Conservation biologists must make on-the-ground decisions for species management based on incomplete and indirect data, necessitating robust yet applicable statistical tools. As a motivating example, we focus on the Central Valley Project (CVP) and State Water Project (SWP) facilities, which are regulated by take of endangered salmonids caused by their drawing water from the California Delta. Both projects salvage fish to reduce take, and salvage data are collected around-the-clock during operations. However, the methods historically used to estimate take from the salvage data are statistically deficient, hindering management.
To address this issue, we developed a Partially Observed Markov Process (POMP) model for estimating fish take at CVP and SWP. POMP provides a flexible modeling framework that allows us to mechanistically describe the processes of fish salvage and sample collection. Recent mathematical and computational developments leveraging particle filtration allow us to obtain robust estimates of model likelihood, despite our model being non-linear, non-normal, time-series, and partially observed. Using our POMP model, managers can flexibly estimate take and salvage at relevant timescales (i.e., daily and yearly), quantify the probability that certain triggers have been reached, and respond accordingly. As a proof of concept, we simulated two years of realistic data from Chinook salmon at CVP, which we then analyzed at daily and yearly time scales.
Our model is able to address the technical issues with previous methods used to estimate take; it can estimate take when zero salvage is observed, account for uncertainty in model parameters, and estimate take flexibly at multiple time scales. However, our evaluation highlighted critical issues with existing parameters that hinder take estimation, regardless of the model. Specifically, survival rates for fish passing through the facilities were estimated using inappropriate statistical methods based on small samples collected in uncontrolled conditions, and are therefore poorly bounded (e.g., 17%-100%). As a result, the estimation of take was highly uncertain. For example, when four fish were salvaged, the expected value of daily take was 34 fish, yet the 95% credible interval covered three orders of magnitude (4 to 105). Even when no fish were salvaged, the 95% credible interval for daily take included over 10 fish. Taken together, our evaluation suggests that >50% of the uncertainty in daily take estimation results from poorly bounded parameters. Our study therefore underscores the need to develop robust models as well as the need to refine parameter estimates for use in on-the-ground conservation management.