Analytical Bayesian models to quantify pest eradication success or species absence using zero-sighting records

It is not possible to establish the absence of a population with certainty using imperfect zero-sighting records, but absence can be inferred. In this paper we use Bayesian methods to formulate analytical inferred distributions and statistics. When such formulations are available, they offer a highly efficient and powerful means of analysis. Our purpose is to provide accessible and versatile formulations to support an assessment of population absence for management decisions, using data from a series of regular and targeted surveys with zero-sightings. The stochastic processes considered here are prior population size, growth and imperfect detection, which are combined into a single distribution with sufficient flexibility to accommodate alternative distributions for each of the driving processes. Analytical solutions formulated include the inferred mean and variance for population size or number of infested survey-units, the probability of absence, the probability of a series of negative surveys conditional on presence, and the probability a population is first detected in a given survey, although we also formulate other statistics and provide explicit thresholds designed to support management decisions. Our formulation and results are straightforward to apply and provide insight into the nonlinear interactions and general characteristics of such systems. Although motivated by an assessment of population absence following a pest eradication program, results are also relevant to the status of threatened species, to 'proof-of-freedom' requirements for trade, and for inferring population size when a population is first detected.