Age and growth of the sandbar shark, Carcharhinus plumbeus, in Hawaiian waters through vertebral analysis

Age and growth estimates were determined for the sandbar shark, Carcharhinus plumbeus, from Oahu, Hawaii in the central Pacific Ocean. Age estimates were obtained through vertebral centra analysis of 187 sharks. We verified our age estimates through marginal increment analysis of centra and oxytetracycline marking methods of at liberty sandbar sharks. Sizes of sampled sharks ranged from 46 to 147 cm pre-caudal length. Four growth models were fitted to length-at-age data; two forms of the von Bertalanffy growth model, the Gompertz growth model, and a logistic growth model. Males and females exhibited statistically significant differences in growth, indicating that females grow slower and attain larger sizes than males. Growth parameter estimates revealed slower growth rates than previously estimated (based on captive specimens) for Hawaiian sandbar sharks. The von Bertalanffy growth model using empirical length-at-birth provided the best biological and statistical fit to the data. This model gave parameter estimates of L _∞ = 138.5 cm PCL and k = 0.12 year⁻¹ for males and L _∞ = 152.8 cm PCL, k = 0.10 year⁻¹ for females. Male and female sandbar sharks mature at approximately 8 and 10 years of age, respectively.     

Age,growth and reproductive biology of the silky shark,Carcharhinus falciformis,and the scalloped hammerhead,Sphyrna lewini,from the northwestern Gulf of Mexico

Synopsis The silky shark, Carcharhinus falciformis, and scalloped hammerhead, Sphyrna lewini, represent >80% of the shark by-catch of the winter swordfish/tuna longline fishery of the northwestern Gulf of Mexico. This catch represents a potential supplemental fishery, yet little is known of the life histories of the two species. This report relates reproductive biology data to age and growth estimates for 135 C. falciformis and 78 S. lewini. Unlike other regional populations, C. falciformis in the Gulf of Mexico may have a seasonal 12 month gestation period. Males mature at 210–220 cm TL (6–7 yr); females at >225 cm TL (7–9 yr). Application of age at length data for combined sexes produced von Bertalanffy growth model parameter estimates of L_∞ = 291 cm TL, K = 0.153, t₀ = −2.2 yr. Adult male S. lewini outnumbered adult females in catches because of differences in the distributions of the sexually segregated population. Males mature at 180 cm TL (10 yr); females at 250 cm TL (15 yr). von Bertalanffy parameter estimates for combined sexes of this species were L_∞ = 329 cm TL, K = 0.073, t_o = −2.2 yr.     

Age and growth of the bonnethead shark, Sphyrna tiburo, from northwest Florida, with comments on clinal variation

Age and growth rates of the bonnethead shark, Sphyrna tiburo, from northwest Florida were estimated from vertebrae collected between October 1992 and October 1995. The von Bertalanffy growth equation was fit to male and female vertebral age data. Initial growth was rapid (≈ 200 mm TL) for both sexes from age 0–1. At age 2 growth slowed for males but continued for females. Similar to many species of sharks, females grew slower than males (K = 0.28 and K = 0.69, respectively) but attained a larger maximum size (L_∞=1226 and L_∞=897). Maximum age was estimated in males and females to be 8+ and 12+ years, respectively. Growth of young-of-year sharks was 21 to 30 mm TL per month determined by three different methods. A comparison of age and growth estimates from populations at more southerly latitudes suggest that clinal variation in total length may be evident among bonnethead sharks in the Gulf of Mexico with females reaching larger sizes in northern areas as compared to south Florida. This revised version was published online in July 2006 with corrections to the Cover Date.     

Age, growth and reproduction of the humpback red snapper Lutjanus gibbus off Ishigaki Island, Okinawa

The humpback red snapper Lutjanus gibbus (Lutjanidae) is an important species for fisheries in the Kagoshima and Okinawan region of Japan. The present study estimated the age, growth and reproduction of this lutjanid species in the waters around Ishigaki Island, southern part of Okinawa. An opaque zone was formed on the otolith every year, and this formation correlated with their spawning season; these zones were identified as annual rings. Maximum ages of 21 and 24 years were observed for males and females, respectively. The von Bertalanffy growth parameters clarifying the age–fork length relationship were as follows: L _∞ = 390.5 mm, K = 0.210 year⁻¹ and t ₀ = −1.88 year for males, and L _∞ = 303.4, K = 0.256 year⁻¹ and t ₀ = −3.05 year for females. The main spawning season was estimated as between May and October, since greater values of gonadosomatic index for females as well as maturation oocytes and/or postovulatory follicles were observed during those six months.     

