Longer time series with missing data improve parameter estimation in a state-space model in coral reef fish...

Analysis of time series data is fundamental in ecology for understanding community dynamics, and the mechanisms driving such dynamics. However, ecological time series commonly contain missing values, which can arise due to methodological changes in monitoring programs, poor weather conditions, logistical constraints, or human error. State-space models are a useful suite of techniques for analyzing ecological time series with missing data. Such models can estimate the unobserved true abundances as latent variables, even for putative census occasions that lack observations. Nevertheless, the impact of missing data on parameter accuracy and precision in these state-space models remains poorly investigated, particularly in species-rich systems. We evaluated the performance of a multivariate process-based state-space model for time series of varying lengths and sampling frequencies, using simulated data informed by empirical counts of reef fish communities from the Great Barrier Reef in Australia. We found that despite containing missing data, the models fitted to longer time series produced more accurate and precise parameter estimates compared to shorter, complete-case time series. Additionally, higher spatial replication with uneven census intervals enhanced parameter precision more than maintaining census frequency at the expense of reducing the number of sites. Analysis of reef fish community data revealed attenuation in intrinsic population growth parameters and weaker intraspecific density dependence when modeling longer time series whose inter-census intervals change, while estimates of variability in species' population growth parameters due to environmental fluctuations remained consistent regardless of sampling design. Nonetheless, analyses of shorter, complete-case time series still produced reliable parameter estimates. Our findings highlight the robustness of Bayesian state-space models to missing data, demonstrating that flexibility in long-term monitoring programs does not compromise ecological inference from these models.