A Framework to Unify the Relationship Between Numerical Abundance, Biomass, and Environmental DNA

Does environmental DNA (eDNA) concentration correlate with numerical abundance (N) or biomass in aquatic organisms? We hypothesize that eDNA can be adjusted to simultaneously reflect both. Building on frameworks developed from the Metabolic Theory of Ecology, we derive two equations to adjust eDNA data to simultaneously reflect both N and biomass using population size structure data and allometric scaling coefficients. We also demonstrate that these equations share model parameters, necessitating the joint estimation of regressions between adjusted eDNA, N, and biomass. Furthermore, our framework can be extended to model how other variables (temperature, taxa, diet, trophic level, etc.) might impact relationships between eDNA, N, and biomass in natural ecosystems. We applied our framework to data from two previously published studies correlating eDNA to Brook Trout (Salvelinus fontinalis) N and biomass. In both case studies, point estimates of the scaling coefficient (b) reflected allometric processes (b = 0.51 and 0.37 for Case Study 1 and 2, respectively), with credible intervals indicating that b likely differed from zero (i.e., eDNA scales with N) and one (i.e., eDNA scales with biomass). Directly estimating the value of b improved estimates of N and biomass relative to assuming b equals 0, which particularly affected the capacity to estimate biomass. However, models assuming eDNA production scaled with biomass (i.e., b = 1) were largely similar to estimating b, implying that assuming eDNA scales linearly with biomass might be a sufficient approximation for some systems. Nevertheless, the framework demonstrates that correlating eDNA directly with either N or biomass (as is commonly done in many studies) inherently necessitates an adjustment to infer the other metric if populations exhibit size structure variation. Collectively, we demonstrate that quantitative eDNA data is unlikely to correspond exactly to either population N or biomass but can be adjusted to simultaneously reflect both.