Title: Optimal management of an annual Weed: a stochastic dynamic programming approach
Abstract: Weeds are ecologically and economically disastrous. Invasive species in general are considered the greatest cause of global biodiversity loss after habitat destruction, and agricultural weeds cost the Australian economy $4 billion annually on average. Weed eradication is difficult. Managers must operate with limited budgets and search costs can increase as weed density decreases. Even if all plants are successfully removed, a seedbank may persist, leading to future outbreaks. Thus complete eradication is often an unrealistic target and the question becomes one of how much control is enough. The decision of what level of management resources to invest must not rely solely on management costs, but also take into account plant population dynamics in the context of a stochastic environment. Here we examine ongoing management of a contained annual weed with an established seedbank, which as a “sleeper” weed may yet escape and cause harm. Using stochastic dynamic programming, we find the optimal management effort of controlling the weed population, trading off expected costs of escape versus costs of searching and removal. The optimal removal effort increases non-linearly with the density of emerging plants until management becomes futile at high population densities. Most of the state space nevertheless recommends complete removal of emergent plants. The solution is most sensitive to population growth rate, the escape probability function and the relative costs of escape and management. Our simple model leads to valuable insights for the ongoing control of a sleeper weed. In our study we have assumed that immediate eradication is elusive. Nonetheless, continued long-term management may gradually deplete the seedbank and allow the possibility of eradication; thus the management time horizon (i.e., the length of the control program) can influence the optimal strategy. The net costs of management versus escape are also important whereas population dynamics – in this case the relentless growth of a sleeper weed’s seedbank – become more important over the long-term. It is therefore important to include both economics (costs of management and escape) and biology (population dynamics and escape probability) in seeking optimal weed control strategies. [Baxter, P. W. J., Wilcox, C., McCarthy, M. A. and Possingham, H. P. (2007). Optimal management of an annual weed: A stochastic dynamic programming approach. In: Oxley, L. and Kulasiri, D., Natural Resources and Biodiversity Management. International Congress on Modelling and Simulation Land, Water & Environmental Management: Integrated Systems for Sustainability, Christchurch, (2223-2229). 10-13 Dec 2007.]