Some New Investigations on the Dynamic Biocompetitive Ecological Model (DBEM): A Nonautonomous Framework for Planetary Overshoot

Seven of nine planetary boundaries have been transgressed and anthropogenic mass now exceeds all living biomass, yet existing collapse models assume ecological regeneration—contradicting tipping-point evidence—while integrated assessment models rely on smooth damage functions that preclude irreversibility. We introduce the dynamic biocompetitive ecological model (DBEM), a three-variable nonautonomous dynamical system coupling human population, technosphere mass, and a novel quantity—effective structural capacity—that represents the fraction of Earth’s life-support systems still functional. The DBEM’s central innovation is irreversible capacity decay: Once structural capacity is lost through technosphere metabolism, it does not regenerate. Calibrated to published 2025 data and recast in a nondimensional form, the model yields a single overshoot ratio of 1.23, confirming that the technosphere exceeds sustainably supported capacity by 23 percent. Two collapse thresholds emerge with fundamentally different time scales: an overshoot threshold, already crossed, that drives accelerating biosphere degradation, and a reproductive failure threshold, orders of magnitude more distant, that would constrain human population directly. Between them lies an intermediate regime—absent from all existing collapse and integrated assessment models—in which structural capacity is eroding but population dynamics remain unconstrained. This regime constitutes a policy-relevant window whose duration depends on the rate of capacity degradation and whose stabilization requires simultaneously reducing the material scale of the technosphere and arresting further biosphere erosion.