Van Tienderen recently published a method that links selection gradients between a phenotypic trait and multiple fitness components with the effects of these fitness components on the population growth rate (mean absolute fitness). The method allows selection to be simultaneously estimated across multiple fitness components in a population dynamic framework. In this paper we apply the method to a population of red deer living in the North Block of the Isle of Rum, Scotland. We show that (1) selection on birth date and birth weight can operate through multiple fitness components simultaneously; (2) our estimates of the response to selection are consistent with the observed change in trait values that we cannot explain with environmental and phenotypic covariates; (3) selection on both traits has fluctuated over the course of the study; (4) selection operates through different fitness components in different years; and (5) no environmental covariates correlate with selection because different fitness components respond to density and climatic variation in contrasting ways.