Geospatial statistics strengthen the ability of natural geochemical tags to estimate range-wide population connectivity in marine species

Using calcified structures as natural geochemical tags to estimate levels of population connectivity is becoming increasingly common. However, the technique suffers from several logistical and statistical problems that constrain its full application. Foremost is that only a subset of potential sources is sampled, often compounded by under-sampling within locations at an overly coarse spatial scale. This introduces unknown error and prevents the creation of a range-wide connectivity matrix. To address this issue, we analyzed the natural geochemical tags of embryonic statoliths in the whelk Kelletia kelletii (Forbes, 1850). We sampled from 23 sites over the entire geographic range in 2004 and 2005 from Monterey (California, USA) (36 degrees N) to Isla Asuncion, (Baja California, Mexico) (27 degrees N). We then used geospatial statistics (kriging) to make continuous along-coast maps of embryonic statolith chemistry. This allowed us to estimate chemistry at unsampled locations. We used this new continuous assignment method to estimate the spatial error associated with assignment by the classic method of discriminant function analysis (DFA). Then, we compared the performance of the 2 methods at classifying unknown embryonic statoliths. We found large spatial errors often associated with DFA assignments, even when traditional DFA accuracy assessments indicated the method was performing well. The continuous method provided an improved assessment of uncertainty in assignments. It outperformed the DFA method in classifying unknown embryos to the vicinity of their true source. Geospatial statistics also provided useful information on other range-wide variables, such as adult reproductive abundance. As a proxy for larval supply, such information can aid future assignments of recruits. Our combined analyses help inform sampling designs and motivate the development of a new approach for population connectivity studies.