Innovations in Survey and Sampling Design in the Chilean Crustacean Swept Area Assessments

"Not to be cited without prior reference to the authors" ICES CM 2012/F:12

Innovations in survey and sampling design in the Chilean Crustacean Swept Area Assessments

E. Acuña1, R. Alarcón2, L. Cid3 and A. Cortés1.

Abstract

Three crustacean species are subject of yearly swept area assessments off Northern-Central Chile: a pandalid shrimp (Heterocarpus reedi) and two munidid squat lobsters (Cervimunida johni and Pleuroncodes monodon).

One of the first improvements of these studies, was establishing the latitudinal and longitudinal distributions of the three species in their fishing grounds, using all positive survey and commercial tows irrespective of the catch obtained, providing useful information to decide the best sampling strategy. Innovations in swept area assessment surveys included changing the original systematic sampling with longitudinal transects design, the introduction of an adaptive sampling strategy due to a requirement of intensifying sampling effort in the areas of higher abundance of the species and finally, adopting the stratified random sampling for the three resources. Methodological approaches related to tow duration, determination of tow beginning and end, are also addressed.

Keywords: Squat lobsters, deepsea shrimp, trawl research surveys, Chile.

Contact author: Enzo Acuña, Dept. Biología Marina, U. Católica del Norte, Casilla 117 Coquimbo, Chile. [email protected]

1 Depto. de Biología Marina. Universidad Católica del Norte. Casilla 117- Coquimbo, Chile. Phone-Fax 56 51 209814, [email protected], [email protected] 2 CEPES. Centro de Estudios Pesqueros. Phone 56 2 9644583 [email protected] 3 Depto. de Estadística. Universidad del Bío Bío. Concepción, Chile. Phone 56 41 3111141, [email protected]

Introduction

The yellow squat lobster Cervimunida johni, red squat lobster Pleuroncodes monodon and deepsea shrimp Heterocarpus reedi fisheries, are important crustacean fisheries in northern-central Chilean lower shelf and upper slope, between 150 to 500 m depth. The shallowest species is the red squat lobster which is found normally between 120 and 250 m, the yellow squat lobster is found between 180 and 300 m and the deepsea shrimp is found between 250 and 500 m depth and from 24 to 38°S (Acuña et al., 2007).

Since 1993, the Fisheries Research Fund (Fondo de Investigación Pesquera, FIP) has financed bottom trawl research surveys to determine the biomass and abundance of these three crustacean resources: the two squat lobsters and the deepsea shrimp found in northern-central Chilean waters. Different research teams have performed these studies and made some changes in the research protocol through time; we make a review of these studies, complementing a previous study required by this financing agency (Acuña et al., 2007).

The objective is to determine the optimal sample size and randomization strategy, considering survey costs and sampling variability. The baseline of a sampling strategy being to gather the maximum amount of information (regarding the parameters to be estimated) with the minimum possible sample size (i.e. the minimum cost).

Bottom trawl surveys provide stock assessment models and age and size composition information with fishery-independent estimates of relative abundance based on catch per unit effort (CPUE), . Precision of these CPUE estimates is in part affected by variability in the sampling efficiency of the trawl, to minimize such variability, survey scientists pay close attention to the maintenance of strict fishing procedures, such as gear deployment, retrieval, and towing speed (Weinberg et al., 2002).

One of the core issues in bottom trawl survey methodology and in other experimental trawling situations is standardizing and measuring the fishing effort. Whether survey results are used to prepare “area swept” estimates of absolute abundance, to compute indices of relative abundance, or to calculate other fishing efficiency statistics, controlling and quantifying tow duration, and tow distance are considered important. The significance of these factors is comparable to others, such as the construction and rigging of the gear, adherence to a specified towing speed, and other operational protocols (Stauffer, 2004). There are several examples of bottom trawl surveys programs, like the MEDITS survey program, which are intended to produce basic information on benthic and demersal species in terms of population distribution and demographic structure, on the continental shelves and along the upper slopes at a global scale in the Mediterranean (Bertrand et al., 2002), which had, as one of its main challenges, the adoption of common standardized sampling protocols.

The sampling protocols for many groundfish trawl surveys define tow duration as the period between the time the trawl is determined to be on the bottom and in a stable fishing configuration and the time the trawl winches are engaged to retrieve the gear (usually at the end of some fixed, predetermined sampling period). In such cases, the towing distance is similarly defined as the distance transited by the vessel between the starting point and end point of the tow as previously defined (Wallace & West, 2006).

