On the estimation of population size-A comparison of capture-recapture and multiplier-benchmark methods

Approaches to population size estimation are of importance across a wide spectrum of disciplines, especially when census and simple random sampling are impractical. The capture-recapture method and the multiplier-benchmark method are two commonly used approaches that use data that partially capture the target population and overlap in a known way. Due to similarities in required data structures, the approaches are often used interchangeably without a critical appraisal of the underlying assumptions, especially in the two-sample case. Here, we describe the similarities and differences of the sampling mechanisms and assumptions underlying both approaches. We emphasize that the capture-recapture method assumes data sources as random samples and describes two-way inclusion histories, while in multiplier-benchmark method, one source captures a fixed sub-population, and the one-way inclusion histories are modeled. We also discuss the implications of these differences through simulation and real data to guide the choice of method in practice. A careful study of the data structures, relationships, and data generation processes is crucial for assessing the appropriateness of using these methods.