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): 125133. https://doi.org/10.3897/aiep.52.80093

Growth in body size is a key lifehistory 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 datalimited 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 firstprinciple equation that is most widely used to estimate growth is the one proposed by
L_{t} = L_{∞} (1 − e^{−K (t − t0)})) [Eq 1]
The hypothetical age at zero length t_{0} typically has a negative value which is small compared to the maximum age. Different values of t_{0} shift the growth curve along the ageaxis without changing the values of L_{∞} or K. For the sake of simplicity in datalimited methods, t_{0} 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), preanal 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 (L_{max}), maximum age (t_{max}), and length (L_{m}) and age (t_{m}) at first maturity were extracted from FishBase 08/2021 (
Solving Equation 1 for K and omitting t_{0} gives Equation 2
$K=\frac{\mathrm{ln}\left(1\frac{{L}_{t}}{{L}_{\infty}}\right)}{t}$ [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 t_{max} is reached and reported at about 95% of L_{∞} (
$K=\frac{\mathrm{ln}(10.95)}{{t}_{\mathrm{max}}}=\frac{3.0}{{t}_{\mathrm{max}}}$ [Eq 3]
If several estimates of t_{max} 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 t_{max} with 95% confidence limits. Since the main source of uncertainty in Equation 3 is the estimate of t_{max}, 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/t_{max} and 4.6/t_{max}. For example, for an observed t_{max} = 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 (t_{m}), L_{t} with the corresponding length L_{m}, and L_{∞} with L_{max}/0.95
$K=\frac{\mathrm{ln}\left(10.95\frac{{L}_{\mathrm{m}}}{{L}_{\mathrm{max}}}\right)}{{t}_{\mathrm{m}}}$ [Eq 4]
Similar to Equation 3, approximate 95% confidence limits of K can be obtained from observed confidence limits of t_{m} or L_{m}. 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 t_{m} can be construed as 0.67t_{m}–1.33t_{m}. For example, for observed values of t_{m} = 3 years, L_{m} = 40 cm and L_{max} = 110 cm, Equation 4 would predict K = 0.14. Setting t_{m} 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 lengthfrequency 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 datalimited 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 (t_{m}) and length (L_{m}) at first maturity and maximum length (L_{max}), 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 t_{m} 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 datarich methods (gray dots) and from maximum length and length and age at maturation (black dots with indication of plausible ranges), in loglog space. The doubledots 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 (t_{max}) and maximum length (L_{max}), 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 t_{max} 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 PuysegurSnares  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 L_{m} and t_{m}  from t_{max}  
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
$K=\frac{\left(\frac{3.0}{{t}_{\mathrm{max}}}\frac{\mathrm{ln}\left(10.95\frac{{L}_{\mathrm{m}}}{{L}_{\mathrm{max}}}\right)}{{t}_{\mathrm{m}}}\right)}{2}$ [Eq 5]
For example, maximum age (t_{max} = 20 years) and maturation (t_{m} = 6 years, L_{m} = 445 cm WD, L_{max} = 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.