About 7,000 species of fishes are used by humans for food, sports, the aquarium trade, or are threatened by environmental degradation. However, life history parameters such as growth and size at first maturity, which are important for management, are known for less than 2,000 species. We therefore created a life history ‘Key Facts’ page that strives to provide estimates with error margins of important life-history parameters for all fishes (select a species and click on the Key facts link). It uses the ‘best’ available data in FishBase as defaults for various equations, as explained below. Users can replace these defaults with their own estimates and recalculate the parameters. For most parameters, we present the range of the standard error of the estimate, which contains about 2/3 of the range of the observed values. We will gradually replace these with estimates of the 95% confidence limits, derived from the standardized residuals. We hope the Key Facts will prove useful to managers and conservationists in species-rich and data-poor tropical countries.

Life history parameters

L infinity: This is the length (L_inf) that the fish of a population would reach if they were to grow indefinitely (also known as asymptotic length). It is one of the three parameters of the von Bertalanffy growth function: L_t = L_inf (1 – e ^–K(t-to)); where L_t is the length at age t (see below for definitions of K and t₀). If one or more growth studies are available in FishBase, L_inf of the population with the median Ø’ (see definition below) is taken. Users can click on ‘Growth data’ to see a list of the different estimates of L_inf for different populations, i.e. from different localities, of the species in question. If no growth studies are available, L_inf and the corresponding 95% confidence interval are estimated from maximum length using an empirical relationship between L_inf and L_max (Froese and Binohlan 2000). Users can change the L_inf value and click the Recalculate button to update all parameters depending on L_inf.

K: This is a parameter of the von Bertalanffy growth function (also known as growth coefficient), expressing the rate (1/year) at which the asymptotic length is approached. The default value of K is calculated using the L_inf provided above and a median value of Ø’ = log K + 2 log L_inf (see Pauly et al. 1998) from growth studies available in FishBase for the species. Users can click on the 'Growth data' link to see different estimates of K and Ø’ for different populations. Users can change the value of Ø’ and click the 'Recalculate' button to update the values of K, t₀ (see below), natural mortality, life span, and generation time. If no growth studies but data on L_m and t_m are available for a species, these are used to estimate K from the approximation: K = -ln(1 - L_m / L_inf) / (t_m - t₀). If there are no available growth and maturity data but an estimate of maximum age (t_max) is available, this is used to calculate K from the equation K = 3 / (t_max - t₀). If data for maturity or maximum age are not available in FishBase, users can enter their own estimates to calculate growth. Pauly et al. (1998) have shown that closely related species have similar values of Ø’, even if their L_inf and K values differ. We are working on an option to estimate K, in the absence of data, from the maximum length, and the median Ø’ of species from the same genus or family and in the same climate zone.

t₀: This is another parameter of the von Bertalanffy growth function which is defined as the hypothetical age (in years) the fish would have had at zero length, had their early life stages grown in the manner described by the growth equation¾ which in most fishes is not the case. Basically it is a constant inserted to improve the fit and its effect is to move the whole growth curve sideways along the X-axis without affecting either L_inf or K. Many growth studies use methods that do not provide realistic estimates of t₀ and thus result in ‘relative’ age at length. To improve the estimation of life span and generation time below, we use an empirical equation (Pauly 1979) to estimate a default value for t₀ from L_inf and K. This has the form: log (-t₀) = -0.3922 - 0.2752 log L_inf - 1.038 log K. Users can replace the default value and recalculate life span and age at first maturity.

Natural mortality: The instantaneous rate of natural mortality (M; 1/year) refers to the late juvenile and adult phases of a population and is calculated here from Pauly’s (1980) empirical equation based on the parameters of the von Bertalanffy growth function and on the mean annual water temperature (T), using a re-estimated version that analyzes a larger dataset and provides confidence limits. The Growth data link shows other estimates of M and water temperature. Users can change the values for L_inf, K and annual water temperature and recalculate the value of M. If no estimate of K is available, M is calculated from the preliminary empirical equation: M = 10^(0.566 - 0.718 * log(L_inf) + 0.02 * T (Froese et al. in prep.). Note that the length type for calculating M has to be fork length for scombroids (tuna and tuna-like fishes) and total length for all other fishes. Length is used here mainly as a ‘proxy’ for weight. Thus, natural mortality will be underestimated in eel-like fishes and overestimated in sphere-shaped fishes.

