Parameter uncertainty and elasticity analyses of a population model: setting research priorities for shearwaters

Abstract

The difference between parameter uncertainty and elasticity analyses of a deterministic matrix model was evaluated using the Short-tailed Shearwater ( Puffinus tenuirostris) as a case study. A total of 5000 simulations of the model were run with input parameters randomly selected from uniform distributions between the upper and lower 95% confidence limits for each parameter. A multiple regression equation was used to relate population growth to all input parameters, two-way interactions and quadratics. Elasticity and parameter uncertainty coefficients were estimated as the percent change in population growth rate when the minimum and maximum value of each parameter were substituted into the regression equation, with all other parameters set at their mean values. Minimum and maximum values were set at the 95% confidence limits for the parameter uncertainty analysis, and at ±5% of both mean survival and mean mortality estimates for the elasticity analyses. Parameter rankings differed among the uncertainty and two elasticity analyses. Probability of pre-breeders staying in the colony and probability of first breeding ranked highly in the parameter uncertainty analysis. Survival rates had higher elasticity coefficient rankings when ±5% of mean survival was used because altering proportions close to one results in a wider parameter range. The importance of interactions was explored but their importance in this example was found to be low. Incorporating breeding age specific data more closely approximated observed population demographic structure but had little effect on the magnitude or rankings of the elasticity or parameter uncertainty coefficients. The utility of parameter uncertainty and elasticity analyses differ. The former determines how uncertainty in parameter estimation influences model outcomes and is therefore valuable for setting research priorities. The latter determines the effect on model outcomes of altering parameter input levels, so is more valuable for ranking the potential effectiveness of alternative management strategies.