Improved estimation of intrinsic growthr_maxfor long‐lived species: integrating matrix models and allometry

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.

Perspectives on the intrinsic rate of population growth

“…Differences between methods 2, 3 and 6 and methods 4 and 5 were more accentuated for fast-growing populations, suggesting that the ad hoc treatment or omission of fecundity in methods 4 and 5, respectively, can have a large effect on estimates. It is also important to note that Method 5, which is based on allometric scaling relationships, will underestimate r max if optimal survival is overestimated, whereas Method 6 (the Euler-Lotka equation) and its derivations (methods 2 and 3) will overestimate r max if optimal survival is overestimated, which points to the fact that either of these methods (allometric vs. demographic models) should probably not be used alone (Dillingham et al 2016). A recent expansion of the DIM method that draws strength from both allometric and life table models (Dillingham et al 2016) has the potential to generate improved estimates and more realistic depictions of uncertainty in the population growth rate and could thus be tested across a variety of populations with different life histories to provide improved conservation and management advice.…”

“…and can be solved iteratively. Niel & Lebreton (2005) found that a rT % 1 for birds and Dillingham et al (2016) recently found that a rT % 1 for several vertebrate taxa (birds, mammals and elasmobranchs); thus, r max can be obtained from knowledge of a and s only.…”

“…Indeed, r max is used to quantify extinction risk in conservation contexts or to assess the dynamics of terrestrial and aquatic animal populations. While population growth rates can be estimated with a variety of direct methods, including visual surveys, transects or regression-based approaches among others (Skalski, Ryding & Millspaugh 2005), series of abundance estimates are notoriously difficult to obtain for aquatic organisms, especially for long-lived, latematuring marine species (Dillingham et al 2016). For these species, population growth rates are instead typically derived from models based on survival and fecundity schedules, which may not necessarily reflect optimal conditions and thus not represent the maximum, or intrinsic, growth rate.…”

Sturgeon and paddlefish life history and management: Experts' knowledge and beliefs

“…Population growth rates represent the population-specific intrinsic rate of increase, or the per-capita rate to which a particular population is capable of increasing under optimum environmental conditions (Huston, 1979). An intrinsic population growth rate is a difficult parameter to estimate, especially in long-lived species such as sturgeons (Dillingham et al, 2016). Reflecting the lack of consensus on the probable intrinsic population growth rate in sturgeons and paddlefish, the majority of respondents (53%) were unsure of the proper response, indicating that the population growth rate concept is not fully comprehended within the scientific community.…”

Life‐history constraints on maximum population growth for loggerhead turtles in the northwest Atlantic

“…of Commerce 2001) and population viability analyses (Merrick & Haas, 2008;Snover & Heppell, 2009). For many long-lived and late-maturing species, the maximum rate of population growth is unknown or inestimable using direct methods (e.g., analysis of trends in abundance indices) because of data limitations (Dillingham et al, 2016). In such cases, demographic models, such as life tables and projection matrices, are used to represent population dynamics and to generate estimates of population growth (Caswell, 2001;Zerbini, Clapham, & Wade, 2010).…”