Modeling the persistence of plant populations in fragmented ecosystems

Ecosystem fragmentation is one of the main threats to species persistence via habitat reduction and isolation which often lead to species extinctions. A question that has long been of interest is the minimum habitat size that can sustain viable populations in fragmented landscape. Despite numerous empirical and theoretical efforts on this topic, most studies fail to address this central question, and our mechanistic understanding of and capacity to predict the effects and outcomes associated with fragmentation stressor is still illusive. We develop an ordinary differential equation (ODE) based framework that incorporates the effect of the patch area on the net population growth rate for a plant species in fragmented ecosystem via a general net growth function. We investigate the minimum patch area needed to sustain a given plant species. We use data from the Amazonian herb Heliconia acuminata to test our model. Furthermore, we compare the performance ODE model and a linear matrix model to predict the observed data. We provide a general formula for a threshold value for the fragment area, below which a plant population is not viable. For Heliconia acuminata, our ODE-based model predicts a value for the minimum fragment area of ≈0.7ha, which reflects the observed data and is smaller than the value obtained using the matrix projection model. Our findings suggest that the Heliconia’s mortality rate responds more negatively to fragmentation. Furthermore, we found that the ODE-based model can serve as an alternative to the linear demographic model.