Estimates of population parameters and consumption / biomass ratio for fishes in reservoirs , Paraná State , Brazil

Consumption, natural mortality, and growth are important parameters for the construction for both fisheries and ecosystems models. We estimated k (growth constant of the von Bertalanffy’s function), Loo 1(asymptotic length), Woo (asymptotic weight), Ar (caudal fin index), M (natural mortality), and Q/B (consumption/biomass ratio) for several fish species inhabiting reservoirs. We explored possible relationships among these parameters for 135 fish species sampled in thirty reservoirs in the State of Paraná, southern Brazil. Maximum length (Lmax) varied from 2.60 to 79.00 cm, Loo from 2.73 to 85.05 cm, Woo from 0.23 to 9,490.26 g, k from 0.01 to 2.38 yr-1, Ar from 0.03 to 3.60, M from 0.16 to 2.82 yr-1, and Q/B from 3.31 to 67.18. Significant correlations were observed between most pairs of parameters, except for Ar and k, Ar and Loo , and for M and Q/B. The estimates presented here may be useful for constructing Ecopath models, both in Brazil and other tropical regions, where the use of ecosystem modeling is growing.


Introduction
Estimates of growth parameters for fish species are important not only to understand their life history and behavior, but also to manage fishery resources, since they allow estimating the potential productivity (Nikolsky, 1969;Gulland, 1977).Several studies point out to the lack of important biological parameters to estimate yield and give support to management, especially for tropical fish (Pauly, 1998a(Pauly, , 1998b;;Beverton, 1998;Holt, 1998).Worldwide, it is known approximately 28,000 fish species (Nelson, 2006), among these only 1,400 (5%) have information on growth available (Binohlan & Pauly, 2000); in the Neotropical region such information should be even less available.
The knowledge of growth parameters (e.g.von Bertalanffy growth constant k and asymptotic length L oo , maximum reported length and age (L max and t max , respectively) as well as the consumption/biomass ratio (Q/B), and natural mortality (M) are important parameters for building ecosystems models (e.g.Ecopath; Christensen & Pauly, 1993), several other fishery models and, consequently, managing fishery resources (Froese & Pauly, 2000;Froese & Binohlan, 2000, 2003).In addition, these parameters allow testing life history theories and obtaining preliminary estimates of other parameters from those already available (Froese & Binohlan, 2000, 2003;Stergiou & Karpouzi, 2002;Stergiou & Karachle, 2006).
Examples of use of empirical equations for parameters estimation described above include asymptotic length from maximum reported length, natural mortality from growth parameters, optimum exploitation length from asymptotic length or length at first maturity, length at first maturity from asymptotic length and/or von Bertallanfy growth constant, trophic level from maximum reported length (Pauly, 1980;Froese & Binohlan, 2000;Stergiou & Karpouzi, 2002;Angelini & Agostinho, 2005a).
Recently, there has been an increase in the number of studies using the ecosystem approach, which justifies compiling the cited parameters values for future use in the building of Ecopath models.Moreover, information on Neotropical fishes can be uploaded to online databases, such as the FishBase (Froese & Pauly, 2010).Thereby, in this study, we estimated/compiled the parameters k (growth constant of the VBGF), L oo (asymptotic length), L max (maximum reported length), W oo (asymptotic weight), Ar (caudal fin index), M (natural mortality) and Q/B (consumption/biomass) for 135 Neotropical fish species collected in 30 reservoirs in the State of Paraná, southern Brazil.In addition, we evaluated possible significant relationships between k and L max , k and L oo k and W oo , k and M, k and Ar, k and Q/B, L oo and Q/B, W oo and L max , M and Ar, and M and L max .Finally, we made a trophic categorization for all species considered in this study.All analyses were performed aiming at detecting patterns in the life history of those fish species.

