Survey abundance indices in a tropical estuarine lagoon ... · weighted back transformation (Krige, 1981) for the ... Kriging interpola-tions were evaluated through jackknife cross-validation,

ICES Journal of Marine Science, 58: 1219–1231. 2001doi:10.1006/jmsc.2001.1122, available online at http://www.idealibrary.com on

Survey abundance indices in a tropical estuarine lagoon and theirmanagement implications: a spatially-explicit approach

Mario Rueda and Omar Defeo

Rueda, M., and Defeo, O. 2001. Survey abundance indices in a tropical estuarinelagoon and their management implications: a spatially-explicit approach. – ICESJournal of Marine Science, 58: 1219–1231.

We estimated the spatial population structure and biomass of Eugerres plumieri, Mugilincilis, and Cathorops spixii in a tropical estuarine lagoon in Colombia, based onsurvey data carried out seasonally in 1993–1994 and 1997. Geostatistical techniquesand the swept area method were used to map and estimate fish biomass, whereasuncertainty in spawning biomass was estimated by Monte Carlo analysis to assess thestatus of the fishery. Biomass tended to be spatially autocorrelated and populationswere distributed in high-biomass patches of 2–15 km in diameter. The spatialdependence was variable among species and seasons. High-biomass patches did notoverlap in space between species, which could be viewed as a way of reducing oravoiding potential interactions. However, the occurrence of highest biomass for E.plumieri and M. incilis during the same season might be directed to overcome the effectof a widely fluctuating environment such as occurs in estuarine lagoons. Selectivityexperiments were performed to account for the effect of fishing gear vulnerability inbiomass estimates. Application of the encounter probability model showed increasingprobabilities of capture with individual size and differential avoidance behaviouramong species. Risk analysis, used for testing a biological reference point defined interms of harvesting and spawning biomass, suggested the need to take immediatemanagement actions for E. plumieri.

� 2001 International Council for the Exploration of the Sea

Keywords: fish biomass, geostatistical mapping, selectivity, limit reference points,tropical estuarine lagoon, Colombia.

Received 28 February 2001; accepted 23 July 2001.

M. Rueda and O. Defeo: Laboratorio Biologıa Pesquera, CINVESTAV IPNUnidad Merida, A.P. 73 Cordemex, 97310 Merida, Yucatan, Mexico. M. Rueda:Instituto de Investigaciones Marinas y Costeras, Apdo. 1016, Santa Marta, Colombia.Correspondence to M. Rueda: fax: 5299-812334; e-mail: [email protected]

Introduction

Estimates of fish biomass in estuarine tropical lagoonsoften rely on commercial cpue as an index of abundance.However, these estimates are highly problematic: theusually highly aggregated distribution patterns maycause cpue to remain relatively stable while stock abun-dance is being depleted (Caddy, 1999). Thus, assessmentof abundance should ideally come from direct methodsconsisting of intensive surveys aimed at capturing theusually highly aggregated patterns of population distri-bution in a variable estuarine environment (Whitfield,1993). Nevertheless, there is a conspicuous lack ofnon-cpue-based population estimates from tropicalestuaries because of the absence of directed surveys. Thefew published studies are based on multispecific esti-mates that do not consider spatially-explicit variations in

1054–3139/01/061219+13 $35.00/0

biomass for each species (mapping) and the inherentuncertainty in stock estimates (Blaber, 1997; Whitfield,1999). This is crucial to assess the status of a fishery andto formulate risk-averse management strategies directedto prevent overfishing.

Geostatistical techniques are useful in providingestimates of the variance-covariance structure andmapping of the spatial distribution of abundance ofhighly aggregated organisms (Conan, 1985; Simardet al., 1992; Petitgas, 1993; Pelletier and Parma, 1994;Maynou et al., 1998). Such approaches were used todescribe the spatial structure and provide biomassestimates of the three dominant fish species, Eugerresplumieri, Mugil incilis and Cathorops spixii (Santos-Martınez and Viloria, 1998), exploited in the CienagaGrande de Santa Marta (CGSM). This artisanal fishery
is one of most important of Colombia, with 3500 fishers,
� 2001 International Council for the Exploration of the Sea

