Accounting for temporal variation and correlation in environmental DNA sampling can improve ecological inferences.

Environmental DNA (eDNA) concentration varies through space and time, and measurements collected close together are often correlated. Ignoring this dependence can inflate the rate of incorrect ecological inferences (Type I error rate). Although spatial correlation in eDNA has received considerable attention, temporal correlation has been less well studied. Statistical models and study designs that account for temporal correlation are increasingly important to understand time-dependent effects in complex systems. We developed a hierarchical model that separates temporal ecological variation from variability stemming from sampling and laboratory processes and applied it to four single-site eDNA time series collected over 17-24 days, three of which provided sufficient information for parameter estimation. We then used the empirically estimated parameter magnitudes in a simulation study to evaluate alternative temporal sampling designs that considered (1) how a fixed number of samples are allocated across different numbers of sampling times with different levels of temporal replication and (2) equally spaced versus cluster-spaced sampling (short bursts separated by longer gaps). Across the three time series sufficient for analysis, we observed substantial sampling variability, temporal variability, and temporal correlation, although correlation was estimated imprecisely (large coefficient of variation). Simulations showed that when sampling intervals were shorter than the effective temporal correlation range, models that ignored temporal dependence produced inflated Type I error rates and frequently detected spurious temporal trends. Accounting for temporal correlation substantially reduced this inflated Type I error rate. Optimal sampling strategies depended on study objectives. Clustered sampling most effectively estimated temporal correlation. When temporal dependence was negligible, evenly spaced sampling maximized power to detect trends. Estimating sampling variability required concentrating effort into fewer sampling times with more replicates per time, whereas estimating temporal variance was most precise with intermediate levels of replication. Together, these results indicate that temporal dependence can strongly affect inference from quantitative eDNA time series when sampling intervals approach the correlation timescale. Designs that ignore this dependence risk inferring ecological change or difference where none exists. Our framework provides practical guidance for allocating sampling effort in temporally intensive eDNA monitoring and for interpreting trends from short time series.