The swept area method requires quantitative information on the effective pathwidth of a trawl to estimate absolute densities of groundfish (Ramm & Xiao, 1995). Effort in trawl surveys is standardized by using a common gear and fixing haul duration and vessel speed. Such

standardization should result in a fairly constant distance trawled and area or volume swept (Adlerstein & Ehrich, 2002).

Variability in trawl efficiency due to vessels and gears can be controlled by keeping these factors constant or adjusted for by applying corrections based on comparative fishing experiments when changes are made. Similarly, keeping surveys within similar time periods in each year can control seasonal variability. Conversely, diel variability can be more difficult to control, especially in the face of the logistical constraints of marine ecosystem sampling that often requires fishing to occur during both day and night (Benoît & Swain, 2003).

Pennington & Vølstad (1991) pointed out several benefits fromdecreasing tow duration, like saving survey time, increasing the number of stations with higher precision of abundance estimates, reducing operating expenses, since gear and equipment wear is a function of tow length, so it is fuel consumtion while dragging a trawl. There is also less chances that an obstruction will cause a tow to be aborted or damage the gear. Smaller catches require less sorting time and allow more time for taking other biological measurements, gear saturation, the filling of the sampler with animals or debris before the tow is completed. Godø et al. (1990) analyzing data for cod, haddock and long rough dab had determined that short tows are at least as efficient as long tows in catching fish of any size and based on their results suggested that the efficiency of trawl surveys can be increased by reducing tow duration. Somerton et al. (2002) observed in the eastern Bering Sea (EBS) bottom trawl survey that, due to recent population increases of several fish species, 30 min tows often produced catches that were too large to be feasibly sorted in their entirety. These require subsampling procedures that are time-consuming and may result in increased sampling variability and bias, suggesting that one way to reduce the need for subsampling is to reduce tow duration.

Stocks of Pandalus borealis off West Greenland have been assessed using a research trawl survey since 1988 (Carlsson et al., 2000). The survey has used a design of randomly placed stations, stratified (on depth data where available, using small blocks elsewhere), with sampling effort proportional to stratum area. In some years, a two-stage adaptive sampling scheme was used to place more stations into strata with large first-stage variation in catches. The design of the survey was reviewed in 1998 (Carlsson et al., 2000, Folmer & Pennington, 2000). Four modifications to the survey were proposed during the first phase of the review: (1) increasing the number of stations sampled by shortening tow duration from 60 to 15 min, (2) reallocation of effort from areas of historically low density to areas of high abundance, (3) pooling strata to increase the sample size in the resulting (combined) strata and (4) abandonment of two-stage sampling. In 1998, tow duration was reduced from 1 h to 30 min at 25% of the stations, two stage adaptive sampling was discontinued, and sampling effort was reallocated (Folmer & Pennington, 2000).

Relative abundance indices and their variances derived from trawl surveys were often estimated in the past from standard mean and variance calculations. This method is referred to as Normal in comparison with those in use for particular distributions. For a given species, hauls generally show an irregular distribution with many zero values and some very large catches (Caverivière, 1993). Presently, the Delta Distribution system of analysis, seems best suited to increase the efficiency in mean and variance calculations for trawl surveys (Pennington, 1983 and 1986).

Delta Distribution treats positive values separately, under the assumption that they have a simple lognormal distribution, and then the zero values are included. A hyper-geometric function, which can easily be computed, is used. The efficiency of Delta Distribution depends on the number of trawl tows, on the proportion of zero values and on the variability range for positive values (Smith, 1988).

Since the late 1980´s and during the 1990’s, geostatistics has been widely used for the estimation of abundance of demersal resources (Maynou, 1998). It has also been used by to study the spatial distribution of other munidids like Munida intermedia and M. sarsi on the Galician continental shelf in NW Spain (Freire et al., 1992) and for mapping, estimating biomass and optimizing sampling programs in the northern shrimp, Pandalus borealis (Simard et al., 1992). Over the past 10 years, fisheries scientists gradually adopted geostatistical tools when analyzing fish stock survey data for estimating population abundance. First, the relation between model-based variance estimates and covariance structure enabled estimation of survey precision for non random survey designs. The possibility of using spatial covariance for optimizing sampling strategy has been a second motive for using geostatistics. Kriging also offers the advantage of weighting data values, which is useful when sample points are clustered (Petitgas, 2001).

This article reviews the characteristics of the survey design and sampling strategies, tow duration, and in general the methodology used to assess the biomass and abundance, of the two squat lobsters and the pandalid shrimp populations in Chilean waters, and the improvements made through time in different aspects of the trawl surveys.

