This paper is about mechanisms and models, and how they interact. In part, it is a response to recent discussion in philosophy of biology regarding whether natural selection is a mechanism. We suggest that this debate is indicative of a more general problem that occurs when scientists produce mechanistic models of populations and their behaviour. We can make sense of claims that there are mechanisms that drive population-level phenomena such as macroeconomics, natural selection, ecology, and epidemiology. But talk of mechanisms and mechanistic explanation evokes objects with well-defined and localisable parts which interact in discrete ways, while models of populations include parts and interactions that are neither local nor discrete in any actual populations. This apparent tension can be resolved by carefully distinguishing between the properties of a model and those of the system it represents. To this end, we provide an analysis that recognises the flexible relationship between a mechanistic model and its target system. In turn, this reveals a surprising feature of mechanistic representation and explanation: it can occur even when there is a mismatch between the mechanism of the model and that of its target. Our analysis reframes the debate, providing an alternative way to interpret scientists’ “mechanism-talk”, which initially motivated the issue. We suggest that the relevant question is not whether any population-level phenomenon such as natural selection is a mechanism, but whether it can be usefully modelled as though it were a particular type of mechanism.