Reliability of conservation actions based on elasticity analysis of matrixmodels

Matrix population models have entered the mainstream of conservation biolog y, with analysis of proportional sensitivities (elasticity analysis) of dem ographic rates becoming important components of conservation decision makin g We identify areas where management applications using elasticity analysis potentially conflict with the mathematical basis of the technique, and we use a hypothetical example and three real data sets (Prairie Chicken [Tympa nuchus cupido], desert tortoise [Gopherus agassizii], and killer whale [Orc inus orca]) to evaluate the extent to which conservation recommendations ba sed on elasticities might be misleading. First, changes in one demographic rate can change the qualitative ranking of the elasticity values calculated from a population matrix, a result that dampens enthusiasm for ranking con servation actions based solely on which rates have the highest elasticity v alues. Second, although elasticities often provide accurate predictions of future changes in population growth rate under management perturbations tha t are large or that affect more than one rate concurrently, concordance fre quently fails when different rates vary by different amounts. In particular , when vital rates change to their high or low values observed in nature, p redictions of future growth rate based on elasticities of a mean matrix can be misleading, even predicting population increase when the population gro wth rate actually declines following a perturbation. Elasticity measures wi ll continue to be useful tools for applied ecologists, but they should be i nterpreted with considerable care. We suggest that studies using analytical elasticity analysis explicitly consider the range of variation possible fo r different rates and that simulation methods are a useful tool to this end .