Extraordinary growth in tiger sharks Galeocerdo cuvier from the South Atlantic Ocean

Two tagged‐and‐recaptured tiger sharks Galeocerdo cuvier, measuring 172 and 304 cm total length (L_T) and at age 0·75 and 3·50 years, exhibited unmatched growth rates of 118·4 and 55·5 cm year^?1, respectively. The larger fish was nearly mature, indicating that G. cuvier off Brazil could mature considerably earlier than conspecifics from other regions.     

Growth and mortality of bigeye tuna <Emphasis Type="Italic">Thunnus obesus</Emphasis> (Scombridae) in the eastern and central tropical Pacific Ocean

Biological parameters such as age, growth and age (or size) at maturity are vital for stock assessment and management. Aging is essential in yielding such information. However, limited aging studies have been conducted for large tropical pelagic species in the eastern and central tropical Pacific Ocean. The objective of this study is to conduct a length frequency analysis for estimating growth and mortality of bigeye tuna in the eastern and central tropical Pacific Ocean using samples from the Chinese longline fishery during February to November 2006. The von Bertalanffy growth parameters of asymptotic fork length L _∞ and growth coefficient k were estimated at L _∞ = 207.4 cm fork length, k = 0.23 year^-1, and theoretical age at zero length t ₀ = −0.40 year. The total mortality rate (Z) was estimated to be 0.60; the fishing mortality rate (F) and the natural mortality rate (M) were 0.25 year^-1 and 0.35 year^-1, respectively. The exploitation rate (E) was 0.16. This study provides the estimates of growth and mortality rate for bigeye tuna in the eastern and central tropical Pacific Ocean, which can be used as biological input parameters in further stock evaluations in this region. However, age analysis, further validation of the age composition and stock structure are needed for future studies.     

Age and growth of Schizopygopsis younghusbandi younghusbandi in the Yarlung Zangbo River in Tibet, China

Schizopygopsis younghusbandi younghusbandi is an endemic species whose distribution is restricted to the middle reaches of the Yarlung Zangbo River, being one of the most important commercial fishes in this area. Age and growth of 606 specimens captured between October 2002 and April 2005 were studied. The range in standard length (L) was 65.7–387.3 mm and total weight (W) was 3.3–772.0 g. The relationship between L and W was W = 0.000909L^2.2493 for males and W = 0.000259L^2.4781 for females. Age, determined from anal scales and lapillus otoliths, ranged from 3 to 18 years. The parameters of von Bertalanffy growth functions, estimated by back-calculated length, were L_￥ = 442.7mm  LL_\infty = 442.7mm\;L, k = 0.0738 year⁻¹ and t ₀  = −1.4 year for males, and L_￥ = 471.4mm  LL_\infty = 471.4mm\;L, k = 0.0789 year⁻¹ and t ₀ = 0.2 year for females. Males and females exhibited statistically significant differences in growth. χ ²-test indicated that von Bertalanffy growth functions could well describe the growth of S. y. younghusbandi. The longevities were 39.2 and 38.2 years for males and females, respectively. Growth inflexion points were 10.2 and 12.0 years for males and females, respectively, but 84.8% of the captures were at the smaller ages. So conservation and management schemes for this population should be considered urgently. In addition, we found that populations from the upstream of the Lhasa River, the downstream of the Lhasa River and the middle reaches of the Yarlung Zangbo River showed statistically significant differences in growth patterns.     

Toxicity of dodecylpyridinium and cetylpyridinium clorides against phosphate-accumulating bacterium

The antibacterial effect of cationic surfactants against the pure culture of phosphate (P)-accumulating bacterium Acinetobacter junii was investigated. The estimated EC₅₀ values of the N-dodecylpyridinium chloride (DPC) for growth inhibition was 1.4±0.5 × 10⁻⁶ mol L⁻¹ and for the inhibition of the P-uptake rates 7.3±2.6 × 10⁻⁵ mol L⁻¹. The estimated EC₅₀ values of the N-cetylpyridinium chloride (CPC) for growth inhibition was 4.9±1.3 × 10⁻⁷ mol L⁻¹ and for the inhibition of the P-uptake rates 7.7±2.9 × 10⁻⁶ mol L⁻¹. This suggests the importance of controlling the amounts of cationic surfactants in influent of the wastewater treatment systems in order to avoid the possible failure of the biological P removal from wastewaters.     

