Multi-species attributes as the condition for adaptive sampling of rare species using two-stage sequential sampling with an auxiliary variable

Assessing populations of rare species is challenging because of the large effort required to locate patches of occupied habitat and achieve precise estimates of density and abundance. The presence of a rare species has been shown to be correlated with presence or abundance of more common species. Thus, ecological community richness or abundance can be used to inform sampling of rare species. Adaptive sampling designs have been developed specifically for rare and clustered populations and have been applied to a wide range of rare species. However, adaptive sampling can be logistically challenging, in part, because variation in final sample size introduces uncertainty in survey planning. Two-stage sequential sampling (TSS), a recently developed design, allows for adaptive sampling, but avoids edge units and has an upper bound on final sample size. In this paper we present an extension of two-stage sequential sampling that incorporates an auxiliary variable (TSSAV), such as community attributes, as the condition for adaptive sampling. We develop a set of simulations to approximate sampling of endangered freshwater mussels to evaluate the performance of the TSSAV design. The performance measures that we are interested in are efficiency and probability of sampling a unit occupied by the rare species. Efficiency measures the precision of population estimate from the TSSAV design relative to a standard design, such as simple random sampling (SRS). The simulations indicate that the density and distribution of the auxiliary population is the most important determinant of the performance of the TSSAV design. Of the design factors, such as sample size, the fraction of the primary units sampled was most important. For the best scenarios, the odds of sampling the rare species was approximately 1.5 times higher for TSSAV compared to SRS and efficiency was as high as 2 (i.e., variance from TSSAV was half that of SRS). We have found that design performance, especially for adaptive designs, is often case-specific. Efficiency of adaptive designs is especially sensitive to spatial distribution. We recommend that simulations tailored to the application of interest are highly useful for evaluating designs in preparation for sampling rare and clustered populations.