1220 M. Rueda and O. Defeo

1300 canoes and a catch of 5334 t in 1994. The CGSM ispart of a lagoon-delta ecosystem classified as Type I(river-dominated, arid, low tidal; Thom, 1984), contain-ing fringe, basin and riverine mangroves together withsmaller lagoons, creeks, canals and mangrove swamps(Botero and Salzwedel, 1999). To the north, the lagooncomplex is separated from the Caribbean Sea by abarrier island, which has an inlet on its eastern and thatconnects the lagoon directly to the sea. Seasonal changesin salinity, due mainly to variability in inputs from riversand precipitation, influence the distribution, maturationand spawning rates of the main fish species (Rueda andSantos-Martınez, 1999; Rueda, in press). Even thoughthese fish populations show highly complex aggregatedpatterns of distribution (Sanchez, 1997; Bateman, 1998;Rueda, in press), there is no quantitative analysis of theconsequence of spatial variations in abundance on theprecision of population estimates. To address this issue,we undertook experimental fishing surveys to estimatethe biomass of these species, using the swept areamethod and geostatistics. Probabilities of exceedinglimit reference points (sensu Caddy and Mahon, 1995),defined in terms of harvestable and spawning biomass,were estimated taking into account spatial and seasonalpopulation variability together with the vulnerability of
each species to the fishing gear.
Methods

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Figure 1. Cienaga Grande de Santa Marta (CGSM), Colombia, showing the fixed grid of 115 stations sampled during eachseason. Coordinates of the stations correspond to the universal transverse mercator projection (UTM) from the 18th zone inColombia.

Study area and fishing surveysThe CGSM is the largest (450 km2) estuarine lagoon ofColombia (Figure 1). Four seasons affect the populationdynamics of the fish fauna in this lagoon: (I) ‘‘majorrainy’’ from September to November; (II) ‘‘major dry’’from December to April; (III) ‘‘minor rainy’’ from Mayto June and (IV) ‘‘minor dry’’ from July to August(Santos-Martınez and Acero, 1991; Rueda andSantos-Martınez, 1999; Sanchez and Rueda, 1999). Fourseasonal fishing surveys were conducted in two annualcycles (1993–1994 and 1997), based on a systematicdesign of 115 stations spaced 2000 m apart and locatedwith a GPS NAV 5000D, covering the whole CGSM(Figure 1). At each station, a haul was carried out usinga ‘‘boliche’’ or encircling gillnet of 5-cm mesh size, whichenclosed an average circular area of 5000 m2. Eightcanoes with outboard motor were used simultaneouslyto conduct each survey, which took approximately eighthours to complete. Individuals of E. plumieri, M. incilisand C. spixii collected at each station were counted,measured and weighed. Afterwards, fishes were sexedand maturity stages were determined by macro-scopic observation of the fresh gonad. A total of 9241specimens were measured during the study.

1221Survey abundance indices in a tropical estuarine lagoon

Modelling the spatial structure of the population

The intensive systematic sampling used in this study wassuitable for the application of geostatistics. The spatialprocess of fish biomass B(x) was observed in each seasonby means of 115 observations measured at a location x[Z(xi)], where x was defined by latitude and longitude ina two-dimensional space. Plots of fish biomass per haulof each species versus distance did not show spatialtrends along the geographical components for allseasons (�0.11<r<0.09; p>0.05). This satisfied theassumption of second-order stationarity, i.e. themathematical expectation of mean biomass was assumedconstant over the study area, with covariance betweentwo adjacent stations depending solely on samplinginterval (Warren, 1998). We did not find a proportionaleffect between local [i.e. any point sampled, Z(xi)] meanbiomass and local standard deviation (r<0.15 in allcases; p>0.05). This enabled the description of thespatial structure of biomass per species through exper-imental semivariograms �(h) for each season (Matheron,1971), using log-transformed data [log(x+1)], becauseraw data did not follow a normal distribution:

