The Humboldt Current System (HCS) in the South Pacific Ocean (SPO) is among the most productive in the world (Gilly et al., 2013). Chile has a continental coastline of around 4,200 km with a north–south orientation, crossing different environmental conditions strongly associated with latitude, and whose atmospheric circulation is forced by the Pacific anticyclone.

This system, characterized by its high climatic variability, makes small pelagic populations fluctuating, with alternating inter- and intra-annual preponderance leading to relatively dense shoal formations with a marked daily cycle. Shoalings are highly aggregated during the day and dispersed at night together with less dense surface aggregations (Castillo et al., 2009). Catches show marked seasonality with maximums between February and May, supported by the annual summer season recruitment impulse (Cubillos et al., 2002). This incorporation of juveniles, dominated by the zero age group, defines the highest catches for the first half of the year (Aranis et al., 2016). This links the activity closely to recruitments, which are highly variable and vulnerable, as growing and maturing individuals are mostly removed from the population (Aranis et al., 2015). These high recruitment fluctuations make these populations especially difficult to manage, further complicated by environmental conditions that play an important role in all stages of their life cycle and in determining the success of reproduction and recruitment (Hjort, 1914; Lasker, 1975; Iles and Sinclair, 1982; Cury and Roy, 1989; Yáñez et al., 1990; Bakun, 1996; Cubillos, 1999; Cubillos and Arcos, 2002; Arcos et al., 2004; Castillo-Jordán et al., 2010).

These small pelagic species have a coastal distribution within 50 nautical miles (nm) from the coast. Biological productivity is generally high due to seasonal upwelling events, mainly from mid-September to March, the austral spring–summer period (Arcos and Navarro, 1986; Arcos, 1987; Cubillos et al., 2001). Spatial expression of spawning (eggs and larvae) does not exceed 20 nm and 20–30 nm in the case of juveniles and adults, mainly on the continental shelf, whose catches do not exceed 500-m depth in the water column, preferably between 3 and 80 m (Castillo et al., 1995; Frimodt, 1995; Cubillos et al., 2007; Castillo et al., 2009). Araucanian herring, Strangomera bentincki (Norman, 1936), and anchovy, Engraulis ringens (Jenyns, 1842), are more abundant within the first 5–10 nm associated with upwelling foci and the mouth of rivers (Cubillos and Arancibia, 1993). Industrial and artisan catches are clearly focused on the continental shelf, mainly in the Biobío Region (62%) and secondarily in the Araucanía and Los Ríos Regions (35%). From an environmental, oceanographic, and biological perspective, differences exist between both areas. North of Punta Lavapié (37° 08' 57"S, 73° 35' 00"W), the coastline tends toward the northwest, platform width is greater than 130 nm, cut by the Biobío Canyon, the Itata Canyon, the Arauco Gulf, and the Concepción and Coliumo Bays.

Administratively, extraction has been regulated since 2001 through fishing quotas and biological reproductive and recruitment periods since 1996. Although these measures strongly regulate fishing, they also led to periods of different intensities both in the industrial and artisan sectors (Aranis et al., 2015).

Total pelagic landings in the zone were sustained for some 15 years by Araucanian herring stock, a resource that spurs fishing operations mixed with anchovy. The average catch from 2010 to 2016 was 479,000 t, mainly by the artisan fleet (78%). A hegemonic presence of the species is evidenced in artisan fishery, partly reflecting the magnitude ratio of biomass and assigned quotas.

Recruitment or entry processes of juvenile Araucanian herring have been detected since 1999 using hydroacoustic methods (Castillo et al., 2010), while spawning biomass has been evaluated since 2002 via the daily egg production method (Cubillos et al., 2007), which incorporates reproductive dynamics and egg production. Such studies have yielded data on Araucanian herring spatial distribution of different developments in the southern region, as well as abundance quantifications, spatial spawning, and recruitment characterization (Castro et al., 1997; Castillo et al., 2010).

