MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
https://doi.org/10.47193/mafis.3522022010508 275
ORIGINAL RESEARCH
A data-limited approach to determine the status of the artisanal
fishery of sea silverside in southern Chile
PAULO MORA1, 2, GUILLERMO FIGUEROA-MUÑOZ1, 3, 4, LUIS A. CUBILLOS1,5,* y POLIANA STRANGE-OLATE1
1Programa de Magíster en Ciencias Mención Pesquerías, Facultad de Ciencias Naturales y Oceanográficas, Universidad de
Concepción, Chile. 2Instituto de Fomento Pesquero, Valparaíso, Chile. 3Núcleo Milenio INVASAL and Genomics in Ecology,
Evolution and Conservation Laboratory (GEECLAB), Departamento de Zoología, Facultad de Ciencias Naturales y Oceanográficas,
Universidad de Concepción, Concepción, Chile. 4Departamento de Ciencias Biológicas y Químicas, Facultad de Recursos Naturales,
Universidad Católica de Temuco, Rudecindo Ortega 02950, Temuco, Chile. 5Centro COPAS COASTAL, Departamento de
Oceanografía, Facultad de Ciencias Naturales y Oceanográficas, Universidad de Concepción, Casilla 160-C, Concepción, Chile.
ORCID Paulo Mora https://orcid.org/0000-0002-8172-1533, Guillermo Figueroa-Muñoz https://orcid.org/0000-0001-7446-
9934, Luis A. Cubillos https://orcid.org/0000-0003-0641-3722.
ABSTRACT. Artisanal fisheries are essential, but for most the status of the stock
supporting the fishing activity remains unknown due to lack of data and difficult
access to sampling. For example, the artisanal fishery of sea silverside Odontesthes
(Austromenidia) regia, in Los Lagos administrative region in Chile, requires a data-
limited approach to determine its status because the fishery administration has not
invested in its monitoring. The approach consisted of estimating the spawning
potential ratio (SPR) from length-frequency data collected in 2019 using length-
based spawning potential ratio (LBSPR) and biological reference points using the
only-catch optimized method (OCOM) to catch data covering the period from 1960
to 2020. In addition, five age-structured sea silverside populations were simulated
considering uncertainty in recruitment and utilizing life-history parameters estimated
by FishLife. According to LBSPR, the SPR was 0.58 (95% confidence intervals: 0.5-
0.7), suggesting a fully exploited fishery status. The OCOM result was inconsistent
with the life-history parameters and was discarded as a valid sea silverside stock
assessment. The age-structured population simulations indicated evidence of a
reduction in the spawning stock biomass close to 75% of the unexploited condition
in 1960. Thus, the underexploited status reached a probability close to 49.4%, and
the fully exploited status was 41.2%. The framework for a data-limited stock-
assessment approach and results obtained here for the sea silverside are starting
essential steps that may be emulated in other artisanal data-limited fisheries.
Key words: data-poor, assessment, small-scale fishery, simulations, life-history.