where Z(xi) is the biomass per species in a station xi,Z(xi+h) is another biomass value separated from xi by adiscrete distance h (measured in meters) and N(h) is thenumber of pairs of observations separated by h. We usedweighted back transformation (Krige, 1981) for thepurpose of mapping and to provide fish abundanceestimates in the original arithmetic scale, which providesmore reliable population estimates than simple back-transformations (GS+, 1998). Non-directional semi-variograms were appropriate because the same spatialstructure existed in all directions after checkinganisotropy. Analysis of directional variograms wereconsistent with isotropy, which thus represented themost parsimonious model of spatial structure. Amongseveral theoretical models, spherical and exponentialones best explained the spatial structure of biomass, andthus were used to fit the experimental semivariograms.The models provided the following parameter estimates(Cressie, 1991): the nugget effect (Co), which reflects thepresence of microscale variation; the sill (Co+C), whichdefines the asymptotic value of semivariance; and therange (Ao), defined as the distance at which biomassceases to be correlated. Goodness of fit criteria formodel fitting were the reduced sum of squares (RSS), thecoefficient of determination (r2) and the high number ofpairs near the semivariogram origin. An analysis of theresidual sum of squares (ARSS: Chen et al., 1992) wasalso performed to compare the semivariogram models
fitted for each species and season.
Biomass estimates per species and season for eachyear Z|(Xo) were obtained by ordinary point kriging,using the observed values Z(Xi) in the surroundingneighborhood as follows (Matheron, 1971):

where �i is the vector of observations that minimizesthe prediction error (Cressie, 1991). Maps of biomasswere performed over a 424�414 m regular interpolatinggrid covering the whole area (450 km2), whereas theneighborhood comprised at least 16 nearest neighboursrestricted on a radius of 20 000 m. Kriging interpola-tions were evaluated through jackknife cross-validation,fitting observed (O) and estimated (E) values to a linearregression of the form O=�+�E. Departures from aone-to-one line through the origin indicate modelinadequacy, and thus the significance of � and � wastested with standard t-tests under the null hypothesesthat �=0 and �=1 (Power, 1993). The estimated krigingstandard deviation was used as a precision indexdirected to delineate the area within which reliableglobal estimates could be estimated (Maynou et al.,1998). Seasonal variations in fish biomass per haul (rawdata) were also tested using a two-way ANOVA, withseasons and species as main effects. Assumptions ofnormality and homoscedasticity were tested and datawere log-transformed when necessary. When significantdifferences were found, Newman–Keuls test comparisonswere performed.

Estimation of global harvestable biomass

Global harvestable biomass and the standard deviationper species and seasons were estimated by (a) blockkriging (Bk) (Matheron, 1971) and (b) the swept areamethod (Bh) (King, 1995). In block kriging, we directlyestimated the mean and standard deviation of biomassin each discrete area (block) around an interpolationpoint. Thus, the discrete summation of mean estimatesprovided the total biomass over the sampled area.Estimates of kriging standard deviations (SDtk) wereobtained following the same reasoning. A formalcomputational treatment can be found in Journel andHuijbregts (1978) and Maynou et al. (1998).

The swept area method was applied as follows:

where C is the mean catch per area a enclosed by the net(5000 m2), A is the stock area (450 km2), and v is thevulnerability, defined as the proportion (of each fishspecies) retained within the area of influence of the gear


(King, 1995). The standard error (SEh) of the mean wasderived from the variance estimate (s2):

where n is the number of stations where hauls werecarried out and Ci is the catch per haul. Thus, the SEh

was estimated as SEh=s/√n (King, 1995).

Selectivity experiments

In order to diminish the estimation error derived fromglobal kriging and swept area methods, biomass esti-mates were corrected by the vulnerability parameter v,which takes into account the vulnerability of eachspecies to the sampling gear. To quantify v, selectivityexperiments were carried out during two seasons of1994, using two nets (one enclosing the other) with meshsizes of 5.0 and 1.9 cm in inner- and outer-net, respect-ively (see also Rueda et al., 1997). The encounterprobability model (Tokai, 1998) was applied to estimategear vulnerability, defined as the available-selection pro-cess (Millar and Fryer, 1999), proportional to thecontact-selection multiplied by the probability that a fishcontacts the gear given that it is available to the gear(length-independent encountering probability):

where P is the probability that a fish encounter theinner-net and the backeted term is the length-dependentcontact-selection curve of mesh selectivity (sensu Millarand Fryer, 1999). Species-specific estimates of par-ameters a, b, and P were obtained by maximizing thelog-likelihood function which gave the lowest value ofAkaike’s Information Criterion (AIC) (Tokai et al.,1996). It was impossible to obtain georeferenced lengthdata from the surveys. Thus, estimates of length-dependent vulnerability were averaged for each speciesbased on the length-dependent distribution of biomassin order to correct the biomass estimates derivedfrom geostatistical (B=Fish biomass/v) and swept area[Equation (3)] methods and to provide unbiased globalestimates of harvestable fish biomass.

