Searching for non-indigenous species: rapidly delimiting the invasion boundary

Aim At first detection, little information is typically known about an invader's characteristics, true arrival date or spatial extent. Yet, before management options such as control or eradication can be considered, we need to know where a nuisance species has already spread. This is particularly difficult because of stochastic processes. Here, we develop an approach that requires little a priori information, yet accurately delimits the range of a biological invader. Location We used a simulated landscape, subjected to stochasticity inherent in establishment and spread, to test novel theory for delimiting locally spreading populations. Methods We distinguish three stages to identify the boundary of an invasion, which we term Approach, Decline, Delimit (ADD). Our ADD algorithm uses general characteristics of the invasion pattern, obtained during a search for occupied sites, in combination with sampling and probability theory to delimit the invasion. We compare ADD against four naive delimitation strategies, for long and normal dispersal kernels. Results Our results illustrate the potential difficulty in delimiting invasions. Naive strategies, such as stopping when the invader is absent, typically failed to properly delimit the invasion. In contrast, ADD operated relatively efficiently, and was robust to habitat heterogeneity and knowledge of the true epicentre, but was sensitive to the sparseness of the invasion. For long-distance dispersal kernels, ADD had 80% accurate delimitations when c. 5% or more of the cells were occupied within the invasion boundary; for normal dispersal kernels, ADD had 95% accurate delimitations when c. 2.5% or more of the cells were occupied. Main conclusions There is virtually no existing theory for delimiting invasions. ADD is efficient and accurate, even with unknown time of invasion, unknown dispersal kernels, stochastic establishment dynamics and spatial heterogeneity, except for very low invasion densities.