Un enfoque de datos-limitados para determinar el estatus de la pesquería
artesanal de pejerrey de mar en el sur de Chile
RESUMEN. Las pesquerías artesanales son esenciales, pero para la mayoría de ellas
se desconoce el estado de las poblaciones que sustentan la actividad pesquera debido
a la falta de datos y al difícil acceso a los muestreos. Por ejemplo, la pesquería
artesanal del pejerrey de mar Odontesthes (Austromenidia) regia, ubicada en la
región administrativa de Los Lagos de Chile, requiere un enfoque con datos limitados
para determinar su estado debido a que la administración pesquera no ha invertido en
su monitoreo. El enfoque consistió en estimar la razón de potencial de desove (SPR)
a partir de datos de frecuencia de talla recolectados en 2019, utilizando la relación de
potencial de desove basada en la talla (LBSPR) y puntos biológicos de referencia
utilizando el método optimizado de sólo-captura (OCOM) sobre los datos de captura
entre 1960 y 2020. Además, se simularon cinco poblaciones de pejerrey de mar
estructuradas por edad bajo incertidumbre en el reclutamiento y utilizando
parámetros de historia de vida estimados por FishLife. Según el LBSPR, el SPR
fue de 0,58 (intervalos de confianza del 95 %: 0,5-0,7), lo que sugiere un estado de
*Correspondence:
lucubillos@udec.cl
Received: 9 March 2022
Accepted: 22 March 2022
ISSN 2683-7595 (print)
ISSN 2683-7951 (online)
https://ojs.inidep.edu.ar
Journal of the Instituto Nacional de
Investigación y Desarrollo Pesquero
(INIDEP)
This work is licensed under a Creative
Commons Attribution-
NonComercial-ShareAlike 4.0
International License
276 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
explotación plena. El resultado del OCOM fue inconsistente con los parámetros de historia de vida y se descartó como
una evaluación válida del stock de pejerrey de mar. Las simulaciones de la poblacionales estructurada por edades
mostraron una reducción en la biomasa desovante cercana a 75% de una condición no explotada en 1960. Así, el estado
subexplotado alcanzó una probabilidad cercana a 49,4%, y el estado de explotación plena de 41,2%. El marco para un
enfoque de la evaluación de stock con datos limitados, y los resultados obtenidos aquí para el pejerrey de mar, están
iniciando pasos esenciales que podrían emularse en otras pesquerías artesanales limitadas en datos.
Palabras clave: Datos limitados, evaluación, pesquería artesanal, simulaciones, historia de vida
INTRODUCTION
Global total marine catches were 84.4
million metrics tons in 2018, from which 78.7%
came out from biologically sustainable stocks.
In 2017, this fraction reached 65.8%, and stocks
fished biologically unsustainably were 34.2%
(FAO, 2018). Unfortunately, there are problems
with artisanal fisheries, either because they are
difficult to sample or because information on
them is generally incomplete, or both, increasing
the uncertainty of global fishery statistics.
Nevertheless, artisanal fisheries are essential
mainly because they are not only an indispensable
source of food for human consumption, but also
generate employment for fishers, providing
economic well-being for all agents involved in
the socio-ecological system resulting from these
fisheries (Salas et al. 2007; Pomeroy and Neil
2011).
In Chile, artisanal fisheries contributed almost
38% to the national landings in 2020, industrial
fisheries 21 % (mainly pelagic fish) and aqua-
culture 41 % (mainly salmon and mussel aqua-
culture) (SERNAPESCA 2020). Almost 61% of
the artisanal fisheries landings are fish, 29%
seaweed, 6% mollusks, and the rest are crusta-
ceans, sea urchin, and tunicates (SERNAPESCA
2020). The silverside Odontesthes
(Austromenidia) regia Humboldt, 1821, is a small
pelagic fish that supports an artisanal fishery,
inhabiting marine coastal waters in the Humboldt
Current System, from northern Peru to southern
Chile (Brian and Dyer 2006; Arellano and
Swartzman 2010; Deville et al. 2021). Silversides
are small, slender and elongated fish which live
between 1 and 4 years, and their spawning season
lasts between two and five months (Moresco and
Bemvenuti 2006; Pajuelo and Lorenzo 2000;
Arrieta et al. 2010). Thirteen species of
silversides have been described in Chile, with
representatives of the subgenus Austromenidia
(including Odontesthes regia) being the most
abundant in the marine ecosystem (Dyer and
Gosztonyi 1999). Sea silverside has high genetic
diversity and at least two co-distributed genetic
groups (Deville et al. 2021). The species can
inhabit diverse marine environments, such as
estuaries, beaches, sandy bottoms, and moves in
small schools near the coast, between 0 and 50 m
depth (Cifuentes et al. 2012).
