Relationships among variables and their equilibrium values: caveats of time-less interpretation

In biology, the researcher often manipulates some variables of a system and observes its other variables, or investigates relationships among naturally occurring variable values. The studied variables are often measured at equilibrium. It is therefore important to know what we can learn from these equilibrium values and how much information they provide about the fundamental properties of the system. We argue that this information is very limited and that statistical relationships that include equilibrium values may lead to grossly incorrect inferences. A number of simple systems are discussed in order to provide examples of such inferential errors and advice is given about how to avoid them in practice. In conclusion, the potential importance of measure theory in biological sciences in considered.