The value of volunteer surveillance for the early detection of biological invaders

Early detection of invaders requires finding small numbers of individuals across large landscapes. It has been argued that the only feasible way to achieve the sampling effort needed for early detection of an invader is to involve volunteer groups (citizen scientists, passive surveyors, etc.). A key concern is that volunteers may have a considerable false-positive and false-negative rate. The question then becomes whether verification of a report from a volunteer is worth the effort. This question is the topic of this paper. Since we are interested in early detection we calculate the Z% upper limit of the one sided confidence interval of the incidence (fraction infected) and use the term maximum expected plausible incidence for this. We compare the maximum plausible incidence when the expert samples on their own, q_E∼, and the maximum plausible incidence when the expert only verifies cases reported by the volunteer surveyor to be infected, q_V∼. The maximum plausible incidences q_E∼ and q_V∼. are related as, q_V∼=θ_fp1-θ_fnq_E∼ where θ_fp and θ_fn are the false positive and false negative rate of the volunteer surveyor, respectively. We also show that the optimal monitoring programme consists of verifying only the cases reported by the volunteer surveyor if, T_XT_N<θ_fp1-θ_fn, where T_N is the time needed for a sample taken by the expert and T_X is the time needed for an expert to verify a case reported by a volunteer surveyor. Our results can be used to calculate the maximum plausible incidence of a plant disease based on reports of passive surveyors that have been verified by experts and data from experts sampling on their own. The results can also be used in the development phase of a surveillance project to assess whether including passive surveyor reports is useful in the early detection of exotic invaders.