Uncertainty and variability in demography and population growth: A hierarchical approach
Estimates of uncertainty are the basis for inference of population risk. Uncertainty is estimated from models fitted to data that typically include a deterministic model (e.g., population growth) and stochastic elements, which should accommodate errors in sampling and any sources of variability that affect observations. Prediction from fitted models (of, say, demography) to new variables (say, population growth) requires propagation of these stochastic elements. Ecological models ignore most forms of variability, because they make statistical models complex, and they pose computational challenges. Variability associated with space, time, and among individuals that is not accommodated by demographic models can make parameter estimates and growth rate predictions unrealistic. I adapt a hierarchical approach to the problem of estimating population growth rates and their uncertainties when individuals vary and that variability cannot be assigned to specific causes. In contrast to an overfitted model that would assign a different parameter value to each individual, hierarchical models accommodate individual differences, but assume that those differences derive from an underlying distribution - they belong to a "population." The hierarchical model can be implemented in classical (frequentist) and Bayesian frameworks (I demonstrate both) and analyzed using Markov chain Monte Carlo simulation. Results show that population growth models that rely on standard propagation of estimation error but ignore variability among individuals can misrepresent uncertainties in ways that erode credibility.
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