Age and growth estimates of the bull shark,Carcharhinus leucas,from the northern Gulf of Mexico

Synopsis Length at age and growth rates for 59 bull sharks, Carcharhinus leucas, collected from the northern Gulf of Mexico were estimated from the band patterns formed seasonally in the vertebral centra. The combined age at length data for both sexes were applied to a von Bertalanffy growth model producing parameter estimates of L = 285 cm TL, K = .076, t₀ = –3.0 yr. Lengths at age for males and females were similar except that males did not attain as great a length as females. Growth was apparently slow and varied among individuals, but in general, was estimated to be 15–20 cm yr^–1 for the first five years, 10 cm yr^–1 for years 6–10, 5–7 cm yr^–1 for years 11–16, and less than 4–5 cm yr^–1 thereafter. Males mature at 210–220 cm TL or 14–15 yr of age; females mature at>225 cm TL or 18+ yr of age. The largest male (245 cm TL) was 21.3 yr old; the largest female (268 cm TL) was 24.2 yr old.     

Age, growth, mortality and sex ratio of sand smelt, Atherina boyeri Risso, 1810 (Pisces: Atherinidae) in the estuary of the Mala Neretva River (middle-eastern Adriatic, Croatia)

The present study investigated the age, growth, mortality and morphometry of the sand smelt, Atherina boyeri, in the Mala Neretva River estuary (mid‐eastern Adriatic Sea). The study of scale annuli showed that the population is up to 4 years of age. However, most sand smelt are in their first and second year; the numbers of older individuals are very low because they migrate upstream and are heavily fished. The von Bertalanffy parameters for the total sample of sand smelt were found to be L_∞ = 13.5 cm, K = 0.37 year^?1 and t₀ = ?0.97. Overall total mortality was estimated at 1.81 year^?1, natural mortality was 0.90 year^?1 and fishing mortality was 0.91 year^?1.     

Growth and production of the bivalve <Emphasis Type="Italic">Macoma balthica</Emphasis> (Linnaeus, 1758) (Cardiida: Tellinidae) in the southeastern part of the Baltic Sea

The growth and production of the Baltic clam Macoma balthica in the southeastern part of the Baltic Sea were studied. The shell length of M. balthica reached 23.5 mm, the maximum age was 13+ years. The linear growth was described by the von Bertalanffy equation for shallow-water area (depths 9–40 m): L _τ = 23.99(1 − e ^{−0.1293(τ − (−0.9578))}), and for the deep-water area (41–81 m): L _τ = 20.61(1 − e ^{−0.1813(τ − (−0.5608))}). The annual production was lower (25.35 ± 1.72 kJ/m²) in the shallow-water area than in the deep-water area (71.23 ± 4.48 kJ/m²), with values of P _s /B ratio 0.44 and 0.38, respectively.     

Using otoliths to estimate age and growth of a large Australian endemic monocanthid, <Emphasis Type="Italic">Nelusetta ayraudi</Emphasis> (Quoy and Gaimard, 1824)

Nelusetta ayraudi (the ocean leatherjacket) is an endemic Australian monacanthid species distributed from North West Cape (Western Australia) south to southern Queensland. The commercial and recreational fisheries targeting Nelusetta ayraudi have expanded substantially along the coast of New South Wales (NSW) in recent years but there exists little biological information on which to base effective management of this growing fishery. World-wide, only a few studies have aged monacanthids. Of these, researchers have interpreted periodic increments in bony structures such as vertebrae and anterior dorsal spines in preference to those found in otoliths. In this study we estimated age of N. ayraudi by counting growth increments in sectioned otoliths. The periodicity of increment formation was validated using a vital stain, (oxy-tetracycline), injected into young-of-the-year fish. Growth was rapid especially as juveniles with N. ayraudi attaining approximately 220 mm after 1 year and 340 mm after 2 years. No differences in growth rates were detected between sexes or between fish captured at different latitudes (zones). The largest male (605 mm, Total Length—TL) and female (656 mm, TL) were both recorded from northern NSW, with both sexes attaining the maximum age of 6+ years from northern and southern NSW. The von Bertalanffy parameters describing growth for N. ayraudi were L_￥ {L_\infty }  = 591 mm (TL), k = 0.377 year⁻¹ and t _o = −0.247 years.     

