Statistical Analysis on Isotopic Data of Atlantic Salmon Otoliths

Stable oxygen and carbon isotope ratio analyses (¹⁸O/¹⁶O or δ¹⁸O, and ¹³C/¹²C or δ¹³C) of otoliths have provided a powerful tool in fisheries science and management, but little is known about the essential features of otolith data and few attempts have been made to explore appropriate statistical methods that could be used for data analysis. In this paper, we report a pilot study on δ¹⁸O and δ¹³C data from otoliths of Atlantic salmon (Salmo salar), an anadromous fish that is currently listed as an endangered species under the federal Endangered Species Act. The otolith samples were collected from five separate Atlantic salmon production hatcheries located in different watersheds throughout the State of Maine, some facilities used different diet formulations to feed the young salmon (fry or smolts). The results showed that none of the δ¹⁸O and δ¹³C data were normally distributed, so that the commonly-used statistical tests such as linear discriminant function analysis, ANOVA and t-test may not be appropriate. Among the five production hatcheries, we were able to discriminate the water sources from three watersheds (from δ¹⁸O) and food sources from two different diets (from δ¹³C). Our analysis also indicated that the sample sizes required to estimate the δ¹⁸O and δ¹³C means based on the different variability (between groups or within group) and precision levels (≤ ±5.0%) were not large. These results and conclusions not only address the statistical considerations of isotopic data from otoliths, but have practical importance for Atlantic salmon management as well.