In Los Lagos administrative region, southern
Chile, the sea silverside is a species of great
commercial interest for artisanal fishers, where
landings represent 90 % of the total landings of
the species (SERNAPESCA 2020). Overall, the
main fishing gear used for the silverside fishery
corresponds to gillnets (2-3 m deep, 3-4 cm mesh
size), which are positioned in the coastal zone
(SUBPESCA 2003). The official records of sea
silverside artisanal landings in Chile increased
from 58 t in 1960 to 661 t in 2020. In Los Lagos,
landings started in 1965 attaining peaks of 4420 t
and 3271 t in 1990 and 1999, respectively.
However, after the last peak, sea silverside
landings declined to only 4 t in 2011 and started
to recover until 2020 (Figure 1).
There are concerns about the status of the
artisanal sea silverside fishery. Therefore, a data-
limited approach was used to determine the status
of the fishery in the Los Lagos Region. The sea
silverside reproductive aspects, age, and growth
were studied in Peruvian waters by Villavicencio
and Muck (1984), Gómez Alfaro et al. (2006),
Arrieta et al. (2010), and Campos León et al.
(2020). Plaza et al. (2011) described sea
silverside as an asynchronous multiple-spawner
with an extensive spawning season in Chile.
Pavez et al. (2008) studied biological and fishery
aspects of sea silverside in Los Lagos administra-
tive region. These authors concluded that catches
were supported by the spawning stock, particular-
ly reproductive aggregations near shore, and the
fishery could be affecting the reproductive
potential since sea silverside is a low-fecundity
species.
Most data-limited stock assessment methods
consider commercial catch (Free et al. 2020;
Ovando et al. 2022), body length data (Hordyk et
al. 2014a, 2014b; Prince et al. 2015; Hordyk et al.
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 277
2016), or both. The performance of data-limited
methods is usually evaluated by simulation
considering uncertainty in the population dynam-
ics (Carruther and Hordyk 2018; Zhou et al.
2017a; Free et al. 2020; Sharma et al. 2021). This
paper evaluates the sea silverside status in Los
Lagos administrative region, uses length-
frequency data to compute the spawning potential
ratio, and evaluates the models' performance by
simulating the population dynamics.
Figure 1. Landings of sea silverside in Los Lagos administrative region in Chile during the period 1960-2020.
MATERIALS AND METHODS
Study area and data sources
The study area is referred to as Los Lagos
administrative region in Chile. Total landings
were obtained from official records of the
Servicio Nacional de Pesca y Acuicultura
(SERNAPESCA, https://sernapesca.cl). Biological
data were obtained by sampling the artisanal
activity in four fishing zones during 2019. Punta
Quillahua and Amortajado have zones exposed to
the sea along the continental coast. The other two,
Bahía Ancud and Golfo de Quetalmahue, are
semi-enclosed fishing zones in northern Chiloé
island (Figure 2). The fishing zones are associ-
ated with Ancud as the main port for landings. A
total number of 552 sea silversides were sampled.
For each individual, total mass (W) was measured
using a scale Pesamatic Model WTB 2000 ( 0.01
g) and total length (TL) with a board meter ( 0.1
cm). Sex of individuals (males, n = 338; and
females, n = 214) was determined through macro-
scopic observation of gonads, after dissection.
Biological data analysis
Biological data were grouped according to the
following austral seasons: summer (January-
March), autumn (April-June), winter (July-
September), and spring (October-December).
