Improved estimation of intrinsic growth r_max for long-lived species: integrating matrix models and allometry

Authors

Peter W. Dillingham, University of New EnglandFollow
Jeffrey E. Moore, Marine Mammal and Turtle Division, Southwest Fisheries Science Center, National Marine Fisheries Service, NOAA
David Fletcher, University of Otago
Enric Cortés, Panama City Laboratory, Southeast Fisheries Science Center, National Marine Fisheries Service, NOAA, Panama City, Florida
K. Alexandra Curtis, Marine Mammal and Turtle Division, Southwest Fisheries Science Center, National Marine Fisheries Service, NOAA
Kelsey C. James, University of Rhode Island
Rebecca L. Lewison, San Diego State University

Date of this Version

2016

Citation

Ecological Applications, 26(1), 2016, pp. 322–333

Comments

U.S. Government Work

Abstract

Intrinsic population growth rate (r_max) is an important parameter for many ecological applications, such as population risk assessment and harvest management. However, r_max can be a difficult 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 r max for long- lived species by integrating life- history theory (allometric models) and population- specific 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 r_max , but r_max 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- specific estimates of r_max 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- specific 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 r_max 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 r_max (and other vital rates) that reflect a balance of information from the individual studied population, theoretical expectation, and meta- analysis of other populations. We applied the method specifically to an archetypical petrel (representing the genus Procellaria ) and to white sharks ( Carcharodon carcharias ) in the context of estimating sustainable fishery bycatch limits.