Overcoming the constraints of low sample sizes to produce age and growth data for rare or threatened sharks

Abstract

1. Many sharks are listed as data deficient in assessment and management reports owing to a lack of basic life history data, making decisions about conservation management difficult. As such, the collection of these data is a priority. However, rare or threatened species with populations that are already small can be difficult to sample. Thus there is a need for techniques that permit the use of small sample sizes to provide preliminary information on life history parameters such as age and growth.2. In this study, growth curves were fitted to length-at-age data for five rare or difficult to sample sharks from north-eastern Australia: Carcharhinus coatesi (n = 56), Carcharhinus fitzroyensis (n = 39), Carcharhinus macloti (n = 37), Eusphyra blochii (n = 14) and Hemipristis elongata (n = 14) to provide the first estimates of growth for these species. Vertebral centra from field collections were aged to obtain length-at-age data, and partial age adjustments were used to increase the precision of age estimates. In addition, back calculation techniques were applied to add interpolated data to fill gaps in the growth curves caused by missing length classes.3. Back calculation techniques did not substantially alter the growth curves of the species, which had an even spread of data across size classes (C. fitzroyensis, E. blochii and H. elongata). However, the back calculation techniques considerably improved the growth curves for C. coatesi and C. macloti where juveniles were missing from the samples. 4. Small sample sizes often provide a barrier to conducting growth studies because of the perception that growth estimates can only be obtained from 'large' sample sizes. However, by including individuals across all of the species length classes and maximizing the use of all available exogenous information using back calculation and partial age adjustments, as well as through judicious choice of growth models, it is possible to obtain practical estimates of growth, even when sample sizes are extremely limited.

Growth of Tropical dasyatid Rays Estimated Using a Multi-Analytical Approach

“…We then used nonlinear least squares to compare a range of growth models to determine if a particular model best described the growth data [23]. Estimated ages and observed sizes ( W D ), were fitted to four commonly used models (Table 2): the three-parameter von Bertalanffy (VBGF) [24,25], the modified two-parameter von Bertalanffy (2VBGF) [26],, the logistic (after [9]) and the three-parameter Gompertz (GGF) [27]. Akaike’s information criterion (AIC) with a bias correction (AIC c ) due to small sample sizes (<200) was used to determine the best model fit [9,28].…”

“…Estimated ages and observed sizes ( W D ), were fitted to four commonly used models (Table 2): the three-parameter von Bertalanffy (VBGF) [24,25], the modified two-parameter von Bertalanffy (2VBGF) [26],, the logistic (after [9]) and the three-parameter Gompertz (GGF) [27]. Akaike’s information criterion (AIC) with a bias correction (AIC c ) due to small sample sizes (<200) was used to determine the best model fit [9,28]. Models were ranked according to AIC differences (Δ) where models with a Δ value of between zero – two were considered to have the highest support, while any higher Δ values were considered to have lower support [29].…”

“…While such techniques are generally reliable, accurate and common-place, the acquisition of adequate sample sizes remains a major challenge [6], particularly for those species that are poorly represented in commercial fisheries (the most common method for sourcing specimens) [7] due to gear selectivity [8,9] and/or spatially/temporally restricted sampling [10]. Low sample sizes hinder age and growth studies because they present challenges for the estimation of growth parameters using conventional analytical approaches.…”

Age and growth of the highly exploited narrownose smooth-hound (Mustelus schmitti) (Pisces: Elasmobranchii)

“…To model growth, we used partial ages because they have been shown to be more accurate than rounded ages (Smart et al, 2013). To calculate the partial ages, we used the fraction of the year that had elapsed from the time of birth to the time each individual was collected.…”

Nearshore movement ecology of a medium-bodied shark, the creek whaler Carcharhinus fitzroyensis

“…Teleosts and crustaceans constitute the majority of its diet [20]. Size at birth is approximately 500 mm total length (TL); males mature at approximately 800 mm TL and females 900 mm TL; maximum size is approximately 1,350 mm TL [20,25]. Females give birth every year with one to seven pups per litter (mean = 3.7) [20].…”