Predicting when seed dispersal matters for scaling up reforestation from sites to landscapes
Due to the social and ecological benefits of tropical reforestation, policymakers have set ambitious goals to reforest millions of hectares of degraded land. Forest landscape restoration will require predicting appropriate reforestation techniques over large spatially-heterogeneous areas. However, general predictions for reforestation dynamics are hindered by high variability between empirical studies. Differences in landscape structure may underlie these divergent results, but are difficult to control in small-scale empirical studies. Seed arrival is one ecological process that can determine reforestation rate and depends on landscape elements beyond the scale of most field studies. We use mathematical models to quantify how seed arrival determines rates of secondary succession in spatially heterogeneous landscapes. We ask how time to canopy closure varies (1) with different rates of seed arrival, (2) with feedbacks between canopy area and seed arrival, and (3) with between-patch interactions in heterogeneous landscapes. We first develop an analytically tractable model for time to tree canopy closure with constant seed rain. We then extend our model to include positive feedbacks between seed arrival and either the canopy area of individual trees (internal reproduction) or total canopy area in the plot (directed dispersal). Finally, we use a multipatch version of the model to quantify effects of between-patch interactions on canopy closure.
In a single patch model with a constant rate of seed arrival, sensitivity of canopy closure to seed arrival is high only for a narrow range of relatively low seed arrival. In models with feedbacks between canopy area and seed arrival, we found that feedbacks only impact canopy closure when small increases in canopy area result in an initially high response of seed arrival. In the multipatch model, between-patch interactions only impact canopy closure in simulations with intermediate levels of global seed rain. By replicating landscapes, our mathematical models provide insight into why some empirical studies reveal a strong effect of seed dispersal on secondary succession while others do not. We suggest that seed dispersal is critical for canopy closure only under a narrow range of conditions, including low seed arrival, directed dispersal and intermediate levels of global seed rain. Ultimately, we show that mathematical models can inform spatially-targeted interventions for forest landscape restoration, including where passive restoration will be sufficient to restore forest cover and where active restoration will be necessary.