Breeding, growth and exploitation of Brachyplatystoma rousseauxii Castelnau, 1855 in the Caqueta River, Colombia

The main life history traits of the large Amazonian migratory catfish Brachyplatystoma rousseauxii were determined in the Caqueta River, Colombia. The breeding season occurred during the rising and falling water periods. The size at first sexual maturity was significantly larger for females (88.5 cm Ls) than males (81.7 cm). Both males and females reproduce for the first time between their third and fourth year. The growth characteristics were estimated using length frequency analyses. Females grew systematically larger than males, the difference being about 9% after the first year and increasing to 12% for ten years old individuals. Mortality estimates, calculated from different models, some taking into account the effect of body size, ranged from 0.32 to 0.42 year-1 for natural mortality and from 0.72 to 0.82 year-1 for fishing mortality, indicating high fishing pressure in the Caqueta River, higher than in the Peruvian Amazon. Resulting exploitation rates (0.63 to 0.72) pointed towards overexploitation of the species in the Caqueta. The situation calls for a concerted management between the countries sharing this resource (Brazil, Colombia, and Peru) and potential solutions are proposed.

Introduction the large catfishes in the Caqueta region (Muñoz-Sosa, 1993;Agudelo, 1994;Celis, 1994;Gómez, 1996;Agudelo et al., 2000), but almost nothing is known about their growth and mortality characteristics. This also applies to B. rousseauxii, whose catches have been decreasing in the region (Rodríguez, 2010), although very preliminary information about growth and mortality were provided by Muñoz-Sosa (1996). Yet, for such commercially important species, this knowledge is fundamental for the development of proper management strategies (Sparre & Venema, 1995). The present study aims at filling this gap, by providing new information about the reproduction, growth and mortality patterns of B. rousseauxii in the Caqueta River.

Material and Methods
Study area. Fish were sampled between 1995 and early 1998 in La Pedrera district and its area of influence, situated north of the Amazonas Department, on the right margin of the Caqueta River in the Colombian Amazon, close to the Brazilian border at about 1°18' S and 69°37' W ( Fig. 1). Located about 90 m a.s.l., the mean annual temperature is about 27°C, with minimum values (20°C) in January and June and maximum (35°C) in November (Celis, 1994). Fish were caught by local fishermen in two main zones (Agudelo et al., 2000): between Maria Manteca and Puerto Córdoba, an extension of about 250 km and between Puerto Córdoba and the Brazilian border in Villa Betancourt and Serrinha, an extension of about 50 km. Although the data set is from the period between 1995 and 1998, it is very important because there are no other available data for the Caqueta River. Obtaining such a comprehensive data set (allowing the estimation of the reproductive, growth and mortality parameters) for any river is almost impossible nowadays as fish are almost always eviscerated and beheaded directly on the fishing grounds. Moreover, a scientific sampling for so many specimens would be impractical (i.e., time and costs) and unethical. It must also be emphasized that the results obtained from this relatively old data set will provide a suitable basis for future comparisons on the resource status. Given the life cycle of this particular species, where the smallest fish are in Amazon estuary area, no specimen smaller than 38 cm could be caught during this study.
Data. For this study, data of the Colombian Instituto Amazónico de Investigaciones Científicas SINCHI, used in Agudelo et al. (2000), were re-analyzed to take into account methodological flaws pointed out in Garcia et al. (2009a) and provide new information regarding reproduction, growth, and mortality parameters. Between September 1995 and December 1997, B. rousseauxii were collected during daily sampling in the main landing zones of commercial fishermen in La Pedrera. Every landed specimen was measured and, whenever possible, weighed and sexed (during the whole sampling period, most specimens arrived already eviscerated at the landing zones).
