Optimising passive eDNA sampling: A theoretical framework for time-dependent eDNA accumulation

1. Environmental DNA (eDNA) methods are developing rapidly for ecological surveys, and passive eDNA sampling has emerged as a promising approach for integrating DNA signals over deployment time. However, how deployment duration affects the amount of detectable DNA retained by a sampler remains poorly understood. 2. Here, an analytical model was developed to examine how DNA input, degradation, finite substrate capacity and residual retention of degraded DNA shape passive eDNA accumulation. The model distinguishes detectable adsorbed DNA from degraded, non-detectable DNA that may remain on the substrate and continue to occupy capacity. The residual-retention parameter, {theta}, represents the fraction of degraded DNA that remains capacity-occupying, with {theta}=0 corresponding to complete replacement and {theta}=1 to complete non-replacement. 3. The model predicts three key behaviours. First, when degraded DNA does not occupy substrate capacity ({theta}=0), detectable eDNA accumulates monotonically towards equilibrium, but equilibrium recovery increases less than proportionally with DNA input. Thus, passive-sampler measurements can compress quantitative differences in environmental DNA supply. Second, when degraded DNA remains capacity-occupying ({theta}>0), detectable eDNA can reach a finite peak and subsequently decline. Higher DNA input increases peak yield but shifts the peak earlier, whereas greater substrate capacity increases peak yield and delays the peak. Third, under prolonged deployment with {theta}>0, a higher-input condition can yield less detectable eDNA than a lower-input condition, reversing the expected input-rate ranking. 4. These results show that passive eDNA recovery can follow saturating, unimodal or intermediate dynamics depending on substrate capacity and post-adsorption DNA fate. Thus, retrieval time cannot be optimised by adjusting deployment duration alone. Although investigators can choose deployment duration and sampler design, including substrate capacity, optimisation also requires calibration or explicit assumptions about ambient DNA supply, DNA degradation rate and residual retention of degraded DNA.