Modernising fish and shark growth curves with Bayesian length-at-age models

Age and growth of the blue shark Prionace glauca (Linnaeus, 1758) in the Ecuadorian Pacific: Bayesian multi-models

The blue shark Prionace glauca plays a critical role as a predator in marine ecosystems but is threatened by by-catch. To obtain more precise biological data, a Bayesian approach was used, and 536 vertebrae samples collected during 1 year at the landing stage called "Playita Mía" Manta, Ecuador, were analysed. The objective was to estimate the age and growth parameters of the species. The size of the specimens varied between 116 and 310 cm in total length (TL). Using a Bayesian approach based on the Markov Chain Monte Carlo (MCMC) method, growth parameters were evaluated. The von Bertalanffy model was the one that best fitted the data and provided more adequate estimates (females: L ∞ = 325.50 cm,L 0 = 53.23 cm, and k = 0.12 years; males: L ∞ = 331.47 cm,L 0 = 51.59 cm, k = 0.12 years -1; combined sexes: L ∞ = 329.65 cm,L 0 = 53.64 cm, k = 0.11 year-1). The results indicated that females and males have a similar growth, and that the species has a slow growth. Further studies using multi-model Bayesian approaches and covering a broader range of sizes in the Pacific Ocean are suggested. These studies will provide crucial information for the management and conservation of this species.

Size structure, age, and growth of the blue shark, Prionace glauca (Linnaeus, 1758) in southern Brazil

The blue shark is a highly migratory species with a worldwide distribution, making it susceptible to multiple fishing fleets across the globe. In southern Brazil, it is an important target, comprising up to 40% of the total biomass landed by the commercial surface longline fleet. This study aims to contribute to a better understanding of how the species uses the region and to update its life-history information available for future assessments. Over five consecutive years (2018-2022) of landings and onboard monitoring, we gathered size data and vertebral samples to describe the species size composition in the region, as well as its seasonal and interannual variability and to update estimated life-history parameters. The results showed that southern Brazil is mainly inhabited by large juvenile males that arrive during winter (July-September) and stay until spring (October-December), when their frequency decreases. Small adult males are present throughout the year but in higher frequencies during summer. A small number of adult females are present with higher frequencies during spring and summer, which decreases during the austral autumn and winter. Some variability in the presence of each life stage was observed among years. The estimated life-history parameters were as follows: L∞: 255.02 cm fork length (FL), k: 0.20, L0:35.68 cm FL for males; L∞: 246.47 cm FL, k: 0.23, L0:36.77 cm FL for females; and L∞: 269.58 cm FL, k: 0.18, L0:36.19 cm FL for pooled sexes. However, the estimated values must be cautiously interpreted, as the obtained samples cannot be construed as representative of the entire harvested stock due to the lack of consistent presence of some life stages in the study region.

Life-history traits of an exploited skate: The short-tail yellownose skate Zearaja brevicaudata (Chondrichthyes: Rajiformes)

The short-tail yellownose skate, Zearaja brevicaudata, occurs off southern Brazil and along the Argentine continental shelf, including waters surrounding the Islas Malvinas and the upper slope, and is very frequently caught by trawl fisheries throughout its range. The age, growth, and maturity of Z. brevicaudata were investigated using 204 individuals collected by commercial fishing vessels from northern Argentina, between March 2016 and September 2019. Age was determined on a sample comprising vertebrae from 151 individuals, 60 males, ranging in size from 391 to 956 mm total length (TL), and 91 females, ranging in size from 324 to 1060 mm TL. Maximum ages determined for males and females were 22 and 29 years, respectively. A Bayesian framework was employed with a set of three candidate models to estimate growth parameters (von Bertalanffy, Gompertz, and Logistic). The von Bertalanffy model had the best fit, and the sexes showed undistinguishable growth parameters. For sexes combined, derived growth mean parameters (± S.D.) were L∞ = 1081 mm ± 64.34 mm, k = 0.09 ± 0.01 years-1, and L0 = 248 mm ± 23.52 mm. The age at maturity was estimated at 13.15 and 14.66 years for males and females, respectively.