Risk analysis

Seasonal harvestable (Bk, Bh) and spawning (Bsk, Bsh)biomass estimates were used to quantify the risk offalling below an undesirable biomass threshold. Tocompute Bs, the species-specific proportion of matureindividuals in each length class for E. plumieri (Ruedaand Santos-Martınez, 1999), M. incilis (Sanchez et al.,1998) and C. spixii (Tıjaro et al., 1998) was multiplied bythe corresponding estimate of total harvestable biomassat size. This short-term risk analysis was done with a

limit reference point (LRP) defined by two ratios (1)Bs/Bh=0.3 and (2) Bs/Bh=0.1, representing twoscenarios of fishery status. The scenario Bs/Bh=0.3 couldbe considered as risk-averse, whereas Bs/Bh=0.1 is risk-prone, on the basis of the concept of average resiliencedefined by Caddy and Mahon (1995), which consider30% of an unfished stock level as a recruitment-basedLRP. Monte Carlo analysis was used to explicitlyaccount for the uncertainty associated with natural andunpredictable variations in the parameters of Equation 3in order to quantify the Bs/Bh risk of falling below theLRPs above mentioned (theoretical managementscenarios: Seijo and Caddy, 2000). For this purpose, Cand v were randomly generated by Monte Carloresampling with lognormal and normal probabilitydensity functions, respectively, because the observed Cidata followed a lognormal distribution (Chi-square 7.06,d.f.=3; p=0.07), whereas vulnerability values per specieswere normally distributed (K-S test: p>0.05). MonteCarlo runs consisted of 1000 simulation trials for eachspecies and season, which produced the probabilitydistributions in Bh and Bs and the corresponding ratiosthat were used as LRP to evaluate fishery status.

Results

Spatio-temporal population structure

Semivariograms revealed that fish populations werespatially structured in 16 of the 24 seasonal surveys. Inthe remaining eight, among which five were carried outduring the minor rainy season, the lack of spatialautocorrelation was reflected in flat semivariograms(Figure 2), because of a pure nugget effect (Table 1).Spherical and exponential models successfully explainedspatial correlations of seasonal fish biomass, and thesame type of model tended to be consistent withinseasons and among years for a given species (Table 1).The spherical model best explained 11 of the 16 exper-imental semivariograms, reaching an asymptote at dif-ferent ranges (which could be considered as an estimateof patch size); whereas the remaining ones wereexplained by exponential models (Table 1), suggesting acontinuous decay of spatial correlation with distance.

Levels of spatial autocorrelation varied betweenspecies and seasons, which was reflected by a spatiallystructured biomass component [C/(Co+C)] (varianceexplained by the spatial models) that ranged between50% and 98% (Table 1). The location of high-biomasspatches did not overlap between species (Figures 3–5),and the distribution patterns for each species variedacross seasons. This high variability determined that thesemivariance significantly varied between seasons(ARSS analysis: F-test >100; p�0.001) and suggestedinstability in the spatial structure of the populations(Figure 2).


Mean biomass of E. plumieri was lowest in the minorrainy season of each year, when spatial autocorrelationwas not detected (Tables 1 and 2). The highest meanbiomass mainly occurred in the major rainy season of1993–1994 (74 kg km�2) and in the major dry of 1997(203 kg km�2). The kriging maps (Figure 3) showed adecrease in the size of the patches or even an absence ofpatches during the seasons of low biomass levels. M.incilis had the highest mean biomass in the major rainyseason of 1993–1994 (134 kg km�2) and in the minordry of 1997 (166 kg km�2), whereas the lowest biomassconsistently occurred during the minor rainy seasons(Table 2). In the remaining seasons, biomass turnedout to be relatively homogeneous within low levels(Figure 4). C. spixii did not show a defined spatialstructure in major rainy (1993–1994) and minor dry(1997) seasons, when mean biomass was lowest (Tables 1and 2). The highest biomass of C. spixii occurred inthe minor rainy season of 1993–1994 (54 kg km�2)and in the major rainy of 1997 (97 kg km�2), whenkriging maps evidenced strong aggregated distribution(Figure 5).

