Rapid Ecological Risk Assessment. J. Hajagos, SUNY Stony Brook; J. Damuth, UC Santa Barbara; and S. Ferson, Applied Biomathematics
Using a stochastic model of Malthusian population growth, we can compute the probability that a species will fall below some abundance within a specified time. To do so, we require estimates of three quantities: current population size, low-density population growth rate (commonly known as "little r" or "r max"), and temporal variance of that growth rate. Although these empirical requirement is minimal, and certainly modest, it is still a significant hurdle when the species of concern has not been the focus of prior local study. We show how allometries (i.e., regressions of a species-specific parameter on the typical organism body size for several species) can be used to estimate the needed quantities. Fenchel’s now classical allometry for little r can be supplemented by newly assembled information on both little r and its temporal variance. A more recently described allometry characterizes the typical ecological density of a species as a function of its body size. This allometry can be used as an estimate of the species’ current abundance, or perhaps as the carrying capacity, which could parameterize a generalized Malthusian model incorporating density dependence. The allometries are typically power relations that are linear under log-log transformations. The tightness of the allometries for hundreds of species over twenty orders of magnitude in body size is remarkable, but there is still considerable residual uncertainty about the vital parameters. We discuss how this uncertainty can be propagated through the analysis to yield conservative estimates of the risks of population decline useful for screening risk assessments.
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