Material and Methods
Study area.The study reservoirs were located in six river basins (Paranapanema, Tibagi, Ivaí, Piquiri, Iguaçu, and Leste) throughout the State of Paraná and its borders with the States of São Paulo and Santa Catarina (Fig. 1; Table 1).Although the main purpose of these reservoirs is energy production, they are also used for water supply, and for fishing and leisure.Reservoirs were selected to include a diversity of areas, morphometries, hydraulic retention times and distribution throughout the state.More detailed description of some characteristics of each reservoir is presented in Table 1.
Sampling.Fishes were sampled in 30 studied reservoirs (Table 1); two samplings were carried out, one in July and another in November 2001.Samplings were conducted in the lacustrine zone of the reservoirs (following Thornton et al., 1990) with 20-m-long gillnets of diverse mesh sizes (2.4, 3, 4, 5, 6, 7, 8, 9, 10, 12, and 14 cm opposite knots), set for 24 h and checked every 8 h.Seine nets (20 m long and 0.8 cm mesh) were used during the day in the littoral.
For species with more than 50 individuals the parameters k and L oo were estimated from the sampled data.Growth parameters were obtained by fitting von Bertalanffy's growth constant function (VBGF;Ricker, 1975), which calculates the parameters k (growth constant) and L oo (asymptotic length), as follows: , where L t is the total fish length (cm) at age t, L oo is the asymptotic length (cm), k is VBGF's inclination or growth rate (year -1 ), and t 0 is the age intercept (fish age is assumed to be zero).Asymptotic length (L oo ) and k were calculated, whenever possible, using length-frequency data and FISAT's ELEFAN I routine (Sparre et al., 1989;Gayanilo & Pauly, 1997), with the option of scanning for k-values.This routine estimates VBGF's adherence to length frequency data.Sometimes, the bestfitted k value was corroborated by the literature or by FISAT's routine "by eye", which fits the VBGF visually.When the collected data did not allow fitting, we used published data (Perez Lizama & Vazzoler, 1993;Angelini & Agostinho, 2005a;Froese & Pauly, 2010; Table 2).When it was not possible to obtain VBGF parameters, L oo was estimated using the length of the largest individual of the population sample: L oo = L max * 1.05 (Angelini & Agostinho, 2005a).
Production, according to Ivlev (1945), is the "total quantity of tissue elaborated by a fish population during a stated period of time, although not all individuals survive until the end of that period".As the production/biomass (P/B) ratio is hard to estimate directly, it can be considered equivalent to total mortality [Z = fishing mortality (F) + natural mortality (M)] (Pauly et al., 2000).The study reservoirs have negligible fishing activity, if any.Thus, as shown by Allen (1971) under equilibrium conditions, the P/B ratio is similar to natural mortality (M), which was calculated with the empiric regression of Pauly (1980): where M is natural mortality (year -1 ), k and L oo are the VBGF's parameters, and T is the average annual water temperature (average for the 30 reservoirs; in ºC).
There are several empirical approaches to estimate consumption/biomass ratio (Q/B), and this parameter is relatively easy to estimate for fish populations (Palomares & Pauly, 1989, 1998;Pauly, 1989;Pauly et al., 1990;Jarre et al., 1991).It is interesting to notice that Q/B values for the same species vary as a result of using different empirical formulas and predictor parameters; for example, there might be variation in measurements of proportion and asymptotic weight, as well as in the type of food consumed by a species.To estimate Q/B we used the empiric regression model proposed by Palomares & Pauly (1998), as follows: logQ/B=7.964-0.204logWoo -1.965T'+0.083Ar+0.532H+0.398Dwhere Q/B is consumption/biomass rate (year -1 ), W oo is the asymptotic weight (wet weight in g, estimated based on the length/weight relationship for L oo ); T' is the inverse of the average annual water temperature (T'=1000/G+273.15),where G is the average water temperature of the 30 reservoirs ( o C); Ar is the caudal fin index (Ar=h 2 /s, where h is the caudal fin height (mm) and s is the caudal fin surface area (mm 2 ), extending to the narrowest part of the caudal peduncle) and a measure of the swimming and metabolic activity of the fish (Palomares & Pauly, 1998).Ar values were estimated by measurements of five individuals, when possible, per species (analyzed individuals were deposited in the collection of Museu de Ictiologia, Nupélia).Variables H and D refers to feeding behavior, i.e., H=1 for herbivorous, D=1 for detritivorous and H=D=0 for carnivorous.Values of average annual water temperature, for both equations listed above, were provided by the limnology laboratory of Nupélia (Table 1).
We tested significant relationships between k and L max , k and L oo , k and W oo , k and M, k and Ar, k and Q/B, L oo and Q/ B, W oo and L max , M and Ar, and M and L max with linear regressions.All these relationships are relevant to the study of life history (Jensen, 1997;Froese & Pauly, 2000;Froese & Binohlan, 2000, 2003).

