The analysis of stable isotopes of carbon, nitrogen, hydrogen, and oxygen has been a key tool in ecology for decades. Heavy vs light isotopes react at slightly different rates, and the consequences of these different rates have been used for myriad purposes, including pinpointing human activity as the main driver of climate change, reconstructing past climate, reconstructing food webs, and inferring nitrogen fluxes that are difficult to measure directly. The theory we use to interpret stable isotopes has deep roots in chemistry, and works well in the original systems for which it was derived. Unfortunately, many systems to which stable isotope theory is now applied, such as many aspects of ecology and biogeochemistry, differ in critical ways from the original systems. Here, we use analytical and numerical techniques to explore the consequences of some of these differences for our understanding of stable isotopes in ecology and biogeochemistry, focusing on a model of the soil nitrogen cycle. Specifically, because it is common to use steady state assumptions when interpreting isotopic data, we ask: How does assuming that stable isotope ratios are at steady state influence our ability to make inferences?
Results/Conclusions
Our results show that isotope ratios change for a long time after masses are near equilibrium. After an event like a rainstorm (time 0), inorganic nitrogen mass is near equilibrium (95% of the way) within 11 days. The stable isotope ratio, however, is still moving away from its equilibrium at 11 days, and does not approach its equilibrium until 25 days. In many places rainstorms are rarely 25 days apart, so isotope ratios are likely rarely near equilibrium. In addition to taking longer to approach equilibrium, our results show that the approach time to equilibrium is asymmetric: It takes longer for isotope ratios to equilibrate following perturbations that increase the isotope ratio than it does for perturbations that decrease the isotope ratio. Because of this asymmetry, the average of measurements across time gives a biased estimate of the equilibrium value. Finally, we find that the approach time to equilibrium is much longer when soil nitrogen saturates biotic demand than when it limits biotic demand. Because of this finding, isotope-based inferences might not be comparable across fertility gradients or across fertilization treatments. We discuss the implications of these findings along with productive ways to move forward.