Oblique transmission occurs when a trait is passed to offspring from non-parental members of the parental generation. This can occur, for example, via social learning, mobile genetic elements, epigenetics, and the microbiome. We (i.e. Drs Ram, Uri Liberman, and Marcus Feldman) developed a model in which both vertical (i.e. from parent to offspring) and oblique transmission occur in a population evolving under fluctuating selection. Our analytical and numerical results highlight scenarios in which oblique or vertical transmission are likely to evolve; surprisingly, in some cases, oblique transmission does not evolve, even though it increases population mean fitness. We also examine the effect of the transmission mode on maintenance of diversity in the population.