Material and Methods

Sampling strategies

Although several sampling strategies have been used, the randomization of the sampling selection needs to be conditioned by the spatial distribution of the species, which, for these species, has one of two characterizations. One in which the distribution of the species consists of clearly detectable fishing grounds (squat lobsters), and other in which there is a continuous abundance band, in which it is difficult to distinguish fishing grounds (deepsea shrimp). In both cases, we divided the area of abundance into sampling grids consisting of 1 nm x 1 nm cells, which were defined as the sampling units. Within each sampling unit, a tow was executed and the biomass captured was considered as representation of the abundance of the entire cell.

Considering the fact that species are distributed in narrow bands parallel to the coast, running north to south along central Chile, up to year 2003, the sampling strategies considered a systematic sampling with longitudinal transects. This had a twofold objective, firstly to achieve a complete coverage of the area of the fishery, from 24 to 38ºS with transects located every 10º of latitude and secondly, to have an almost complete longitudinal coverage of the abundance bands (Figure 1.1.). The randomness of the selection was achieved by randomly selecting the location of the first transect. The transect consisted of a strip of sampling units with longitudinal orientation (east to west) to cover the entire abundance band width. Within this transect one of every two or every three units were trawled, and the abundance estimated for the tow was assumed to be the same for the entire unit.

A further refinement of the systematic sampling was the introduction of an adaptive strategy. This scheme was used due to the requirement of intensifying the sampling effort in the areas of higher abundance of the species. The adaptive strategy increased the number of transects in those areas where a predefined minimum capture for a given species was obtained.

When in a given transect such minimum was reached, two additional transects, located 5 nm north and south of the first transect, were obtained (Figure 1.2.). The same procedure was used in all cases where the capture was higher than the minimum. Although this is a well documented procedure,

there were two main drawbacks, one was that this type of strategy is designed for clustered populations (Francis 1984, Thompson 1988, 1990, 1991a, 1991b, 1992, Thompson et al. 1992), and second, that it is not possible to previously define the sample size, which is a major drawback in researches with limited budget, which allows but a fixed amount of tows. This dynamic allocation of stations also had some logistic inefficiencies of extra steaming and back-tracking to add stations in areas already sampled, which reduced the cost-efficiency ratio, as was also observed by Carlsson et al. (2000) in the Pandalus borealis fishery off Greenland, therefore this allocation was abandoned and only a predetermined design was used.

Since some species are not distributed in clusters, but in a more uniform way along their abundance bands, systematic sampling was not considered to be an appropriate strategy, then simple random sampling was used along the entire band of abundance (Figure 1.3.). This strategy has been documented as more effective than systematic, stratified random and adaptive sampling for the cases of uniform distribution (Cochran, 1977, Thompson, 1992).

In contrast with previous randomization strategies, stratified random sampling has been successfully used in the last ten years for the squat lobster species, which have clearly delimited fishing grounds, particularly when there exists a requirement of intensifying the sampling effort precisely in those fishing grounds. For that purpose, a stratified randomization was defined, using the historic fishing grounds determined from previous data as strata, with each fishing ground being defined as a different stratum. The number of samples was allocated in each stratum proportionally to its size and using simple random sampling within the stratum.

As an alternative stratification method, the abundance gradient of the species was used to define the strata. In such cases, the allocation of number of samples was determined by the species density instead of the size of the strata, as shown in Figure (2). In this case, the abundance gradient has a latitudinal orientation.

Resampling

As mentioned, to estimate the total biomass of the species, the abundance estimated for the tow was assumed to be the same for the entire unit. Being this assumption rather ambitious, we explored into the between tows variability within each sampling unit. For this purpose we replicated the tows within a number of unitary cells. We replicated the tows up to five times within each of a number of cells, and the results were analyzed using variance component analysis. The data collected did not allow us to conclude the distribution within cells was non homogeneous, although this result need to be further explored.

Tow duration and Swept area determination

To implement some of the benefits listed by Pennington and Vølstad (1991) and Godø et al. (1990) in Chilean crustacean research trawl surveys, shorter tows were implemented since 2003, replacing the 30 min tows previously used, by 15 min tows. The trawl bottom contact, which is considered the beginning of the effective tow duration or towing time (min), was determined by acoustic instrumentation (NETMIND tilt sensor) installed in the bottom of the trawl (Figure 3).

