Optimizing ecological survey effort over space and time

Abstract

Summary Previous studies that optimize allocation of surveillance resources over space have assumed that detection rates are constant over time and that travel or survey costs are the same for all sites. Other recent research explicitly accounts for stochastically varying detection rates and distinct travel costs but restricts attention to the optimal number of visits to a single site. Here, we integrate these approaches to construct a model that optimizes the allocation of surveillance effort over both space and time. The solution defines the budget that should be allocated to each site and the number of visits over which that search budget should be expended. We show that the solution has close affinities with that of Hauser and McCarthy (Ecology Letters, 12, 2009, 683), which ignored temporal variation in detection rates and travel costs. We illustrate our approach by finding the optimal allocation of survey effort over space and time that maximizes the expected number of detections of the cascade treefrog (Litoria pearsoniana) in a region. In deriving our model, we also solve an alternative model to Moore et al. (PLoS One, 9, 2014) that considers the trade‐off between the number of visits and length of each visit when the detection rate at a site varies over time. We compare the predictions of the original model of Moore et al. (PLoS One, 9, 2014) and the new model using experimental data on detections of two species, showing the two models perform similarly well. Interestingly, when variable detection rates and travel costs are considered using our model, the form of the resulting objective function is very similar to the case in which they are ignored; in both cases, the probability of failed detection at each site is a negative exponential function of effort. However, travel costs impose a discontinuity into the solution space making the decision variables semi‐continuous (i.e. the optimal surveillance effort at each site is either zero or a value greater than the travel cost). This discontinuity complicates the task of finding the optimal solution. We propose a straightforward algorithm that finds very good approximate solutions.