Stability and resilience of a forest bio-economic equilibrium under natural disturbances

Natural disturbances play a key role in the long-term evolution of a forest but are by essence unforeseeable. If a sustainable management is fixed in a forest, where the harvest is equal to the forest growth (such as at maximal sustainable yield), natural disturbances could jeopardise the established equilibrium by modifying the future forest growth and possibility to harvest timber. This paper aims at studying the stability of a bio-economic equilibrium, where a forest is first managed in a sustainable way and has reached an equilibrium between the timber market and biological timber production. So far in forestry, sustainable management schemes do not appropriately integrate disturbance regimes. To overcome this issue, we describe a bio-economic equilibrium that includes a forest inventory, a local unregulated timber market (whose variations are defined by an equilibrium-displacement model), and natural disturbances. The paper investigates the short- and long-term effects following a disturbances. For reasonable descriptions of both forest evolution and timber market equilibrium, we show that there exists a critical forest inventory under which it is impossible to find a stable state where the forest inventory persists in the long term. For a forest inventory larger than this critical level, the equilibrium is what we call "meta-stable", because while the forest inventory does often persist in the long term, there always exists a certain level of natural disturbance able to destabilize the equilibrium and, ultimately, exhaust the forest inventory. However, this threshold is often too large to threaten real forests. Finally, we derive the maximum frequency between hazards that ensures the long-term sustainability of the forest.