Maximum intrinsic rate of population increase in sharks, rays, and chimaeras: the importance of survival to maturity

Abstract

The maximum intrinsic rate of population increase r max is a commonly estimated demographic parameter used in assessments of extinction risk. In teleosts, r max can be calculated using an estimate of spawners per spawner, but for chondrichthyans, most studies have used annual reproductive output b instead. This is problematic as it effectively assumes all juveniles survive to maturity. Here, we propose an updated r max equation that uses a simple mortality estimator which also accounts for survival to maturity: the reciprocal of average lifespan. For 94 chondrichthyans, we now estimate that r max values are on average 10% lower than previously published. Our updated r max estimates are lower than previously published for species that mature later relative to maximum age and those with high annual fecundity. The most extreme discrepancies in r max values occur in species with low age at maturity and low annual reproductive output. Our results indicate that chondrichthyans that mature relatively later in life, and to a lesser extent those that are highly fecund, are less resilient to fishing than previously thought.

Quantifying the known unknowns: estimating maximum intrinsic rate of population increase in the face of uncertainty

“…Instantaneous natural mortality M was estimated using the reciprocal of average lifespan (M = 1 /ω), with average lifespan ω defined as the midpoint between age at maturity and maximum age (ω = αmat+αmax 2 ), for rationale see Pardo et al (2016). Given that we obtained a distribution of age at maturity values for each population (see above), we used this uncertainty in age at maturity as the basis to estimate uncertainty in M , thus uncertainty of M was iteratively estimated using the same age at maturity distribution described above.…”

“…In this study, we use an unstructured derivation of the Euler-Lotka demographic model, which estimates the maximum intrinsic rate of population increase r max (Myers et al, 1997;Pardo et al, 2016;Cortés, 2016). We address how measurement error in life history traits affects (1) uncertainty in productivity estimates, and (2) sensitivity of these estimates to uncertainty in each trait.…”

“…We used a Monte Carlo simulation model ( Fig. 1) based on published information on the biology of a species to iteratively estimate maximum intrinsic rate of population increase r max using a derivation of the Euler-Lotka model (Cortés, 2016;Pardo et al, 2016). The model starts with the data required (Values for age at maturity α mat , maximum age α max , litter size l, and breeding interval i ("Data" section in Fig.…”

Evidence for systemic age underestimation in shark and ray ageing studies

“…These examples, while simplistic, highlight the potential ways that (2014)), current perceptions of population dynamics, including key areas such as fisheries productivity reference points and extinction risk, are strongly shaped by comparative life history studies (Cortés, 2000;Frisk, Miller, & Dulvy, 2005;Frisk, Miller, & Fogarty, 2001;Pardo, Kindsvater, Reynolds, & Dulvy, 2016) and meta-analyses (García, Lucifora, & Myers, 2008;Hutchings, Myers, García, Lucifora, & Kuparinen, 2012;Zhou, Yin, Thorson, Smith, & Fuller, 2012) that draw heavily upon age and growth studies.…”

“…(c) The apparent loss of age-structure due to age underestimation may be inadvertently attributed to or indistinguishable from the effects of fishing. of population productivity (Pardo et al, 2016;Smith, Au, & Show, 1998), is frequently obtained from the inverse of a growth curve at length-at-maturity, meaning it too would be susceptible to biased growth parameters. Sidestepping the use of biased parameters altogether is also difficult.…”