Body and scale growth of wild Atlantic salmon smolts during seaward emigration

The relationship between scale and body growth for emigrating Atlantic salmon, Salmo salar, smolts was previously not understood and therefore was examined in this study using mark-recapture techniques. The size of smolts at time of recapture was significantly greater than when marked (P = 0.0002). The growth in length of smolts emigrating 5 km over an average of 20 days was 7.7 ± 6.1 mm per day. Instantaneous somatic growth (G _body) ranged from 7.0 × 10⁻⁴ to 5.1 × 10⁻³ (mean = 2.7 × 10⁻³ ± 1.3 × 10⁻³). The mean number of plus growth circuli present per scale was significantly greater for smolts when recaptured compared to when marked (P = 0.0014). The instantaneous growth rate of scales (G _scale) ranged from 1.4 × 10⁻³ to 11.5 × 10⁻³ (mean = 6.6 × 10⁻³ ± 4.3 × 10⁻³). The relationship between body size and scale radius showed positive allometry rather than isometry. The relationship of G _scale with G _body showed positive allometry indicating that scales grew at a slightly faster rate than the body during the emigratory period.     

Toxicity of anionic and cationic surfactant to Acinetobacter junii in pure culture

The harmful effects of surfactants to the environment are well known. We were interested in investigating their potential toxicity in a pure culture of Acinetobacter junii, a phosphate (P)-accumulating bacterium. Results showed a high acute toxicity of sodium dodecyl sulfate (SDS) and hexadecyltrimethylammonium bromide (HDTMA) against A. junii. The estimated EC₅₀ values of the HDTMA for the inhibition of CFUs in the pure culture of A. junii was 3.27 ± 1.12 × 10⁻⁷ mol L⁻¹ and for the inhibition of the P-uptake rates 2.47 ± 0.51 × 10⁻⁶ mol L⁻¹. For SDS, estimated EC₅₀ values for the inhibition of CFUs in the pure culture of A. junii was 5.00 ± 2.95 × 10⁻⁶ mol L⁻¹ and for the inhibition of the P-uptake rates 3.33 ± 0.96 × 10⁻⁴ mol L⁻¹. The obtained EC₅₀ values in the standardised yeast toxicity test using Saccharomyces cerevisiae were 3.03 ± 0.38 × 10⁻⁴ and 4.33 ± 0.32 × 10⁻⁵ mol L⁻¹ for SDS and HDTMA, respectively. These results emphasized the need to control concentrations of surfactants entering the activated sludge system. The negative effects of these toxicants could greatly decrease populations of P-accumulating bacteria, as well as eukaryotic organisms, inhabiting activated sludge systems, which in turn could result in the decrease of the system efficiency.     

Size, growth and reproductive biology of the giant mudskipper, Periophthalmodon schlosseri (Pallas, 1770), in Malaysian waters

The size, growth and reproductive biology of the giant mudskipper, Periophthalmodon schlosseri, was studied in the inter‐tidal mudflat of a mangrove swamp along a 0.4–0.6 × 5 km stretch of the Sepang coastal waters, Selangor Malaysia. The size ranges of the giant mudskipper specimens caught in the study area were between 10–27.5 cm TL (20.6 ± 3.1 cm) for males and 14.5–28.5 cm TL (21.9 ± 2.3 cm) for females. Male to female sex ratio during the study was 1 : 1.1. The estimated von Bertalanffy growth parameters were L_∞ = 29 cm and K = 1.4 year^?1, with a growth performance index of Ø′ = 3.1. Otolith microstructure analysis revealed a strong correlation (Female: r = 0.920, n = 35; Male: r = 0.943, n = 41, P < 0.05) between the number of daily rings (number of days old) over the respective size ranges of male (8.5–19.5 cm SL) and female fish (11.8–22.3 cm SL). Four maturity stages were described to follow gonadal development based on external features; these stages were further validated through histological examination of the ovary and oocyte diameter measurements. The gonadal development cycle of P. schlosseri was asynchronous, as marked by the random mixture of early stages oocytes (diameter: 70.7 ± 14.9 μm) to matured stages (356.9 ± 20.2 μm), and had a prolonged spawning season extending from June to October. Monthly fluctuation of the gonadosomatic and hepatosomatic indices for this species was highly correlated (r = 0.126, P < 0.05).     