Results
L max varied from 2.60 to 79.00 cm.L oo from 2.73 to 85.05 cm.The values of L oo for 34 species (Table 2) were compiled from the literature; among these species C. modestus, A. altiparanae, P. britskii, A. gymnogenys, G. brasiliensis, H. aff. malabaricus, R. quelen and S. melanodermatum showed L oo less than the L max recorded in this study.W oo from 0.23 to 9,490.26 g, k from 0.01 to 2.38 yr -1 , Ar from 0.03 to 3.60, M from 0.16 to 2.72 yr -1 , and Q/B from 3.31 to 67.18 (Table 2).
Various relationships were apparent with the VBGF.In this sense, k was significant negatively related to maximum length, and asymptotic length and weight (F = 45.00,F = 62.80 and F = 59.60, respectively; Figs.2a, b, c).The piscivorous species R. quelen showed low annual growth rate (k = 0.01 year -1 ; Table 2) and low natural mortality, whereas O. niloticus (k = 2.38 year -1 ; Table 2) showed the opposite trend; both were considered outliers (Fig. 2).On the other hand, relationships between k and caudal fin index, and natural mortality (F = 458.38;Fig. 2e) and consumption/biomass ratio (F = 30.43;Fig. 2f) were positive.
The relationship between k and caudal fin index was not significant (F = 0.02; Fig. 2d).The fin shape of knifefishes G. sylvius and E. trilineata strongly affected the relationship (Fig. 2d); but even after their exclusion the relationship was still non-significant (F = 0.16; p = 0.68).Rhamdia quelen and O. niloticus did not follow the general relationship between k and consumption/biomass ratio (Fig. 2f).
The relationship between asymptotic length and consumption/biomass ratio was negative (F = 78.33;Fig. 3a).
Interestingly, the species above the regression line in Figure 3a represent small-and medium-sized species that are mostly detritivorous and have high population growth rates.The relationship between maximum length and asymptotic weight was positive (F = 563.14;Fig. 3b).The species M. salmoides (located below the regression line) and L. macrocephalus (located above the regression line) were outliers.
The relationship between natural mortality and maximum length was negative (F = 136.37;Fig. 3c).The species L. macrocephalus was an outlier; when this fish was removed, the relationship showed stronger non-linear tendency (Spearman U= -0.80; p < 0.05).The relationship between natural mortality and caudal fin index was not significant (F = 0.09; Fig. 3d), following the same trend observed for the relationship between k and caudal fin index.Similarly, after exclusion of the knifefishes, the relationship was still non-significant (F = 0.06; p = 0.80).