The role of predation risk in structuring life-history traits of crucian carp (Carassius carassius) in a series of small boreal lakes

Predation is a major evolutionary force determining life-history traits in prey by direct and indirect mechanisms. This study focuses on life-history trait variation in crucian carp (Carassius carassius), a species well known for developing a deep body as an inducible morphological defence against predation risk. Here, the authors tested variation in growth and reproductive traits in 15 crucian carp populations in lakes along a predation risk gradient represented by increasingly efficient predator communities. Lakes were located in south-eastern Norway and were sampled in summer 2018 and 2019. The authors expected crucian carp to attain higher growth rate, larger size, and later age at maturity with increasing predation risk. In the absence of predators, they expected high adult mortality, early maturity and increased reproductive effort caused by strong intraspecific competition. They found that the life-history traits of crucian carp were clearly related to the presence of piscivores: with increasing predation risk, fish grew in body length and depth and attained larger asymptotic length and size at maturity. This growth was evident at young age, especially in productive lakes with pike, and it suggests that fish quickly outgrew the predation window by reaching a size refuge. Contrary to the authors' predictions, populations had similar age at maturity. High-predation lakes also presented low density of crucian carp. This suggests that fish from predator lakes may experience high levels of resource availability due to reduced intraspecific competition. Predation regulated life-history traits in crucian carp populations, where larger size, higher longevity and size at maturity were observed in lakes with large gaped predators.

Downsized: gray whales using an alternative foraging ground have smaller morphology

Describing individual morphology and growth is key for identifying ecological niches and monitoring the health and fitness of populations. Eastern North Pacific ((ENP), approximately 16 650 individuals) gray whales primarily feed in the Arctic/sub-Arctic regions, while a small subgroup called the Pacific Coast Feeding Group (PCFG, approximately 212 individuals) instead feeds between northern California, USA and British Columbia, Canada. Evidence suggests PCFG whales have lower body condition than ENP whales. Here we investigate morphological differences (length, skull, and fluke span) and compare length-at-age growth curves between ENP and PCFG whales. We use ENP gray whale length-at-age data comprised of strandings, whaling, and aerial photogrammetry (1926-1997) for comparison to data from PCFG whales collected through non-invasive techniques (2016-2022) to estimate age (photo identification) and length (drone-based photogrammetry). We use Bayesian methods to incorporate uncertainty associated with morphological measurements (manual and photogrammetric) and age estimates. We find that while PCFG and ENP whales have similar growth rates, PCFG whales reach smaller asymptotic lengths. Additionally, PCFG whales have relatively smaller skulls and flukes than ENP whales. These findings represent a striking example of morphological adaptation that may facilitate PCFG whales accessing a foraging niche distinct from the Arctic foraging grounds of the broader ENP population.

Re-estimation of juvenile Isurus oxyrinchus growth in the Mexican Pacific through a multimodel inference approach and verification of growth band periodicity

