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Evolution as Complex Adaptive System: a Mathematical Framework

18 September 2025   20:30 Diperbarui: 18 September 2025   20:30 50
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Simulations proceeded in discrete generations. Each individual's phenotype was derived from its genotype using the mapping described in Section III.A. Predators engaged in probabilistic predation events against prey, with success determined by trait-dependent hunting probability (Section III.B). Survivors reproduced with probability proportional to their fitness, subject to mutation and recombination. In prey-evolving variants, prey traits were updated under analogous replicator--mutator dynamics. Bottleneck scenarios were implemented by reducing predator population size to 10% for ten generations at specified times. Spatial variants employed a 50 50 lattice with local reproduction and dispersal.

Observables

At each 10--50 generation interval, we recorded allele frequencies, linkage disequilibrium, haplotype diversity, trait means and variances, multivariate trait covariances, fitness distributions, predator and prey abundances, and predation rates. Emergence of coordinated adaptations was detected by clustering of phenotype vectors and by threshold-crossing of a composite adaptation index. Temporal dynamics were characterized by autocorrelation, cross-correlation between predator and prey traits, and spectral analysis to detect oscillatory regimes.

Analysis

Ensemble results were analyzed using nonparametric tests (Mann--Whitney, Kolmogorov--Smirnov) for between-variant comparisons, generalized additive models for sensitivity analysis, and survival analysis for time-to-event outcomes. Statistical significance was evaluated with bootstrap confidence intervals. Empirical calibration was addressed by comparing simulated linkage disequilibrium and co-selection signatures with genomic data from Falco peregrinus and related species.

Implementation and Reproducibility

Forward-time genetic simulations were implemented in SLiM 3.0, with driver scripts in Python 3.8 for parameter control, data storage, and analysis. Ensemble jobs were executed on a high-performance computing cluster under SLURM scheduling. Outputs were archived in HDF5 format with metadata including random seeds, parameter values, and software versions. Analysis pipelines were version-controlled (Git) and containerized (Docker/Singularity) to ensure reproducibility.

D. Emergent Attractors and Synchronized Adaptations

A central prediction of the CAS framework is that evolution does not merely accumulate isolated improvements, but converges toward emergent attractors --- coherent sets of traits that stabilize as functional wholes. In the case of the peregrine falcon, such attractors correspond to trait configurations enabling the stooping hunting strategy, where vision, respiration, neuromuscular control, and wing morphology operate in synchrony.

1. Coordinated Trait Bundling

In our simulations, coordinated adaptation was measured as the joint improvement of multiple interdependent traits beyond thresholds that render them functional as a package. For example, enhanced wing morphology (T4T_4T4) alone may not significantly increase predation success unless complemented by sufficient visual acuity (T1T_1T1) and neuromuscular control (T3T_3T3). Once these traits cross synergistic thresholds, fitness gains become multiplicative, creating a strong attractor basin around the coordinated phenotype.

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