Replacement distance controls growth at long wavelengths in a coevolving spatial network

Abstract

When an agent leaves a spatial network, its replacement removes old contacts and may transport population to a new location. The frequency of replacement alone therefore does not determine how turnover changes spatial organization. We study diffusing agents joined by persistent attractive contacts, with the total pull on each agent bounded. At fixed population, successors appear at the departure position, within a surrounding disk, or anywhere in the system. We ask whether small differences between dense and dilute regions grow or fade. The theory separates an exactly calculable diffusion and replacement contribution from an approximate attraction contribution obtained by averaging the contact network. Paired simulations find similar attraction contributions under the three rules at all nine sampled wavelengths. Changing only the replacement location reverses the broadest tested pattern: it grows with replacement at the departure position but fades under both displaced rules. An independent radius scan traces this change from growth to decay. Under displaced replacement, intermediate wavelengths grow between sampled long and short scales with decay. Rates measured in the earliest finite window are compatible with the prediction at long and intermediate wavelengths; discrepancies are already present at short wavelengths. Replacement distance thus helps determine which spatial density contrasts are initially amplified.