Neurons are precisely and reproducibly assembled into complex networks during development. How genes collaborate to guide this assembly remains an enduring mystery. In humans, large numbers of genes have been implicated in neurodevelopmental disorders that are characterized by variable and overlapping phenotypes. The complexity of the brain, the large number of genes involved and the heterogeneity of the disorders makes understanding the relationships between genes, development and neural function challenging. Waddington suggested the concept of canalization to describe the role of genes in shaping developmental trajectories that lead to precise outcomes. Here, we show that members of the δ-protocadherin family of homophilic adhesion molecules, Protocadherin-19 and Protocadherin-17, contribute to developmental canalization of visual circuit assembly in the zebrafish. We provided oriented visual stimuli to zebrafish larvae and performed 2-photon calcium imaging in the optic tectum. The latent dynamics resulting from the population activity were confined to a conserved manifold. Among different wild type larvae, these dynamics were remarkably similar, allowing quantitative comparisons within and among genotypes. In both Protocadherin-19 and Protocadherin-17 mutants, the latent dynamics diverged from wild type. Importantly, these deviations could be averaged away, suggesting that the loss of these adhesion molecules leads to stochastic phenotypic variability and introduced disruptions of circuit organization that varied among individual mutants. These results provide a specific, quantitative example of canalization in the development of a vertebrate neural circuit, and suggest a framework for understanding the observed variability in complex brain disorders.