The swept area is obtained as the product between the effective tow duration (ETD) and the wing spread (WS). Both measures are obtained by acoustic instrumentation (NETMIND Wing Spread sensors) installed in the wings of the net. In the last five years, almost in 70% of the tows the wing spread has been measured with the NETMIND. However, in the case when both vessels (the

5 artisanal and the industrial) operate at the same time, we use the NETMIND in one of them, preferably the artisanal. Then, to calculate the swept area, we developed a functional model for the wing spread with General Linearized Models (GLM) using depth (m), trawl speed (knots) and length of the net cable (LNC, m) as (in R language):

glmWS ~ Speed  LNCDepth ,: family  gaussian

Sampling gear and onboard procedures

The standard device is a bottom trawl, including all the material and its rigging from the doors to the codend of the net. Its codend mesh size is 40 - 50 mm (stretched mesh).

The chosen fishing gear used by the vessels is the same bottom trawl used commercially and has remained with almost no modifications over the history of the surveys (Acuña et al., 2007).

Along the coast two different areas were sampled, a strip of 5 nautical miles (nm) which is reserved by law for the artisanal fishermen, where an artisanal boat i.e. less than 18 m total length must be used, and the area outside the previous one where industrial vessels can be used. Chartered fishing vessels were used, and as much as possible, the same vessels were used every year in each area.

The depth of the sampling locations varied from 50 to 450 m depth allowing, encompassing the whole depth range of the two squat lobsters in the area of study. In the case of the deep sea shrimp, the set depth of the sampling locations varied from 100 to 600 m depth allowing, encompassing the whole depth range of this species.

The total weights of the catch of the target species and their by-catch were obtained on board, but the samples from the target species and their by-catch for biological purposes, were analyzed in the laboratory. A subsample from each tow was used to measure , individual length, weight and sex (including sexual maturity stage) for each target species. Fecundity was also normally determined.

Spatial distribution of target species

In the geostatistical literature, an autocorrelated variable is termed a regionalized variable (Maynou, 1998). The example of regionalized variable which is used in our bottom trawl surveys is the density of P. monodon, C. johni (squat lobsters) or H. reedi (deep-sea shrimp) over the fishing grounds off northern-central Chile.

The fishing grounds limits were determined applying the transitive geostatistical method. The analysis was performed independently for either squat lobster species or the deepsea shrimp. The use of this approach was based in the fact that the sampling design (tows) implies going beyond the limits of the species distribution, and that all sampled values are considered, including zeros. We also assumed that the population densities systematically decrease towards the geographical limits of the species distribution.

Biomass and abundance estimates

Several methods have been used to determine the biomass and abundance of the two squat lobsters or deep-sea shrimp, according to the mean density estimator in an historical order are: arithmetic mean, ratio estimator, Δ distribution (Pennington, 1983, 1996), geostatistical estimator (Matheron, 1971,

Petitgas, 1993). The behavior of those methods in relation to the zero values in the data was analyzed.

At present we use the geostatistical method. The function of covariance describing the spatial autocorrelation is called structure function (Maynou, 1998), in this case the variogram. To compute the geostatistical experimental variograms we used Maynou’s (1998) procedure using various R packages (Ihaka & Gentleman, 1996; http://www.r-project.org)

Results

Only some selected results for the two squat lobster species as an example are shown, since the main objective of this research was precisely to review some of the aspects involved in the changes implemented in the bottom trawl crustacean surveys, namely the associated sampling strategies. The impact of the stratified random sampling design in comparison with the adaptive design previously used in terms of the number of species positive samples, i.e. samples where the red or yellow squat lobsters were captured are shown in Table 1. In both species the number of species positive samples obtained were higher, but in 2005 for P. monodon.

Besides the number of positives samples, i.e. samples where one or the two species of squat lobsters were captured, that were obtained using a stratified random sampling design, was always higher than 67.9%. We did not have access to the same type of data from previous studies for comparison purposes (Table 1).

The fishing grounds limits for both squat lobster species in part of the study area are shown in Figures 4 and 5, where three different ways of representing these areas are presented.

Biomass and abundance estimates

The sample mean is recognized as an unbiased estimator of the mean population density independent of the underlying distribution from which random sample is taken. However, in studies of swept area the probability distribution of the local density is often highly skewed, representing serious problems for its use as an estimator of the mean population (Grosslein, 1971, Pennington, 1996). In this case, the sample mean itself has a skewed distribution converging to a symmetric normal distribution only when the sample size becomes infinitely large (asymptotically normal).