Life span: This is the approximate maximum age (t_max) that fish of a given population would reach. Following Taylor (1958), it is calculated as the age at 95% of L_inf, using the parameters of the von Bertalanffy growth function as estimated above, viz.: t_max = t₀ + 3 / K.

L maturity: This is the average length (L_m) at which fish of a given population mature for the first time. The value and its standard error are calculated from an empirical relationship between length at first maturity and asymptotic length L_inf (Froese and Binohlan 2000). Additional information on maturity, when available, can be displayed by clicking on the Maturity data link.

Age at first maturity: This is the average age at which fish of a given population mature for the first time. It is calculated from the length at first maturity using the inverse of the von Bertalanffy growth function, viz.: t_m = t₀ - ln(1 - L_m / L_inf) / K.

L max. yield: This is the length class (L_opt) with the highest biomass in an unfished population, where the number of survivors multiplied with their average weight reaches a maximum (Beverton 1992). A fishery would obtain the maximum possible yield if it were to catch only fish of this size. Thus, fisheries managers should strive to adjust the mean length in their catch towards this value. They can also use L_m and L_opt to evaluate length-frequency diagrams for signs of growth overfishing (capturing fish before they have realized most of their growth potential) and recruitment overfishing (reducing the number of parents to a level that is insufficient to maintain the stock and hence the fishery; see Fig. 33). If no growth parameters are available, L_opt and its standard error are estimated from an empirical relationship between L_opt and L_inf (Froese and Binohlan 2000). Otherwise, L_opt is estimated from the parameters of the von Bertalanffy growth function and natural mortality as: L_opt = L_inf * (3 / (3 + M/K)) (Beverton 1992).

Relative yield-per-recruit: The main reason why fisheries scientists study the growth of fishes and describe it in the form of the von Bertalanffy growth function, is to perform stock assessment using the yield-per-recruit (Y/R) model of Beverton and Holt (1957). We implemented the simplified version that estimates relative yield-per-recruit (Y’/R) as a function of the mean length at first capture (L_c), L_inf, M, K and the exploitation rate (E; see below) (Beverton and Holt 1964). The value for exploitation rate is set at E = 0.5 as a default, but see discussion below. The default value for L_c is set equal to 40% of L_inf. This is based on a preliminary investigation of the L_c / L_inf ratio for 34 stocks ranging in size from 15 to 184 cm maximum length and which give a range of L_c/L_inf values between 0.15 and 0.74. Users can enter other values for their respective fisheries and calculate the corresponding relative yield-per-recruit. For the respective L_c the corresponding maximum and optimum exploitation rates and fishing mortalities (F) are shown (see next paragraph for discussion). Relative yield-per-recruit values can be transformed to absolute yield-per-recruit in weight by the relationship: Y/R = Y’/R * (W_inf * e^-(M(t_r-t₀))); where W_inf is the asymptotic weight and t_r is the mean age at recruitment. The Y’/R function can be used to estimate the proportion by which the relative yield will increase if the mean size at first capture is closer to L_opt and the exploitation rate is closer to the one producing an optimum sustainable yield (see discussion of exploitation rate below). Note that yield-per-recruit analysis assumes relatively stable recruitment even at very small stock sizes, which is often not the case (see paragraph on resilience / productivity below).

