Comparative demography of plants based upon elasticities of vital rates

Elasticities of matrix elements from population projection matrices are commonly used to analyze the relative contributions of different life history transitions (birth, survival, growth) to the finite rate of increase (lambda). Hitherto, comparative demography based on matrix models has relied upon decomposing elasticity matrices into blocks, each containing matrix elements deemed to represent recruitment, stasis, or progression to larger size classes. Elasticities across an entire matrix always sum to unity, and different populations and species can be compared on the basis of the relative proportions of these three variables. This method has been widely used, but it contains a weakness in that the value of matrix elements is a function of more than one vital rate. For example, transitions representing progression to larger size classes involve a survival rate as well as a growth rate. Ideally, then, demographic comparisons between populations should be made using elasticities of vital rates themselves, rather than elasticities of matrix elements that are compounds of those rates. Here, we employ the complete set of general equations for the elasticity of vital rates in an entirely new analysis of matrices for 102 species of perennial plants. The results show a surprising similarity to an earlier analysis based upon matrix element elasticity and provide important confirmation of general patterns of correlation between plant life history and demography. In addition, we show that individual vital rate elasticities cannot, on their own, predict variation in life history. Therefore, all three demographic processes (survival, growth, and reproduction) are necessary to account for life history variation. The new analysis provides a firmer foundation for comparative demography.