Size structure is a key biological trait of the population. To be contrasted correctly with other structures of different strata, it requires weighing upon capture. Hence, frequency-to-size measurements expand from catch in weight or number, representing the biomass or abundance by size class. This procedure requires the concurrence of the three main sampling components, catch or landing, length, and weight of the specimens. However, the imbalance of catch magnitudes affects the correct representation and entails uncertainty about the correct decision when integrating data that can vary spatially, temporally, and in relation to origin (artisan-industrial). In this context, average weights are not always available, though these data are essential for estimating various indices, functions, and statistics. To solve this problem, it is necessary to establish decision criteria regarding the feasibility of finding or obtaining alternative information and assessing another potential and representative solution that replaces the missing one. Lacking any of these estimates implies that significant volumes of catch or fraction landed cannot be processed, with potentially important consequences for the assessment of population structure, demographic fractions, and state of the fisheries. This has led to the need to define criteria for a different estimate of the length–weight relationship, first allowing to resolve the relevance of integrating data and second to offer the best solution for correct integration and representation. In sum, to set a goal for evaluating the validity of integrating pelagic fish length information from samples obtained from various sources, exploring, designing a statistical procedure that allows integrating different data sources or clusters, and incorporating the meta-analysis approach (Pearson, 1904; Plackett, 1958; O’Rourke, 2007; Nordmann et al., 2012) to estimate size distribution by combining catch data from commercial vessels and research fisheries are key. However, to integrate information from commercial and artisan vessels in order to apply the meta-analysis to estimate size distribution, we need to face zero-probability estimates due to non-catch of certain lengths, since zero probability does not indicate the non-existence of a specific length. To solve this issue before the meta-analysis, we carried out a Bayesian estimation of the capture probability for each length. To our knowledge, this is the first study using the meta-analysis technique to estimate the length distribution of Araucanian herring, integrating samples of different types of vessels. This procedure can be used in other fish species sampled in the catch.

In this section, we introduce the data set and study area where the samples have been collected. Afterward, we present the Bayesian procedure to estimate the probability of catch of each length and describe the meta-analysis method to estimate the length distribution. Finally, we present the meta-regression used to test whether there are significant differences between vessel types for each length.

The data used to estimate Araucanian herring catch for 19 lengths for each of the 18 vessels through meta-estimation are detailed in Table 3 . Of the 18 vessels, three (13, 16, and 17) were commercial fishing. Many lengths exhibited zero captures. Due to the presence of 0 values ( Table 3 ), the probability of capture for each length of each vessel was estimated through the Bayesian methods. The variance of each estimate was calculated using a sample size of 10,000 from the posterior distribution for each vessel.

After obtaining the Bayesian estimates for each length {8, 8.5, 9, … ,16.5, 17}, the estimates for each of the 18 vessels were combined using the previously described meta-analysis methodology. The process was repeated 19 times for each length. The meta-estimate was first performed by separating the data from the samples obtained by each type of vessel (commercial and research ones). Then, a meta-estimate was performed considering the samples jointly from both types of vessels. Figure 2 shows the distribution of the probability estimate for each length for research ( Figure 2A ), commercial ( Figure 2B ), and research and commercial ( Figure 2C ) vessels. Differences in the estimation of some probabilities between the research and commercial catch vessels are evidenced.

Research catch vessels showed a higher probability of catching Araucanian herring of lengths ranging from 9 to 13 cm. Commercial catch vessels showed a higher probability of catching Araucanian herring of lengths from 12.5 to 15.5 cm. To verify the existence of statistically significant differences in the probability of capture for the different lengths, a meta-regression was used considering a covariate that indicated the type of vessel. Figure 3 shows the contrast p-values for each length. Statistically significant differences in the estimation of capture probability were evidenced for 11 lengths (light blue dot).

Results show differences in the distribution of Araucanian herring length between fishing with commercial and research catch levels for certain sizes.

The meta-analysis methodology combined with Bayesian methods provides a framework to integrate information on Araucanian herring lengths from commercial and research catch vessels in order to estimate the size distribution structure. Our findings were applied in the reports that are delivered to the undersecretary of fisheries and its scientific committee in order to define the modifications of the biological closures of recruitment. According to the results, there are differences in the distribution of Araucanian herring length between commercial and research catch fishing related to certain sizes.

The correct application of a method that overcomes the feasible integration difficulties of sizes in pelagic fish will allow solving a technical issue. Results will also be applied in practical terms for better data interpretation and management, especially for recruitment processes in which diverse population components coexist, making analysis and result difficult. In sum, these results allow to improve, integrate, or segregate information under an objective statistical criterion. For example, this has been applied to the commercial fishing activity and studies under design and scientific methods; it also allows verifying the correct use of information from different vessels, fleets, and fishing gear.

Particular attention should be paid to data corresponding to oceanographic thermal anomalies that could alter biological conditions, especially average specimen weights. It is important to be careful with successive approximations when data are inserted in studies during a warm event (El Niño), when biological processes change strongly, probably resulting in weight decreases of some species. Additionally, care must be taken to exclude years with abnormal processes or estimates.

The practical application can be useful for similar studies of fishery analysts or of another nature, in which there must be contrasted levels of information that are very dissimilar in terms of the size of the sample or universe that they represent, being relevant a priori to see the real feasibility of integrating that information or not.

The original contributions presented in the study are included in the article. Further inquiries can be directed to the corresponding author.

Conceived and designed the study: AA, RDLC, and CM. Data curation: AA, MR, LC, AG, and KW. Analyzed the data: RDLC. Interpreted the data and wrote the paper: AA, RDLC, CM, MR, LC, AG, and KW. All authors reviewed the article. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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