The only large mainland colony of southern elephant seals (Mirounga leonina) is on Península Valdés, at 42°S, in Argentine Patagonia. Censuses of pups have been carried out regularly there since 1970, and the population grew five-fold by 2010. Here we use Bayesian modeling tools to make rigorous estimates of the rate of population growth, r, and to estimate survival and recruitment parameters that could account for the growth, incorporating observation error across different census methods. In the 1970s, r= 8%/yr, but has slowed to <1%/yr over the past decade. Using explicit demographic models, we established that the high growth of the 1970s was consistent with adult and juvenile survival at the upper end of published values (0.87/yr adult female survival; 0.40 juvenile survivorship to age four); the decline in the rate of population growth from 1970 to 2010 can be described by density-dependent reductions in adult and juvenile survival that fall well within published variation. Extrapolating empirical models of population growth rate backwards illustrates that the population could have been an established colony, with 100 pups born per year, between 1915 and 1945, consistent with qualitative observations prior to 1950. We conclude that the Valdés colony was founded by a few immigrants early in the 20th century and has been growing mostly by internal recruitment, with unknown density-dependent processes causing a reduction in growth and stabilization at 15,000–16,000 pups born.