Optimal Planting Distance in a Simple Model of Habitat Restoration With an Allee Effect

Abstract

Ecological restoration is emerging as an important strategy to improve the recovery of degraded lands and to combat habitat and biodiversity loss worldwide. One central unresolved question revolves around the optimal spatial design for outplanted propagules that maximizes restoration success. Essentially, two contrasting paradigms exist: the first aims to plant propagules in dispersed arrangements to minimize competitive interactions. In contrast, ecological theory and recent field experiments emphasize the importance of positive species interactions, suggesting instead clumped planting configurations. However, planting too many propagules too closely is likely to waste restoration resources as larger clumps have less edges and have relatively lower spread rates. Thus, given the constraint of limited restoration efforts, there should be an optimal planting distance that both is able to harness positive species interactions but at the same time maximizes spread in the treated area. To explore these ideas, here we propose a simple mathematical model that tests the influence of positive species interactions on the optimal design of restoration efforts. We model the growth and spatial spread of a population starting from different initial conditions that represent either clumped or dispersed configurations of planted habitat patches in bare substrate. We measure the spatio-temporal development of the population, its relative and absolute growth rates as well as the time-discounted population size and its dependence on the presence of an Allee effect. Finally, we assess whether clumped or dispersed configurations perform better in our models and qualitatively compare the simulation outcomes with a recent wetland restoration experiment in a coastal wetland. Our study shows that intermediate clumping is likely to maximize plant spread under medium and high stress conditions (high occurrence of positive interactions) while dispersed designs maximize growth under low stress conditions where competitive interactions dominate. These results highlight the value of mathematical modeling for optimizing the efficiency of restoration efforts and call for integration of this theory into practice.