Sensitivity analysis to guide population recovery: Prairie-chickens as an example

Calculation of elasticities in matrix population models is a formal type of sensitivity analysis that is used increasingly to guide recovery of declining populations. Results presumably allow recovery efforts to focus on the life stage most responsible for change in population growth, as indexed by the highest elasticity. Specifically, the highest elasticity denotes the vital rate whose proportionate change exerts the largest proportionate effect on the finite rate of increase (λ). We examined the utility of this analysis given uncertainly in parameter estimates and random variation in vital rates. We modeled these conditions to test the hypothesis that nest success and brood survival exert the greatest effect on population growth of greater prairie-chickens (Tympanuchus cupido pinnatus). We calculated elasticity associated with each age-specific vital rate contained in 1,000 randomly- generated replicates of a Leslie matrix model, and regressed λ on each randomly varying rate. Age 0 survival (S(o)) was associated with highest elasticity for 100% of the replicates and accounted for most of the variation in λ (r² = 0.95). Within S(o), nest success and brood survival accounted for more variation in λ than other life stage combinations. These results demonstrate the utility of sensitivity analysis, but additional results point to its limitations. For example, the vital rate consistently associated with the second highest elasticity (S₁) accounted for minuscule variation in λ (r² = 0.0009), implying that rank of elasticities can fail to index the magnitude of a vital rate's effort on λ when vital rates vary simultaneously and disproportionately. To ensure that results are reliable, we recommend that sensitivity analysis be performed across the range of plausible vital rates, that stimulations involve randomization of values within these ranges, and that elasticities be calculated in tandem with regression analysis to fully illuminate potential relations of vital rates with λ. A critical assumption is that variance of vital rates is estimated accurately.