Malthusian kinetics while the second one can reproduce with Malthusian or autocatalytic replication or with a combination of both reproducing strategies. The model consists of two coupled, nonlinear, autonomous ordinary differential equations. We investigate analytically and numerically the phase plane dynamics and the bifurcation scenarios of this ecologically coupled system, focusing on the outcome of competition for several degrees of intraspecific cooperation, σ, in the second population of replicators. We demonstrate that the dynamics of both populations can not be governed by a limit cycle, and also that once cooperation is considered, the topology of phase space does not allow for coexistence. Even for low values of the degree of intraspecific cooperation, for large enough autocatalytic replication rates, the second population of replicators is able to outcompete the first one, having a wide basin of attraction in state space. We characterize the same power law dependence between the outcompetition extinction times, τ, and the degree of intraspecific cooperation for both populations, given by τ∼ciσ−1. Our results suggest that, under some kinetic conditions, the appearance of autocatalysis might be favorable in a population of replicators growing with Malthusian kinetics competing with another population also reproducing exponentially.

Suggested Citation

  • Fontich, Ernest & Sardanyés, Josep, 2009. "Dynamical role of the degree of intraspecific cooperation: A simple model for prebiotic replicators and ecosystems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(9), pages 1867-1878.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:9:p:1867-1878
    DOI: 10.1016/j.physa.2009.01.020
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    References listed on IDEAS

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    1. Bärbel M. R. Stadler & Peter F. Stadler, 2003. "Molecular Replicator Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 47-77.
    2. David H. Lee & Kay Severin & Yohei Yokobayashi & M. Reza Ghadiri, 1997. "Emergence of symbiosis in peptide self-replication through a hypercyclic network," Nature, Nature, vol. 390(6660), pages 591-594, December.
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