Work to date on biological invasions and the spread of biological control agents has been focused on the explicitly spatial aspects, such as rate of spread and shape of the wave front. There has been relatively little attention paid to the influence of dispersal on the rate of increase of local populations. We use a simple general model for logistic local growth and one-dimensional diffusive dispersal to show that dispersal can act as a substantial drain on local populations. Local increase at a site of introduction is always slower than would be expected in the absence of dispersal, while the rate of increase of other populations is initially enhanced, then reduced by dispersal. This may have an important effect when estimating population parameters for invading organisms or biological control agents during the initial stages of their spread, and helps explain the “latent period” typically observed in biological invasions.