Growth Parameters and Mortality Rates Estimated for Seven Data-Deficient Fishes from the Azores Based on Length-Frequency Data

Given the scarcity of information suitable for stock assessments, the growth and mortality of seven exploited marine fishes in Azorean waters were estimated based on length-frequency data. The studied species were Trachurus picturatus, Sparisoma cretense, Scomber colias, Scorpaena scrofa, Serranus atricauda, Seriola spp. and Aphanopus carbo. The growth parameters L∞ (cm), k (year−1) and ϕ’ estimated through the ELEFAN_GA_boot routine were set at 55.87, 0.08 and 2.39 for T. picturatus; 55.03, 0.11 and 2.53 for S. cretense; 55.93, 0.18 and 2.76 for S. colias; 61.11, 0.11 and 2.61 for S. scrofa; 52.10, 0.12 and 2.51 for S. atricauda; 107.33, 0.12 and 3.18 for Seriola spp.; and 133.16, 0.09 and 3.19 for A. carbo; respectively. The total mortality rate estimated using the length–converted catch curve method was 0.22, 0.35, 0.58, 0.32, 0.31, 0.39 and 0.22 year−1; the natural mortality included 0.15, 0.20, 0.30, 0.20, 0.21, 0.21 and 0.16 year−1; and fishing mortality rate 0.07, 0.15, 0.28, 0.12, 0.10, 0.18 and 0.06 year−1, respectively, for the species mentioned. The relatively large sizes and slow growth with a low natural mortality rate indicate a high vulnerability to overfishing. Therefore, assessment and management initiatives are highly encouraged to ensure the sustainability of the resources.


Introduction
Knowledge of fish population dynamics (e.g., recruitment, growth and mortality) is essential for improving stock assessment and fisheries management [1,2]. Failure to manage fish populations efficiently may have devastating consequences for biodiversity as well as the livelihoods and socioeconomic situations of millions of people who rely heavily on these resources. Management strategies that successfully conserve the stocks and maximize sustainable yields are based on sufficient knowledge to understand the population dynamics and infer causal linkages between management measures (e.g., harvest control rules) and a fish population [3,4].
Growth parameters and mortality rates of fishes are crucial inputs for stock assessments. This is because they provide valuable information on the variation of fish size over time and the decline in population biomass due to fishing and/or natural causes [1,5]. Traditional methods for determining the growth parameters include direct readings of rigid structures (e.g., otoliths, spines and vertebrae) to estimate the age of fish or indirect estimations based on length distribution data over time [1]. While well-conducted growth studies using otoliths, scales or other rigid structures should produce more accurate growth estimates than studies using solely length-frequency data, length-based approaches are highly desirable, mainly when age data collection is resource-demanding or accurate aging is not possible [6][7][8]. Mortality estimates may be determined by assessing changes in the  Notes: DR-direct reading; BC-back-calculation; IM-indirect method; MX-mixing; EF-empirical formula; n-number of individuals; L T -total length; L F -fork length; L ∞ -asymptotic length (cm); k-growth coefficient (year −1 ); φ -growth performance index; Z-total mortality rate (year −1 ); M-natural mortality rate (year −1 ); F-fishing mortality rate (year −1 ).

Data Collection
Fish species (blue jack mackerel T. picturatus, parrotfish S. cretense, Atlantic chub mackerel S. colias, red scorpionfish S. scrofa, blacktail comber S. atricauda, amberjacks nei Seriola Life 2022, 12, 778 4 of 14 spp. and black scabbardfish A. carbo) landed at the Azorean fish markets were sampled under the European Commission's data collection framework (DCF) [37]. DCF sampling design and protocols were developed in accordance with the recommendations of the International Council for the Exploration of the Sea (ICES) working groups on commercial catches (WGCATCH; https://www.ices.dk/community/groups/Pages/WGCATCH.aspx; accessed on 10 January 2022) and biological parameters (WGBIOP; https://www.ices.dk/ community/groups/Pages/WGBIOP.aspx; accessed on 10 January 2022) [38]. For fish species with a forked tail, the fork length (L F ) was obtained instead of the total length (L T ). Table 2 summarizes the number of individuals sampled by species, sampling time and measure of fish size.