Fine-root mass, growth and nitrogen content for six tropical tree species

Although fine roots might account for 50% of the annual net primary productivity in moist tropical forests, there are relatively few studies of fine-root dynamics in this biome. We examined fine-root distributions, mass, growth and tissue N and C concentrations for six tree species established in 16-year-old plantations in the Caribbean lowlands of Costa Rica in a randomized-block design (n = 4). The study included five native species (Hyeronima alchorneoides, Pentaclethra macroloba, Virola koschnyi, Vochysia ferruginea and Vochysia guatemalensis) and one exotic (Pinus patula). Under all species >60% of the total fine-root mass to 1 m deep was located in the uppermost 15 cm of the soil. Fine-root live biomass and necromass (i.e., the mass of dead fine-roots) varied significantly among species but only within the uppermost 15 cm, with biomass values ranging from 182 g m⁻² in Pinus to 433 g m⁻² in Hyeronima plots, and necromass ranging from 48 g m⁻² in Pinus to 183 g m⁻² in Virola plots. Root growth, measured using ingrowth cores, differed significantly among species, ranging from 304 g m⁻² year⁻¹ in Pinus to 1,308 g m⁻² year⁻¹ in Hyeronima. These growth rates were one to five times those reported for moist temperate areas. Turnover rates of fine-root biomass ranged from 1.6 to 3.0 year⁻¹ in Virola and Hyeronima plots, respectively. Fine-root biomass was significantly and positively correlated with fine-root growth (r = 0.79, P < 0.0001), but did not correlate with fine-root turnover (r = 0.10, P = 0.20), suggesting that fine-root accumulation is a function of growth rate rather than mortality. Fine-root longevity was not correlated (r = 0.20, P = 0.34) and growth was negatively correlated with root N concentration across species (r = −0.78, P < 0.0001), contrary to reported trends for leaves, perhaps because N was relatively abundant at this site.     

Age, Growth Rates, Sex Change and Feeding Habits of Notothenioid Fish Eleginops Maclovinus from the Central-southern Chilean Coast

The róbalo, Eleginops maclovinus, a protandrous hermaphrodite species, is an important component of the ichthyofauna in the coastal areas and estuaries of southern Chile. However, there are many aspects about its life history that are unknown. Three hundred and eighty-three specimens of E. maclovinus (19–79 cm total length, TL) were collected between November 2002 and December 2003 from central-southern Chile. Marginal increment analysis from sagittal otoliths showed a single annual minimum in March, demonstrating that a single growth ring is formed each year. The growth of E. maclovinus was described by the von Bertalanffy growth model by following parameters: L _∞ = 105.4 cm TL, K = 0.08 per year, and t ₀ = −1.03 years. E. maclovinus can live for 10 years. The length and age at which the 50% of the males in the population transformed into females was estimated at ~36 cm TL and ~5-years old. A total of 27 prey items were identified. The most important prey items were the crustaceans Hemigrapsus crenulatus and Emerita analoga associated with estuarial and marine habitats respectively. Ontogenetic changes in the diet were related to the spatial distributional pattern of males (1–4 years old, in the estuary) and females (5–8 years old, in the sea). Also, diet changes are associated with the type of available prey in each habitat occupied, indicating a generalized opportunist strategy.     

Reproduction, growth, mortality and yield of Tilapia mariae Boulenger 1899 (Cichlidae) in a Nigerian rainforest wetland stream

