Bayesian Spatial Modeling of Data from Unit‐Count Surveys of Fish in Streams

We describe a framework for spatial modeling of data from surveys of stream‐dwelling fish species in which repeated counts are made of animals within a sample of habitat units. Using Bayesian modeling with Markov chain‐Monte Carlo (MCMC) algorithms, it is possible to estimate fish population size from repeated‐count survey data while allowing fish detection probabilities to vary across the stream. We propose the use of conditional autoregressive models for modeling the spatial dependence of density across the habitat units of the stream. The spatial dependence model can be used along with covariate models for density and detection to predict density at unsampled units and thereby estimate total abundance across the stream. We apply these models to data sampled from an intensive repeated‐count survey of juvenile coho salmon Oncorhynchus kisutch in McGarvey Creek, Northern California. Spatial dependence in fish density was detected, and models that account for spatial dependence produced more precise predictions at unsurveyed units, and thus more precise estimates of total stream abundance, than models that assumed spatial independence. Through a small simulation study, we show that ignoring heterogeneity in detection probabilities can lead to significant underestimation of total abundance. Inclusion of heterogeneity by means of a random effect in the detection component of the model can lead to numerical instability of the MCMC method, and we stress the importance of accounting for heterogeneity by incorporating covariates in modeling detection probability.