SENSITIVITY ANALYSIS TO GUIDE POPULATION RECOVERY - PRAIRIE-CHICKENS AS AN EXAMPLE

Calculation of elasticities in matrix population models is a formal ty pe of sensitivity analysis that is used increasingly to guide recovery of declining populations. Results presumably allow recovery efforts t o focus on the life stage most responsible For change in population gr owth, as indexed by the highest elasticity Specifically, the highest e lasticity denotes the vital rate whose proportionate change experts th e largest proportionate effect on the finite rate of increase (lambda) . We examined the utility of this given uncertainty in parameter estim ates and random variation in vital rates. We modeled these conditions to test tile hypothesis that nest success and brood survival exert the greatest effect on population growth of greater prairie-chickens (Tym panuchus cupido pinnatus). We calculated elasticity associated with ea ch age-specific vital rate contained in 1,000 randomly-generated repli cates of a Leslie matrix model, and regressed lambda on each randomly- varying rate. Age 0 survival (S-0) was associated with highest elastic ity for 100% of tile replicates and accounted for most of the variatio n in lambda (r(2) = 0.05), Within S-n, nest success and brood survival accounted for more variation in gamma than other life stage combinati ons. These results demonstrate the utility of sensitivity analysis, bu t additional results point to its limitations For example, the vital r ate consistently associated with the second highest elasticity (S-1) a ccounted for minuscule variation in gamma (r(2) = 0.0009), implying th at rank of elasticities can fail to index the magnitude of a vital rat e's effect on gamma when vital rates vary simultaneously and dispropor tionately. To ensure that results are reliable, we recommend that sens itivity analysis be performed across the range of plausible vital rate s, that simulations involve randomization of values within, these rang es, and that elasticities be calculated in tandem with regression anal ysis to lull illuminate potential relations of vital rates with gamma. A critical assumption is that variance of vital rates is estimated ac curately.