An update of the age and growth for juveniles of the short fin mako shark (I. oxyrinchus) from the Mexican Pacific is presented, based on the analysis of growth band counts from dorsal vertebrae of 198 individuals [110 females, 74-231 cm of total length (TL) and 88 males, 72-231 cm TL) caught during 2008-2018. New available information on vertebral growth band periodicity (biannual deposition in juveniles) and the convenience of using vertebrae form the dorsal region over the cervical region to count growth bands, as well as a multimodel approach, were used. The von Bertalanffy (VB) growth model, Gompertz, logistic and two parameters of VB (2-VB) were fitted to the length-at-age. Only ages ≤6 years were used for the fitting of the models and their performance was compared with the small-sample bias-corrected form of the Akaike information criterion (AICc), their differences ( ∆ i ) and weights ( w i ). Following a multimodel inference approach, the model averaged asymptotic length ( L ¯ inf ), length-at-age 0 ( L ¯ 0 ) and their unconditional standard error ( SE ¯ ), were estimated for each sex scenario using the three-parameter version of each model. The precision of growth band counts was acceptable for the different methods used and by two different readers. The centrum edge analysis (CEA) and marginal increment analysis (MIA) did not support the hypothesis of biannual band pair formation for juveniles, likewise for adults the periodicity could not be verified due to the small sample of large animals. Age was estimated assuming the formation of two pairs of growth bands per year during the first 5 years and one pair of bands per year afterwards considering direct validation information. The estimated ages in years ranged from 0-14 for females and 0-6 for males. The Kimura likelihood ratio test showed no differences in the growth curves of juveniles by sex (P > 0.05). According to the AICc, the 2-VB model better fitted the length-at-age data for combined sexes (L_inf  = 386.4 cm, k = 0.12 years^-1 , L₀  = 70 cm). The model averaged L ¯ inf and L ¯ 0 were 378.3 cm ( SE ¯ = 64.5 ) and 69.5 cm ( SE ¯ = 6.3 ), respectively. The growth parameters determined for juveniles of I. oxyrinchus are similar to those estimated in other regions, showing relatively fast growth rate as previously reported, medium longevity in comparison to other shark species and natural mortality close to that reported in the last stock assessment for the North Pacific Ocean. These life-history parameters should be considered to evaluate the population in the region and to develop better fishery management and conservation measures.

Further description of the Kerguelen sandpaper skate Bathyraja irrasa (Rajiformes: Arhynchobatidae) based on additional specimens, including egg cases and embryos

Adult specimens, additional juvenile specimens, egg cases and embryos were used to provide a more detailed anatomical description of the Kerguelen sandpaper skate Bathyraja irrasa, a species of skate endemic to the Kerguelen Plateau and listed as Vulnerable by the IUCN Red List of Threatened Species. The morphological and meristic data reveal a relatively high level of intraspecific variation, mostly related to size. Egg cases are described for the first time and were shown to vary in colour and fouling depending on the length of time spent in the marine environment. Embryos removed from egg cases represent all stages of embryonic development in this species and include the largest embryo recorded for this species, i.e., 230 mm total length (L_T ), which increases the range of size at hatching of B. irrasa to 178-230 mm L_T . A number of morphometric and meristic characters varied ontogenetically in B. irrasa, in particular relative tail length, number of tail thorns in the median row and the size of orbits. This study highlights the importance of describing intraspecific variation in species and the importance of egg cases to taxonomic and biological research on oviparous species.

Age, growth and maturity of Southern Ocean skates (Bathyraja spp.) from the Kerguelen Plateau

Three species of Southern Ocean skates, Bathyrajaeatonii,Bathyrajairrasa and Bathyrajamurrayi, are commonly caught as incidental by-catch in fisheries around Heard Island and McDonald Islands of the Kerguelen Plateau. We used length-at-age data to present the species’ life history information (age, growth and maturity for the first-time). Length- and age-at-maturity analyses revealed that B.irrasa matured at > 6 years old and > 1000 mm total length (TL), which was older and larger than B.murrayi (> 5 years old and > 400 mm TL) but similar to B.eatonii (> 5 years old and > 900 mm). We fitted growth models using a multi-model Bayesian framework. Our findings support the assumption that B.irrasa is slow growing and late maturing compared to B.eatonii and B.murrayi, consequently putting it at greater risk to fishery-induced increases in mortality compared to other species (e.g., B.murrayi). This is the first-time age and growth has been estimated for these species, however sample sizes for B.murrayi and B.eatonii were small and hence growth models should be interpreted with caution. Our results represent vital information for population projection models and can therefore assist in the development and/or revision of current by-catch limits to inform ongoing management strategies and conservation efforts.

