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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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The CAS framework provides a natural resolution by reframing both divergence and convergence as emergent outcomes of shared attractor dynamics.

1. Divergent Evolution as Attractor Partitioning

In CAS terms, divergent evolution arises when an ancestral population disperses across a rugged adaptive landscape with multiple basins of attraction. Subpopulations, shaped by stochasticity, local environments, and demographic contingencies, fall into distinct basins, stabilizing around alternative adaptive packages. In this framing, divergence is not merely linear accumulation of differences, but partitioning of populations across multiple emergent attractors.

2. Convergent Evolution as Attractor Recurrence

Convergent evolution, by contrast, occurs when lineages separated in space or time nonetheless enter the same attractor basin, producing strikingly similar trait combinations. This phenomenon is common in high-performance predators: falcons, hawks, and even unrelated lineages like bats or large predatory fish display functionally equivalent adaptations for speed, vision, and strike precision. The CAS model predicts such outcomes because attractor basins are recurrent solutions, shaped by universal constraints of physics, ecology, and genetic architecture.

3. Unified Explanation of Both Patterns

By embedding both divergence and convergence within the same dynamical system, CAS eliminates the need to treat them as opposites. Divergence and convergence are not mutually exclusive; they are complementary modes of population movement within and across adaptive landscapes. Divergence reflects the distribution of populations across multiple attractors, while convergence reflects the recurrence of stable attractors across lineages and conditions.

4. Peregrine Falcon as Case in Point

The peregrine falcon exemplifies this reconciliation. Divergently, the Falconidae family shows wide morphological and ecological diversity, with many lineages stabilizing in different niches. Yet convergently, peregrine-like hunting designs---steep-winged morphology, high visual acuity, reinforced keel---emerge across unrelated raptor clades. CAS theory explains both patterns as consequences of the same underlying dynamics: stochastic divergence into different basins, and deterministic recurrence of specific basins that are especially deep and evolutionarily stable.

In sum, CAS reframes the debate: divergence and convergence are not contradictory, but are two aspects of a single process governed by emergent attractor structures. This perspective situates evolutionary patterns within a broader theory of complex systems, offering a unified explanatory language for phenomena traditionally considered distinct.

C. Trade-offs and Red Queen Dynamics in a Unified Framework

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