Dynamic Natural-Capital Accounting under Tipping Risk and Spatial Contagion: A Regenerative Forest Network Model

Abstract Classical renewable-resource models value the biological stock that remains after current extraction, whereas ecological resilience theory emphasizes the possibility of alternative regimes separated by tipping boundaries. This paper combines these perspectives in a networked forest-management problem with two continuous ecological states---harvestable biomass and resilience---and a discrete ecological regime for each patch. Harvesting lowers biomass and resilience and increases the endogenous intensity of a harmful regime shift; regenerative effort rebuilds ecological capital and reduces that intensity. The hazard also rises with exposure to degraded neighboring patches, generating spatial contagion. The planner solves an infinite-horizon controlled piecewise-deterministic Markov decision problem. Rather than assuming positive ecological shadow values, we derive them from primitive order conditions by monotone dynamic programming. Six structural results follow. The model nests Clark's classical target-stock problem; sufficiently large expected tipping losses generate \emph{regenerative inactivity}, with zero harvest and positive restoration; the optimal harvest rule contains a direct tipping-risk precautionary wedge; degraded neighbors can induce preventive closure before local collapse; a next-generation matrix yields a spectral threshold for early-stage landscape cascades; and Perron--Frobenius sensitivity identifies the patches at which restoration most effectively reduces systemic ecological risk. A stylized numerical illustration shows how restoration can move a connected forest from a supercritical to a subcritical cascade regime. The framework extends the economics of endogenous regime shifts by making resilience a managed state and by adding network contagion and systemic restoration targeting. JEL codes: C61; Q23; Q28; Q57. MSC 2020: 90C39; 90B15; 91B76; 92D40.