Jackknife cross-validation showed that kriging predic-tions for fish biomass were statistically significant, given

that the null hypotheses �=0 and �=1 were neverrejected (p>0.05, Table 1). This was corroborated bykriging standard deviations values, which were alwayslowest close to the sampling stations.

The mean biomass per haul (Table 2), significantlydiffered between seasons (F7,2718=48.8; p�0.01) andspecies (F2,2718=27.7; p�0.01). The season x speciesinteraction was also significant (F14,2718=26.6; p�0.01).E. plumieri presented higher seasonal biomass in 1997than in 1993–1994 (Newman–Keuls test: p�0.01),except for the major rainy season, when the meanbiomass per haul did not differ between years (p>0.05).Biomass of M. incilis showed the same patterns asE. plumieri, while biomass per sampling unit of C. spixiidid not differ between seasons and years (p>0.05),except for the 1997 major rainy season when biomasshad the highest value of the whole period (p�0.01).

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Figure 2. Semivariograms computed for fish biomass estimates for (I) major rainy, (II) major dry, (III) minor rainy and (IV) minordry in 1993–1994 (—�—) and 1997 (– – –�– – –) in the CGSM. Fitted models are presented in Table 1. All points include morethan 150 pairs.

Selectivity experiments and harvestable biomassestimates

The encounter probability model described by the three-parameter sigmoid function [Equation (5)] successfullyexplained the retention probability at size for the three


species (Figure 6). Non linear fitting of Equation (5)provided in all cases significant a, b and P parametersthat minimized AIC values. The selectivity of the inner-net was a function of species size, even though some fishlarger than 20 cm (e.g. C. spixii) succeeded in escapingfrom the inner-net, probably due to their digging behav-ior. Encounter probabilities to the inner-net for E.plumieri, M. incilis and C. spixii were estimated as 0.72,1.00 and 0.84 respectively, thus avoiding the net inproportions of 0.28, 0.00, and 0.16 (Figure 6). It wasassumed that the encounter probability to the outer-netwas 1.00, thus providing conservative estimates ofharvestable biomass. The resulting vulnerability thatincludes the selectivity curve and the encounter prob-ability was 0.5, 0.43, and 0.40 for E. plumieri, M. incilisand C. spixii, respectively. Kriging estimates of globalharvestable biomass were on average 16% lower than

swept area estimates when corrected by the aboveestimates of vulnerability for each species (Table 2).

Table 1. Parameters, goodness of fit criteria and cross-validation of the (Exp) exponential and (Sph)spherical models, fitted to fish biomass (kg 5000 m�2) experimental semivariograms during (I) majorrainy, (II) major dry, (III) minor rainy, and (IV) minor dry seasons in the CGSM. (Co) nugget effect,(Co+C) sill, (Ao, in m) range, (%) spatially structured component, (r2) coefficient of determination,(RSS) reduced sum of squares, (�) intercept, (�) slope, (r) coefficient of correlation. For all surveys, �and � were not significantly different from 0 and 1, respectively, and r was significant (p<0.05), bothfor the geostatistical models fitted and the jackknife cross-validation.

Season/yearSpecies Model

Parameters Goodness of fit Cross validation

Co Co+C Ao % r2 RSS � � r

(I)/93–94E. plumieri Sph 0.045 0.118 13 020 61 0.99 5�10�5 0.05 1.00 0.40M. incilis Sph 0.089 0.322 15 490 72 0.93 3�10�3 0.06 1.25 0.45C. spixii none — — — — — — — — —(II)/93–94E. plumieri Exp 0.007 0.036 1 760 78 0.53 9�10�5 0.01 0.97 0.45M. incilis none — — — — — — — — —C. spixii Sph 0.009 0.056 3 910 84 0.60 1�10�4 �0.08 0.86 0.33(III)/93–94E. plumieri none — — — — — — — — —M. incilis none — — — — — — — — —C. spixii Sph 0.016 0.088 3 460 80 0.55 3�10�4 �0.16 1.35 0.52(IV)/93–94E. plumieri Sph 0.003 0.024 3 030 84 0.37 2�10�5 0.03 0.70 0.26M. incilis Sph 0.004 0.010 12 650 61 0.92 2�10�6 0.00 1.07 0.46C. spixii Exp 0.001 0.065 2 350 98 0.98 1�10�5 �0.08 1.32 0.63

