Rainer
Froese, Maria Lourdes D. Palomares and Daniel Pauly
m.palomares@cgiar.org
pauly@fisheries.com
World
Wide Web electronic publication, http://www.fishbase.org/Download/keyfacts.zip,
version of 14.2.2000.
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, available on the Internet at http://www.fishbase.org/search.cfm
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 there 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 replace this soon with a more appropriate
estimate giving 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.
Max. length: The maximum size of an organism is a strong
predictor for many life history parameters (e.g. Blueweiss et al. 1978). The
default value used here is the maximum length (Lmax) ever reported
for the species in question, which is in principle available for all species of
fish. If no other data are available, this value is used to estimate asymptotic
length (Linf), length at first maturity (Lm), and length
of maximum possible yield (Lopt), as defined in more detail below.
However, Lmax may be much higher than the maximum length reached by
the fish population being studied by the user, in which case the derived
estimates will be unrealistically high. If additional maximum size estimates
for different areas are available in FishBase, a click on the 'Max. size data'
link displays a list that can be used to replace the Lmax value with
more appropriate estimates. If the 'Recalculate' button in the ‘Max. length’
row is clicked, Linf , Lm and Lopt are
recalculated.
L
infinity: This is the length (Linf)
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: Lt = Linf (1 –
e –K(t-to)); where Lt is the length at age t (see
below for definitions of K and t0). If one or more growth studies
are available in FishBase, Linf 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 Linf for different
populations, i.e. from different localities, of the species in question. If no
growth studies are available, Linf and the corresponding 95%
confidence interval are estimated from maximum length using an empirical
relationship between Linf and Lmax (Froese and Binohlan,
in press). Users can change the Linf
value and click the 'Recalculate' button to update all parameters depending on
Linf.
K: This is a parameter of the von Bertalanffy
growth function (also known as the growth coefficient), expressing the rate
(1/year) at which the asymptotic length is approached. The default value of K
is calculated using the Linf provided above and a median value of
Ø’ = log K + 2 log Linf (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 Lm and tm are available for a species, these are
used to estimate K from the equation: K = ‑ln(1 ‑ Lm / Linf) / (tm
‑ t0). If there are no available growth and maturity
data but an estimate of maximum age (tmax) is available, this is
used to calculate K from the equation K = 3 / (tmax
‑ 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 Linf and K values differ. We are working on an option
to estimate K, in the absence of other ‘relevant’ data, from the median Ø’
of species from the same genus or family and 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 equation - which in most fishes is not the case. Its
effect is to move the whole growth curve sideways along the X-axis without
affecting either Linf 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 Linf and K. This has the form: log (‑t0) =
‑0.3922 ‑ 0.2752 log Linf ‑
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 data set and provides
confidence limits. The 'Growth data' link shows other estimates of M and water
temperature. Users can change the values for Linf, K, and annual
water temperature and recalculate the value of M. If no estimate of K is
available, M is calculated from the empirical equation: M = 10^(0.566
‑ 0.718 * log(Linf) + 0.02 * T (Froese and
Binohlan, in prep.). Note that the length type for calculating M has to be in
fork length for scombrids (tuna and tuna-like fishes) and in total length for
all other fishes. Length is used here mainly as an approximation 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 (tmax)
that fish of a given population would reach. Following Taylor (1958) it is
calculated as the age at 95% of Linf, using the parameters of the
von Bertalanffy growth function as estimated above, viz.: tmax =
t0 + 3 / K.
L maturity: This is the average length (Lm) 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 Linf (Froese and Binohlan, in
press). 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 parameters of the von Bertalanffy growth function, viz.: tm =
t0 ‑ ln(1 ‑ Lm / Linf) /
K.
