Survivorship curves and their impact on the estimation of maximum population growth rates

Previous efforts to use the Euler equation to estimate maximum population growth rates (variously symbolized as either r, [r.sub.m], or [r.sub.max]) have used simplified models of survivorship that neglect differences in survivorship schedules among species. In particular, several recent analyses have used either an exponential model of survivorship or a step function model in which all individuals live until a fixed age of death. Using a flexible alternative based on the beta distribution and a compiled data set of mammalian survivorship curves for 58 species, we explore the influence of survivorship shape and scale on the estimation of r. We show that the Euler equation paired with an exponential model of survivorship can be used to calculate an unbiased estimate of r over a large range of body sizes, whereas the more commonly used step function survivorship model results in severely inflated estimates of r, especially for mammals with large maximum population growth rates. Finally, we demonstrate that, despite producing different absolute estimates of r, the three survivorship models examined yield similar allometric scaling coefficients relating r to biomass. These allometric scaling relationships are highly sensitive to the inclusion or exclusion of bats (Chiroptera), which exhibit life-history traits (long life spans, small litter sizes, and relatively long litter intervals) inconsistent with their small body size. Key words: allometry; beta distribution; Cole approximation; Euler equation; life history; maximum population growth rate; metabolic theory; survivorship.