Growth and life history variability of the grey reef shark (Carcharhinus amblyrhynchos) across its range

For broadly distributed, often overexploited species such as elasmobranchs (sharks and rays), conservation management would benefit from understanding how life history traits change in response to local environmental and ecological factors. However, fishing obfuscates this objective by causing complex and often mixed effects on the life histories of target species. Disentangling the many drivers of life history variability requires knowledge of elasmobranch populations in the absence of fishing, which is rarely available. Here, we describe the growth, maximum size, sex ratios, size at maturity, and offer a direct estimate of survival of an unfished population of grey reef sharks (Carcharhinus amblyrhynchos) using data from an eight year tag-recapture study. We then synthesized published information on the life history of C. amblyrhynchos from across its geographic range, and for the first time, we attempted to disentangle the contribution of fishing from geographic variation in an elasmobranch species. For Palmyra’s unfished C. amblyrhynchos population, the von Bertalanffy growth function (VBGF) growth coefficient k was 0.05 and asymptotic length L∞ was 163.3 cm total length (TL). Maximum size was 175.5 cm TL from a female shark, length at maturity was estimated at 116.7–123.2 cm TL for male sharks, maximum lifespan estimated from VBGF parameters was 18.1 years for both sexes combined, and annual survival was 0.74 year-1. Consistent with findings from studies on other elasmobranch species, we found significant intraspecific variability in reported life history traits of C. amblyrhynchos. However, contrary to what others have reported, we did not find consistent patterns in life history variability as a function of biogeography or fishing. Ultimately, the substantial, but not yet predictable variability in life history traits observed for C. amblyrhynchos across its geographic range suggests that regional management may be necessary to set sustainable harvest targets and to recover this and other shark species globally.


Frisk, Miller, and Fogarty (2001) length at maturity
Frisk, Miller, and Fogarty [1] quantified the relationship between body size (total length) and length at maturity and age at maturity for 150 elasmobranch species including requiem sharks.
Length at maturity L m was significantly related to maximum length L max " = 0.70 "() + 3.29. (1.1) The linear relationship between L m and L max is particularly strong for individuals with L max < 200 cm, which includes C. amblyrhynchos.

Francis (1988) growth model
The Francis [2] formulation of the von Bertalanffy growth function (VBGF) for tag-recapture data describes the expected growth from a fish of initial length L over some time period Δ : where < and = are the mean annual growth increments of a species at reference lengths and (which should be chosen to include a substantial proportion of by the tagging data within their range). We set Δ =1 and standardized growth to an annual timestep. Parameters < and = can be used to estimate the conventional parameters @ and k of the VBGF by the equations 3) The Francis model is flexible in that it allows the addition of additional parameters. Assuming that the growth of a shark of length L over some time period is normally distributed with mean and standard deviation , then growth variability can be described using a single parameter v where = . (2.4) If this mean-variance relationship results in inadequate model fit, then additional parameters can be introduced [2], but this was not necessary for our data. Outliers can also bias growth model parameters, but may represent true values that should not necessarily be discarded. The contamination probability p can be added to ensure that extreme data points have minimal effect on growth parameters (as long as outliers are somewhat rare). Finally, mean m and standard deviation s of measurement error in ∆ can be modeled, and the log likelihood function can be rewritten as R is the range of observed growth increments M and the likelihood is summed over all observed growth increments. We estimated the model using the grotag function with limited memory, bound-constrained BFGS maximization in the fishmethods package [3] to find the set of parameters that maximizes .

Jolly-Seber annual survival ( )
Royle and Dorazio [4] formulated the Jolly-Seber (JS) for capture-recapture data as a restricted dynamic occupancy model where individuals can be in one of three states: "not yet entered", "alive", "dead" [5]. Transitions between these states are determined by the ecological processes entry and survival, which are estimated. We were interested in the probability of annual survival sampling available in the R package rjags [6].

Hoenig (1983) total mortality (Z)
The Hoenig [7] method of estimating total mortality (Z) is parameterized around the observed relationship between longevity (T max ) and mortality. The equation takes the form = + ( "() ), (4.1) where a and b are fitted parameters, and T max is the maximum observed age in the catch. The equation is parameterized separately for teleost fishes (a = 1.46, b = -1.01) and cetaceans (a = 0.941, b = -0.873), both of which have been used for sharks [8,9]. We assumed that Z was equal to natural mortality M given the absence of fishing at Palmyra. T max was estimated as the time required to attain >99% of @ as T max = 5•Ln(2)•k -1 [61], using the k estimate from equation 2.3.