L max. yield: This is the length class (Lopt) 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 Lm and Lopt
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 Figure 1). If no
growth parameters are available, Lopt and its standard error are
estimated from an empirical relationship between Lopt and Linf
(Froese and Binohlan, in press). Otherwise Lopt is estimated from
the von Bertalanffy growth function as: Lopt = Linf *
(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 (Lc), Linf, 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 Lc is set equal to 40% of Linf. This is based on a
preliminary investigation of the Lc / Linf ratio for 34
stocks ranging in size from 15 to 184 cm TL and which give a range of Lc/Linf
values between 0.15 – 0.74. Users can enter other values for their respective
fisheries and calculate the corresponding relative yield-per-recruit. For the
respective Lc the corresponding maximum and optimum exploitation
rates and fishing mortalies (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 * (Winf *
e^‑(M(tr‑t0))); where Winf is the
asymptotic weight and tr 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 Lopt
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 Eopt =
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 (EMSY) may be unrealistically high. We
therefore provide an estimate of the exploitation rate Eopt
corresponding to a value that is slightly lower than EMSY and which
is the exploitation rate corresponding to a point on the yield-per-recruit
curve where the slope is 1/10th of the value at the origin of the
curve. Users are able to change the value of Lc and calculate the
corresponding values of EMSY and Eopt. We also provide
the corresponding values of FMSY and Fopt through the
relationship: F = M * E / (1 – E).
Estimation of
exploitation rate from mean length in catches: Beverton and Holt (1956) showed that for fish
that grow according to the von Bertalanffy growth function, total mortality (Z)
can be expressed by: Z = K * (Linf – Lmean) / (Lmean
– L’) , where Lmean is the mean length of all fishes caught at sizes
equal or larger than L’, which is the smallest size in the catch and here assumed
to be the same as Lc, which is the mean length at entry in the
fishery, assuming knife-edge selection, and thus the same as used under Yield
per Recruit above. All other parameters are as defined above. Users can enter
observed values of Lc and Lmean for a given fishery, as
may be estimated from length-frequency samples, and calculate total mortality
Z, fishing mortality F = Z – M, and exploitation rate E = F / Z. The estimate
of F or E can then be compared with those at maximum sustainable yield and optimum
yield as given in the Relative Yield per Recruit section, thus obtaining a
preliminary indication of the status of the fishery. Note, however, that the
length-frequencies from which Lc and Lmean
are derived must be to the furthest extent possible representative of the
length-structure of the population under equilibrium, as may be obtained by
averaging a long time series of length-frequency samples.
Table 1. Values of selected life history parameters suggested for classifying the resilience / productivity of fish populations or species. See text for definitions and discussion.
Generation time: This is the average age (tg) of
parents at the time their young are born. In most fishes Lopt (see
above) is the size class with the maximum egg production (Beverton 1992). The
corresponding age (topt) is a good approximation of generation time
in fishes. It is calculated using the parameters of the von Bertalanffy growth
function as tg = topt = t0 ‑
ln(1 ‑ Lopt / Linf) / K. Note that
in small fishes (< 10 cm) maturity is often reached at a size larger than Lopt
and closer to Linf. 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 then Lm, viz.: Lm100 =
Lm + (Linf ‑ Lm) / 4, and
calculate generation time as the age at Lm100. This is applied
whenever Lm >= Lopt.
Length-weight: This equation can be used to estimate the
corresponding wet weight to any given length. The default entry is Linf,
thus calculating the asymptotic weight for the fish of the population in
question. The parameters ‘a’ and ‘b’ are taken from a study in FishBase with a
median value of ‘a’ and with the same length type (TL, SL, FL) as Linf.
Users can click on the 'Length-weight' link to see additional studies. Users
can change the length or the values of ‘a’ and ‘b’ and recalculate the
corresponding weight.
Trophic level: The rank of a species in a food web can be
described by its trophic level (troph), which can be estimated as: Troph =
1 + mean trophs of food items; where the mean troph is weighted by the
contribution of the various food items (Pauly and Christensen 1998). The
default value and its standard error as shown in the Key Facts sheet are
derived from the first of the following options that provides an estimate of
troph based on: 1) diet information in FishBase, 2) food items in FishBase, and
3) an ecosystem model.
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) / K1(t)] / [WtNtdt]
integrated between the age at which fish recruit (tr) and the
maximum age of the population (tmax); where Nt is the
number of fishes at age t, Wt their mean individual weight, and K1(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 Winf –
1.965T’ + 0.083A + 0.532h + 0.398d; where Winf (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 Winf is taken either
from Linf and the length-weight relationship (see above) or from Wmax
(maximum weight ever recorded for the species) when an independent estimate of
Winf 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 5 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 all 8 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 Winf and A are
re-entered, e.g., in cases where no possible/guessed values of Winf
are available in FishBase.
The
Key Facts page is still very much under construction and we welcome comments
and suggestions for its further improvement to any of the authors (see e-mail
addresses above).
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.