Then, the average, standard deviation, and range
of total length (cm) and body weight (gr) were
computed by season and sexes. Besides, param-
eters of the length-weight relationship (LWR)
were determined, in which the body is a potential
function of total length (Froese 2006):
where W is the total body weight, L is the total
length (cm), and a and b are unknown parameters to
be estimated. Although the LWR is a non-linear
model and the parameters could be estimated
through a non-linear least-square approach, the
body weight violates the linearity and homosce-
dasticity. Froese (2006) and Ogle (2016) stated that
bodyweight follows a log-normal distribution, and
therefore a multiplicative error term could be a
better choice. Hence, linearizing the equation by
applying logarithms makes the error additive,
stabilizes the variance, and the unknown parameters
278 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
Figure 2. Study area in Chile (A) showing sampling locations in northern Chiloé island, and (B) zoom of sampled
locations during 2019 (C).
can be estimated using a linear model. The log-
normal and gamma distributions were fitted to
observed body weight data using maximum
likelihood estimation implemented in the func-
tion fitdistr of the R-package MASS (Venables
and Ripley 2002). According to the log-
likelihood and Akaike information criterion
(AIC) (Akaike 1974), body weight of sea
silverside follows a gamma distribution (log-
likelihood = -2206.2, AIC = 4416.4) rather than a
log-normal distribution (log-likelihood = -2209.7,
AIC = 4423.4). Therefore, unknown parameters
(a and b) of the LWR were estimated using a
generalized linear model (GLM) with gamma
family and natural logarithm as link function. The
following linear predictor was used:
where is the intercept, the slope, SEX is a
factor for males and females, SEASON is a factor
for summer, autumn, winter, and spring. The R-
package (DHARMa) (Harting 2022) for residual
diagnostics was utilized, which uses a simulation-
based approach to create standardized residuals
for a fitted GLM. After testing residuals, normal
residuals followed. An ANCOVA was used with
a Chi-squared test to evaluate significant effects
of fixed groups, i.e., SEX and SEASON (Lai and
Helser 2004). A submodel consisted of removing
one of the fixed factors resulting non-significant
and represented by a model with different
intercepts and fixed slope (model 1), a model with
changes in the slope and fixed intercept (model
2), and a model with changes in both the intercept
and slopes simultaneously (model 3) (e.g., Nahdi
et al. 2016). The best submodel was selected with
AIC (Akaike 1974), and the Nagelkerke pseudo-
r2 (Nagelkerke 1991) was computed. The R-
package MASS was utilized to fit GLMs
(Venables and Ripley 2002) and the R-package
rcompanion (Mangiafico 2015) for computing
the Nagelkerke pseudo-r2.
Once LWR was analyzed, the condition factor
among seasons and sexes was studied. The
relative condition factor (Le Cren 1951) was
computed as , where Kn is the allom-
etric condition factor, W is the body weight, L is
the total length, and b is the allometric exponent
of the LWR (Nahdi et al. 2016).
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 279
Status of the fishery
Length-based spawning potential ratio
Annual length-frequency data were utilized to
apply the length-based spawning potential ratio
(LBSPR) model of Hordyk et al. (2014a, 2014b).
The LBSPR is a steady-state stock assessment
model that estimates the spawning potential ratio
as an index of status. In addition, the method also
estimates the parameters of a logistic selectivity
curve (Hordyk et al. 2016). The input is one or
more length-frequency data, the von Bertalanffy
(VB) asymptotic length (l), the ratio between the
natural mortality (M) and the VB growth
coefficient (M/k) (Prince et al. 2015), and the
length at first maturity (lm) obtained from Pavez
et al. (2008) (Table 1).
Catch data analysis
The only-catch stock assessment model called
OCOM (Optimized Catch-Only Method) of Zhou
et al. (2017a) as implemented in the package
'datalimited2' (Free 2018) for the software R
(https://www.r-project.org) was applied to
determine the status of the sea silverside artisanal
fishery in Los Lagos administrative regions. As
mentioned, landing data covered the period from
1960 to 2020 (Figure 1) assuming they are a
proxy of the catch since landings could be less or
equal to the catches.
The OCOM uses Schaefer's logistic surplus
production:
where Bi is the biomass at the beginning of the
year i, r is the intrinsic growth rate, K is the
carrying capacity, and Ci is the observed catch
during year i. The unknown parameters to be
estimated are r and K, and the estimation
procedure utilizes a prior for r to solve K through
the ratio Bi/K or stock saturation, i.e., s = Bi/K.
