From static to dynamic: Embracing dynamics in isotopic diet estimation.

Isotopic mixing models are widely used in ecology to quantify the diets of organisms. Most of these models assume that stable isotopic systems remain stable over time (a premise known as the steady-state hypothesis) and are therefore referred to as static mixing models. However, evidence shows that temporal dynamics-such as variations in isotopic turnover rates, diet shifts, and fluctuations in the isotopic signatures of both sources and consumers-can introduce significant bias into model outputs. Despite the recognition of such dynamics, the factors influencing bias and its implications remain underexplored. This study uses modelling and in silico experiments to characterize bias in mixing models resulting from temporal dynamics and to develop a dynamic mixing model that accounts for these effects. The results revealed that bias is strongly influenced by the interaction between the isotopic turnover rate and sampling frequency, emphasizing the importance of time variability in isotopic turnover. Additional sources of bias include the consumer's isotopic signature prior to a dietary shift, which reflects the distance from equilibrium with the new diet. This bias can be further amplified by temporal fluctuations in source signatures. Our study also evaluates previously recommended strategies to mitigate bias, confirming their effectiveness in reducing errors in static models and providing additional guidelines for their application. Furthermore, it improves access to a dynamic mixing model, enabling direct comparison with static approaches and demonstrating its robustness and accuracy in estimating diets under dynamic conditions.