Information on change in population size over time is among the most basic inputs for population management. Unfortunately, population changes are generally difficult to identify, and once identified difficult to explain. Sources of variald (patterns) in population data include: changes in environment that affect carrying capaciyy and produce trend, autocorrelative processes, irregular environmentally induced perturbations, and stochasticity arising from population processes. In addition. populations are almost never censused and many surveys (e.g., the North American Breeding Bird Survey) produce multiple, incomplete time series of population indices, providing further sampling complications. We suggest that each source of pattern should be used to address specific hypotheses regarding population change, but that failure to correctly model each source can lead to false conclusions about the dynamics of populations. We consider hypothesis tests based on each source of pattern, and the effects of autocorrelated observations and sampling error. We identify important constraints on analyses of time series that limit their use in identifying underlying relationships.