Discussion
In this study we obtained significant relationships among various biological parameters.These relationships can be useful to obtain other estimates, such as yield per recruit (Y/R), which can be easily calculated from L max , W max , t max , and Ar, among others.Significant negative relationships were established between the parameters k and L max , k and L oo and k and W oo .On Table 1.Some characteristics of the study reservoirs ( a -Perimeter estimated in Google TM Earth.Depth = maximum depth, R.T. = Hydraulic retention time, A.A.W.T. = average annual water temperature).Consulted references : Júlio Jr. et al. (2005) Vazzoler (1993), in a review on marine and freshwater fish growth in Brazil, observed the same trend in the relationship between L oo and k.
The negative correlation between k and L oo and k and W oo seems to be a recurrent pattern in fishes (Beverton & Holt, 1959;Pauly, 1998aPauly, , 1998b;;Froese & Pauly, 2000).
The relationship between k and L oo should provide the slope value equal to -0.33, when assuming the isometric growth (Jensen, 1997).Stergiou & Karachle (2006) updated the slope value for all Greek fish stocks and found the value of -0.3006, close to the theoretical -0.33.We found a slope value of -0.6195, which differed greatly from the theoretical value, as well as a correlation coefficient (r = -0.57),which is higher than verified by Stergiou & Karachle (2006) for Greek Seas fish stocks (r = -0.34).In addition, if we remove R. quelen and O. niloticus (which deviated from the regression line) from the analysis, the value of the slope becomes even higher (-0.8211; r = -0.64).Vazzoler (1993).*For species in which k was calculate, Rn (goodness of fit index) was greater than 0.6.
The parameters estimated here are consistent with other studies, which found that smaller species have higher k values (Pauly, 1998a(Pauly, , 1998b;;Angelini & Agostinho, 2005a).According to Pauly (1998a), the same asymptotic size may be associated with various k values.In addition, the same author showed that tropical fishes tend to be confined within a space defined by the smaller asymptotic size and higher k values than fish from temperate regions.Angelini & Agostinho (2005a) estimated the k values for 35 fish species from the upper Paraná River floodplain and Itaipu reservoir and verified that fishes with smaller asymptotic lengths showed higher k values.In this study, 55% of species showed k value greater than 0.50; among these, except H. derbyi and P. mesopotamicus, all are considered small and medium-sized species.In addition, in reservoirs, the fish assemblage is composed basically by small-sized fishes (Dias et al., 2005;Agostinho et al., 2007).Those findings intensified the pattern highlighted by Pauly (1998a) for tropical fish.The large number of small and medium-sized species with fast growth is associated with the higher temperatures recorded in the tropics.Pauly (1998a) affirm that metabolic rates increase with temperature and that growth is limited by respiratory metabolism.Thus, tropical fishes should generally remain small.Rhamdia quelen is a catfish species, prefers calmer and deeper water along banks and vegetation with a sand or mud bottom (Silva et al., 2011).Despite the large distribution of this species, from northern Mexico to southern Argentina (Graça & Pavanelli, 2007), studies on the biological aspects of this species have been primarily conducted on captive adult fish for farming purposes (Silva et al., 2011).Thus, comparative studies on the growth parameters for R. quelen were not found in field.On the other hand, Oreochromis niloticus showed rapid growth, reaching adult size in small interval of time, exhibit relatively short reproductive cycles, tolerate a variety of environmental conditions, have high capacity for hybridization and high Table 2 (cont.).Demographic and biological attributes of 135 fish species captured in 30 reservoirs in the State of Paraná, southern Brazil, in July and November 2001.N = number of individuals captured, TC = species' trophic category, L max = maximum length (cm), L oo = asymptotic length (cm; values with asterisk were obtained of the literature), W oo = asymptotic weight (g), k = growth constant from von Bertalanffy's equation (year -1 ), Ar = caudal fin index (Palomares & Pauly, 1998), M = natural mortality (year -1 ) and Q/B = consumption/biomass ratio (year -1 ). a - Froese & Pauly (2010), b -Angelini & Agostinho (2005a), c  -Perez Lizama & Vazzoler (1993).*For species in which k was calculate, Rn (goodness of fit index) was greater than 0.6.resistance to diseases and infection (Coward & Bromage, 2000).These biological features might have favored the rapid growth of O. niloticus populations in the reservoirs studied.
