A Bayesian hierarchical model of postlarval delta smelt entrainment: integrating transport, length composition, and sampling efficiency in estimates of loss

Hydrodynamic models have been used to estimate rates of ichthyoplankton transport across marine and estuarine environments and subsequent geographic isolation of a portion of the population (i.e., entrainment). Combining simulated data from hydrodynamic models with data from fish populations can provide more information, including estimates of regional abundance. Entrainment of postlarval delta smelt (Hypomesus transpacificus), a threatened species endemic to California's Sacramento-San Joaquin Delta, caused by water export operations, was modeled using a Bayesian hierarchical model. The model was fit using data spanning years 1995-2015 from multiple sources: hydrodynamic particle tracking, fish length composition, mark-recapture, and count data from entrainment monitoring. Estimates of the entrainment of postlarval delta smelt ranged from 10 (SD = 23) in May 2006 to 561 791 (SD = 246 423) in May 2002. A simulation study indicated that all model parameters were estimable, but errors in transport data led to biased estimates of entrainment. Using only single data sources rather than integration through hierarchical modeling would have underestimated uncertainty in entrainment estimates or resulted in bias if transport, survival, or sampling efficiency were unaccounted for.