Mixture models for the species apportionment of hydroacoustic data, with echo-envelope length as the discriminatory variable

Abstract

Abstract For this side-looking, 200 kHz, split-beam sonar application, echo-envelope length has been shown to be predictive of fish size. In this study, this relationship is exploited to estimate the abundance of (large) chinook salmon (Oncorhynchus tshawytscha) in the presence of (smaller) sockeye salmon (Oncorhynchus nerka). The echo-length to fish-size relationship is too imprecise to ascertain the species of individual fish in the classic sense. However, the frequency distribution of echo-length measurements contains information on the relative abundance of chinook and sockeye salmon. The use of echo-length measurements in a mixture model is explored in order to estimate the proportion of total fish passage that comprised chinook salmon. Inputs to the model include empirical estimates of the length–frequency distribution for each species, parameter estimates from the regression relationship of echo-length to fish-length, and echo-length measurements from individual, ensonified fish. Outputs are estimates of the proportions of chinook and sockeye salmon in the river. The advantages of the mixture-model approach over threshold-based discrimination are discussed. Conditional maximum likelihood and Bayesian versions of the model are described. The method can be generalized to other hydroacoustic measurements, including target strength and other discrimination problems.