The standard length (Ls), standard corporal length (CLs): from the posterior part of the opercula to the end of the hypural plates) and body mass (W) of each fish were measured to the nearest 1 cm and 50 g, respectively. The standard corporal length was taken to determine the standard length of specimens landed beheaded, using a linear regression between Ls and CLs (CLs = 0.750*Ls -1.260, r² = 0.952, P < 0.001). Gonads were macroscopically checked for maturity stage determination. The maturity scale of gonadal maturation stages followed Nuñez & Duponchelle (2009). Briefly, for females, the stages of gonadal maturation were: stage 1, immature; stage 2, maturing; stage 3, advanced maturation; stage 4, ripe; stage 5, spent and stage 5-1 describes gonads of resting females. For males, stage 1 corresponds to immature fish, stage 2 to maturing or resting individuals and stage 3 to ripe fish. The breeding season was determined using only fishes above the mean size at first maturity. The breeding season was estimated from the monthly proportions of females' gonadal maturation stages 3 and 4 combined.
The size at first sexual maturity (L m ) is defined as the standard length at which 50% of the individuals are at an advanced maturation stage during the breeding season (i.e., at least stage 2 for females and males). L m is estimated by fitting the fraction of mature individuals per 10 mm Ls intervals to a logistic regression function (Barbieri et al., 1994;Duponchelle & Panfili, 1998): %M = 1(1 + e (-a(L-Lm)) ) -1 where %M = percentage of mature individuals by 10 mm size class, L = central value of each size class, and a and L m = constants of the model. The % of mature individuals in each size class was weighted by the total number of individuals in the same size class.
Age and growth characteristics were estimated from the modal progressions of standard length frequency distributions (King, 1995) using the ELEFAN (Electronic Length Frequency Analysis) routine (Pauly & David, 1981) provided in the FiSAT II (FAO-ICLARM Fish Stock Assessment Tools) package (Gayanilo et al., 2005). The set of parameters that best corresponded to the breeding patterns observed for the species (i.e., which gave an estimated birth date corresponding to the breeding peak) and that best described the distributions (i.e., which went through the largest number of large modes and yielded the largest Score = "goodness-offit" parameter of the ELEFAN routine) was selected (Garcia et al., 2009a). This process also permitted to diminish the tendency of ELEFAN method to underestimate K and overestimate Loo (Moreau et al., 1995). The growth parameters were calculated by the von Bertalanffy Growth Function (VBGF) equation fitted by the ELEFAN method: L t = Loo (1-e (-K (t-t0) ) where L t is the mean length at age t, Loo is the asymptotic length, K the growth coefficient and t o the theoretical age at size 0. t 0 was calculated using the empirical formula proposed by Pauly (1979): log 10 (t 0 ) = -0.392 -0.275 log 10 Loo -1.038 log 10 K Fig. 1. Map of the Colombian Amazon, its constitutive departments and the principal fishing zones for Brachyplatystoma rousseauxii (based on Agudelo et al., 2000;Murcia et al., 2007).
The age at first sexual maturity (A m ) was calculated from the VBGF as follows (Duponchelle et al., 2007): A m = {-ln[1-(L m Loo -1 )]K -1 } + t o where L m is the size at first sexual maturity and Loo and K are parameters from the VBGF.
The longevity (t max ) was calculated as the age at 95% of L " from the equation of Taylor (1958): where t 0 , and K are the VBGF parameters and p is a fraction of Loo (in this case 0.95). The longevity was also calculated from the equation of Froese & Binohlan (2000): log 10 t max = 0.5496 + 0.957 log 10 (A m ) where A m is the age at first sexual maturity.
Mortality parameters were also estimated using procedures provided in the FiSAT II package. Total mortality (Z) was estimated by the method of the length-converted catch curves (LCC) (Pauly, 1983). Natural mortality (M) is one of the most complicated life history parameters to estimate in natural populations (Vetter, 1988;Brodziak et al., 2011) and several empirical models linking M to life history attributes such as age at maturity or growth were proposed for fish (reviews in Simpfendorfer et al., 2005;Gislason et al., 2010). These empirical relationships assume that M is a species-or stock-specific constant, and users generally apply the estimate to all exploited ages and sizes of the species or stock under study. One of the most commonly used models is Pauly's (1980) equation linking M to Loo , K and the mean annual environmental temperature (T) for the species concerned. Hence, natural mortality was evaluated using Pauly's equation, as implemented in the Fisat package, for a mean annual temperature of 27°C. In order to verify the accuracy of natural mortality estimate using Pauly's equation and the consequences on the estimation of fishing mortality and exploitation rate, however, M was also estimated using Richter and Efanov's formula (Sparre & Venema, 1995), relating mortality to the age at which 50% of the population is mature (estimated by A 50 ), as implemented in the FiSAT II package. Additionally, natural mortality was also estimated using Jensen (1996)'s formulas (Simpfendorfer et al., 2005): M = 1.65/A 50 and M = 1.6 x K, K being the VBF growth coefficient.