The prior for r is based on natural mortality (M),
and prior for the stock saturation is based on a
boosted regression trees (BRTs) model
developed by Zhou et al. (2017b). The estimation
considered n=10000 values for r and s, and the
optimization function solved viable r-K pairs to
set upper and lower K values, which are not part
of a prior range. Derived quantities are MSY =
rK/4 and FMSY = r/2 based on optimized r-K pairs.
Simulation of sea silverside age-structured
populations
In addition to the known life-history param-
eters of Pavez et al. (2008) for the sea silverside,
other life-history parameters were obtained by
applying the FishLife package developed by
Thorson et al. (2017) and Thorson (2020) for the
software R. FishLife is an efficient method to
estimate life-history parameters for little-studied
species. It is based on a multivariate model that
utilizes a comprehensive evolutionary model of
life-history parameters fitted to longevity,
growth, natural mortality, maturity, and tempera-
ture data from FishBase (Froese and Binohlan
2000; Froese and Binohlan 2003; Froese and
Pauly 2022). FishLife utilizes stock-recruitment
parameters and population parameters from the
RAM Legacy Database (https://www.ramlegacy.
org) (Ricard et al. 2012). According to a multi-
variate normal distribution, the model predicts a
vector of life-history parameters along phyloge-
netic lineages, with lower taxonomic levels
having more precise parameters than higher
levels.
Based on FishLife, additional derived parame-
ters were obtained for sea silverside such as the
von Bertalanffy age at length zero (Pauly 1983),
the assumed coefficient of variation of length at
age, shape of maturity (based on 95% maturity,
Pavez et al. 2008), the spawning time as year
fraction (i.e., the month starting the reproductive
period according to Plaza et al. 2011), and the
length-weight parameters based on cube law
(Froese 2006) (Table 1). Once all the parameters
were obtained, five age-structured sea silverside
population models were simulated for the period
1965-2020 (Table 2). The simulations considered
uncertainty in unexploited recruitment level and
interannual variability. The unexploited recruit-
ment (R0) scales the population level, specifically
the unexploited spawning stock biomass (SSB0) at
the beginning of 1965. The interannual variability
is a process error impacting the trajectory of the
population from 1965 to 2020, given the observed
catch history. The steepness (h), standard devia-
tion of deviations of log recruitment (
R), and
autocorrelated annual deviations (
R) allowed us
to estimate the stock-recruitment model of
Beverton and Holt parameterized by Punt and
Cope (2019), as:
280 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
where
i are the annual deviations of recruitment,
which are autocorrelated, as
where
R is the serial correlation coefficient and
(Thorson et al. 2014; Hawkshaw
and Walters 2015). The simulation approach
consisted of selecting the lower limit for R0, on
a log scale (logR0), and projecting forward from
1965 to 2020, while solving the fishing mortality
rate (Fi) given the observed catch, selectivity
(vj), and the projected vulnerable biomass (Vi) of
the population (Table 2). The Baranov catch
equation was utilized to compute the fishing
mortality rate through the Newton-Raphson
algorithm (Gulland 1965; Quinn and Deriso
1999). The basic idea that underlies each
simulation is to reconstruct possible trajectories
of stock change from the start of the fishery to
the most recent year, given population dynamics
(i.e., the stock-recruitment model, recruitment
variability, and survival) (Table 2), selectivity
(vj), and observed catches.
Once R0's lower limit was determined, R0's
upper range was defined using two times .
Five sea silverside populations were simulated,
each with 1000 alternative and equally probable
trajectories of recruitment, and hence for the state
variables of the population. Invalid trajectories,
e.g., those resulting in extinction before 2020,
were discarded. With valid trajectories, the ratio
between the spawning biomass in 2020 and the
unexploited spawning biomass, i.e., SSBi/SSB0,
allowed to estimate the following status condi-
tion: depletion (SSBi/SSB0 < 0.25), over-exploi-
tation (0.25 SSBi/SSB0 < 0.4), fully exploitation
(0.4 SSBi/SSB0 < 0.75), and under-exploitation
(SSBi/SSB0 > 0.75). The status categories are in
agreement with the Chilean Law (Payá et al.
