Abstract
Adaptation and evolution are quasi synonymous in popular language, it is hence little surprising that the theory of Darwinian evolution is infused with complex systems concepts. We will discuss when a species will manage to successfully mutate while escaping its local fitness optimum, or when it may spiral towards extinction in the wake of an “error catastrophe”. Venturing into the mysteries surrounding the origin of life, we will investigate the possible advent of a quasispecies in terms of mutually supporting hypercycles. The basic theory of evolution is furthermore closely related to game theory, the mathematical theory of socially interacting agents, viz of rationally acting economic persons. The tragedy of the commons occurring in this context describes the over-exploitation of resources.
We will learn in this chapter that complex systems come with respective individual characteristics. For Darwinian evolution the core notions are fitness, selection and mutation. On this basis, generic concepts from dynamical systems theory unfold, like the phenomenon of stochastic escape. Furthermore we will show that evolutionary processes affect not only the welfare of an individual species, but the pattern of species abundances of entire ecosystems, which will be discussed in this context the neutral theory of macroecology.
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Notes
- 1.
Evolutionary processes transcending a single species, like the radiation of lineages, would be the domain of “macroevolution”.
- 2.
Point mutations can be thought to correspond to “single-nucleotide mutations” (SNM).
- 3.
The probability to find a state with energy E in a thermodynamic system with temperature T is proportional to the Boltzmann factor \(\exp (-\beta \,E)\). The inverse temperature is \(\beta =1/(k_B T)\), with \(k_B\) being the Boltzmann constant.
- 4.
In classical thermodynamics, the Hamiltonian \(H(\alpha )\), or energy function, determines the probability that a given state \(\alpha \) is populated. This probability is proportional to the Boltzmann factor \(\exp (-\beta H(\alpha ))\), where \(\beta =1/(k_B t)\) is the inverse temperature.
- 5.
Any system of binary variables is equivalent to a system of interacting Ising spins, which retains only the classical contribution to the energy of interacting quantum mechanical spins (the magnetic moments).
- 6.
- 7.
The notion of life at the edge of chaos features prominently in Chap. 7.
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- 9.
- 10.
A sequence of elements is summable if the sum does not diverge when the length is successively increased. For vectors, the sum of the squared entries is of relevance.
- 11.
This detailed out in exercise (8.2).
- 12.
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- 14.
- 15.
The occurrence of self-organized criticality in the sandpile model is discussed in Chap. 6.
- 16.
References
Azaele, S., et. al. (2016). Statistical mechanics of ecological systems: Neutral theory and beyond. Reviews of Modern Physics, 88, 035003.
Blythe, R. A., & McKane, A. J. (2007). Stochastic models of evolution in genetics, ecology and linguistics. Journal of Statistical Mechanics: Theory and Experiment, P07018.
Bull, J. J., Meyers, L. A., & Lachmann, M. (2005). Quasispecies made simple. PLoS Computational Biology, 1, e61.
Drake, J. W., Charlesworth, B., & Charlesworth, D. (1998). Rates of spontaneous mutation. Genetics, 148, 1667–1686.
Drossel, B. (2001). Biological evolution and statistical physics. Advances in Physics, 2, 209–295.
Eigen, M., & Schuster, P. (2012). The hypercycle – A principle of natural self-organization. Springer.
Gros, H. (2023). Generic catastrophic poverty when selfish investors exploit a degradable common resource. Royal Society Open Science, 10, 221234.
Heasley, L. R., Sampaio, N. M., & Argueso, J. L. (2021). Systemic and rapid restructuring of the genome: A new perspective on punctuated equilibrium. Current Genetics, 67, 57–63.
Higgs, P. G., & Lehman, N. (2015). The RNA world: Molecular cooperation at the origins of life. Nature Reviews Genetics, 16, 7–17.
Jain, K., & Krug, J. (2006). Adaptation in simple and complex fitness landscapes. In U. Bastolla, M. Porto, H. E. Roman, & M. Vendruscolo, (Eds.), Structural approaches to sequence evolution: Molecules, networks and populations. AG Porto.
Schweitzer, F., Behera, L., & Mühlenbein, H. (2002). Evolution of cooperation in a spatial prisoner’s dilemma. Advances in Complex Systems, 5, 269–299.
Sigmund, K. (2017). Games of life: Explorations in ecology, evolution and behavior. Courier.
Volkov, I., Banavar, J. R., Hubbell, S. P., & Maritan, A. (2003). Neutral theory and relative species abundance in ecology. Nature, 424, 1035–1037.
Wilkinson, D. M., & Sherratt, T. N. (2016). Why is the world green? The interactions of top-down and bottom-up processes in terrestrial vegetation ecology. Plant Ecology & Diversity9, 127–140.
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Gros, C. (2024). Darwinian Evolution, Hypercycles and Game Theory. In: Complex and Adaptive Dynamical Systems. Springer, Cham. https://doi.org/10.1007/978-3-031-55076-8_8
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DOI: https://doi.org/10.1007/978-3-031-55076-8_8
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