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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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Inovasi. Sumber ilustrasi: PEXELS/Jcomp

Experiment 1 --- Baseline dynamics

Variant A runs, 30 replicates, horizon 10,000 generations. Record allele frequency dynamics, trait means/variances, predation rate, population sizes.
Experiment 2 --- Epistasis / Pleiotropy effect

Variant B vs A. Measure time to reach a coordinated phenotype cluster (e.g., threshold composite index), compare distributions of times across replicates.
Experiment 3 --- Full coevolution (Red Queen)

Variant C: enable prey evolution. Compute cross-correlation between predator trait mean and prey trait mean; measure sustained oscillations vs convergence.
Experiment 4 --- Bottleneck acceleration

Variant D: impose bottleneck at generation tbt_btb (e.g., generation 2,000) reducing NPN_PNP to 10% for 10 generations. Compare time to coordinated fixation pre/post bottleneck.
Experiment 5 --- NK ruggedness sweep

Variant E: run K in {0,2,4,6}. For each K, run ensemble; compute frequency of punctuated shifts and distribution of adaptive peak heights.
Experiment 6 --- Spatial structure

Variant F: run on 5050 grid with local mating neighborhood and migration rate mmm in {0, 0.01, 0.05}. Evaluate local vs global adaptation and emergence of multiple local attractors.
Experiment 7 --- Sensitivity & robustness

Latin hypercube sampling across ,s,NP,E,M\mu, s, N_P, \sigma_E, \sigma_M,s,NP,E,M. Fit response surfaces (e.g., time to emergence as function of parameters).
6. Observables and diagnostics (what to record)

For each replicate and at regular intervals (e.g., every 10--50 generations):

Genetic metrics: allele frequencies per locus; linkage disequilibrium (pairwise r2r^2r2); haplotype diversity; heterozygosity HHH; (nucleotide diversity analog).
Phenotypic metrics: mean and variance for each trait TT_\ellT; multivariate trait covariance matrix; principal components of phenotype space.
Fitness metrics: distribution of individual fitness www; mean population fitness w\bar ww.
Ecological metrics: NP(t),Nprey(t)N_P(t), N_{prey}(t)NP(t),Nprey(t); predation rate \phi; prey trait distribution.
Emergence diagnostics: cluster analysis of phenotype vectors (k-means or DBSCAN) to detect attractor formation; time to first appearance of "coordinated phenotype" defined as composite index I=wTT,ancSD(T)I = \sum w_\ell \frac{T_\ell - T_{\ell,anc}}{SD(T_\ell)}I=wSD(T)TT,anc crossing threshold.
Dynamical metrics: autocorrelation, cross-correlation predatorprey, spectral analysis (power spectrum) to detect oscillations.
Event logging: bifurcation events (sudden changes in mean trait > N SD in < G generations), population crashes, fixation events.
All recorded data should be timestamped and stored in a standardized format (compressed HDF5 / NetCDF) with metadata documenting parameter set and RNG seed.

7. Statistical analysis & hypothesis testing

HALAMAN :
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