2014) and consider a target reference point to be
50 % of the unexploited spawning biomass, i.e.,
SSBtarget = 0.5SSB0, with a range between 0.4 and
0.75 of SSB0. The limit reference point was the
half of the target, i.e., SSBlim = 0.25SSB0.
Table 1. Life-history parameters estimated for sea silverside according to Pavez et al. (2008), and life-history
parameters estimated by FishLife. Additional derived parameters needed for simulation of a population
dynamics highlighted by an asterisk (see text).
Process
Parameter
Symbol
Units
Pavez et al.
(2008)
FishLife
Growth
Asymptotic length
cm
24.0
29.0
Asymptotic weight
g
95.0
241.0
Growth coefficient
k
year-1
1.047
0.597
year
0.632
-0.274*
Coefficient of variation of length at
age
-
n.a.
0.05*
Mortality
Natural mortality rate
M
year-1
1.2
1.1
Maximum Age
year
3+
5
Maturity
Age at maturity
year
n.a.
1.3
Length at maturity
cm
15.8
16.9
Shape maturity at length
cm
2.0
0.5*
Spawning time
-
0.583*
Stock-recruitment
Steepness
-
-
0.815
Standard deviation of recruitment
deviations
-
-
0.567
Autocorrelation of recruitment
deviations
-
-
0.352
Length-weight
relationship (LWR)
Intercept LWR
a
gcm-b
0.0050
0.0098*
Allometry coefficient LWR
b
3.1
3*
Average temperature
Temperature
T
°C
12.6
18.1
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 281
Table 2. Equations of the age-structured simulation model for sea silverside in Los Lagos region, Chile.
Process or state
Equation
N°
Length at age
1
Maturity at size l
2
Maturity at age j
3
Selectivity at size l
, where
4
Selectivity at age j
Weight at age
5
Abundance
6
Total biomass at
beginning of year i
7
Spawning biomass
8
Vulnerable biomass
9
Unexploited spawning
biomass
10
Reproductive potential
without fishing
; where
11
Reproductive potential at
fishing mortality F
;
where:
12
RESULTS
Biological data
The total length of sea silverside ranged
between 14.8 and 24.0 cm for females and 15.4
and 23.4 cm for males, showing similar total
length and weight averages and standard
deviations (Table 3). Nevertheless, the length-
frequency evidenced the most extensive range of
sea silverside specimens in summer, from 15 to
24 cm (Figure 3).
The general model for the length-weight
relationship (LWR) showed no significant differ-
ences between males and females. Indeed, the
factor sex showed no effects in the intercept
(SEX, P = 0.083), nor in the slopes (SEX ,
P = 0.334), neither in the intercept among sex by
season (SEX SEASON, P = 0.547) or in the slope
by season (SEX SEASON , P = 0.070).
Discarding SEX from the general model and
considering only seasonal effects, the AIC values
for models 1, 2, and 3 were 3008.2, 3007.4, and
3008.7, respectively. Although the AIC was close
among competing models, the best model for the
LWR was model 2 (Table 4), with a fixed
intercept and different slopes among seasons
(Nagelkerke pseudo-r2 = 0.921). The highest
expected weight at a given length occurred in
summer and the lowest in autumn for fish larger
than 20 cm (Figure 4A). This result was a
consequence of different seasonal slopes for the
LWR, with a slope higher in summer and lower
in autumn (Table 4). According to the standard
error, the slope was not different from 3, and the
lowest 95 % confidence interval was 2.901 while
the highest equaled 3.058. Accordingly, the
allometric condition factor (Kn) did not show
significant differences among seasons for males
and females, but females showed a lower range in
autumn and larger in spring (Figure 4B).