Recent theory and empirical studies on natural mortality indicate that M scales with individual body size (McCoy & Gillooly, 2008;Gislason et al., 2010;Brodziak et al., 2011) and that while the assumption of a constant K may be a valid approximation when only mature individuals are targeted by the fishery, size dependence should be taken into account when immature are caught (Brodziak et al., 2011). Given that important proportion of immature individuals are exploited in the Caqueta River, natural mortality was therefore also estimated, for comparison purposes, separating the immature and mature individuals using: where Loo and K are the VBGF parameters and L the body length (cm) for which the M estimate would apply. Practically, L was fixed as the mean standard lengths of immature (L = 82.5, 75 and 82 cm for females, males, and sexed and unsexed individuals combined) and mature individuals (L = 102, 94 and 100 cm for females, males, and sexed and unsexed individuals combined) in the data set. Fishing mortality (F) was calculated as F = Z-M (Pauly, 1980). The exploitation rate was calculated as E = F.Z -1 . For comparison purposes, both F and E were calculated for the different estimates of M.
Statistical analyses .Analysis of covariance (ANCOVA) was used to test for differences in the log-transformed lengthmass relationships between sexes, using log 10 W as the dependent variable, log 10 L s as the covariate, and sex as categorical variable.
Differences of mean standard length or mass for each sex among years were tested with Kruskal-Wallis One Way Analysis of Variance and Dunn's all pairwise post-hoc test, using Bonferonni correction to keep the experiment-wide error rate at the desired á (0.05, 0.01 or 0.001). Differences in mean standard length and mass between sexes for each year were tested with a Mann-Whitney Rank Sum Test.
For each sex, logistic regression models provided an estimate of the L m ± standard deviation. Sizes at maturity between sexes were compared using Student t-tests (degrees of freedom calculated from the number of size classes).
Breeding season. The breeding season of Brachyplatystoma rousseauxii in the Caqueta River occurs during an extended period of about six months, encompassing the rising and receding water periods (Fig. 2). Some variations were observed among years: it started earlier (March) and finished sooner (September) in 1996 than in 1997 (April-May to September).
Age and growth characteristics. For females, males and the combination of sexed and unsexed individuals, the best fitting models obtained from the ELEFAN routine gave mean birth date corresponding to the peak of the breeding season (June for females and August for males, Fig. 3). The VBGF parameters are presented in Table 2. Females had a better growth than males at every age class (Table 3). The difference between females and males gradually increased from ~9% at one year old to 12% at twelve years old.
The estimated longevity for B. rousseauxii varied according to the model used (Table 2) and ranged between 11 and 13 years. Computing age from the VBGF parameters, the youngest individuals collected, a male of 38 cm, was 10.9 months old, whereas the smallest female sampled (45 cm) was 12.6 months old. The largest male (129 cm) was 11.7 years old and the largest female (143 cm) was 12.9 years old.
Age and size at first sexual maturity. Over the study period, females reached the first sexual maturity (Fig. 4) at a significantly larger size (88.5 cm ± 0.1) than males (81.7 cm ± 0.01) (t-test, t = 15.1, P<0.001). Both males and females reached maturity between their third and fourth year, at 3.3 and 3.4 years, respectively.

Mortality and Exploitation.
