Methods for estimating a critical value for determining the freshwater/estuarine habitat residence of American eels from otolith Sr:Ca data

Linear discriminant analysis (LDA) and habitat discrimination critical value (HDCV) methods are alternatives for evaluating the migratory history, such as the proportion of residence in freshwater (%fwr) and estuarine/marine habitats, of individual American eels (Anguilla rostrata) via the analysis of otolith Sr:Ca data. The LDA process requires Sr:Ca data from both freshwater and estuarine/marine groups while the mean + cSD method requires only a freshwater standard. For the two group (freshwater, estuarine/marine), single predictor variable (Sr:Ca) case, the LDA process defaults to Fisherʹs linear discriminant where the HDCV equals the average of the group mean Sr:Ca values. The difference between freshwater and estuarine resident eel mean otolith Sr:Ca values, based on 13 published studies and the current study (n = 14), decreased with increasing freshwater group otolith mean (r = 0.80, p < 0.001), reflecting a relatively constant estuarine group mean (r = 0.38, p = 0.17). A process is proposed for estimating a HDCV from freshwater group otolith Sr:Ca mean and SD values based on empirical linear relations between the LDA, HDCV and freshwater mean (n = 14, r = 0.90, p < 0.0001) and c and SD (n = 14, r = −0.89, p < 0.0001) from the equation HDCV = mean + cSD. Variation in the sample sizes of otolith Sr:Ca values used in the discriminant process of estimating a HDCV, while statistically significant, had trivial effect sizes that were likely of little biological consequence. However, larger sample sizes are preferred over smaller sample sizes. Estimates of %fwr increased with increases in the HDCV. Differences in %fwr estimates over a range of HDCVs were highly statistically significant and effect sizes increased with increased HDCV difference. As HDCV levels increased, growth rate estimates increased for a given %fwr value. A HDCV difference of ≤0.5 × 10−3 produced a small effect size. Accurate estimation of a HDCV is fundamental to the assessment of the habitat residence and inter-habitat movement of American eels and perhaps of other diadromous fishes and helps minimize bias in dependent estimates of other useful statistics such as the percentage of freshwater residence (%fwr) and growth rate.