282 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
Table 3. Summary of total length (cm), body weight (g), and minimum (Min) and maximum (Max) values of sea
silverside. Standard deviation shown in parenthesis.
Total Length (cm)
Body weight (g)
Sex
Season
n
Mean (cm)
Min
Max
Mean (g)
Min
Max
Female
Summer
61
20.2 (2.4)
14.8
23.8
59.1 (20.1)
23
94
Autumn
46
20.3 (1.1)
18.6
23.4
52.7 (9.3)
39
78
Winter
45
20.9 (1.3)
17.4
23.9
61.8 (12.3)
36
95
Spring
62
20.1 (1.4)
17.6
24.0
54.6 (12.5)
37
89
Annual
214
20.3 (1.7)
14.8
24
57.0 (14.9)
23
95
Male
Summer
76
19.6 (2.0)
15.4
23.4
54.0 (15.1)
23
82
Autumn
43
20.2 (1.1)
17.5
22.3
52.5 (8.7)
38
70
Winter
68
20.4 (1.0)
18.5
22.8
57.9 (10.1)
41
85
Spring
151
19.6 (1.1)
17.2
23.2
49.9 (8.9)
34
84
Annual
344
19.8 (1.4)
15.4
23.4
52.8 (11.2)
23
85
Both
Annual
558
20.0 (1.5)
14.8
24
54.4 (12.9)
23
95
Table 4. Coefficients for the best model describing the length-weight relationship of sea silverside. Model 2 estimated
by generalized linear model, family gamma and natural logarithm as link function. Nagelkerke pseudo-r2 = 0.921,
likelihood ratio test: -708.5 (p<0.01).
Coefficients
Estimate
Standard Error
t-value
P-value
Intercept
-4.926
0.114
-43.39
<0.01
Length*Summer
2.983
0.038
78.43
<0.01
Length*Autumn
2.953
0.038
78.06
<0.01
Length*Winter
2.976
0.038
79.15
<0.01
Length*Spring
2.971
0.038
77.90
<0.01
Status of the fishery
Length-based spawning potential ratio
The fit of the steady-state LBSPR model to the
annual length-frequency of sea silverside per-
formed well (Figure 5A). The resultant spawning
potential ratio (SPR) was 0.58, with 95 %
confidence intervals (CI) between 0.5 and 0.7.
The ratio fishing to natural mortality (F/M) was
3.1 (CI: 1.9 - 4.3), and the logistic selectivity
parameters were L50 = 19.7 cm (CI: 19.1-20.2 cm),
and L95 = 22.6 cm (IC: 21.8 - 23.4 cm). The
resultant selectivity curve was to the right of the
maturity ogive (Figure 5B), suggesting that on
average a significant proportion of fish were
spawning before being caught.
The only-catch stock assessment model
Population parameters and biological
reference points obtained using the optimized
only-catch model (OCOM) indicated a median
carrying capacity (K) of 8197 t and a median intrin-
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 283
Figure 3. Length-frequency data of sea silverside by sex and seasons during 2019.
sic growth rate (r) of 0.342 (Table 5). The
maximum sustainable yield (MSY) was 700 t,
and the fishing mortality rate at MSY (FMSY) was
0.171 (IC: 0.083 - 0.542). Finally, the saturation
(B2020/K) showed a reduction of 0.313 in biomass
in 2020, slightly above the limit biomass and
equivalent to B2020/BMSY = 0.575 (IC: 0.192-
1.175) (Figure 6C).
According to the selected r-K pairs, biomass
trajectories revealed no effect of fishing between
1960 and 1990. However, overfishing occurring
in 1989-1990 impacted the sea silverside popula-
tion negatively (Figure 6). After that, a slight
recovery occurred until 1999, but the overfishing
between 1999 and 2005 determined a depletion.
Eventually, the sea silverside exhibited a re-
covery from 2005 to 2020 with increased
uncertainty.
