The role of variability and uncertainty in testing hypotheses involving parameters in stochastic demographic models

Hierarchical/random effect models provide a statistical framework for estimating variance parameters that describe temporal and spatial variability of vital rates in population dynamic models. In practice, estimates of variance parameters (e.g., process error) from these models are often confused with estimates of uncertainty about model parameter estimates (e.g., standard errors). These two sources of "error" have different implications for predictions from stochastic models. Estimates of process error (or variability) are useful for describing the magnitude of variation in vital rates over time and are a feature of the modeled process itself, whereas estimates of parameter standard errors (or uncertainty) are necessary for interpreting how well we are able to estimate model parameters and whether they differ among groups. The goal of this comment is to illustrate these concepts in the context of a recent paper by A.W. Reed and N.A. Slade (Can. J. Zool. 84: 635-642 (2006)). In particular, we will show that their "hypothesis tests" involving mean parameters are actually comparisons of the estimated distributions of vital rates among groups of individuals.