SDM meets eDNA: optimal sampling of environmental DNA to estimate species–environment relationships in stream networks

Species distribution models (SDMs) are frequently data‐limited. In aquatic habitats, emerging environmental DNA (eDNA) sampling methods can be quicker and more cost‐efficient than traditional count and capture surveys, but their utility for fitting SDMs is complicated by dilution, transport, and loss processes that modulate DNA concentrations and mix eDNA from different locations. Past models for estimating organism densities from measured species‐specific eDNA concentrations have accounted for how these processes affect expected concentrations. We built off this previous work to construct a linear hierarchical model that also accounts for how they give rise to spatially correlated concentration errors. We applied our model to 60 simulated stream networks and three types of species niches in order to answer two questions: 1) what is the D‐optimal sampling design, i.e. where should eDNA samples be positioned to most precisely estimate species–environment relationships? and 2) How does parameter estimation accuracy depend on the stream network's topological and hydrologic properties? We found that correcting for eDNA dynamics was necessary to obtain consistent parameter estimates, and that relative to a heuristic benchmark design, optimizing sampling locations improved design efficiency by an average of 41.5%. Samples in the D‐optimal design tended to be positioned near downstream ends of stream reaches high in the watershed, where eDNA concentration was high and mostly from homogeneous source areas, and they collectively spanned the full ranges of covariates. When measurement error was large, it was often optimal to collect replicate samples from high‐information reaches. eDNA‐based estimates of species–environment regression parameters were most precise in stream networks that had many reaches, large geographic size, slow flows, and/or high eDNA loss rates. Our study demonstrates the importance and viability of accounting for eDNA dilution, transport, and loss in order to optimize sampling designs and improve the accuracy of eDNA‐based species distribution models.