The biology and fisheries of Tilapia mariae, the only tilapiine cichlid fish in the Iba Oku (Uyo, Nigeria) wetland stream was studied. There were more females than males in the population. The smallest sexually mature female fish was 11.0 cm total length (TL) while the size at 50% maturity was 17.1 cm TL. Absolute fecundity (F_e) ranged from 953 to 3200 eggs and was positively correlated with TL. The fish bred year‐round with peaks in November, March–April and July–September. The seasonalized von Bertalanffy growth function (VBGF) was fitted to the 12 consecutive months length–frequency data (n = 2439) to obtain a VBGF with the following parameters: L∞ (asymptotic length) = 30.4 cm TL, K (growth coefficient) = 0.4 year^?1, C (amplitude of growth oscillation) =0.4, and WP (winter point) = 0.9. The seasonalized length‐converted catch curve method gave Z (instantaneous total mortality coefficient) as 1.75 year^?1, M (instantaneous natural mortality coefficient) was 0.99 year^?1 while F (instantaneous fishing mortality coefficient) was 0.76 year^?1 and E (=F/Z the current exploitation rate) was 0.43. Length at first capture (Lc) was 17.7 cm TL. The fish was recruited to the fishery year‐round with two pulses. From the Beverton and Holt relative yield per recruit analysis via the selection ogive procedure, E_max (predicted maximum exploitation rate) was 0.54. The stock was not overexploited, since E < E_max. This study also showed that the fish is an r‐selected species with a few K‐selected traits.     

Population structure,growth and production of the yellow clam <Emphasis Type="Italic">Mesodesma mactroides</Emphasis> (Bivalvia: Mesodesmatidae) from a high-energy,temperate beach in northern Argentina

The yellow clam Mesodesma mactroides (Bivalvia: Mesodesmatidae) was once the most abundant intertidal species on the Atlantic coast of northern Argentina and an important commercial resource in South America. This study of a population inhabiting the intertidal zone of the sheltered-dissipative sandy beach Santa Teresita documents the species’ population biology, including demographic structure, growth and production during December 2004 and December 2006, and adumbrates the critical state of M. mactroides at present. A total of 3,015 M. mactroides were collected and measured, whereas individuals were found with an anterior–posterior shell length between 2 and 64 mm. A von Bertalanffy growth function with an asymptotic length (L _∞) of 85 mm and a growth constant (K) of 0.47 year⁻¹ was established from length–frequency distributions. The longevity of the species is estimated at approximately 6 years, and instantaneous mortality rate was about three times higher than 40 years ago. Besides, this study confirmed that the overall growth performance index (OGP) is habitat-specific and can be used to group M. mactroides and M. donacium from different areas into temperate and upwelling species. Furthermore, OGP is inversely correlated with the latitudinal distribution of Mesodesma populations. The intertidal biomass ranged between 0.06 and 0.07 g AFDM m⁻² year⁻¹. Individual production was observed to be highest at 47 mm length (0.35 g AFDM m⁻² year⁻¹), and annual production ranged between 0.12 and 0.19 g AFDM m⁻² year⁻¹, resulting in productivity values (P/B) between 1.84 and 2.93. The comparison of the results of the present study with those of growth studies conducted on M. mactroides 40 years ago revealed the following considerable differences in the population structure of M. mactroides, indicating the conservation status of this intertidal bivalve as endangered: (1) present growth rates are faster, but that the maximum length attained has decreased, (2) the numbers of individuals per square metre were many times higher in the past than in the present, (3) bivalves from the present work never reached the ‘commercial size’ of 60 mm and (4) 40 years ago, the population of M. mactroides was composed of up to three cohorts, whereas in this study, there was only one single cohort visible.     

Life history characteristics of an invasive cyprinid fish (Carassius gibelio) in Chimaditis Lake (northern Greece)

The life history characteristics of an invasive cyprinid fish, the Prussian carp (Carassius gibelio) were examined in Lake Chimaditis (northern Greece). The population is dominated by females that are able to reproduce gynogenetically. Fish samples were collected using trammel nets from August 2004 to July 2005. Their total length (TL) ranged between 21.9 and 37.0 cm. The length–weight relationship was W = 0.0336TL^2.81 (r² = 0.92, n = 600) and the mean Fulton condition factor exhibited monthly variation from 0.172 (May) to 0.186 (August). According to the annual growth marks present, the lifespan of the Prussian carp in Lake Chimaditis is 6 years. The growth parameters were estimated as L_∞ = 34.46 cm, K = 0.297 year^?1, t₀ = ?1.994 year. Absolute fecundity (F_A) ranged between 26 000 and 176 600 oocytes (mean = 66990) and relative fecundity between 78 and 251 oocytes per gram of total weight (mean = 158). Absolute fecundity increased exponentially with length (F_A = 0.286 × TL^3.66, r² = 0.66) and weight (F_A = 17.93 × W^1.36, r² = 0.73) of the fish.