Two-phase stratified random surveys on multiple populations at multiple locations

The two-phase random stratified sampling design proposed by Francis (1984) was designed for situations where prior information is insufficient to ensure an efficient allocation of sampling effort to different strata. It involves taking a first-phase sample, and then using the data from this to allocate a second-phase sample which compensates for any shortcomings of the first-phase sample. Here we generalise this method to situations where several species are sampled simultaneously, and at several locations. The method then uses the first-phase sample results to decide how best to allocate a second-phase sample to locations and strata. We provide the results of a simulation study based on model populations of shellfish which demonstrates the effectiveness of the method. We use a survey of cockles, pipis, and tuatuas on 11 Auckland Fisheries Management Area beaches as an example of its use.