Growth Parameters
Growth parameters were estimated through the von Bertalanffy growth function (VBGF) [7] using monthly length-frequency data (2 cm class interval for S. cretense, S. colias, S. scrofa and S. atricauda; and 3 cm class interval for T. picturatus, Seriola spp. and A. carbo) obtained from commercial landings. Data from Seriola spp. were grouped for this analysis due to a lack of data in some months. As the length data were not separated for males and females, growth parameters were estimated for pooled sexes. The original VBGF model [7] was altered to remove theoretical age at length zero (t 0 ) as follows: where L t is the fish length (cm) at age t (year), L ∞ is the asymptotic length (cm), i.e., the length that the fish of a population would reach if they were to grow indefinitely, and k is the growth coefficient that expresses the rate (year −1 ) at which the asymptotic length is approached. The asymptotic length (L ∞ ), growth coefficient (k) and growth performance index (φ ) were computed by electronic length-frequency analysis using a bootstrapped method with a genetic algorithm (ELEFAN_GA_boot; [39]) within the TropFishR [40,41] and fishboot [39,42] packages in R [43]. Bootstrap experiments based on 1000 resamples.

Discussion
In general, the current investigation indicates a favorable environment for reaching the maximum length compared to all existing records. The maximum LF of 53 cm for T. picturatus and the maximum LT of 47 cm for S. atricauda observed in the present study were close to the maximum LF of 54 cm for T. picturatus observed by Garcia et al. [17] and the maximum LT of 46 cm for S. atricauda reported by Rosa et al. [62]. S. cretense and S. scrofa had maximum LT of 55 cm and 61 cm, respectively, which were greater than the 52 cm reported by Afonso et al. [63] for S. cretense and the 59 cm reported by Rosa et al. [62] for S. scrofa. On the other hand, the maximum LT of 65 cm (60 cm LF) for S. colias [64] and 160 cm (139 cm LF) for Seriola spp. [18] were found in the literature to be greater than the maximum length obtained in this study. The maximum LT of A. carbo ranged between 120 cm [65] and 148 cm [66], implying that the 134 cm LF recorded in this study was near the maximum value. Due to the scarcity of existing data for T. picturatus, S. cretense, S. colias, S. scrofa, S. atricauda, Seriola spp., and A. carbo in the literature, the findings from this study will undoubtedly contribute to the available records.
The growth parameters of fish population dynamics (asymptotic length L∞ and growth coefficient k) are critical for stock assessment and fisheries management. Some reported L∞ for T. picturatus in Madeira and Canaries (Table 1) were shorter than the present findings. However, an L∞ of 55.9 cm LF obtained in this study agreed with the values Figure 3. Estimates of total mortality rate (Z) from the linearized length-converted catch curve method for blue jack mackerel Trachurus picturatus, parrotfish Sparisoma cretense, Atlantic chub mackerel Scomber colias, red scorpionfish Scorpaena scrofa, blacktail comber Serranus atricauda, amberjacks nei Seriola spp. and black scabbardfish Aphanopus carbo in the Azores between 1990 and 2017 (speciesspecific sampling periods are shown in Table 2).

