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

We provide here the full data sets and R-code of the analyses used in this contribution.