Natural mortality (M) in fish is difficult to estimate because its values are strongly correlated with growth parameters, as reported by Pauly (1998a).Fish with fast initial growth (higher k values) present higher M values, whereas fish with higher asymptotic lengths present lower M values.The von Bertalanffy's growth constant and natural mortality were stronger correlated in this study, consequence of the fact that M was calculated using the Pauly's equation and then totally dependent on k.The knifefishes species, as G. sylvius, E. trilineata, and Rhamphichthys hahni, showed the body shape highly specialized.The caudal portion of the body is elongate and it has a long anal fin, there are no dorsal, adipose, or pelvic fins, while the caudal fin is either small or absent (Albert, 2001).Thus, the caudal fin index for these species does not follow the specified pattern for other species.In addition, these species can present large maximum length, with such a high natural mortality, because on the shape of the body.
Consumption/Biomass ratio is defined as the number of times a population consumes its own weight within a year (Pauly, 1986(Pauly, , 1998a(Pauly, , 1998b;;García & Duarte, 2002).García & Duarte (2002) studied Q/B ratio and estimates of Q/B-predictor parameters for Caribbean fish, and Angelini & Agostinho (2005a) studied parameter estimates for fish from the upper Paraná River Floodplain and from Itaipu Reservoir (Brazil), and they found that Q/B varies inversely with L oo and trophic levels (species from low trophic levels showed high Q/B ratio, due to their fast life cycles).Small-sized species, which are normally r-strategists (sensu Winemiller, 1989), showed low asymptotic lengths, short life cycles, high growth rates, early first maturation, high natural mortality, and high fecundity (Vazzoler, 1996).These species usually form the base of food webs, as they are concentrated in the lower trophic levels.Thus, patterns found in this study are similar to those observed previously.
The correlations found between the parameters studied here corroborate the patterns described by Pauly (1998a) and Angelini & Agostinho (2005a), which indicated that k varies inversely with L oo and W oo , as well as Q/B ratio varies inversely with L oo and natural mortality has a high correlation with L max , for tropical fishes and also for fishes from other latitudes and ecosystems (Pauly, 1998b).Furthermore, we emphasize that, as suggested by Pauly (1998a), those correlations allow summarizing and comparing demographic and biological data of fish species from different biogeographic regions.
The estimates presented here should be useful for building Ecopath models.Ecological modeling is under development in tropical regions, such as Brazil (Angelini & Petrere, 1996;Wolff et al., 2000;Angelini & Agostinho, 2005a, 2005b;Angelini et al., 2006;Angelini & Gomes, 2008).Pauly (1998b) pointed out to the need for an adaptation or more precisely a "tropicalization" of the parameters from Beverton and Holt models.Moreover, García & Duarte (2002) suggested that it would be interesting to explore the consistency of published consumption/biomass ratio values for the same species in similar habitats.Those authors compared estimated Q/B values with three empirical models described by Palomares & Pauly (1989, 1998) and by Pauly et al., (1990), and they concluded that parameters vary for a given fish species; this is a clear sign that empirical models must be used with caution.Thus, empirical models obtained with data from temperate areas should be analyzed with attention.Furthermore, we emphasize that empirical models described by Palomares & Pauly (1989, 1998) and by Pauly et al., (1990) should be parameterized with data from tropical areas.

Fig. 1 .
Fig. 1.Location of the 30 reservoirs in the State of Paraná sampled in July and November 2001.

Fig. 2 .
Fig. 2. Relationships between von Bertalanffy's constant (k; Growth rate) and maximum length (L max ; a), asymptotic length (L oo ; b), asymptotic weight (W oo ; c), caudal fin index (Ar; d), natural mortality (M; e) and consumption/biomass ratio (Q/B; f) for 135 fish species in reservoirs from the State of Paraná, southern Brazil, caught in July and November 2001.

Fig. 3 .
Fig. 3. Relationships between some biological parameters of 135 fish species in the State of Paraná, southern Brazil, caught in July and November 2001.Asymptotic length (L oo ) and consumption/biomass ratio (Q/B; a); maximum length (L max ) and asymptotic weight (W oo ; b); maximum length (L max ) and natural mortality (M; c); and caudal fin index (Ar) and natural mortality (M; d).

Table 2 (
cont.).Demographic and biological attributes of 135 fish species captured in 30 reservoirs in the State ofParaná,  southern Brazil, in July and November 2001.