Human Population and Carbon Dioxide

A recently proposed model of human population and carbon utilization is reviewed. Depending on parameter values, one of three possible long-term outcomes obtains. 1. Atmospheric carbon, [CO2]atm, and human populations equilibrate at positive values. 2. The human population stabilizes, while [CO2]atm increases without bound. 3. The human population goes extinct and atmospheric carbon declines to 0. The final possibility is qualitatively compatible with both “consensus” views of climate change and the opinions of those who argue against it. Schaffer – Global Warming 2 In a recent communication to this journal, Lonngren and Bai (2008) proposed what a student of biochemical kinetics would refer to as an “abstract” model (LB) of human population growth and anthropogenic climate change. Phenomenological models, because they omit complicating factors, are incapable of quantitative prediction. At the same time, their cartoon-like simplicity focuses attention on the important task of identifying mechanistic essentials. They are also amenable to mathematical analysis, with the consequence that they can often be understood in detail. By way of contrast, elaborate simulations run the risk of replacing poorly understood systems with models that are likewise opaque (Borges, 1998). This having been said, both the analysis of LB and its derivation warrant comment. The purpose of this note is three-fold: first, to clarify the model’s dynamics; second, to reconsider its assumptions and finally, to suggest a somewhat more general scheme for contemplating the coevolution of carbon and climate. By way of conclusion, we note that LB’s most noteworthy prediction – human extinction and no atmospheric carbon (more accurately, anthropogenic carbon) – is qualitatively consistent with both the consensus view of global warming and the opinions of those who argue against it. The LB Model. The equations proposed by Lonngren and Bai are as follows: