Research Article |
Corresponding author: Rainer Froese ( rfroese@geomar.de ) Academic editor: Wojciech Piasecki
© 2022 Rainer Froese.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Froese R (2022) Estimating somatic growth of fishes from maximum age or maturity. Acta Ichthyologica et Piscatoria 52(2): 125-133. https://doi.org/10.3897/aiep.52.80093
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Growth in body size is a key life-history trait that has coevolved and is interlinked with maturation, maximum age, mortality, generation time, and the intrinsic rate of population growth. Growth parameters are therefore required inputs in the majority of assessment models used in conservation or fisheries management. However, because of the difficulties involved in the proper aging of individuals, growth parameters are unknown for the vast majority of species. Here, two new data-limited methods are presented to estimate somatic growth from maximum length combined with either length or age at maturation or with maximum age. A comparison with existing growth parameters of fishes (Actinopterygii and Elasmobranchii) shows that the estimates of the new methods fall within the range of established methods. The new methods apply to species with indeterminate growth, such as fishes or invertebrates, and were used here to produce the first growth parameter estimates for 110 species of fishes.
age at first maturity, asymptotic length, maximum age, maximum length recruitment, von Bertalanffy growth equation
The speed by which organisms increase in body size determines how fast they reach maturity and maximum size, i.e., the adult size and age range. The mean age of parents when their offspring are born defines generation time, which itself is linked to the intrinsic rate of population growth (
The first-principle equation that is most widely used to estimate growth is the one proposed by
Lt = L∞ (1 − e−K (t − t0))) [Eq 1]
The hypothetical age at zero length t0 typically has a negative value which is small compared to the maximum age. Different values of t0 shift the growth curve along the age-axis without changing the values of L∞ or K. For the sake of simplicity in data-limited methods, t0 is assumed here to be zero and is omitted from the subsequent equations. Also, for easy comparison among species, length in fish is measured in centimeters and age in years, which implies that K has the unit year–1. Note that the type of length, such as total length (TL), fork length (FL), standard length (SL), pre-anal length, or body width (WD) does not affect the estimate of K as long as the species grows roughly isometrically and thus changes its proportions during growth only in a minor way.
While measuring lengths in one of the above length types is straightforward in most species of fish, determining age e.g. from counting rings in hard structures such as scales, otoliths, vertebrae or spines is more demanding and prone to error. As a result, sufficiently large and reliable data sets for fitting Equation 1 [Eq 1] are missing for the majority of species (
Data on asymptotic length (L∞), maximum length (Lmax), maximum age (tmax), and length (Lm) and age (tm) at first maturity were extracted from FishBase 08/2021 (
Solving Equation 1 for K and omitting t0 gives Equation 2
[Eq 2]
To estimate growth from the maximum length and maximum age, Equation 3 replaces age t with reported maximum age for a population and assumes that tmax is reached and reported at about 95% of L∞ (
[Eq 3]
If several estimates of tmax are available for a population, e.g., as the oldest fish observed during periods of one or 5 years over the last 20–40 years, then these numbers can be used to derive a mean estimate of tmax with 95% confidence limits. Since the main source of uncertainty in Equation 3 is the estimate of tmax, its lower and upper confidence limits can be inserted in the equation to derive approximate confidence limits for K. Alternatively, plausible ranges of uncertainty can be derived by assuming that maximum age will be observed and reported in individuals with a body length between 90% and 99% of L∞. Replacing 0.95 in Equation 3 with 0.90 and 0.99, respectively, then yields plausible ranges of K between 2.3/tmax and 4.6/tmax. For example, for an observed tmax = 15 years, Equation 3 would predict K = 0.20. Applying the alternative rules for uncertainty gives plausible ranges of K as 0.15–0.31.
To estimate growth from length and age at maturation, Equation 4 replaces age t in Equation 2 with the age where individuals have reached sexual maturity (tm), Lt with the corresponding length Lm, and L∞ with Lmax/0.95
[Eq 4]
Similar to Equation 3, approximate 95% confidence limits of K can be obtained from observed confidence limits of tm or Lm. Alternatively, plausible ranges of K can be obtained from the observation that in species that mature e.g., on average at 3 years of age, some mature already at two and some at four years of age. Based on this common observation, a typical uncertainty range in the estimate of tm can be construed as 0.67tm–1.33tm. For example, for observed values of tm = 3 years, Lm = 40 cm and Lmax = 110 cm, Equation 4 would predict K = 0.14. Setting tm to 0.67*3 and 1.33*3, respectively, gives a plausible range for K of 0.11–0.21.
Equation 4 can be used more generally for any case where a combination of length and age is known, such as an unusually large year class with a strong visible peak in length-frequency plots, see the example below.
Estimates of K resulting from the new methods are shown with only two significant decimals to avoid the impression of unrealistic high precision, given that these are data-limited methods with wide ranges of uncertainty.
All data and code used in this study are available from https://oceanrep.geomar.de/id/eprint/55916.
Growth estimates derived from maximum length and length and age at maturation. The MATURITY table in FishBase 08/2021 (
The variability in Fig.
List of fifteen species with first estimates of growth parameters (L∞, K), as derived from age (tm) and length (Lm) at first maturity and maximum length (Lmax), with indication of family, locality of the population, and type of length measurements. TL stands for total length, SL for standard length, and WD for body width. Plausible ranges of K were calculated from an assumed uncertainty range of tm of +/– 33%. See the supplement data (https://oceanrep.geomar.de/id/eprint/55916) and the MATURITY table in FishBase (
Family | Species | Locality | Sex | t m | L m | L max | Type | L∞ | K | 95% CL |
---|---|---|---|---|---|---|---|---|---|---|
Acipenseridae | Acipenser dabryanus | Yangtze River | F | 9 | 106 | 250 | TL | 263 | 0.06 | 0.04–0.09 |
Ariidae | Sciades herzbergii | Ceará | F | 2.5 | 50.8 | 94.2 | TL | 98.9 | 0.29 | 0.22–0.43 |
Bothidae | Bothus constellatus | Gulf of Tehuantepec | F | 5.5 | 10.1 | 15.7 | TL | 16.5 | 0.17 | 0.13–0.26 |
Characidae | Gymnocharacinus bergii | Valcheta | M | 1 | 3.7 | 7.5 | TL | 7.88 | 0.63 | 0.48–0.95 |
Valcheta | F | 1 | 3.8 | 7.5 | TL | 7.88 | 0.66 | 0.49–0.98 | ||
Cichlidae | Chaetobranchus flavescens | Rupununi River | F | 1 | 17 | 26 | TL | 27.3 | 0.97 | 0.73–1.46 |
Clupeidae | Nematalosa erebi | Murray River | U | 2.5 | 19.9 | 39 | TL | 41 | 0.27 | 0.20–0.40 |
Gaidropsaridae | Ciliata septentrionalis | Severn estuary and Bristol Channel | M | 1 | 7.18 | 12.2 | SL | 12.8 | 0.82 | 0.62–1.23 |
Gobiidae | Knipowitschia longecaudata | Caspian, Azov, and Black Sea basins | U | 0.75 | 2 | 5 | TL | 5.25 | 0.64 | 0.48–0.96 |
Mobulidae | Mobula birostris | Indo–Pacific | F | 6 | 445 | 680 | WD | 714 | 0.16 | 0.12–0.24 |
Muraenolepididae | Muraenolepis microps | South Georgia | M | 4 | 24 | 35 | TL | 36.8 | 0.26 | 0.20–0.40 |
Notopteridae | Chitala chitala | Ganga River | F | 3 | 75.5 | 122 | TL | 128 | 0.30 | 0.22–0.44 |
Pentacerotidae | Pentaceros wheeleri | Emperor Seamount | M | 6 | 27 | 44 | TL | 46.2 | 0.15 | 0.11–0.22 |
Emperor Seamount | F | 7 | 28 | 44 | TL | 46.2 | 0.13 | 0.10–0.20 | ||
Salmonidae | Stenodus nelma | Arctic Ocean | Mx | 12 | 75 | 150 | SL | 158 | 0.05 | 0.04–0.08 |
Triakidae | Mustelus griseus | Taiwan | F | 5.65 | 72 | 101 | TL | 106 | 0.20 | 0.15–0.30 |
Triakidae | Mustelus punctulatus | Mediterranean | F | 1.95 | 95 | 190 | TL | 200 | 0.33 | 0.25–0.50 |
Comparison of growth parameters L∞ and K derived with various data-rich methods (gray dots) and from maximum length and length and age at maturation (black dots with indication of plausible ranges), in log-log space. The double-dots in some of the species are caused by records with different length or age at maturation for the same population and the same maximum length.
Growth estimates derived from maximum length and maximum age. The POPCHAR table in FishBase 08/2021 contained 744 records with reported maximum age and the corresponding maximum length in the population, for, altogether, 573 species (
The variability in Fig.
List of 105 species with first estimates of growth parameters (L∞, K), as derived from maximum age (tmax) and maximum length (Lmax), with indication of family, locality of the population, sex, and type of length measurements, where TL stands for total length, SL for standard length, FL for fork length, and WD for body width. The plausible ranges of K (CL) were derived from assuming that tmax was observed between 0.9 and 0.99 L∞. See the supplement data (https://oceanrep.geomar.de/id/eprint/55916) and the POPCHAR table in FishBase (
Family | Species | Locality | Sex | t max | L max | L∞ | Type | K | CL |
---|---|---|---|---|---|---|---|---|---|
Acipenseridae | Acipenser sinensis | Yangtze River (below Gezhouba Dam) | F | 33 | 346 | 363.3 | TL | 0.09 | 0.07–0.14 |
Adrianichthyidae | Oryzias sinensis | East Asia | U | 1 | 3 | 3.15 | SL | 3.00 | 2.30–4.60 |
Agonidae | Hemitripterus bolini | Bering Sea and Aleutian Islands | U | 23 | 83 | 87.2 | TL | 0.13 | 0.10–0.20 |
Alepocephalidae | Alepocephalus bairdii | Southern Brittany | Mx | 38 | 93 | 97.7 | SL | 0.08 | 0.06–0.12 |
Aphaniidae | Aphanius baeticus | Spain | U | 2 | 3 | 3.15 | SL | 1.50 | 1.15–2.30 |
Bagridae | Coreobagrus ichikawai | Tagiri River | M | 3 | 10.8 | 11.3 | SL | 1.00 | 0.77–1.53 |
Bagridae | Coreobagrus ichikawai | Tagiri River | F | 4 | 9.35 | 9.8 | SL | 0.75 | 0.58–1.15 |
Bathymasteridae | Bathymaster derjugini | Sea of Okhotsk | U | 8 | 18.1 | 19.0 | TL | 0.37 | 0.29–0.58 |
Bathymasteridae | Bathymaster signatus | N Kurils and SE Kamchatka | F | 9 | 36 | 37.8 | TL | 0.33 | 0.26–0.51 |
Berycidae | Centroberyx gerrardi | Southern Australia | U | 71 | 66 | 69.3 | TL | 0.04 | 0.03–0.06 |
Blenniidae | Salaria fluviatilis | Mediterranean (Europe) | U | 5 | 13 | 13.7 | SL | 0.60 | 0.46–0.92 |
Carcharhinidae | Carcharhinus galapagensis | Circumtropical | F | 24 | 370 | 388 | TL | 0.12 | 0.10–0.19 |
Carcharhinidae | Negaprion brevirostris | Eastern Pacific to Eastern central Atlantic | F | 25 | 320 | 336 | TL | 0.12 | 0.09–0.18 |
Catostomidae | Ictiobus cyprinellus | Ontario | U | 26 | 157 | 165 | TL | 0.12 | 0.09–0.18 |
Cebidichthyidae | Cebidichthys violaceus | Oregon–California | U | 18 | 76 | 79.8 | TL | 0.17 | 0.13–0.26 |
Centrarchidae | Ambloplites rupestris | Ontario | U | 13 | 43 | 45.2 | TL | 0.23 | 0.18–0.35 |
Characidae | Astyanax mexicanus | Tinaja cave | U | 8 | 9 | 9.5 | TL | 0.37 | 0.29–0.58 |
Clupeidae | Alosa killarnensis | Lake Lough Lene | U | 5 | 20 | 21 | SL | 0.60 | 0.46–0.92 |
Clupeidae | Clupeonella abrau | Lake Abrau | U | 2 | 8 | 8.4 | SL | 1.50 | 1.15–2.30 |
Clupeidae | Nematalosa erebi | Lower Murray River | U | 10 | 48 | 50.4 | SL | 0.30 | 0.23–0.46 |
Cobitidae | Cobitis elongatoides | Danube River | F | 5 | 13 | 13.7 | SL | 0.60 | 0.46–0.92 |
Cobitidae | Cobitis ohridana | Moraca River basin | F | 3.5 | 8.3 | 8.7 | TL | 0.86 | 0.66–1.31 |
Cottidae | Gymnocanthus herzensteini | Primorye | F | 17 | 42 | 44.1 | TL | 0.18 | 0.14–0.27 |
Cottidae | Hemilepidotus jordani | Bering Sea and Aleutian Islands | U | 30 | 65 | 68.3 | TL | 0.10 | 0.08–0.15 |
Cyprinidae | Barbus caninus | Europe | U | 5 | 25 | 26.3 | SL | 0.60 | 0.46–0.92 |
Cyprinidae | Gymnocypris firmispinatus | Anning River | M | 9 | 16.3 | 17.1 | TL | 0.33 | 0.26–0.51 |
Cyprinidae | Gymnocypris firmispinatus | Anning River | F | 13 | 24.2 | 25.4 | TL | 0.23 | 0.18–0.35 |
Cyprinidae | Luciobarbus graellsii | Spain | U | 16 | 65 | 68.3 | SL | 0.19 | 0.14–0.29 |
Cyprinidae | Onychostoma barbatulum | Taiwan | U | 7 | 26 | 27.3 | TL | 0.43 | 0.33–0.66 |
Fundulidae | Fundulus heteroclitus | East coast of North America | U | 4 | 10 | 10.5 | SL | 0.75 | 0.58–1.15 |
Galaxiidae | Galaxias olidus | Australia: Goulburn, Torbreck, Howqua, and Taggerty rivers | U | 4 | 13 | 13.7 | SL | 0.75 | 0.58–1.15 |
Gobiidae | Acentrogobius pflaumii | Swan–Canning estuary | Mx | 3.9 | 9.6 | 10.1 | TL | 0.77 | 0.59–1.18 |
Gobiidae | Amblygobius phalaena | Pioneer Bay, Orpheus I. | M | 1.17 | 10.2 | 10.7 | TL | 2.56 | 1.97–3.93 |
Gobiidae | Amblygobius phalaena | Pioneer Bay, Orpheus I. | F | 1.17 | 10.5 | 11.0 | TL | 2.56 | 1.97–3.93 |
Gobiidae | Babka gymnotrachelus | Black, Azov, and Caspian Sea basins | U | 5 | 16 | 16.8 | SL | 0.60 | 0.46–0.92 |
Gobiidae | Economidichthys trichonis | Lake Trichonis, Lysimachia | U | 1.8 | 2.5 | 2.6 | SL | 1.66 | 1.28–2.56 |
Gobiidae | Knipowitschia caucasica | Eurasia | U | 2 | 5 | 5.3 | SL | 1.50 | 1.15–2.30 |
Gobiidae | Knipowitschia croatica | Bosnia–Herzegovina, Croatia | U | 2 | 4.7 | 4.9 | SL | 1.50 | 1.15–2.30 |
Gobiidae | Knipowitschia longecaudata | Caspian, Azov, and Black Sea basin | U | 2 | 4 | 4.2 | SL | 1.50 | 1.15–2.30 |
Gobiidae | Knipowitschia milleri | Acheron River (lower stretch) | U | 2 | 2.6 | 2.7 | SL | 1.50 | 1.15–2.30 |
Gobiidae | Stiphodon percnopterygionus | Okinawa Island | F | 2 | 3.5 | 3.7 | SL | 1.50 | 1.15–2.30 |
Gobiidae | Stiphodon percnopterygionus | Okinawa Island | M | 2 | 3 | 3.15 | SL | 1.50 | 1.15–2.30 |
Gobiidae | Trimma benjamini | Helen Reef (Hotsarihie Reef), Hatohobei State | U | 0.39 | 2.29 | 2.4 | SL | 7.68 | 5.90–11.8 |
Gobiidae | Valenciennea muralis | Pioneer Bay, Orpheus I. | M | 1 | 11.6 | 12.2 | TL | 3.00 | 2.30–4.60 |
Gobionidae | Romanogobio albipinnatus | Northern Caspian basin (Volga, Ural) | U | 5 | 11.5 | 12.1 | SL | 0.60 | 0.46–0.92 |
Gobionidae | Romanogobio belingi | Eastern Europe | U | 5 | 11.5 | 12.1 | SL | 0.60 | 0.46–0.92 |
Gobionidae | Romanogobio benacensis | Italy, Slovenia | U | 4 | 10 | 10.5 | SL | 0.75 | 0.58–1.15 |
Gobionidae | Romanogobio ciscaucasicus | Caspian Sea | U | 6 | 11 | 11.6 | SL | 0.50 | 0.38–0.77 |
Gobionidae | Romanogobio kesslerii | Europe | U | 5 | 11 | 11.6 | SL | 0.60 | 0.46–0.92 |
Gobionidae | Romanogobio tanaiticus | Don River drainage | U | 5 | 10 | 10.5 | SL | 0.60 | 0.46–0.92 |
Gonostomatidae | Cyclothone braueri | Rockall Trough, NE Atlantic (near 55°N, 12°W) | F | 1.25 | 3.8 | 3.99 | SL | 2.40 | 1.84–3.68 |
Heptapteridae | Pimelodella kronei | Southeastern region of Brazil | U | 15 | 15 | 15.8 | TL | 0.20 | 0.15–0.31 |
Hexagrammidae | Pleurogrammus azonus | Northern Sea of Japan | U | 12 | 50 | 52.5 | TL | 0.25 | 0.19–0.38 |
Latridae | Latris lineata | Tasmania | M | 29 | 81.5 | 85.6 | FL | 0.10 | 0.08–0.16 |
Latridae | Latris lineata | Tasmania | F | 43 | 95 | 99.8 | FL | 0.07 | 0.05–0.11 |
Lestidiidae | Lestrolepis japonica | Kagoshima Bay | U | 4 | 19 | 19.9 | SL | 0.75 | 0.58–1.15 |
Leuciscidae | Anaecypris hispanica | Guadiana drainage (Spain, Portugal) | U | 3 | 6 | 6.3 | SL | 1.00 | 0.77–1.53 |
Leuciscidae | Pelasgus minutus | Europe | U | 6 | 5 | 5.25 | SL | 0.50 | 0.38–0.77 |
Leuciscidae | Tropidophoxinellus hellenicus | Peloponnese | U | 4 | 9.3 | 9.8 | SL | 0.75 | 0.58–1.15 |
Liparidae | Liparis fabricii | Barents Sea | U | 6 | 21 | 22.1 | TL | 0.50 | 0.38–0.77 |
Liparidae | Palmoliparis beckeri | Pacific off the North Kuril Islands | U | 8 | 42 | 44.1 | TL | 0.37 | 0.29–0.58 |
Lutjanidae | Etelis radiosus | Lihir Island group (seamount) | U | 14 | 70 | 73.5 | SL | 0.21 | 0.16–0.33 |
Lutjanidae | Paracaesio stonei | Lihir Island group (seamount) | U | 15 | 37 | 38.9 | SL | 0.20 | 0.15–0.31 |
Mobulidae | Mobula birostris | India | U | 20 | 680 | 714 | WD | 0.15 | 0.12–0.23 |
Mobulidae | Mobula japanica | Punta Arenas de la Ventana (24°03′N, 109°49′W), SE Baja California | Mx | 14 | 240 | 252 | WD | 0.21 | 0.16–0.33 |
Muraenidae | Muraena augusti | Northeastern Central Atlantic | Mx | 17.9 | 90 | 94.5 | TL | 0.17 | 0.13–0.26 |
Myctophidae | Diaphus suborbitalis | Suruga Bay | U | 2.5 | 6.7 | 7.0 | SL | 1.20 | 0.92–1.84 |
Myctophidae | Diaphus theta | South Kurile region | U | 6 | 11.7 | 12.3 | SL | 0.50 | 0.38–0.77 |
Myctophidae | Lampanyctus macdonaldi | Rockall Trough, NE Atlantic (near 55°N, 12°W) | U | 6 | 13.5 | 14.2 | SL | 0.50 | 0.38–0.77 |
Oreosomatidae | Allocyttus niger | Tasmanian waters | U | 100 | 47 | 49.4 | TL | 0.03 | 0.023–0.046 |
Oreosomatidae | Allocyttus niger | Chatham Rise and Puysegur-Snares | U | 153 | 45.5 | 47.8 | TL | 0.02 | 0.015–0.030 |
Oreosomatidae | Allocyttus verrucosus | Western coasts of Australia | U | 100 | 42 | 44.1 | TL | 0.03 | 0.023–0.046 |
Oreosomatidae | Neocyttus rhomboidalis | Australia (all states) | U | 100 | 47 | 49.4 | TL | 0.03 | 0.023–0.046 |
Pentacerotidae | Pentaceropsis recurvirostris | Esperance (33°45′S, 121°55′E), Western Australia | M | 43 | 55.3 | 58.1 | TL | 0.07 | 0.05–0.11 |
Pentacerotidae | Pentaceropsis recurvirostris | Esperance (33°45′S, 121°55′E), Western Australia | F | 55 | 64.5 | 67.7 | TL | 0.05 | 0.04–0.08 |
Pentanchidae | Galeus melastomus | Rockall Trough | M | 7 | 64 | 67.2 | TL | 0.43 | 0.33–0.66 |
Percichthyidae | Nannoperca australis | Australia | U | 5 | 8.5 | 8.9 | TL | 0.60 | 0.46–0.92 |
Percichthyidae | Nannoperca variegata | Australia | U | 4 | 6.2 | 6.5 | TL | 0.75 | 0.58–1.15 |
Percichthyidae | Percilia irwini | Andalién and Biobío rivers basins | Mx | 4 | 9.6 | 10.1 | TL | 0.75 | 0.58–1.15 |
Percidae | Gymnocephalus schraetser | Danube River drainage | U | 15 | 25 | 26.3 | SL | 0.20 | 0.15–0.31 |
Polynemidae | Polydactylus macrochir | Northwestern Australia | U | 20 | 170 | 178 | FL | 0.15 | 0.12–0.23 |
Polyprionidae | Stereolepis gigas | California (off Santa Cruz Island) | U | 62 | 220 | 231 | TL | 0.05 | 0.04–0.07 |
Pomacentridae | Stegastes rectifraenum | Lower Baja Peninsula, Gulf of California | U | 11 | 12 | 12.6 | SL | 0.27 | 0.21–0.42 |
Salmonidae | Coregonus danneri | Lake Traunsee | U | 6 | 22 | 23.1 | SL | 0.50 | 0.38–0.77 |
Salmonidae | Coregonus lucinensis | Lake Breiter Luzin | U | 6 | 16 | 16.8 | SL | 0.50 | 0.38–0.77 |
Salmonidae | Coregonus renke | Germany | U | 7 | 29 | 30.5 | SL | 0.43 | 0.33–0.66 |
Salmonidae | Coregonus vandesius | UK | U | 10 | 20 | 21 | SL | 0.30 | 0.23–0.46 |
Salmonidae | Salmo ferox | British Isles | U | 23 | 80 | 84 | SL | 0.13 | 0.10–0.20 |
Salmonidae | Salvelinus alpinus | Circumpolar | U | 32 | 110 | 115 | SL | 0.09 | 0.07–0.14 |
Salmonidae | Salvelinus gracillimus | Lake Leynavatn, on Streymoy Island | U | 8 | 35 | 36.8 | SL | 0.37 | 0.29–0.58 |
Salmonidae | Salvelinus murta | Lake Thingvalla | U | 18 | 48 | 50.4 | SL | 0.17 | 0.13–0.26 |
Salmonidae | Salvelinus struanensis | Loch Rannoch and Loch Ericht | U | 8 | 36 | 37.8 | SL | 0.37 | 0.29–0.58 |
Salmonidae | Salvelinus thingvallensis | Lake Thingvalla | U | 17 | 24 | 25.2 | SL | 0.18 | 0.14–0.27 |
Salmonidae | Salvelinus youngeri | UK Scotland | U | 9 | 25 | 26.3 | SL | 0.33 | 0.26–0.51 |
Schindleriidae | Schindleria praematura | nearshore (27°10′S, 109°20′W) | U | 0.25 | 2.09 | 2.19 | SL | 11.98 | 9.20–18.4 |
Sciaenidae | Cynoscion othonopterus | Colorado River delta, Gulf of California, Sonora | Mx | 8 | 101 | 106 | TL | 0.37 | 0.29–0.58 |
Scorpaenidae | Scorpaena loppei | Balearic Islands | M | 5 | 12.8 | 13.4 | TL | 0.60 | 0.46–0.92 |
Serranidae | Cephalopholis miniata | Kuwait | U | 26 | 34 | 35.7 | TL | 0.12 | 0.09–0.18 |
Serranidae | Cephalopholis miniata | Great Barrier Reef | U | 30 | 47.5 | 49.9 | TL | 0.10 | 0.08–0.15 |
Serranidae | Epinephelus bleekeri | Kuwait | U | 24 | 65 | 68.3 | TL | 0.12 | 0.10–0.19 |
Serranidae | Epinephelus polylepis | Kuwait | U | 41 | 74 | 77.7 | TL | 0.07 | 0.06–0.11 |
Serranidae | Plectropomus pessuliferus | Red Sea | U | 19 | 96 | 100.8 | TL | 0.16 | 0.12–0.24 |
Somniosidae | Somniosus microcephalus | Greenland | F | 392 | 502 | 527 | TL | 0.01 | 0.006–0.012 |
Sparidae | Calamus brachysomus | North Peru | F | 15 | 44 | 46.2 | TL | 0.20 | 0.15–0.31 |
Sparidae | Calamus brachysomus | North Peru | M | 15 | 51 | 53.6 | TL | 0.20 | 0.15–0.31 |
Sparidae | Sparodon durbanensis | Tsitsikamma and Bird Is. | M | 26 | 95 | 99.8 | FL | 0.12 | 0.09–0.18 |
Squalidae | Squalus megalops | Canary Islands | F | 32 | 88 | 92.4 | TL | 0.09 | 0.07–0.14 |
Syngnathidae | Phyllopteryx taeniolatus | Aquarium of the Pacific, Long Beach, CA | U | 3.5 | 38.6 | 40.5 | SL | 0.86 | 0.66–1.31 |
