Incorporating carbon dioxide into a stoichiometric producer-grazer model

Climate change models predict increases in atmospheric carbon dioxide concentration. As ecosystems equilibrate with the atmosphere, stimulation of photosynthesis is expected to occur. However, growth limitation due to soil nutrients may potentially limit sequestration of carbon. Additionally, changes in producer nutritional quality may cause a decline in grazer populations. Here we extend the WKL model to allow for consideration of the impacts of elevated atmospheric carbon dioxide concentration on producer-grazer dynamics. We do so by explicitly tracking the free carbon in the medium and allowing the producer's growth rate to be limited by available carbon instead of light. This model is analyzed using primarily local bifurcation analysis. Overall, these analyses show that carbon sequestration due to increased atmospheric carbon dioxide can be limited by insufficient available phosphorus. Furthermore, increased atmospheric carbon dioxide will cause decreased stoichiometric quality of producers where available phosphorus is limiting.