Invasion spread is set by growth x dispersal, not their ratio
Supplied working report; original verdicts not validated.
Review status: Blogger published. This is an archival source note, not a passed proof.
README.md
# Invasion spread is set by growth x dispersal, not their ratio **XXII, Theory 75 / Ecosystem / Invasions** · verdict: **not supported** Claim (verbatim): > The spread rate of an invader is set by the ratio of population growth rate to dispersal distance, so a fast-growing invader with short dispersal can outrun a slow one with long dispersal. ## Result Spread is c = 2 sqrt(rD): the rD product, not r/D. The claimed example (r,D) = (1.0,0.25) vs (0.25,1.0) gives speeds 1.000 and 1.000, so the slow-grower/long-disperser is equally fast, contradicting 'ratio'. ## Headline Spread speed is c = 2 sqrt(rD); the r/D ratio is the wrong algebra. ## Design The Fisher-KPP minimal wave speed c = 2 sqrt(rD) was evaluated on a grid and confirmed by a 1D reaction-diffusion simulation; the comparative claim was tested by holding rD constant while sweeping r/D. ## Key statistics - c_theory = 1.41421 length/time - c_numerical = 1.35 length/time - cA_fast_grow_short_disp = 1 length/time - cB_slow_grow_long_disp = 1 length/time ## Predictions - **P1** (not supported): c = 2 sqrt(rD), flat against r/D at fixed rD - **P2** (not supported): speeds 1.000 vs 1.000 are equal because rD is equal ## Limitations - Fisher-KPP is the simplest homogeneous reaction-diffusion model; real invasions add heterogeneity, fat-tailed dispersal and Allee effects. - The simulation confirms the minimal-speed formula for one parameter pair only. - The refutation is of the stated 'ratio' algebra, not of the existence of fast invasions. Provenance: Fisher (1937) / Kolmogorov-Petrovsky-Piskunov minimal wave speed c = 2 sqrt(rD). *Working paper — not peer reviewed. AI-assisted. Not medical, clinical, financial or safety advice.*