Exploitation rate: This is the fraction of an age class that is caught during the life span of a population exposed to fishing pressure, i.e., the number caught versus the total number of individuals dying due to fishing and other reasons (e.g., Pauly 1984). In terms of mortality rates, the exploitation rate (E) is defined as: E = F / (F + M); where M is the natural mortality rate and F the rate of fishing mortality. Gulland (1971) suggested that in an optimally exploited stock, fishing mortality should be about equal to natural mortality, resulting in a fixed E_opt = 0.5. This value is still used widely but has been shown to overestimate potential yields in many stocks by a factor of 3-4 (Beddington and Cooke 1983). For small tropical fishes with high natural mortality the exploitation rates at maximum sustainable yield (E_MSY) may be unrealistically high. We therefore provide an estimate of the exploitation rate E_opt corresponding to a value that is slightly lower than E_MSY and which is the exploitation rate corresponding to a point on the yield-per-recruit curve where the slope is 1/10^th of the value at the origin of the curve. Users are able to change the value of L_c and calculate the corresponding values of E_MSY and E_opt. We also provide the corresponding values of F_MSY and F_opt through the relationship: F = M * E / (1 – E).

Resilience / productivity: The American Fisheries Society (AFS) has suggested values for several biological parameters that allow to classify a fish population or species into categories of high, medium, low and very low resilience or productivity (Musick 1999; Tab. 1). If no reliable estimate of r_m (see below) is available, the assignment is to the lowest category for which any of the available parameters fits. For each of these categories, AFS has suggested thresholds for decline over the longer of 10 years or three generations. If an observed decline measured in biomass or numbers of mature individuals exceeds the indicated threshold value, the population or species is considered vulnerable to extinction unless explicitly shown otherwise. If one sex strongly limits the reproductive capacity of the species or population, then only the decline in the limiting sex should be considered. We decided to restrict the automatic assignment of resilience categories in the Key Facts page to values of K, t_m and t_max and those records of fecundity estimates that referred to minimum number of eggs or pups per female per year, assuming that these were equivalent to average fecundity at first maturity (Musick 1999). Note that many small fishes may spawn several times per year (we exclude these for the time being) and large live bearers such as the coelacanth may have gestation periods of more than one year (we corrected fecundity estimates for those cases reported in the literature). Also, we excluded resilience estimates based on r_m (see below) as we are not yet confident with the reliability of the current method for estimating r_m. If users have independent r_m or fecundity estimates, they can refer to Table 1 for using this information.

Intrinsic rate of population increase: The intrinsic rate of population growth (r_m; 1/year) has been suggested as a useful parameter to estimate the capacity of species to withstand exploitation (see above). It also largely simplifies the parametrization of Schaefer models for estimating maximum sustainable yield through the relationship MSY = r_m * B_inf / 4, where B_inf is the maximum biomass of a particular species that a given ecosystem can support (Ricker 1975), often corresponding to the original size of the unfished population. Note that if L_c is close to the average length L_r at which juveniles join the parent stock, then the value of F_MSY (above) can be used to estimate r_m from the relationship r_m = 2 * F_MSY (Ricker 1975). It seems that 0.4 * L_inf is a first approximation of L_r. We are exploring this and other options to estimate r_m. One can calculate the time (t_d) in years that it would take a strongly reduced population to double in numbers if all fishing ends, from t_d = ln(2) / r_m.

Generation time: This is the average age (t_g) of parents at the time their young are born. In most fishes L_opt (see above) is the size class with the maximum egg production (Beverton 1992). The corresponding age (t_opt) is a good approximation of generation time in fishes. It is calculated using the parameters of the von Bertalanffy growth function as t_g = t_opt = t₀ - ln(1 - L_opt / L_inf) / K. Note that in small fishes (< 10 cm) maturity is often reached at a size larger than L_opt and closer to L_inf. In these cases, the length class where about 100% (instead of 50%) first reach maturity will contain the highest biomass of spawning fishes, resulting usually in the highest egg production. As an approximation for that length class we assume that most fish will have reached maturity at a length that is slightly longer than L_m, viz.: L_m100 = L_m + (L_inf - L_m) / 4, and calculate generation time as the age at L_m100. This is applied whenever L_m >= L_opt.

