Validated age and growth estimates are important for constructing age-structured population dynamic models of chondrichthyan fishes, especially those which are exploited. We review age and growth studies of chondrichthyan fishes, using 28 recent studies to identify areas where improvements can be made in describing the characteristics of ageing structures (both traditional and novel) utilized to estimate ages of sharks, rays, and chimaeras. The topics identified that need consistency include the: (1) terminology used to describe growth features; (2) methods used to both verify and validate age estimates from chondrichthyan calcified structures, especially edge and marginal increment analyses; and (3) the functions used to produce and describe growth parameters, stressing the incorporation of size at birth (L 0 ) and multiple functions to characterize growth characteristics, age at maturity and longevity.

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Summary 1.Precise estimates of demographic rates are key components of population models used to predict the effects of stochastic environmental processes, harvest scenarios and extinction probability. 2. We used a 12-year photographic identification library of whale sharks from Ningaloo Reef, Western Australia to construct Cormack-Jolly-Seber (CJS) model estimates of survival within a capture-mark-recapture (CMR) framework. Estimated survival rates, population structure and assumptions regarding age at maturity, longevity and reproduction frequency were combined in a series of age-classified Leslie matrices to infer the potential trajectory of the population. 3. Using data from 111 individuals, there was evidence for time variation in apparent survival ( φ ) and recapture probability ( p ). The null model gave a @ of 0·825 (95% CI: 0·727-0·893) and p = 0·184 (95% CI: 0·121-0·271). The model-averaged annual @ ranged from 0·737 to 0·890. There was little evidence for a sex effect on survival. 4. Using standardized total length as a covariate in the CMR models indicated a size bias in φ . Ignoring the effects of time, a 5-m shark has a @ = 0·59 and a 9 m shark has @ = 0·81. 5. Of the 16 model combinations considered, 10 (63%) indicated a decreasing population ( λ < 1). For models based on age at first reproduction ( α ) of 13 years, the mean age of reproducing females at the stable age distribution ( A ) ranged from 15 to 23 years, which increased to 29-37 years when α was assumed to be 25. 6. All model scenarios had higher total elasticities for non-reproductive female survival [ E ( s nr )] compared to those for reproductive female survival [ E ( s r )]. 7. Assuming relatively slow, but biologically realistic, vital rates ( α = 25 and biennial reproduction) and size-biased survival probabilities, our results suggest that the Ningaloo Reef population of whale sharks is declining, although more reproductive data are clearly needed to confirm this conclusion. Combining relatively precise survival estimates from CMR studies with realistic assumptions of other vital rates provides a useful heuristic framework for determining the vulnerability of large oceanic predators for which few direct data exist.

Age and growth estimates for the shortfin mako, Isurus oxyrinchus, derived from vertebral centra of 258 specimens (118 males, 140 females), ranging in size from 64 to 340 cm fork length (FL) were compared with data from 22 tagrecaptured individuals (74-193 cm FL) and length-frequency data from 1822 individuals (1035 males, 787 females; 65-215 cm FL). Annual bandpair deposition, confirmed by a concurrent bomb radiocarbon validation study, was used as the basis for band interpretation. Validation was further confirmed with a tetracycline-injected male shortfin mako recaptured after being at liberty off South Africa for 1 year and aged at 18 years. Growth rates from tag-recapture analysis (GROTAG) were higher than those derived from vertebral annuli and were only available from sharks up to 193 cm FL at recapture. Modal length-frequency data were used to verify the first four age classes.Growth curves were fit using both von Bertalanffy and Gompertz models. The 3-parameter version of the von Bertalanffy growth function produced the most biologically reasonable values for males, based on observed data (L ¥ = 253 cm FL, K = 0.125 year -1 (estimated longevity = 21 year), and L 0 = 72 cm). The 3-parameter version of the Gompertz growth function produced the most biologically reasonable estimates, for females (L ¥ = 366 cm FL, K = 0.087 year -1 (estimated longevity = 38 year) and L 0 = 88 cm. Males and females were aged to 29 (260 cm FL) and 32 years (335 cm FL), respectively. Both sexes grew similarly to age 11 (207 cm FL, 212 cm FL for males and females, respectively) when the curve leveled in males and continued to rise in females. Age at 50% maturity was estimated at 8 years for males (185 cm FL) and 18 years for females (275 cm FL). The species grows slower, matures later and has a longer life span than previously reported in North Atlantic waters.

Results of demographic analyses of four species of elasmobranchs were compared by use of life-history tables, Leslie matrices, and several stage-based matrix models. Dasyatis violacea, with few age classes, was used to demonstrate the basics of Leslie-matrix and stage-based matrix model calculations. The demography for Carcharias taurus, with a 2-year reproductive cycle, produced higher potential population growth using actual fertility rather than effective annual fertility. The demography for Alopias pelagicus, with continuous reproduction, produced higher potential population growth for a birth-flow than a birth-pulse population. The Carcharodon carcharias example demonstrated only a small difference in potential population growth between step-like and logistic fertility functions. Stage-based models with fixed stage duration produced potential population growths identical to those obtained from a life-history table or Leslie matrix, but the net reproductive rates and generation times differed. Stage-based models with few stages had different dynamics with shorter recovery to the stable age distribution; they underestimated the elasticity of juvenile survival and overestimated the elasticity of adult survival, suggesting that interpretation should be cautious. Elasticity analyses were used to estimate the number of juvenile age classes that could be fished and have the same effect on potential population growth as fishing all the adult age classes.