Dengue is an emerging tropical disease infecting tens of millions of people annually. A febrile illness with potentially severe hemorrhagic manifestations, dengue is caused by mosquito-borne viruses (DENV-1 to -4) that are maintained in endemic transmission in large urban centers of the tropics with periodic epidemic cycles at 3- to 5-year intervals. Puerto Rico (PR), a major population center in the Caribbean, has experienced increasingly severe epidemics since multiple dengue serotypes were introduced beginning in the late 1970s. We document the phylodynamics of DENV-4 between 1981 and 1998, a period of dramatic ecological expansion during which evolutionary change also occurs. The timescale of viral evolution is sufficiently short that viral transmission dynamics can be elucidated from genetic diversity data. Specifically, by combining virus sequence data with confirmed case counts in PR over these two decades, we show that the pattern of cyclic epidemics is strongly correlated with coalescent estimates of effective population size that have been estimated from sampled virus sequences using Bayesian Markov Chain Monte Carlo methods. Thus, we show that the observed epidemiologic dynamics are correlated with similar fluctuations in diversity, including severe interepidemic reductions in genetic diversity compatible with population bottlenecks that may greatly impact DENV evolutionary dynamics. Mean effective population sizes based on genetic data appear to increase prior to isolation counts, suggesting a potential bias in the latter and justifying more active surveillance of DENV activity. Our analysis explicitly integrates epidemiologic and sequence data in a joint model that could be used to further explore transmission models of infectious disease.