Improved estimation of intrinsic growth rmax for long-lived species: Integrating matrix models and allometry

Abstract

Intrinsic population growth rate (rmax) is an important parameter for many ecological applications, such as population risk assessment and harvest management. However, rmax can be a diffi cult parameter to estimate, particularly for long-lived species, for which appropriate life table data or abundance time series are typically not obtainable. We describe a method for improving estimates of rmax for long-lived species by integrating life-history theory (allometric models) and population-specifi c demographic data (life table models). Broad allometric relationships, such as those between life history traits and body size, have long been recognized by ecologists. These relationships are useful for deriving theoretical expectations for rmax, but rmax for real populations may vary from simple allometric estimators for "archetypical" species of a given taxa or body mass. Meanwhile, life table approaches can provide population-specifi c estimates of rmax from empirical data, but these may have poor precision from imprecise and missing vital rate parameter estimates. Our method borrows strength from both approaches to provide estimates that are consistent with both life-history theory and population-specifi c empirical data, and are likely to be more robust than estimates provided by either method alone. Our method uses an allometric constant: the product of rmax and the associated generation time for a stable-age population growing at this rate. We conducted a meta-analysis to estimate the mean and variance of this allometric constant across well-studied populations from three vertebrate taxa (birds, mammals, and elasmobranchs) and found that the mean was approximately 1.0 for each taxon. We used these as informative Bayesian priors that determine how much to "shrink" imprecise vital rate estimates for a data-limited population toward the allometric expectation. The approach ultimately provides estimates of rmax (and other vital rates) that refl ect a balance of information from the individual studied population, theoretical expectation, and meta-analysis of other populations. We applied the method specifi cally to an archetypical petrel (representing the genus Procellaria) and to white sharks (Carcharodon carcharias) in the context of estimating sustainable fi shery bycatch limits.