Growth estimates of young-of-the-year broadnose sevengill shark, Notorynchus cepedianus, a top predator with poorly calcified vertebrae

The broadnose sevengill shark, Notorynchus cepedianus (Péron, 1807), is a large marine top predator in temperate coastal ecosystems. Some aspects of its life history have been determined, but its growth pattern is yet to be fully understood. The authors used a multi-modelling approach and a sensitivity test to estimate growth parameters from young-of-year (YOY) length data collected off San Antonio Cape (SAC), Argentina, a critical habitat in the Southwest Atlantic Coastal Zone (SACZ). The best selected model, a sex-combined logistic growth model, estimated an asymptotic length (L_∞ ) of 92.58 cm TL (95% C.I.: 86.48-105.89 cm), a growth coefficient (K) of 0.006818 days ^-1 (95% C.I.: 0.004948-0.008777) and a size at birth (L₀ ) of 40.73 cm. The predicted annual growth (i.e., L_{1 -} L₀ ) was 43.2 cm TL. Males had smaller L₀ , higher K and achieved larger sizes after 1 year. The YOY in SAC attained a larger L₁ and grew faster than their Australian and South African wild counterparts. The consistent year-round presence of YOY in the SAC highlights the importance of this area as a pupping ground and potential nursery for N. cepedianus; this has direct implications for the allocation of research and management effort for the conservation of this species in the Southwest Atlantic.

Modelling Fish Growth with Imperfect Data: The Case of Trachurus picturatus

Growth modelling is essential to inform fisheries management but is often hampered by sampling biases and imperfect data. Additional methods such as interpolating data through back-calculation may be used to account for sampling bias but are often complex and time-consuming. Here, we present an approach to improve plausibility in growth estimates when small individuals are under-sampled, based on Bayesian fitting growth models using Markov Chain Monte Carlo (MCMC) with informative priors on growth parameters. Focusing on the blue jack mackerel, Trachurus picturatus, which is an important commercial fish in the southern northeast Atlantic, this Bayesian approach was evaluated in relation to standard growth model fitting methods, using both direct readings and back-calculation data. Matched growth parameter estimates were obtained with the von Bertalanffy growth function applied to back-calculated length at age and the Bayesian fitting, using MCMC to direct age readings, with both outperforming all other methods assessed. These results indicate that Bayesian inference may be a powerful addition in growth modelling using imperfect data and should be considered further in age and growth studies, provided relevant biological information can be gathered and included in the analyses.

Age, growth, maturity and extinction risk of an exploited and endangered skate, Atlantoraja castelnaui, from off Uruguay and northern Argentina

The spotback skate Atlantoraja castelnaui (Arhynchobatidae) is a large and threatened skate species subjected to fishing pressure, endemic to the Southwest Atlantic that occurs from Rio de Janeiro, Brazil, to San Jorge Gulf, Argentina. The age, growth, age at maturity and the maximum intrinsic rate of population increase r_max of A. castelnaui were studied using 152 specimens collected from off Uruguay and north Argentina (35°-42° S), between June 2013 and February 2020. Vertebrae from 143 individuals were used for ageing (females: n = 83, size range 404-1300 mm total length, TL; males: n = 60, size range 400-1270 mm TL). Maximum ages determined for females and males were 30 and 28 years, respectively. To fit growth models, non-linear and Bayesian estimation approaches were considered. For the first approach, a set of four candidate growth (size-at-age) models were fitted: three-parameter von Bertalanffy, two-parameter von Bertalanffy with fixed L₀ , Gompertz and Logistic. In the second approach, von Bertalanffy, Gompertz and Logistic were fitted. For non-linear estimation, model selection indicated that the entire set of candidate growth models were supported by the data. The von Bertalanffy was selected as the best model for Bayesian estimation. There were no differences in growth between sexes. For the sexes combined, the von Bertalanffy growth model by Bayesian method was considered the most adequate to describe the growth of A. castelnaui (growth mean parameters ± S.D.: L_∞  = 1210.29 ± 40.68 mm; k = 0.12 ± 0.01 years^-1 ; L₀  = 179.20 ± 11.62 mm). The age at maturity was estimated at 16.21 and 14.04 years for females and males, respectively. The maximum intrinsic rate of population increase r_max was estimated as 0.252 years^-1 . Life-history traits and r_max provided in the present study suggest that this species has a relatively low productivity and may be vulnerable to an intense fishing pressure.