Here, we explore some cognitive mechanisms that support and constrain sequential abilities in non-human animals (hereafter animals). By examining limits in memory for stimulus sequences and how behaviour sequences can be learned, we highlight the combinatorial costs that arise as sequences get increasingly longer, which may hinder the development of cognitive abilities that require faithful representation of sequences, like language. We discuss a trace memory model as a framework for understanding how animals represent stimulus sequences and suggest that animals represent sequences as unstructured collections of decaying memory traces rather than representing order faithfully. The implications of this model challenge traditional interpretations of declarative and rule-based learning in animals. In addition, we explore associative learning models that can account for how animals acquire behaviour sequences without precise memory of stimulus sequences. Current models have proven powerful in accounting for complex behaviour sequences. We end by asking what the value is of anthropocentric models in the study of animal intelligence, if other models provide more accurate predictions of animal behaviour.

This article is part of the Theo Murphy meeting issue ‘Selection shapes diverse animal minds’.