When sampling from a skewed distribution such as trawling data of deep-sea shrimp, yellow and red squat lobsters with a small to moderate sample size (sometimes limited budgetary), the mean population density estimator is quite sensitive to high and infrequent observations which tend to overestimate the population mean. The extent of this overestimation depends largely on how extreme the observation is (Syrjala, 2000). Similarly, the variance estimator of the sample mean is much higher indicating a very low precision of the mean estimate.

Four mean density estimators were compared in relation to their behavior to the presence of zero values. A regular grid was made with density data (Figure 6) and different proportion of zeros. For the arithmetic mean (average), a proportional reduction in the average density is produced when the proportion of positive stations decrease. On the contrary, the confidence interval of the biomass estimation increases when the proportion of positive stations decreases, meaning that the variance also is increased (Figure 7).

The ratio estimator of the mean population density was calculated as the ratio between the catch and the fishing effort (swept area, SA) as:

n Ci i1 CPUAk  n  SAi i1

2 where CPUAk is the mean density (capture per unit of area, t/km ) in the k spatial unit (fishing ground), Ci is the capture (t) in the i trawl inside the spatial unit assessed.

The ratio estimator is highly sensitive to extreme values (outliers) and was considered in this study because it was widely used in the first crustacean surveys and is still used for comparison with such studies. In this case, a reduction of the mean estimator was not observed but an increase in the variability of the biomass estimate was observed which leads to estimations where the estimated variance is 1.2 times the one with 100% positive stations (Figure 8).

To properly use t the mean population density estimator of the Delta distribution to estimate the biomass it should comply one condition, that the probability distribution of the logarithm of non-zero values should be normal (Syrjala, 2000). When this condition occurred, the simulation was considered valid. In that case, when the proportion of positive stations declined a decreasing trend in the mean estimator, similar to the arithmetic mean, was observed (Figure 9).

In the case of the intrinsic geostatistical estimator or just “geostatistical estimator” also a decreasing trend is observed in relationship with the mean density, but with a lower magnitude in comparison with the Delta distribution method (Figure 11). The comparison of the variance of the biomass estimates between the last two methods with respect to the estimation with 100% positive stations shows that with the geostatistical method the change of the variance is almost 2.2 times. On the contrary, with the Delta distribution methods this change can reach up to 18 times (Figure 9).

So, taking into account these results, we consider that the best mean density estimator for biomass calculations is the geostatistical estimator.

Discussion

The methodological changes seen in the bottom trawl research surveys to assess the biomass and abundance of lower shelf and upper slope crustacean in the northern-central Chilean waters, especially in terms of the sampling design are very similar to those reported by Carlsson et al. (2000) for the research trawl survey of the stocks of Pandalus borealis off West Greenland.

In the Chilean experience, the issues addressed, up to this point, are the sampling design, the number of stations (tows), tow duration, reallocation of effort from areas of historically low density to areas of high abundance, several of these also suggested by Folmer and Pennington (2000) in their analysis of the research trawl survey of the stocks of Pandalus borealis off West Greenland.

When estimating the total biomass, the assumption of uniform distribution of the species in the sampling unit area, needs to be further studied. A specific design needs to be used for this purpose,

since it is crucial to extrapolate the result from one tow, which measures less than 1% of the sampling unit area, to the entire cell.

Issues related with the sampling gear have not been addressed yet and only the commercial trawl has been used, however, the same trawl as well as the same fishing vessel has been used during the last eight years. Actually there is an ongoing study analyzing the commercial trawl characteristics which will probably end with a new design for the trawl, which should then be studied with respect to the several aspects related with the sampling gear involved as analyzed by Wallace & West (2006), Ramm & Xiao (1995) and Adlerstein & Ehrich (2002) among others.

An ongoing analysis of the swept area studies performed in Chilean waters since 1993 has the aim to propose a Manual, where all the characteristics of the bottom trawl research studies should be considered with respect to sampling design, the information collected, and the management of the data as far as the data storage (Data Bank) and production of common standardized analyses of the data. There are several examples of bottom trawl surveys program that have produced this kind of Manuals, like the MEDITS survey program (Bertrand et al., 2002, MEDITS, 2007) had as one of its main challenges the adoption of common standardized protocols, the IBTS Group (ICES, 1999) and the Manual of the Baltic International Trawl Surveys (BITS) (ICES, 2007).

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Table 1. Number of positive samples, i.e. samples where one or the two species of squat lobsters were captured and number of species positive samples, i.e. samples where the red (P. monodon) or yellow (C. johni) squat lobsters were captured, obtained with different sampling designs used in trawl research surveys off Chile. *= not available.

