An analytical solution for optimising multi-species detection surveys

When undertaking surveillance for multiple species, the probability of detecting each species at a site for a given level of survey effort is rarely 1. There is a trade-off between the number of sites to survey, and the survey effort per site. This trade off is exceedingly important in conservation, which must meet the objectives on a limited budget. The costs of surveillance can be classified as either site establishment costs or the costs of visiting, surveying and processing data from each site. Here we examine a scenario in which each of s species occupies a fraction of the possible survey sites (ψi) and we define qi as the probability of failing to detect species i, given a unit of survey effort at occupied sites. The establishment of a site has a fixed cost (c) and each survey of a site has a set cost per unit of survey effort (t) which we set to 1 as part of the analysis such that c and B are relative to t. The cost of establishing and surveying is constrained by the total survey budget available (B). We show that the expected number of detections summed across s species is maximised by visiting sites with a particular survey effort (v) that depends on c, ψi, t and qi (but not B (total survey budget)). The multi-species solution is able to determine the optimal survey effort for any number of species when there is heterogeneity in the probability of failed detection or probability of occupancy between species. This ensures surveys can be representative of the species assemblages in the area of interest and that less detectable species can be considered within the optimisation. While much work has been done to examine single-species approaches to survey effort for conservation, here we examine a multi-species approach which optimises the detection of any of the target species, particularly relevant to biosecurity and threatened species conservation. This ensures that researchers can allocate survey effort to maximise the detection of species across multiple sites. To illustrate the application of the method we apply it to a multi-species surveillance program that monitored two species of forest owls and four arboreal marsupials.