Length converted catch curves resulted in total mortality (Z) values of 1.12 year -1 for females, 1.09 for males and 1.14 for sexed and unsexed individuals combined (Fig. 5). Natural mortality (M) estimates, using both size-independent (assuming a constant M for all age and size classes) and size-dependant models (taking into account two size classes: mean length of immature fish and mean length of mature fish in the population) are presented in Table 4. Natural mortality values calculated from Pauly's (1980) equation, as implemented in FiSAT II, were within the range of values obtained from the other size-independent models for females and males. Size-independent models tended to give M values close to the values observed for immature fish and superior to those obtained for mature fish using the size-dependent model of Gislason et al. (2010). On the contrary, sizeindependent models tended to give M values close to those observed for mature fish and inferior to those obtained for mature fish using the size-dependent model of Charnov et al. (2013). All these natural mortality estimates resulted in relatively high values of fishing mortality (F, 0.63 to 0.79 for females and 0.59 to 0.76 for males) and exploitation rate (E, 0.56 to 0.71 for females and 0.54 to 0.70 for males), excluding immature individuals. The highest estimates of both F and E were obtained when considering only mature individuals. Nevertheless, it must be pointed out that even immature individuals had relatively high F and E values. When sexed and unsexed individuals were combined, taking into account the whole database, fishing mortality estimates when even higher and exploitation rates were well above 0.5, even for immature individuals.

Discussion
The maximum observed length in the Caqueta River was 149 cm, similar to those reported by Agudelo et al. (2000) for the Guaviare, Caqueta, Putumayo, and Amazon rivers in Colombia, and about 5 cm smaller than the length observed in the Iquitos region, Peru (Garcia et al., 2009a). It was, however, much shorter than the 167 cm reported in the same river during the period 1992-1993(Muñoz-Sosa, 1996, indicating that larger fishes were caught a few years earlier in the Caqueta river, as was also the case in the Amazon basin (161 cm, Barthem & Goulding, 1997). The fact that from over 4,000 fish sampled here, the largest specimen caught was nearly 20 cm Table 1. Standard length (L s , in cm) and mass (W, in kg) means (± SD), ranges and number of fish sampled each year (n) of females (F), males (M) and total (sexed and unsexed individuals, T).

Fig. 2. Monthly percentages of breeding (stages 3 and 4)
Brachyplatystoma rousseauxii females (white circles) in the Caqueta River, Colombian Amazon, between 1995 and 1997, in relation to the water level (black line). smaller than fish measured earlier in the same river, suggests a decreased maximum size of the species in the Caqueta. In the present study, the observed differences in mean length and body mass among sexes, confirmed the reported size dimorphism in the species in Colombia (Arboleda, 1989;Agudelo et al., 2000), Brazil (Alonso, 2002), and Peru (García et al., 2009a). The timing of the breeding season relative to the hydrological cycle was very different in the Caqueta than in the Iquitos region. It started during the rising waters and stopped at the end of the descending waters, whereas it started during the descending waters and ended during the early rising waters in the Peruvian Amazon (Garcia et al., 2009a). Breeding during the descending waters and dry period had been hypothesized to be an adaptation of the species to avoid the loss of eggs and larvae in the flood plain, hence ensuring that most descendants would reach the Amazon estuary (Garcia et al., 2009a). This strategy, however, does apparently not apply to the Caqueta River, suggesting a more complex picture.
The growth dimorphism previously reported for the species (Alonso, 2002;Garcia et al., 2009a) was also observed in the Caqueta, with females growing larger and faster than males. Models that do not explicitly account for the effects of fishing and size selectivity usually tend to underestimate Loo and overestimate K (Taylor et al., 2005), which in turn can  Table 2. Longevity (t max ) and parameters of the von Bertalanffy growth function of Brachyplatystoma rousseauxii in the Caqueta River, Colombia, as modelled in FISAT II using the ELEFAN procedure. Longevity t max 1 and t max 2 were calculated from Taylor (1958) and Froese & Binohlan (2000), respectively. lead to biased mortality estimates derived from the VBG function. Although fishing and size selectivity effects were not specifically taken into account, the estimate of asymptotic length observed in the present study was about 5 cm larger than the largest fish sampled over 3 years and more than 4000 specimens, suggesting that Loo , hence K estimates were not too biased. Published growth and mortality parameters for B. rousseauxii in the Amazon basin were recently reviewed and discussed (Garcia et al., 2009a), including the most recent and geographically extensive data obtained using otolith analyses (Alonso, 2002). Consequently, the results of the present study will mainly be compared with Garcia et al. (2009a) study, which occurred during the almost exact same period  These parameters, however, were lower in the Caqueta than in the Peruvian Amazon when all specimens (sexed and unsexed) were taken into account (153.3 cm and 0.22 year -1 versus 155 cm and 0.29 year -1 , respectively), and especially the growth coefficient (K). Direct comparisons between the von Bertalanffy growth function parameters may lead to erroneous conclusions, particularly when considered separately (see Zivkov et al., 1999). In the present case, however, these comparisons are supported by important length-at-age differences: during their first eight years, B. rousseauxii in the Peruvian Amazon were between 11 cm and up to 17 cm larger than those from the Caqueta, the difference decreasing progressively later on.
