Social networks can result in directed social transmission of learned information, thus influencing how innovations spread through populations. Here we presented shoals of threespine sticklebacks (
Gasterosteous aculeatus) with two identical foraging tasks and applied network-based diffusion analysis (NBDA) to determine whether the order in which individuals in a social group contacted and solved the tasks was affected by the group's network structure. We found strong evidence for a social effect on discovery of the foraging tasks with individuals tending to discover a task sooner when others in their group had previously done so, and with the spread of discovery of the foraging tasks influenced by groups' social networks. However, the same patterns of association did not reliably predict spread of solution to the tasks, suggesting that social interactions affected the time at which the tasks were discovered, but not the latency to its solution following discovery. The present analysis, one of the first applications of NBDA to a natural animal system, illustrates how NBDA can lead to insight into the mechanisms supporting behaviour acquisition that more conventional statistical approaches might miss. Importantly, we provide the first compelling evidence that the spread of novel behaviours can result from social learning in the absence of social transmission, a phenomenon that we refer to as an untransmitted social effect on learning.