Syngnathidae | Syngnathus abaster | Eastern Atlantic | U | 4 | 19 | 19.9 | SL | 0.75 | 0.58–1.15 |
Tincidae | Tinca tinca | Eurasia | U | 20 | 60 | 63 | SL | 0.15 | 0.12–0.23 |
Triakidae | Mustelus californicus | Eastern Pacific | F | 12 | 163 | 171 | TL | 0.25 | 0.19–0.38 |
Trichomycteridae | Trichomycterus itacarambiensis | Olhos d’Água Cave, Itacarambi, Mina Gerais | U | 7 | 8.3 | 8.7 | SL | 0.43 | 0.33–0.66 |
Valenciidae | Valencia hispanica | Catalonia | M | 3 | 6.7 | 7.0 | TL | 1.00 | 0.77–1.53 |
Valenciidae | Valencia hispanica | Catalonia | F | 4 | 7.1 | 7.5 | TL | 0.75 | 0.58–1.15 |
Valenciidae | Valencia letourneuxi | Albania/western Greece | U | 3 | 7 | 7.4 | SL | 1.00 | 0.77–1.53 |
Comparison of new and previous median estimates of K, where n is the number of estimates for the same species.
Parameter | K | |
---|---|---|
from Lm and tm | from tmax | |
n new | 153 | 628 |
Median new | 0.174 | 0.200 |
95% confidence limits | 0.149–0.231 | 0.187–0.230 |
n previous | 880 | 2814 |
Median previous | 0.19 | 0.243 |
95% confidence limits | 0.18–0.19 | 0.235–0.250 |
The growth parameter estimates derived with the new methods proposed in this study were applicable to a wide range of species, sizes, and habitats (Tables
If data for maturation and maximum age are available for a given population and are deemed equally reliable, then Equations 3 and 4 can be combined
[Eq 5]
For example, maximum age (tmax = 20 years) and maturation (tm = 6 years, Lm = 445 cm WD, Lmax = 680 cm WD) data are available for the Giant manta Mobula birostris from the Indo–Pacific (Tables
The method of estimating growth from the maximum length and a smaller length for which the corresponding age is known is not limited to length and age at maturation (Equation 4) but can be applied to all cases where age is known for a certain length. This also means that Equation 4 is applicable to early maturing species, such as many gadoids, as well as late maturing species, such as sharks. For example, cod (Gadus morhua) in the western Baltic Sea had a string of years (2014–2020) with very bad reproductive success, however, with one intermediate year (2016) where reproductive success was close to the mean value of previous years (
Overall, the growth estimates derived with the new methods presented in this study appear suitable for consideration and preliminary guidance in applications for conservation or management (Figs
Journals should accept growth estimates performed with the new methods as new knowledge if they are the first for a given species. In order to facilitate the conservation and management of natural resources, FishBase (
Thanks are due to the FishBase team for compiling the data behind the Tables and Figures in this study. Thanks are also due to Daniel Pauly and Henning Winker for useful comments on the manuscript. This study was supported by the German Federal Nature Conservation Agency (BfN) with funds from the Federal Ministry of the Environment, Nature Conservation and Nuclear Safety (BMU), under grant agreement FKZ 3521532201.