Background/Question/Methods Regression of log-abundance of a population versus time is often used to estimate the population's trend.  It is not widely realized that such regression carries implicit assumptions about how the trend and the variability in the population abundances arise.  If the statistical model does not adequately describe the process by which the data are produced, the trend estimate can be seriously in error. 

Results/Conclusions   Here we describe three models for estimating population trend.  The three are different stochastic versions of the exponential growth model:  (1) observation error only, (2) environmental process noise only, and (3) a state space model which combines both observation error and process noise. We describe the statistical methods for obtaining parameter estimates, including estimates of trend, for time series abundance data under each of the three models.  Log-abundance regression turns out to correspond to deterministic exponential growth with observation error only, that is, model (1).