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Evolution as Complex Adaptive System: a Mathematical Framework

18 September 2025   20:30 Diperbarui: 18 September 2025   20:30 49
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Which attractors are universally stable across ecological contexts.
How demographic and ecological contingencies bias populations into particular basins.
To what extent multi-scale synchronization explains convergent macroevolutionary patterns.
4. Broader Implications

Pursuing this path positions evolutionary biology more firmly within the domain of complex systems science, where attractors, bifurcations, and feedback loops are not metaphors but formal tools. It also provides a natural bridge to fields such as systems biology, network theory, and theoretical ecology, fostering cross-disciplinary collaboration.

In summary, the CAS framework not only clarifies the peregrine falcon's adaptive puzzle but also sets the stage for a comparative, empirically anchored research program. By integrating genomics, morphometrics, ecology, and complexity science, this approach has the potential to reveal the underlying logic of evolutionary design across the tree of life.

C. Evolutionary Theory Reframed as CAS

The peregrine falcon case illustrates a broader theoretical point: evolution is best understood not as a sequence of isolated trait changes, but as the dynamics of a Complex Adaptive System. By formalizing evolution in terms of attractors, bifurcations, feedback loops, and multi-scale interactions, we reframe the discipline in several fundamental ways:

1. From linear accumulation to emergent coordination. Classical theory emphasizes incremental trait improvement. CAS emphasizes that adaptive packages emerge through the self-organization of interacting traits, producing coherence without foresight.
2. From static landscapes to dynamic attractors. Traditional fitness landscapes are often conceptualized as static topographies. CAS reframes them as moving, deformable surfaces, continuously reshaped by ecological feedback, genetic interactions, and demographic shifts. Evolutionary outcomes are therefore trajectories toward attractors within evolving landscapes.
3. From dichotomies to unification. Long-standing debates---gradualism vs. punctuated equilibrium, divergence vs. convergence, constraints vs. innovation---are unified as complementary expressions of CAS dynamics. Gradual drift and punctuated shifts, divergence across attractors and convergence on shared attractors, are not contradictions but natural system behaviors.
4. From descriptive to predictive theory. By embedding evolution within the formal machinery of complexity science, CAS yields testable predictions: genomic co-selection signatures, trait covariance patterns, oscillatory eco-evolutionary cycles, and conditions for attractor switching. These predictions can be evaluated empirically across taxa, providing a pathway from metaphor to quantitative science.
In this reframed perspective, the peregrine falcon is not an evolutionary anomaly but a paradigmatic example of how coordinated, high-performance designs emerge from the self-organizing dynamics of evolution as a CAS. This shift opens the door to a new synthesis, one that aligns evolutionary biology with the broader study of complex systems in physics, chemistry, and the life sciences.

References

Evolutionary Biology Foundations

Darwin, C. (1859). On the origin of species by means of natural selection. London: John Murray.
Gould, S. J., & Eldredge, N. (1977). Punctuated equilibria: The tempo and mode of evolution reconsidered. Paleobiology, 3(2), 115--151.
Mayr, E. (1982). The growth of biological thought: Diversity, evolution, and inheritance. Cambridge, MA: Harvard University Press.
Wright, S. (1932). The roles of mutation, inbreeding, crossbreeding, and selection in evolution. Proceedings of the Sixth International Congress of Genetics, 1, 356--366.
Futuyma, D. J. (2013). Evolution (3rd ed.). Sunderland, MA: Sinauer.
Laland, K. N., Uller, T., Feldman, M. W., Sterelny, K., Mller, G. B., Moczek, A., ... & Jablonka, E. (2015). The extended evolutionary synthesis: Its structure, assumptions and predictions. Proceedings of the Royal Society B, 282(1813), 20151019.
Complexity Science & CAS Approaches

Holland, J. H. (1992). Adaptation in natural and artificial systems. Cambridge, MA: MIT Press.
Kauffman, S. A. (1993). The origins of order: Self-organization and selection in evolution. New York: Oxford University Press.
Levin, S. A. (1998). Ecosystems and the biosphere as complex adaptive systems. Ecosystems, 1(5), 431--436.
Mitchell, M. (2009). Complexity: A guided tour. Oxford: Oxford University Press.
Nowak, M. A., & Sigmund, K. (2004). Evolutionary dynamics of biological games. Science, 303(5659), 793--799.
Sturmberg, J. P., & Martin, C. M. (2013). Handbook of systems and complexity in health. New York: Springer. (used here for CAS methodology references).
West, G. B. (2017). Scale: The universal laws of growth, innovation, sustainability, and the pace of life in organisms, cities, economies, and companies. New York: Penguin Press.
Evolutionary Game Theory, Red Queen & Predator--Prey Models

Van Valen, L. (1973). A new evolutionary law. Evolutionary Theory, 1, 1--30.
Abrams, P. A. (2000). The evolution of predator--prey interactions: Theory and evidence. Annual Review of Ecology and Systematics, 31(1), 79--105.
Dieckmann, U., & Law, R. (1996). The dynamical theory of coevolution: A derivation from stochastic ecological processes. Journal of Mathematical Biology, 34(5-6), 579--612.
Hofbauer, J., & Sigmund, K. (1998). Evolutionary games and population dynamics. Cambridge: Cambridge University Press.
Geritz, S. A. H., Metz, J. A. J., Kisdi, E., & Meszna, G. (1997). Dynamics of adaptation and evolutionary branching. Physical Review Letters, 78(10), 2024--2027.
Peregrine Falcon Biology (Morphology, Ecology, Genomics)

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