Discussion
In general, the current investigation indicates a favorable environment for reaching the maximum length compared to all existing records. The maximum L F of 53 cm for T. picturatus and the maximum L T of 47 cm for S. atricauda observed in the present study were close to the maximum L F of 54 cm for T. picturatus observed by Garcia et al. [17] and the maximum L T of 46 cm for S. atricauda reported by Rosa et al. [62]. S. cretense and S. scrofa had maximum L T of 55 cm and 61 cm, respectively, which were greater than the 52 cm reported by Afonso et al. [63] for S. cretense and the 59 cm reported by Rosa et al. [62] for S. scrofa. On the other hand, the maximum L T of 65 cm (60 cm L F ) for S. colias [64] and 160 cm (139 cm L F ) for Seriola spp. [18] were found in the literature to be greater than the maximum length obtained in this study. The maximum L T of A. carbo ranged between 120 cm [65] and 148 cm [66], implying that the 134 cm L F recorded in this study was near the maximum value. Due to the scarcity of existing data for T. picturatus, S. cretense, S. colias, S. scrofa, S. atricauda, Seriola spp., and A. carbo in the literature, the findings from this study will undoubtedly contribute to the available records.
The growth parameters of fish population dynamics (asymptotic length L ∞ and growth coefficient k) are critical for stock assessment and fisheries management. Some reported L ∞ for T. picturatus in Madeira and Canaries (Table 1) were shorter than the present findings. However, an L ∞ of 55.9 cm L F obtained in this study agreed with the values previously estimated for the Azores by Garcia et al. [17] through direct otolith readings (58.3 cm L F ). The variations among these Macaronesian islands are probably due to stock differences in spatial scale [67]. For S. cretense, estimates for the Greek coast from scale readings (L ∞ = 38.9 cm L T ) Life 2022, 12, 778 9 of 14 were much lower than those observed for the Azores (L ∞ = 57.9 cm L T ). Longer L ∞ than those reported in the literature for S. colias [12,13,16,22,29] and S. atricauda [30,31] were also observed in this study. These differences are most likely due to the larger specimens present in this study. On the other hand, S. scrofa, Seriola spp., and A. carbo were found to have smaller L ∞ in the Azores compared to other regions in the Atlantic [19][20][21]23,25,26] and Mediterranean [18,35].
Considering the estimated growth coefficients (k) for T. picturatus, S. cretense, S. colias, S. scrofa, S. atricauda, Seriola spp. and A. carbo calculated in the present study, Sparre and Venema [1] proposed that k = 1.0 year −1 indicates fast growth, k = 0.5 year −1 moderate growth and k = 0.2 year −1 indicates slow growth, suggesting that the seven species described here grow at a relatively slow rate. The estimated k values are smaller or approximately equal to those previously observed in the Azores, Madeira and Canaries for T. picturatus; Greece for S. cretense; Azores, Gulf of Cádiz, Alboran Sea, Adriatic Sea and Mauritania for S. colias; Azores and Canaries for S. atricauda; NW Atlantic, Gulf of Mexico and Adriatic Sea for Seriola spp.; and Canaries and Madeira for A. carbo (Table 1). For S. scrofa, the estimated k was higher than that observed by Shahrani and Shakman [35] on the Libyan coast (Table 1).
Within the same species, variations in L ∞ and k can be attributed to various causes, including variations in water conditions, food availability, metabolic rate, fishing pressure and pollution [1]. For example, as fishing gear is selective and oriented toward harvesting larger individuals, large individuals may become rare in overexploited fisheries, and a scarcity of these individuals in a given sample will inevitably underestimate growth parameters [68,69]. On the other hand, while analyzing fish growth, the validation of growth parameter estimations often arises due to the reliability of some of the methodologies employed to produce such estimates. In this regard, the growth performance index (φ') can indicate estimation reliability since it has been suggested that φ' values are similar for the same species and genera [39,70,71]. The values of φ' obtained from this study ( Figure 2) were close to or within the range of values obtained for stocks of T. picturatus, S. cretense, S. colias, S. scrofa, S. atricauda, Seriola spp. and A. carbo from other Atlantic areas and the Mediterranean, which were estimated either by direct or indirect methods ( Table 1).
The natural mortalities (year −1 ) estimated in this study (Table 3) were not in agreement with the natural mortalities found for T. picturatus in Madeira and Canaries, S. cretense on the Greek coast, S. colias in the Azores, Adriatic Sea and Mauritania, and Seriola spp. in the Adriatic Sea (Table 1). Natural mortality varies with age, density, disease, parasites, food supply, predator abundance, water temperature, sex and size; therefore, observed variances could be related to these factors [72]. However, it is interesting to note that the values of natural mortality of the seven fish species in the Azores indicated lower natural mortality, as the values found in this study were mostly at the lower limit of the modal mortality rate (i.e., 0.20) derived from 175 fish stocks as given by Pauly [52]. No reports of mortality parameters for S. scrofa, S. atricauda, or A. carbo are currently available in the literature.
Natural mortality (M) and fishing mortality (F) can denote the indication of an overfishing status [5]. The optimal scenario for a population is when fishing mortality equals natural mortality, which means that fishing operations exploit the portion of the population that would otherwise be lost due to natural mortality [73]. With knowledge of these parameters, one can manage the stocks and establish the optimal exploitation rate (i.e., However, the exploitation status suggested from this study should be treated with caution because, as population growth estimates have, in some cases, large confidence intervals (see Figure 2) as well as fishing-related uncertainties, the mortality rate scenario may be of more concern. For T. picturatus, S. colias and Seriola spp., for example, the total mortality estimates may also be biased due to the different fishing gears operating over this stock (surface nets and longlines for T. picturatus and S. colias [10,32]) or the different species (i.e., S. dumerili and S. rivoliana) grouped as the same stock (i.e., Seriola spp.). This condition may even be associated with the bimodal patterns in length-frequency distribution ( Figure 1) and catch curves (Figure 3) observed for these species and implies that mortality estimates should ideally be estimated by fishery separately or, in the case of Seriola spp., by species. However, the length of data used in this study did not allow this separation, and it should be re-evaluated to make these analyses possible in the future.
For stock assessment, fisheries experts prefer to use age-composition data acquired by reading rigid structures since these data are more likely to reflect the real age composition of the stock than those produced using a proxy for the age composition obtained using length-composition data. However, measuring the length of a fish is significantly less expensive than determining its age, and most of the biological data acquired for Azorean fish populations are in the form of length composition rather than age composition. Therefore, in the absence of otoliths, length-frequency data may be useful for estimating growth parameters and mortality rates for those data-deficient species. Nevertheless, to reduce imprecision and improve accuracy, it would be desirable to confirm these estimations by comparing the results of the analysis to those produced from age-based approaches. This is highly encouraged to be conducted, at least for blue jack mackerel T. picturatus, parrotfish S. cretense, Atlantic chub mackerel S. colias, red scorpionfish S. scrofa, blacktail comber S. atricauda, amberjacks nei Seriola spp. and black scabbardfish A. carbo that are data-deficient and at the same time classified as priority stocks for the region.
Since harvesting of the studied species is not sex-based, stock assessment models should need a single set of population parameters. Nonetheless, the disparities in development between the sexes may require a change in management regulations to limit effort, especially on the target component, which is particularly vulnerable to overexploitation. Future research should therefore investigate these particularities since the dataset used in this study did not allow progress in this way. This is even more important when it involves sequential hermaphroditic species with sexual dimorphism, such as S. cretense [27]. Additionally, captures of resources such as T. picturatus, S. cretense, S. colias, S. atricauda and Seriola spp. are not completely landed since they are also fished for self-consumption or utilized as live bait in tuna fisheries [10,32]. Therefore, samples from the commercial landings may be under-represented, and special attention will need to be given to the sampling design to ensure that representative samples are taken. In addition to that, stock units for all the studied stocks are not clearly defined [10]. As a result, it is impossible to know whether the stocks were fully sampled across their entire range of distribution and dynamic aspects of the population or whether the samples analyzed referred only to a fraction of the population.
Although the results of this study have certain limitations, it adds new information on species for which there is little or no information available. The information reported greatly improve understanding of population structure, mortality and exploitation status of blue jack mackerel T. picturatus, parrotfish S. cretense, Atlantic chub mackerel S. colias, red scorpionfish S. scrofa, blacktail comber S. atricauda, amberjacks nei Seriola spp. and black scabbardfish A. carbo and inform additional stock assessment initiatives. Stock assessment is a long-term and dynamic process, and a complete picture of the situation can only be obtained when the conclusions from one analysis are compared with those of a different analysis and the different results are used critically to gauge conclusions, improve the data and thus enable future assessments to be more accurate [74].

