Animals of the same species exhibit similar behaviours that are advantageously adapted to their body and environment. These behaviours are shaped at the species level by selection pressures over evolutionary timescales. Yet, it remains unclear how these common behavioural adaptations emerge from the idiosyncratic neural circuitry of each individual. The overall organization of neural circuits is preserved across individuals1 because of their common evolutionarily specified developmental programme2-4. Such organization at the circuit level may constrain neural activity5-8, leading to low-dimensional latent dynamics across the neural population9-11. Accordingly, here we suggested that the shared circuit-level constraints within a species would lead to suitably preserved latent dynamics across individuals. We analysed recordings of neural populations from monkey and mouse motor cortex to demonstrate that neural dynamics in individuals from the same species are surprisingly preserved when they perform similar behaviour. Neural population dynamics were also preserved when animals consciously planned future movements without overt behaviour12 and enabled the decoding of planned and ongoing movement across different individuals. Furthermore, we found that preserved neural dynamics extend beyond cortical regions to the dorsal striatum, an evolutionarily older structure13,14. Finally, we used neural network models to demonstrate that behavioural similarity is necessary but not sufficient for this preservation. We posit that these emergent dynamics result from evolutionary constraints on brain development and thus reflect fundamental properties of the neural basis of behaviour.