Using Demographic Models to Determine Intrinsic Rate of Increase and Sustainable Fishing for Elasmobranchs: Pitfalls, Advances, and Applications

Abstract

Abstract.-Leslie matrices and life tables are demographic models commonly used to evaluate the ability of specific elasmobranch life history strategies to sustain given levels and patterns of fishing pressure. These models are generally density independent and provide an instantaneous rate of population growth for a specified set of life history traits that correspond to a specific population size. Many investigators are using these models to compute rates of population growth that they claim are estimates of the maximum population growth rate (r intrinsic ); they then use these estimates to compute purported estimates of maximum sustainable fishing mortality. However, neither a Leslie matrix nor a life table can be used to estimate r intrinsic without additional information, except in the special case where a severely depleted population is modeled. Only in a severely depleted population will competition for resources be at a minimum and both density-dependent compensation and the rate of population growth be at a maximum (i.e., at r intrinsic ). The fundamental problem is to determine the life history parameters that would occur if the population were extremely depleted because extensive observations on extremely depleted populations are rare. In the absence of such data, r intrinsic can only be estimated from these types of density-independent models by extrapolating observed population growth rates toward zero population size. We illustrate the problems in, and describe methods for, estimating r intrinsic and present information on two species of elasmobranch: barndoor skate Dipturus laevis and lemon shark Negaprion brevirostris.Classic demographic analysis, based on a life table or Leslie matrix, provides an estimate of the exponential (or, more properly, geometric) rate of population growth or decline based on a fixed set of life history parameters. Alternatively, the model can be thought of as providing the current (short-term) rate of population change under current conditions. For the elasmobranchs, where many stocks have been severely depleted, the question is to what extent these populations can withstand fishing pressure. Recently, this question has been approached by attempting to use demographic models to determine the intrinsic or maximum rate of population increase (r intrinsic ) and therefore the maximum sustainable fishing pressure. However, fundamental errors in the interpretation of the models are common.Problems in the use of a basic demographic analysis for estimating r intrinsic arise from the density-independent nature of its structure and the use of static life history parameter inputs. In reality, at least some life history traits must be pliable and able to respond to changes in population size. This forms the basic logic behind density-dependent compensation, which explains why populations rarely go extinct and cannot grow beyond the bounds fixed by limiting factors (such as food resources or space) for extended periods (i.e., there is a carrying capacity of the environment).Throughou...

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