Comparative population demography of elasmobranchs using life history tables, Leslie matrices and stage-based matrix models

Abstract

Results of demographic analyses of four species of elasmobranchs were compared by use of life-history tables, Leslie matrices, and several stage-based matrix models. Dasyatis violacea, with few age classes, was used to demonstrate the basics of Leslie-matrix and stage-based matrix model calculations. The demography for Carcharias taurus, with a 2-year reproductive cycle, produced higher potential population growth using actual fertility rather than effective annual fertility. The demography for Alopias pelagicus, with continuous reproduction, produced higher potential population growth for a birth-flow than a birth-pulse population. The Carcharodon carcharias example demonstrated only a small difference in potential population growth between step-like and logistic fertility functions. Stage-based models with fixed stage duration produced potential population growths identical to those obtained from a life-history table or Leslie matrix, but the net reproductive rates and generation times differed. Stage-based models with few stages had different dynamics with shorter recovery to the stable age distribution; they underestimated the elasticity of juvenile survival and overestimated the elasticity of adult survival, suggesting that interpretation should be cautious. Elasticity analyses were used to estimate the number of juvenile age classes that could be fished and have the same effect on potential population growth as fishing all the adult age classes.