Abstract / Summary
Classical population models assume that estimated parameters, such as intrinsic growth rate, depend on the species of interest and its environment, but not on the initial population size N (0). However, it has been theoretically proposed that this dependence is a mathematical consequence of reducing a two‐dimensional system (e.g. for a predator and a prey) into a one‐dimensional model (for the predator only). We test this proposition experimentally with microbial batch cultures where N (0) and the initial amount of food x (0) are manipulated. We use the McKendrick and Pai (1912) model to exemplify this reduction process, which leads to a logistic equation with the estimated growth rate r and equilibrium density K predicted to increase linearly with N (0) and x (0). Our results confirmed the dependence of r and K on the initial conditions. However, contrary to the prediction, r decreased rather than increased with N (0). Firstly, our results provide experimental evidence that the parameters of a reduced model depend on initial conditions, which raises important questions and challenges in their estimation. Secondly, the use of different initial conditions could be a powerful tool for model selection. Using simulated data from consumer‐resource models and fitting the logistic equation to the consumer trajectory, we find that the observed negative dependence of r to N (0) is incompatible with McKendrick and Pai (1912) and with Monod (1942) models (akin to Holling type 1 and type 2 functional response, respectively), but agrees with the Contois model (1959), akin to ratio‐dependence.