Statistical Analysis of Embedded Replicates in Mark–Recovery Experiments

Abstract

This paper examines statistical theory related to a specialized mark–recovery experiment in which a group of fish is marked with coded wire tags (CWTs) cut sequentially from a wire roll. If the roll contains several codes embedded repetitively and if fish are selected randomly for marking, the resulting marked group automatically comprises several random subgroups called "embedded replicate" groups. When the fish are recovered, each subgroup can be identified by a distinct mark. Consequently, embedded replication appears to offer an easy technique for extending the information available from a conventional CWT experiment with only one code. The paper contends, however, that embedded replicate groups inherently provide no useful information beyond that obtained by treating them as a single group. In particular, the use of embedded replicates for variance estimation can be deceptive. Analytical results supporting these claims are presented for two cases of special interest. The paper also provides an overview of statistical methods that can be used, without recourse to embedded replication, to assess uncertainty in parameters commonly measured by mark–recovery experiments.