Bayesian hierarchical modeling of larval walleye (Sander vitreus) abundance and mortality: Accounting for spatial and temporal variability on a large river

Abstract

Larval fish are extremely variable in space and time while sampling of populations is generally restricted and incomplete. However, estimates of abundance and mortality are important for understanding population dynamics, habitat quality, and anthropogenic impacts. Acknowledging and addressing variability during sampling and data analysis are imperative to producing informative estimates. A combination of spatially and temporally distributed ichthyoplankton sampling and Bayesian hierarchical and state-space modeling was used to partition variance and estimate abundance and mortality of larval walleye (Sander vitreus) in the Maumee River during 2010 and 2011. System variability and degree of sampling coverage have a direct impact on the quality of abundance estimates. Small scale factors (i.e., within site and day-to-day) accounted for the most variation in larval walleye densities, therefore sampling should concentrate on capturing these sources. Bayesian state-space modeling can improve estimates by sharing information through time, properly accounting for uncertainty, and producing probability distribution based estimates. Larval fish are highly variable and difficult to sample; however, the application of Bayesian methods during the data analysis process can lead to improved estimates of abundance and informed management actions.