A major goal of evolutionary biology is to identify key evolutionary transitions that correspond with shifts in speciation and extinction rates. Stochastic character mapping has become the primary method used to infer the timing, nature, and number of character state transitions along the branches of a phylogeny. The method is widely employed for standard substitution models of character evolution. However, current approaches cannot be used for models that specifically test the association of character state transitions with shifts in diversification rates such as state-dependent speciation and extinction (SSE) models. Here we introduce a new stochastic character mapping algorithm that overcomes these limitations, and apply it to study mating system evolution over a time-calibrated phylogeny of the plant family Onagraceae. Utilizing a hidden state SSE model we tested the association of the loss of self-incompatibility with shifts in diversification rates. Confirming long standing theory, we found that self-compatible lineages have higher extinction rates and lower net diversification rates compared to self-incompatible lineages. Furthermore, these results provide empirical evidence for the "senescing" diversification rates predicted in highly selfing lineages: our mapped character histories show that the loss of self-incompatibility is followed by a short-term spike in speciation rates, which declines after a time lag of several million years resulting in negative net diversification. Lineages that have long been self-compatible such as Fuchsia and Clarkia are in a previously unrecognized and ongoing evolutionary decline. Our results demonstrate that stochastic character mapping of SSE models is a powerful tool for examining the timing and nature of both character state transitions and shifts in diversification rates over the phylogeny.