We propose a series of simple models of founder effect speciation. In these models, the resulting reproductive isolation (as measured by the proportion of inviable hybrids or the strength of the barrier to gene exchange between populations) can be very high and can evolve with a high probability on the time scale of dozens or hundreds of generations. In developing our theoretical framework, we utilize Dobzhansky's idea that strong selection against hybrids between two genotypes can occur simultaneously with the existence of a chain of genotypes that connect those two and differ only weakly in fitness among themselves. The mathematical models that we have studied are closely related to the verbal schemes of Mayr's "genetic revolutions," Carson's founder-flush process, and Templeton's genetic transilience. For appropriate parameter values, our theoretical models demonstrate that founder effect speciation is plausible; its importance becomes an empirical question.