Efficacy of simple viability models in ecological risk assessment: Does density dependence matter?

One commonly used PVA (population viability analysis) approach applies a diffusion approximation (DA) of population growth to time series of abundance data to estimate population parameters and various metrics of extinction risk. The simplest versions of this PVA assume density-independent population growth, an assumption that is commonly called into question for populations experiencing self-limitation. Using time series data generated from simulations of populations limited by three commonly used forms of density dependence (ceiling, Beverton-Holt, and Ricker) we asked the question: "When do simple density-independent PVA models provide useful guidelines for prioritizing extinction risk despite density-dependence inherent in the underlying real populations?" Simple DA methods severely underestimated maximum growth rates (mu(max)) used to generate time series data for all three forms of density dependence. These methods also underestimated the intrinsic environmental variability in growth rates, or process error (sigma(2)), for the ceiling model, but overestimated this parameter for the Beverton-Holt and Ricker models. Despite misestimation of the intrinsic parameters, the estimated probabilities of 50% and 75% declines were highly correlated with the observed probabilities for populations growing with a ceiling (coefficients of correlation, or R-2 = 0.87-0.93). DA methods were less accurate for populations exhibiting more complex forms of density dependence (R-2 = 0.61-0.79). Although correlations between observed and estimated risks were high, bias (e.g., over and underestimation) was extensive. Estimated probabilities of 50% declines were typically much lower (overly optimistic) than observed probabilities of the same decline. By contrast, accuracy increased substantially for predictions of 75% decline, and the "optimistic" bias was replaced by conservative bias (overestimates of risk). Regardless of the form of density dependence, estimates of risk were least accurate when populations were recovering rapidly but were much more accurate when most needed by conservation practitioners: when the population fluctuated near its carrying capacity, recovered slowly to this abundance level, or declined toward extinction. Finally, when we classified risk in broad categories (e.g., extremely low, low, moderate, high, and extremely high), DA methods correctly or conservatively estimated the risk of a 75% decline for >85% of the parameter combinations, regardless of the form of density dependence followed by the real population.