Length-weight: This equation can be used to estimate the corresponding wet weight to any given length. The default entry is L_inf, thus calculating the asymptotic weight for the fish of the population in question. The parameters ‘a’ and ‘b’ are taken from data in FishBase with a median value of ‘a’ and with the same length type (TL, SL, FL) as L_inf. Users can click on the ‘Length-weight’ link to see additional data. Users can change the length or the values of ‘a’ and ‘b’ and recalculate the corresponding weight.

Food consumption: The amount of food ingested (Q) by an age-structured fish population expressed as a fraction of its biomass (B) is here presented by the parameter Q/B. FishBase contains over 160 independent estimates of Q/B extracted mainly from Palomares (1991) and Palomares and Pauly (1989) and also from Pauly (1989). These estimates were obtained using Pauly’s (1986) equation, viz.: Q/B = [(dW/dt) / K_1(t)] / [W_tN_td_t] integrated between the age at which fish recruit (t_r) and the maximum age of the population (t_max); where N_t is the number of fishes at age t, W_t their mean individual weight, and K_1(t) their gross food conversion efficiency (= growth increment / food ingested). These Q/B estimates are available in FishBase for only 98 species and for most of these, there is only one Q/B estimate per species. In the few species for which several Q/B values are available, the median Q/B value is taken and a ‘Food consumption’ link is provided to the user for viewing the details of these studies. For other species, Q/B is estimated from the empirical relationship proposed by Palomares and Pauly (1999), viz.: log Q/B = 7.964 – 0.204 log W_inf – 1.965T’ + 0.083A + 0.532h + 0.398d; where W_inf (or asymptotic weight) is the mean weight that a population would reach if it were to grow indefinitely, T’ is the mean environmental temperature expressed as 1000 / (C + 273.15), A is the aspect ratio of the caudal fin indicative of metabolic activity and expressed as the ratio of the square of the height of the caudal fin and its surface area, ‘h’ and ‘d’ are dummy variables indicating herbivores (h=1, d=0), detritivores (h=0, d=1) and carnivores (h=0, d=0). The default value for W_inf is taken either from L_inf and the length-weight relationship (see above) or from W_max (maximum weight ever recorded for the species) when an independent estimate of W_inf is not available in FishBase. Values of A were assigned, for each of the different shapes of caudal fins considered here, using the median A values based on 125 records in FishBase of species with A and caudal fin shape data (from left to right: lunate, forked, emarginate, truncate, round, pointed, double emarginate and heterocercal). Note that five of these eight shapes share the same median value, that which is used as the default A value for the empirical estimation of Q/B when an independent estimate is not available. We are working on a method that will better separate categories of caudal fins. Values of the feeding type indicators ‘d’ and ‘h’ are assigned according to which feeding category the species belongs: detritivore, herbivore, omnivore (default) and carnivore. These categories are determined either from the Main food or the Trophic level (detritivores troph < 2.2; herbivores troph < 2.8; carnivores troph > 2.8). When the default category ‘Omnivore’ is highlighted, Q/B is estimated as the mean of the Q/B values obtained for herbivores and carnivores. The temperature used in the estimation of M above is applied in the empirical estimation of Q/B. The Q/B estimate is automatically recalculated when the tail fin shape and/or the feeding types are changed. The Recalculate button is provided when values of W_inf and A are re-entered, e.g., in cases where no possible/guessed values of W_inf are available in FishBase.

The Key Facts page is still very much evolving and we welcome comments and suggestions for its further improvement to any of the authors.

We thank Eli Agbayani for programming the many changes we requested when developing the Key Facts page. We thank the FishBase Team for assembling the data that allowed us to implement this approach.

You get to the KEY FACTS routine by clicking on the respective button in the BIOLOGY window of the species in question.

On the Internet, you get to the ‘Key Facts’ page by clicking the respective link in the ‘More information’ section of the ‘Species Summary’ page. Note that you can save the Key Facts page to your harddisk and that it will function off-line.