(I)/97E. plumieri Sph 0.017 0.056 8 780 70 0.94 5�10�5 0.04 0.88 0.54M. incilis Sph 0.012 0.055 3 510 78 0.83 2�10�5 0.05 0.74 0.26C. spixii Sph 0.021 0.160 6 980 86 0.82 1�10�3 0.06 0.91 0.47(II)/97E. plumieri Exp 0.088 0.177 4 510 50 0.92 3�10�4 0.21 0.83 0.36M. incilis Exp 0.050 0.131 5 570 62 0.83 4�10�4 �0.10 1.27 0.58C. spixii none — — — — — — — — —(III)/97E. plumieri none — — — — — — — — —M. incilis none — — — — — — — — —C. spixii none — — — — — — — — —(IV)/97E. plumieri Sph 0.020 0.138 4 190 85 0.43 2�10�3 0.03 1.30 0.42M. incilis Sph 0.032 0.162 4 040 80 0.63 8�10�4 0.10 0.86 0.39C. spixii Exp 0.008 0.038 2 140 79 0.60 7�10�5 �0.03 1.24 0.44

Risk analysis

Risk analysis using the scenario Bs/Bh=0.3 showed thatthe probability of falling below this undesirablethreshold varied between species and years (Figure 7).Thus (1) for E. plumieri, the ratio varied between 0.10(1993–1994) and 0.82 (1997); (2) for M. incilis, from 0.06(1993–1994) to 0.14 (1997); and (3) for C. spixii, from0.18 (1993–1994) to 0.13 (1997). Consequently, the prob-ability of achieving desirable levels for this biomassindicator was very high in all cases, with the exception ofE. plumieri in 1997, in which there was a high risk offalling below the LRP. The other indicator of the fisherygiven by scenario 2 (B /B =0.1), showed for all cases
s h


probabilities of falling below this LRP lower than 0.05,thus suggesting low probabilities of overexploitation.

Table 2. Swept area and block kriging estimates of fish biomass during (I) major rainy, (II) major dry,(III) minor rainy and (IV) minor dry seasons in the CGSM. Global estimates provided here werecorrected by vulnerability estimates. c and s.e. (kg km�2) are, respectively, the mean and standarderror of the biomass per haul; Bh and ..h are the mean total harvestable biomass (tonnes) and itsstandard error, computed by the swept area method; ck (kg km�2) is the mean biomass estimated byblock kriging and s.d.k its standard deviation; Bk and s.d.tk account, respectively, for the mean totalharvestable biomass (tonnes) and its standard deviation, computed by block kriging.

Season/yearSpecies

Swept area Global kriging

c s.e. Bh s.e.h ck s.d.k Bk s.d.tk

(I)/93–94E. plumieri 74 12 66 11 62 15 52 13M. incilis 134 38 140 40 92 86 92 84C. spixii 37 8 41 9 — — — —(II)/93–94E. plumieri 46 5 41 4 47 5 37 4M. incilis 3 1 3 1 — — — —C. spixii 47 7 53 8 49 11 48 11(III)/93–94E. plumieri 23 3 20 3 — — — —M. incilis 5 2 5 2 — — — —C. spixii 54 12 61 14 56 30 54 32(IV)/93–94E. plumieri 33 4 30 3 35 3 27 3M. incilis 8 3 9 3 7 1 7 1C. spixii 47 7 53 8 46 15 46 16

(I)/97E. plumieri 71 6 64 6 70 9 59 8M. incilis 39 8 40 8 41 7 36 6C. spixii 97 16 109 18 84 34 86 36(II)/97E. plumieri 203 17 182 15 194 24 167 20M. incilis 130 14 136 14 119 28 114 27C. spixii 31 4 35 5 — — — —(III)/97E. plumieri 59 7 53 6 — — — —M. incilis 21 5 22 5 — — — —C. spixii 46 6 52 7 — — — —(IV)/97E. plumieri 98 14 88 12 91 30 69 25M. incilis 166 16 174 17 159 48 141 47C. spixii 30 6 34 7 29 6 30 6