The mean sizes at first sexual maturity were relatively similar in the Caqueta and in the Peruvian Amazon (Garcia et al., 2009a), differing only by 2 cm for females and 1 cm for males for the same period. The mean age at maturity, however, differed more markedly, maturity being reached approximately one year later in the Caqueta (3.3 and 3.4 years for females and males, respectively) than in the Peruvian Amazon (2.7 and 2.5 years, respectively; Garcia et al., 2009a). This maturation delay is mainly explained by the slower growth rate in the Caqueta.
As previously discussed, potential bias on the estimation of growth parameters was probably small. Consequently, potential resulting bias in the estimation of derived natural mortality estimates was reduced. Nevertheless, to minimize the well-known risk of obtaining erroneous estimations of natural mortality (Gislason et al., 2010;Brodziak et al., 2011) and consequently of fishing mortality and exploitation rate, different models were used (some taking into account the effects of body size) in addition to Pauly's (1980) popular equation. As for most previously published instantaneous mortality rates for the species (see Garcia et al., 2009a for review), the natural mortality (M) estimates calculated in the Caqueta River were below 0.5 year -1 and ranged from 0.32 to 0.42 for the whole data set (sexed and unsexed individuals combined), excluding estimation for immature fish, which yielded higher values. In every case, fishing mortality (F) was much higher than natural mortality in the Caqueta (0.72 to 0.82 year -1 ), which was also observed in the Peruvian Amazon (0.64 year -1 ; Garcia et al., 2009a) and along the estuary-Iquitos axis (0.99 year -1 ; Alonso, 2002). The higher values observed in the Caqueta compared to the Peruvian Amazon suggest a higher fishing pressure in the Caqueta, corroborating previous reports on the high fishing pressure supported by this species in the Caqueta River (Rodríguez, 1991;Agudelo, 1994;Celis, 1994;Muñoz-Sosa, 1996;Agudelo et al., 2000;Petrere, 2001;Fabré & Barthem, 2005). The estimated exploitation rates (E), were well above (0.63 to 0.72) the upper limit reference point (0.5) above which the population is considered over-exploited (Rochet & Table 4. Mortality estimates (year -1 ) and exploitation rate (E) for females, males and total (sexed and unsexed individuals combined). Natural mortality (M) was calculated from size-independant (Pauly, 1980;Richter & Evanov, 1997;Jensen, 1996) and size-dependant (Gislason et al., 2010;Charnov et al., 2013) models. Z was calculated from length-converted catch curves illustrated in Fig. 5   . Additionally, it should be pointed out that these results are based on data from almost 15 years ago. Since then, the situation has likely worsened, considering that B. rousseauxii is still a favored target (Petrere et al., 2004;Agudelo, 2007;Agudelo et al., 2009;Rodríguez, 2010) and that its proportion in the catches of the Colombian Amazon have significantly decreased in the last twenty years (Fig. 6). Taken together, decreased maximum sizes, high fishing mortality and exploitation rate and decreased catches probably indicate recruitment overfishing of the species in the Caqueta River. Brachyplatystoma rousseauxii is a large, highly fecund, relatively long-lived migratory species that typically falls within the "periodic strategists" category defined by Winemiller & Rose (1992). Species displaying such suites of life history traits have long been considered, erroneously (see Sadovy 2001), very resilient to fishery exploitation, although they conform poorly to fisheries management models (Winemiller 2005). Among the many evidences against such belief, reviewed in Sadovy (2001), the dire state of the most important commercial marine fish stocks, generally conformed of periodic species, is a particularly strong one (Sadovy, 2001;Winemiller, 2005). In fact, large species, such as B. rousseauxii, have longer generation times and greater vulnerability to exploitation because of their lower potential rates of population increase (Winemiller & Rose, 1992;Jennings et al., 1998;Winemiller, 2005). Additionally, despite their higher compensatory potential, large periodic species performing large migrations are further vulnerable to habitat degradation and dam construction (Winemiller, 2005), a particularly important threat for B. rousseauxii.