Asila, A.A. and J. Ogari. 1988. Growth parameters and mortality rates of Nile perch (Lates niloticus) estimated from length-frequency data in the Nyanza Gulf (Lake Victoria). p. 272-287 In S. Venema, J. Möller-Christensen and D. Pauly (eds.) Contributions to tropical fisheries biology: papers by the participants of the FAO/DANIDA follow-up training courses. FAO Fish. Rep., (389): 519 p.
Beddington, J.R. and J.G. Cooke. 1983. The potential yield of fish stocks. FAO Fish. Tech. Pap. (242), 47 p.
Beverton, R.J.H. and S.J. Holt. 1956. A review of methods for estimating mortality rates in fish populations, with special references to sources of bias in catch sampling. Rapp. P.-V. Réun. Cons. Int. Explor. Mer 140:67-83
Beverton, R.J.H. and S.J. Holt. 1957. On the dynamics of exploited fish populations. Fish. Invest. Ser. II. Vol. 19, 533 p.
Beverton,
R.J.H. and S.J. Holt. 1964. Table of yield functions for fisheries management.
FAO Fish. Tech. Pap. 38, 49 p.
Beverton, R.J.H. 1992. Patterns of reproductive
strategy parameters in some marine teleost fishes. J. Fish Biol. 41(B):137-160
Blueweiss, L., H. Fox, V. Kudzman, D. Nakashima,
R. Peters and S. Sams. 1978. Relationships between body size and some life
history parameters. Oecologia 37:257-272
Froese, R. and C. Binohlan. Empirical
relationships to estimate asymptotic length, length at first maturity, and
length at maximum yield in fishes. (in press)
Gulland, J.A. 1971. The fish resources of the
oceans. FAO/Fishing News Books, Surrey, UK.
Musick, J.A. 1999. Criteria to define extinction
risk in marine fishes. Fisheries 24(12):6-14.
Palomares, M.L.D. 1991. La consommation de nourriture chez les poissons: étude comparative, mise au point d’un modèle prédictif et application à l’étude des reseaux trophiques. Ph.D. Thesis, Institut National Polytechnique de Toulouse, France.
Palomares, M.L. and D. Pauly. 1989. A multiple regression model for predicting the food consumption of marine fish populations. Australian Journal of Marine and Freshwater Research 40:259-273.
Palomares,, M.L.D. and D. Pauly. 1999. Predicting the food consumption of fish populations as functions of mortality, food type, morphometrics, temperature and salinity. Marine and Freshwater Research 49:447-453.
Pauly, D. 1979. Gill size and temperature as governing factors in fish growth: a generalization of von Bertalanffy’s growth formula. Ber. Inst. f. Meereskunde Univ. Kiel. No 63, xv + 156 p.
Pauly, D. 1980. On the interrelationships between natural mortality, growth parameters, and mean environmental temperature in 175 fish stocks. J. Cons. CIEM 39(2):175-192
Pauly, D. 1982. Studying single species dynamics in a multispecies context. p. 33-70 In D. Pauly and G.I. Murphy (eds.) Theory and management of tropical fisheries. ICLARM Conference Proceedings 9, 360 p.
Pauly, D. 1985. Zur Fischereibiologie tropischer Nutztiere: Eine Bestandsaufnahme von Konzepten und Methoden. Ber. Inst. Meereskd. Christian-Albrechts Univ. Kiel 147:1-55.
Pauly, D. 1986. A simple method for estimating the food consumption of fish populations from growth data and food conversion experiments. Fishery Bulletin (US) 84:827-840.
Pauly, D. 1989. Food consumption by tropical and temperate fish populations: some generalizations. Journal of Fish Biology 35 (Supplement A):11-20.
Pauly, D. and V. Christensen. 1998. Trophic
levels of fishes. p. 155 In R. Froese and D. Pauly (eds.) FishBase 1998:
concepts, design and data sources. ICLARM, Manila, Philippines. 293 p.
Pauly, D., J. Moreau and F.C. Gayanilo, Jr. 1998.
Auximetric analyses. p. 130-134 In R. Froese and D. Pauly (eds.) FishBase 1998:
concepts, design and data sources. ICLARM, Manila, Philippines. 293 p.
Ricker, W.E. 1975. Computation and interpretation
of biological statistics of fish populations. Bull. Fish. Res. Board Can.
(191), 382 p.
Taylor, C.C. 1958. Cod growth and temperature. J.
Cons. CIEM 23:366-370