DiscussionWe provide some of the first model-based estimates ofpopulation abundance of fish species from a tropicalestuary. Species-specific biomass estimates are rarelydocumented for such systems, and pooled multispeciesestimates suggest that total fish biomass ranges from5000 to 15 000 kg km�2 (Blaber, 1997). The seasonalmean harvestable biomass for E. plumieri, M. incilis andC. spixii was estimated as 151, 147, and 122 kg km�2,respectively, which were similar to estimates for thesame families from a temperate estuarine lake in SouthAfrica (Whitfield, 1993).

Geostatistical models were useful tools for quantify-ing temporal variations in the spatial populationstructure at a fine resolution. The distribution pattern offish biomass varied between species and there was amarked seasonality in the location of high biomasspatches. Fish were randomly distributed in 33% ofsurveys, especially during the minor rainy season whenthe lowest biomass levels were encountered. In theremaining surveys, fish populations were most abundantand spatially structured in high biomass patches thatvaried from 2–15 km in diameter, particularly in themajor rainy season of 1993–1994 and in the major andminor dry seasons of 1997. Clustered patterns couldbe explained by strong reproductive aggregationsdocumented for the three species, especially close to orduring the major rainy season (Sanchez et al., 1998;


Figure 3. Eugerres plumieri. Ordinary kriging maps of fish biomass (kg 5000 m�2) in major rainy, major dry, and minor dryseasons in the CGSM. Kriged maps were not performed for the minor rainy season due to the lack of spatial autocorrelation.


Figure 4. Mugil incilis. Ordinary kriging maps of fish biomass (kg 5000 m�2) in major rainy, major dry, and minor dry seasons inthe CGSM. Kriged maps were not performed for the minor rainy (both years) and major dry (1997) seasons, due to the lack ofspatial autocorrelation.


Figure 5. Cathorops spixii. Ordinary kriging maps of fish biomass (kg 5000 m�2) in major rainy, major dry, minor rainy, and minordry seasons in the CGSM. Kriged maps were not performed for the major rainy (1993–1994) and major dry and minor rainy (1997)seasons, due to the lack of spatial autocorrelation.


Tıjaro et al., 1998; Rueda and Santos-Martınez, 1999).In this sense, the most abundant E. plumieri andM. incilis had high biomasses during the major rainy(1993–1994) and dry (1997) seasons, coinciding withparticularly high values of primary productivity andflushing of organic matter (Hernandez and Goke, 1990).

High biomass patches were located at sites that variedamong species (Figures 3–5), and this was especiallynoticed for the dominant E. plumieri and M. incilis,which had concurrent biomass peaks. Even though theopportunistic feeding behaviour enables these species tocope with a range of prey (Galvis, 1983; Blanco, 1983;Arenas and Acero, 1992), diet overlap between speciesare probably reduced by these differential distributionalpatterns within the estuary and by different habitatpreferences (Rueda and Santos-Martınez, 1999; Rueda,in press). The above could also suggest that the differ-ential location of high-biomass patches is the result ofspace partitioning as a way of reducing or avoidingecological interdependencies.

Harvestable biomass corrected by selectivity indicatedthat estimates by geostatistical techniques were onaverage 16% lower than for swept area estimates (seeTable 2). Variances have not been compared, because of

the inappropriateness of comparing design- and model-based estimators (Warren, 1998). Differences betweenestimates can be explained by the weighed effect ofkriging standard deviation for establishing size of areaswithin which reliable global estimates can be estimated.

Monte Carlo simulations, incorporating the uncer-tainty associated to resource abundance and vulner-ability consistently indicated that, with the exception ofE. plumieri for 1997, the spawning biomass to harvest-able biomass ratio (Bs/Bh) had low probabilities (i.e.<0.18) of falling below 0.3. However, E. plumieri in 1997shows some indication of overexploitation, given a pre-cautionary approach (Bs/Bh=0.3). This is consistentwith the increase in juvenile bycatch from 56% in1993–1994 to 83% in 1997, which could result in recruit-ment overfishing, as suggested by yield and biomass perrecruit analyses (Rueda and Santos-Martınez, 1999).For M. incilis (62%) and C. spixii (63%), juvenilebycatch remained fairly constant at high levels(Sanchez et al., 1998; Tıjaro et al., 1998; Rueda andSantos-Martınez, 1999). The open access nature of thefishery in the CGSM aggravates the above scenario, andcalls for a management redundancy framework (sensuCaddy, 1999) through a combination of operationalmeasures (e.g. controls over fishing effort, gear selec-tivity, and mean length at capture) and explicit rights ofaccess within specific area-season windows (e.g. controlsbased in spatial information on fish distribution).