Project number and citation Sampling design Tows Total Positive P. monodon FIP Nº 2000-05 Esc. Cs. del Mar (2000) Adaptive/transects 792 * 186 (23.5%) FIP Nº 2001-06 Canales et al. (2002) Adaptive/transects 682 * 228 (33.4%) FIP Nº 2002-06 Canales et al. (2003) Adaptive/transects 1168 * 158 (13.5%) FIP Nº 2003-31 Bahamonde et al. (2004) Adaptive/transects 719 * 127 (17.7%) FIP Nº 2003-03 Acuña et al. (2004) Randomly Stratified 271 188 (69.4%) 115 (42.4%) FIP Nº 2004-11 Acuña et al. (2005) Randomly Stratified 876 595 (67.9%) 266 (44.7%) FIP Nº 2005-09 Acuña et al. (2006) Randomly Stratified 807 594 (73.6%) 196 (24.3%) FIP Nº 2006-04 Acuña et al. (2007) Randomly Stratified 847 650 (77.8%) 288 (34.0%) FIP Nº 2007-19 Acuña et al. (2008) Randomly Stratified 709 491 (69.3%) 218 (30.8%) FIP Nº 2008-16 Acuña et al. (2009) Randomly Stratified 658 538 (81.8) 285 (43.3%) FIP Nº 2009-15 Acuña et al. (2010) Randomly Stratified 566 507 (89.6%) 247 (43.6%) FIP Nº 2011-01 Acuña et al. (2012) Randomly Stratified 630 483 (76.7%) 300 (47.6%)

Project number and citation Sampling design Tows Total Positive C. johni FIP Nº 2000-05 Esc. Cs. del Mar (2000) Adaptive/transects 792 * 298 (37.6%) FIP Nº 2001-06 Canales et al. (2002) Adaptive/transects 682 * 266 (39.0%) FIP Nº 2002-06 Canales et al. (2003) Adaptive/transects 1168 * 330 (28.3%) FIP Nº 2003-31 Bahamonde et al. (2004) Adaptive/transects 719 * 276 (38.4%) FIP Nº 2003-03 Acuña et al. (2004) Randomly Stratified 271 188 (69.4%) 397 (45.3%) FIP Nº 2004-11 Acuña et al. (2005) Randomly Stratified 876 595 (67.9%) 327 (40.5%) FIP Nº 2005-09 Acuña et al. (2006) Randomly Stratified 807 594 (73.6%) 368 (43.5%) FIP Nº 2006-04 Acuña et al. (2007) Randomly Stratified 847 650 (77.8%) 368 (43.5%) FIP Nº 2007-19 Acuña et al. (2008) Randomly Stratified 709 491 (69.3%) 323 (45.6%) FIP Nº 2008-16 Acuña et al. (2009) Randomly Stratified 658 538 (81.8) 338 (51.4%) FIP Nº 2009-15 Acuña et al. (2010) Randomly Stratified 566 507 (89.6%) 268 (47.3%) FIP Nº 2011-01 Acuña et al. (2012) Randomly Stratified 630 483 (76.7%) 198 (31.4%)

Figure 1. Sampling designs used in the bottom trawl surveys to assess crustacean resources in Chile. 1. Systematic transects. 2. Adaptive transects and 3. Stratified random sampling.

Figure 2. Latitudinal variation of H. reedi CPUE (kg/ km) analysis used to define sampling stratification in relation to local abundance.

Figure 3. Screen view of measurements of wing spread and beginning of bottom contact of the trawl by acoustic instrumentation (NETMIND tilt sensor).

Figure 4. Fishing grounds (densities, ton/km2) of squat lobsters in the crustacean research assessments in northern Chilean waters.

Figure 5. Fishing grounds (densities, ton/km2) of squat lobsters in the crustacean research assessments in northern Chilean waters, in 3D and contours.

(A) (B)

Figure 6. Simulated random sampling grid. (A) 100% positive stations. (B) 70% positive stations.

(A) (B)

Figure 7. Reduction of the arithmetic mean (average) of the population density (A) and confidence intervals for the biomass estimation using the arithmetic mean (B).

(A) (B)

Figure 8. Variability of the ratio estimator of the mean density (A) and variance (times) of the biomass estimation related to 100% positive stations (B).

Figure 9. Estimator of the mean density (A) and change ratio of the variance of the biomass estimation (B) by the Delta distribution and geostatistical method.