Population Intelligence: Smallest-Model Numerical Experiment

Abstract

We introduce a minimal individual based model for population intelligence that retains three structures absent from standard single agent descriptions: a manifold valued intelligence state, endogenous population turnover, and heritable lineage dependent reproductive fitness. The validated S^1 intelligence diffusion was extended with neutral logistic birth death dynamics. Each individual occupies an angle on the circle S^1; noisy mean field attraction produces collective synchronization; logistic birth death dynamics regulate population size; and reproductive rates can depend on lineage and position relative to designated safe or unsafe directions. This nested construction is intentionally small enough to admit an analytic equilibrium benchmark while remaining capable of selection, invasion, and safety transitions. Population size returned toward carrying capacity from (N(0)=200,800,1600), with tail means (775.7,800.3,805.1) for K=800. Across K=100 to 1600, the intelligence equilibrium error scaled as K^{-0.513} , consistent with the canonical K^{-1/2} fluctuation rate, while the extinction rate was zero in 120 runs over the simulated horizon. The mean order parameter remained close to the original theoretical (r*=0.7242), as neutral demography predicts. Directional reproductive selection shifts a safety score to +0.7447 or -0.7448 while synchronization remains approximately 0.75, demonstrating that coordination is not equivalent to safety. These are controlled numerical results, not asymptotic proofs.