We discuss a log-linear model for series of regular bird counts taken at a number of survey sites. The model is parameterized in terms of annual growth rates rather than actual indices of abundance, as is more frequently done. This not only permits easy estimation of and inference about these rates, but also allows us to model the effects upon population growth of covariates, such as the local presence of a competitor or predator, which may themselves vary in space and over time. A recursive relationship permits the expected count at a site to be functionally dependent upon the expected count at the previous visit. We discuss the advantages of using this relationship, rather than replacing the latter with their observed counterparts, as has been used previously.