Exploring the Relationship between Abundance and Temperature with a Chemostat Model

Although there is a well developed theory on the relationship between the intrinsic growth rate r and temperature T, it is not yet clear how r relates to abundance, and how abundance relates to T. Many species often have stable enough population dynamics that one can talk about a stochastic equilibrium population size N*. There is sometimes an assumption that N* and r are positively correlated, but there is lack of evidence for this. To try to understand the relationship between r, N*, and T we used a simple chemostat model. The model shows that N* not only depends on r, but also on the mortality rate, the half-saturation constant of the nutrient limiting r, and the conversion coefficient of the limiting nutrient. Our analysis shows that N* positively correlates to r only with high mortality rate and half-saturation constant values. The response curve of N* vs. T can be flat, Gaussian, convex, and even temperature independent depending on the values of the variables in the model and their relationship to T. Moreover, whenever the populations have not reached equilibrium and might be in the process of doing so, it could be wrongly concluded that N* and r are positively correlated. Because of their low half-saturation constants, unless conditions are oligotrophic, microorganisms would tend to have flat abundance response curves to temperature even with high mortality rates. In contrast, unless conditions are eutrophic, it should be easier to get a Gaussian temperature response curve for multicellular organisms because of their high half-saturation constant. This work sheds light to why it is so difficult for any general principles to emerge on the abundance response to temperature. We conclude that directly relating N* to r is an oversimplification that should be avoided.