Abstract. Simple mathematical models of population dynamics have long been features in ecology and natural resource management textbooks. These models, bearing the names of Verhulst-Pearl, Ricker, Lotka-Volterra, and so on, have mainly been regarded as simple quantitative illustrations of ecological concepts. Somewhere during an ecologist's education, however, comes the realization that these models were not intended to pertain to particular real systems. One difficulty with applying mathematical models to practical situations has been that the connections between the models and ecological data were never specified in the textbooks.

In this presentation, I discuss a set of techniques for connecting mathematical population models with ecological time series data. The techniques involve converting the deterministic population equations into stochastic versions by modeling how the variability in the data arose. An explicit likelihood function, the connection between model and data, provides for parameter estimation, statistical hypothesis testing, model selection, and model evaluation. With these statistical techniques, the textbook models become ecological hypotheses that can be confronted by data, as well as potentially useful tools for ecological management.