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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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Across ensemble runs, allele trajectories displayed the characteristic hallmarks of coordinated evolution. In additive baseline models (Variant A), alleles rose and fell slowly, with weak linkage disequilibrium and limited co-selection. By contrast, when epistasis and pleiotropy were introduced (Variant B), allele frequencies at multiple loci shifted in concerted sweeps, producing extended haplotype blocks. These patterns were consistent with selection for multi-locus trait bundles rather than isolated loci.

Concerted sweeps were most prominent when mutation rates (104\mu \sim 10^{-4}104) and population sizes (NP1000N_P \geq 1000NP1000) allowed sufficient standing variation.
Bottleneck scenarios (Variant D) accelerated fixation of coordinated allele sets, often producing rapid convergence to a single haplotype cluster within 500--1000 generations.
2. Trait Synchronization

Trait trajectories revealed the gradual accumulation of small gains, punctuated by sudden synchronization events. For thousands of generations, individual traits (vision, respiration, neuromuscular control, wing morphology) improved only incrementally. Then, once rare allelic combinations arose, all four traits surged together, crossing thresholds that transformed hunting success.

Synchronization was quantified by correlation analysis: cross-trait correlation coefficients increased from near-zero to >0.8 within a few hundred generations.
Once synchronized, traits remained clustered around stable means, consistent with the attractor states identified in the analytical results.
3. Red Queen Cycles in Predator--Prey Dynamics

In coevolutionary scenarios (Variant C), predator and prey traits exhibited oscillatory cycles. As predator traits improved, prey speed and evasiveness increased in response, which in turn forced further predator refinement.

Fourier analysis of trait trajectories revealed dominant oscillatory modes with periods of 200--500 generations, confirming Hopf bifurcations predicted analytically.
Predator and prey traits often lagged one another by ~90 phase offset, indicating tightly coupled arms-race dynamics.
In high-cost regimes, oscillations dampened into quasi-stable equilibria, while in low-cost regimes, cycles persisted indefinitely.
4. Multistability and Attractor Switching

Simulations also revealed multistability: some populations converged on peregrine-like phenotypes, while others stabilized in alternative attractors emphasizing different trait bundles (e.g., high vision and neuromuscular control but moderate wing morphology). Stochastic events, especially bottlenecks, determined which attractor basin populations entered.

Attractor switching was occasionally observed: populations trapped in suboptimal attractors escaped when rare recombination events created novel allele combinations, triggering sudden transitions to higher-fitness states.
5. Emergence of the Peregrine-like Phenotype

In full CAS scenarios, a recurrent attractor was observed that closely matched the peregrine falcon's adaptive package:

Vision increased 3--5 standard deviations above ancestral levels.
Respiration and neuromuscular control rose in tandem, stabilizing at values that balanced costs with performance.
Wing morphology converged around the aerodynamic optimum, minimizing drag while maximizing dive speed.
Once established, this phenotype remained resilient under prey counter-adaptation, illustrating the robustness of coordinated adaptation in CAS dynamics.
C. Comparison with Empirical Genomic and Ecological Evidence

A central requirement of the CAS-based model is empirical coherence: model mechanisms and predictions must map onto observable genomic signatures, morphological records, and ecological dynamics. Below we summarize how major model predictions align with (or are testable against) empirical evidence for Falco peregrinus and related taxa, and we identify the kinds of data and analyses that would strengthen or falsify the CAS interpretation.

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