Using survival analysis to develop models for estimating size‐at‐detection of invasive species under surveillance

Invasive non‐native species are organisms that can significantly harm societal and natural values, such as agriculture, social amenities, the environment, and native species and ecosystems. To efficiently prepare for the incursion of invasive species and incursion response, it is essential to predict their potential impacts across this range of values. Several critical system‐level factors influence these impacts, including the introduction pathways, the availability of host material, climate suitability, and the extent and vulnerability of affected agricultural or environmental assets. A crucial factor that is incursion‐specific and therefore unpredictable beforehand is the size of an outbreak at the time that it is detected. How large the established invading population is will curtail the range of viable management options: if it is small then eradication may be affordable and provide net benefits, whereas if it is too large then eradication may be impossible. We propose a statistical model for this random variable that enables its use in decision‐support systems. Our study concentrates on surveillance systems that use fixed traps to detect mobile organisms. Using survival analysis, we analyze the relationship between surveillance and the detection event of a pest, where the detection event is held to be analogous to a failure event in survival analysis. This allows us to link the probability density function (PDF) of infestation size at detection to the instantaneous probability of detecting an incursion, assuming it has not been detected earlier, namely the hazard function. This allows us to capture or integrate out the consequent uncertainty of the maturity of the incursion at the time of detection. We then introduce an approximation using the Weibull distribution. We show that the approximation is supportable when dealing with a small fixed number of traps ( n ) or a lower probability of detection per trap ( p ). Furthermore, by assuming a relationship between the population size at detection and the time it remains undetected, we can estimate the PDF for the population's duration of occupancy. Finally, a computer program is developed for the analysis, using the Mediterranean fruit fly (medfly) as a case study, to demonstrate its application. By modeling the population size of an invasive species at the moment it is first detected, we offer insights that can guide effective control and eradication measures and inform broader invasivespecies management practices.