Applied Mathematics, University of Waterloo
The forest transition and ecological thresholds: resilience, recovery, and predictions
A central topic in modeling land use change is to understand the “forest transition” from deforestation to net reforestation. Agricultural land use change is the main driver of this phenomenon; classically, agricultural land expands considerably to feed a growing population, and then declines as efficiency gains are realized, marginal farmland is abandoned, and rural populations move to cities. As a result, existing models have focused on the socioeconomic and demographic factors that drive agricultural intensification. However, these models often neglect the role of ecological feedback effects and thresholds.
We develop and analyze a differential equation model that incorporates both agricultural intensification and ecological thresholds, and is calibrated to empirical parameters. Our analysis shows that there is a risk of total forest collapse (via a cusp bifurcation), which can be induced by large changes in almost any parameter and typically occurs around 25% forest cover. We estimate model parameters at multiple points along historical time series, which allows us to infer the risk of collapse (overcoming a lack of early warning signals otherwise available) and identify historical patterns.
One major takeaway is that the agricultural abandonment rate is a key advance predictor of collapse at long time horizons, but at the brink of a crisis forest collapse can best be avoided by reducing the forest conversion rate. We argue that ecological threshold effects should be acknowledged in forest transition models not only for ecological accuracy but also to ensure prudent forest management, particularly in the face of emerging risks such as climate change.