In summary, we showed that experimental surveyswith design- and model-based estimates of biomass canbe effective fishery assessment tools in tropical estuaries.It must be emphasized that the simple equipment usedand the active participation of fishers during the surveysand in the selectivity experiments enabled the acquisitionof a complete database at very low research costs. This isparticularly important for managing small artisanal fish-eries in developing countries, where cost-effectivenessis essential to develop assessment tools for effectivemanagement frameworks and avoid overfishing.

0.030

1.0

Length (cm)5 10 15 20 25

0.2

0.4

0.6

0.8C. spixii

AIC = 59.9P = 0.84a = –11.97b = 0.69

0.030

1.0

Ret

enti

on p

roba

bili

ty

10 15 20 25

0.2

0.4

0.6

0.8M. incilis

AIC = 25.7P = 1.00a = –11.78b = 0.52

0.025

1.0

5 10 15 20

0.2

0.4

0.6

0.8E. plumieri

AIC = 54.0P = 0.73a = –12.09b = 0.92

Avoidance

Encounterprobability

Figure 6. Selectivity curves estimated for fish species in theCGSM. AIC: Akaike’s Information Criterion. Parameterestimates a, b, and P from Equation (5) are also shown.

AcknowledgementsThis paper is part of the PhD thesis of M.R. atCINVESTAV-IPN U. Merida. The INVEMAR,COLCIENCIAS (Grant No 2105-09-028-94), and GTZprovided logistical and financial support for fieldwork inColombia. We wish to express our gratitude to J. F.Caddy and T. Tokai for valuable suggestions to improveour manuscript. Two anonymous referees providedvaluable suggestions to the final manuscript. Thefirst author thanks J. Mendo and A. Santos-Martınezfor initial advice, and the ‘‘CGSM’s Fisheries Group’’ ofthe INVEMAR for field and laboratory assistance.Native fishers of the CGSM contributed, with theirfishing skills and their empirical knowledge of the area,to the success of the fishing surveys.


0.0000.96

Bs/Bh

Pro

babi

lity

0.100

Frequ

ency

0.020

0.040

0.060

0.080

0.100

0.32 0.53 0.75

20

40

60

80

100p = 0.18

Cathorops spixii

0.0000.96

Bs/Bh

Pro

babi

lity

0.100

Frequ

ency

0.020

0.040

0.060

0.080

0.100

0.32 0.53 0.75

20

40

60

80

100

p = 0.06

Mugil incilis

0.0000.96

Bs/Bh

Pro

babi

lity

0.100

Frequ

ency

0.050

0.100

0.150

0.200

0.300

0.32 0.53 0.75

50

150

250

300p = 0.10

Eugerres plumieri

0.0000.53

Bs/Bh

Pro

babi

lity

0.100

Frequ

ency

0.040

0.080

0.120

0.160

0.21 0.32 0.42

40

80

160p = 0.13

0.250

1993–1994

100

200

120

0.0000.53

Bs/Bh

Pro

babi

lity

0.100

Frequ

ency0.040

0.060

0.100

0.120

0.21 0.32 0.42

40

80

120p = 0.14

100

0.0000.53

Bs/Bh

Pro

babi

lity

0.100

Frequ

ency

0.040

0.080

0.160

0.200

0.21 0.32 0.42

40

80

200p = 0.82

120

0.020

0.080

20

60

0.120

160

1997

Figure 7. Risk analysis. Probability of falling below the LRP (shaded bars, p values are shown) given by the ratio Bs/Bh=0.3,defined as the lowest permissible limit. Probabilities of falling below this undesirable threshold are based on 1000 Monte Carlosimulation trials for 1993–1994 and 1997.

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