This situation therefore calls for adaptive management strategies, as a collapse of B. rousseauxii's fisheries would lead to important socio-economical problems in the region. Fishing is the first most important economic activity of rural communities in the Caqueta (Rodríguez, 1991;Muñoz-Sosa, 1993;Castro & Santamaría, 1993;Agudelo, 1994;Celis, 1994;Gómez, 1996) and B. rousseauxii is the target species (Agudelo, 1994;Celis, 1994). But B. rousseauxii and the other large pimelodid catfishes are also responsible for more than 80% of the fish-related commercial shipments between the Colombian Amazon and the interior of the country (Agudelo, 2007;Agudelo et al., 2009). Given its extensive migratory behavior along the entire Amazon basin, however, efforts at managing this species would make sense only at a regional scale. A good starting point would be the tri-frontier zone between Brazil, Colombia, and Peru including the Putumayo, Caqueta and Amazon rivers, in association with Ecuador, where common fishing rules, mesh size, no-fishing periods and fishing gear recommendations could be implemented. Such concerted management strategy between countries could increase reproductive success by allowing fish to migrate upriver using temporal suspensions of specialized fishing fleets. Limiting the capture of large breeding individuals might also help them to grow older and larger (mega-spawners), ultimately improving the resilience of the species to exploitation (Froese, 2004). Environmental and fishing authorities, together with fishermen's unions and associations in each country should promote a regional management strategy instead of using one-sided and uncoordinated minimum size and fishing gear regulations for this species and other large catfishes. Indeed, a recent study of fisheries patterns in the Colombian Amazon concluded that, to date, fisheries regulation had not succeeded in avoiding yield decrease of some formerly important species, which were progressively replaced by other species, evidencing a selective collapse of catches (Agudelo, 2007). Similar conclusions were made for the Peruvian Amazon, where catches of all the largest species, including B. rousseauxii and B. filamentosum, had strongly decreased to be progressively replaced by species with faster turnover, feeding lower in the food web and of lower commercial value (Garcia et al., 2009b). In order to avoid a collapse of the fishery and to promote the sustainable use of B. rousseauxii in the region, Colombia and the neighboring countries should urgently establish a multilateral process of participative coordination for the large catfish fisheries in the tri-frontier region (Petrere et al., 2004;Fabré & Barthem, 2005;Agudelo, 2007;Agudelo et al., 2009).
The observed differences in the timing of reproduction, age at maturity and growth of B. rousseauxii between the Peruvian Amazon and the Caqueta suggest the existence of distinct populations adapted to particular environmental conditions within the Amazon basin. Although genetic studies did not clearly support population structure (Batista & Gomes, 2006;Batista, 2010), recent genetic analyses in the Upper Madera (Bolivian Amazon) and Western Amazon (Iquitos) provided strong evidence for the existence of a complex population structure of B. rousseauxii in the Amazon basin (Carvajal-Vallejos, 2013). This emphasizes our lack of knowledge about this economically and ecologically important migratory species and its close relatives of the genus Brachyplatystoma, and the need for recent and more comprehensive information on their life histories and genetic structure at the Amazonian scale. Studies on their life histories, however, are becoming ever more difficult owing to their decreasing abundance (Petrere et al., 2004;Garcia et al., 2009b) and the fact that they arrive almost always eviscerated and beheaded at the markets. Yet, simple monitoring of their growth and mortality patterns, which are essential for management strategies, are still possible to implement, providing good length-frequency data are collected. In addition to the management recommendations expressed above, we stress the importance, for national fishery organizations, of collecting good length-frequency data for large catfishes, in order to keep monitoring the dynamic changes of their populations. Recently published evidence (Petrere et al., 2004;Garcia et al., 2009a) and this study, all based on data collected more than ten years ago, demonstrate the urgent need for recent information on these exceptional resources.