It is intriguing that conspicuous colour morphs of a prey species may be maintained at low frequencies alongside cryptic morphs. Negative frequency-dependent selection by predators using search images ('apostatic selection') is often suggested without rejecting alternative explanations. Using a maximum likelihood approach we fitted predictions from models of genetic drift, migration, constant selection, heterozygote advantage or negative frequency-dependent selection to time-series data of colour frequencies in isolated populations of a marine snail (Littorina saxatilis), re-established with perturbed colour morph frequencies and followed for >20 generations. Snails of conspicuous colours (white, red, banded) are naturally rare in the study area (usually <10%) but frequencies were manipulated to levels of ~50% (one colour per population) in 8 populations at the start of the experiment in 1992. In 2013, frequencies had declined to ~15-45%. Drift alone could not explain these changes. Migration could not be rejected in any population, but required rates much higher than those recorded. Directional selection was rejected in three populations in favour of balancing selection. Heterozygote advantage and negative frequency-dependent selection could not be distinguished statistically, although overall the results favoured the latter. Populations varied idiosyncratically as mild or variable colour selection (3-11%) interacted with demographic stochasticity, and the overall conclusion was that multiple mechanisms may contribute to maintaining the polymorphisms.