Conclusions
The seven fish species examined (i.e., blue jack mackerel T. picturatus, parrotfish S. cretense, Atlantic chub mackerel S. colias, red scorpionfish S. scrofa, blacktail comber S. atricauda, amberjacks nei Seriola spp. and black scabbardfish A. carbo) are economically important food fish, and therefore, the estimated population parameters constitute a landmark in the development of stock assessment studies. This information can be implemented into age-structured or length-based models and allow understanding of the dynamics of marine resources and estimating the sustainable yield of the target population. However, uncertainties regarding the representativeness of commercial landing samples in this study have been raised for some species, particularly those that escape the auction control or are used as live bait in other fisheries. In addition, natural mortality and growth patterns are often associated with the ecosystem, species behavior and fishing pressure. As a result, further study should focus on feeding habits, predation-prey relationships, migration patterns, recruitment and the reliability of the current sampling programs for these species. The latter is critical for integrating different data sources to guarantee that small, medium and large individuals are included in the analyses and prevent misleading results. Finally, studies focused on stock delimitation are essential in the stock assessment process because they will allow to estimate reliable population parameters, develop optimal harvest and monitoring strategies, and propose effective conservation measures.

Institutional Review Board Statement:
No ethical approval was required as this study is nonexperimental, and the data analyzed came from commercial fishery activities.

Data Availability Statement:
The data underlying this article will be shared upon reasonable request to the corresponding author.