284 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
Figure 4. A) Length-weight relationships by seasons and B) condition factor by sex and seasons of sea silverside (2019).
Figure 5. A) LBSPR fitted (continuous line) to the annual length-frequency data (bar); and B), the logistic selectivity
curve (continuous line) obtained and compared with the maturity ogive (segmented line) of Pavez et al. (2008).
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 285
Table 5. Estimates of the logistic surplus production
model (r, K) and biological reference points for
sea silverside based on the OCOM model applied
to the catch history in Los Lagos region, Chile
(1960-2020).
Parameter
Median
Lower
Limit
Upper
Limit
r
0.342
0.014
0.463
K
8197
7007
13625
MSY
700
466
812
BMSY
4098
3504
6813
FMSY
0.171
0.133
0.232
B2020/K
0.313
0.222
0.583
Simulations of age-structured sea silverside
populations
The minimum value for the unexploited recruit-
ment (logR0) was 4.8, and according to R = 0.567,
the upper limit for logR0 was 5.6 (Figure 7). From
this range, the level of unexploited recruitment
was selected at random. Simulations of the state
variables were summarized by utilizing the
percentile at 10, 50, and 90 %. The five popula-
tions share identical life-history parameters
(Table 2), and they differed only in R0 and
interannual recruitment variability (Figure 7A).
Higher catches in 1990, 1999-2000, and 2003,
negatively affected the total biomass (Figure 7B),
particularly the spawning stock biomass (Figure
7C).
The spawning potential ratio, SSBi/SSB0,
showed similar performance in the five simulated
populations (Figure 8). The status in 2020 was
similar and fluctuated between 72.7 and 76.9 %
among the five simulated sea silverside popula-
tions. Considering the underlying uncertainty in
the spawning stock biomass, the probabilities for
under-exploited and fully exploited status were
higher (Table 6).
Figure 6. A) Results of the only-catch optimized method: changes in sea silverside biomass, and B) fishing mortality,
C) relative changes in biomass, D) relative changes in fishing mortality regarding the target biological reference
points (segmented line) associated with the logistic surplus production maximum sustainable yield. The dotted
line in panel A and C is the limit biological reference point.
286 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
Table 6. Performance of the simulated age-structured population model under uncertainty during the recruitment
process of sea silverside given by the observed catch history (1960-2020). The effective number of viable
population trajectories shown in parenthesis.
Populations simulated
Indicator
1
(723)
2
(419)
3
(924)
4
(695)
5
(462)
Weighted
average
Status
SSB2020/SSB0
73.9
76.9
76.6
72.7
73.2
74.7
Collapse
Pr[SSB2020/SSB0<0.25]
0.6
1.7
0.9
1.3
2.6
1.3
Overexploitation
Pr[0.25SSB2020/SSB0<0.4]
8.2
9.3
7.9
7.6
7.6
8.0
Fully exploitation
Pr[0.4 SSB2020/SSB0<0.75]
42.3
37.7
39.5
43.9
42.2
41.2
Under exploitation
Pr[SSB2020/SSB0>0.75]
49.9
51.3
51.6
47.2
47.6
49.4
Figure 7. Simulations of age-structured of sea silverside populations (columns) based on the uncertainty in recruitment
(A), resulting total biomass (B), spawning stock biomass (SSB) (C), conditioned to the observed catch history
(1960-2020) (D). The grey area represents percentile intervals at 90 %, and the continuous line indicates the
median of simulations per recruitment scenarios (columns).
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 287
Figure 8. Reproductive potential indicator for sea silverside status, consistent in the ratio between the spawning stock
biomass in a given year (SSBi) and its unexploited level (SSB0). The grey area represents percentiles at 90 %,
and the continuous line is the median of alternative and equally probable spawning biomass trajectories.
DISCUSSION
This study aims to develop a data-limited
approach to determine the status of the sea
silverside stock in Los Lagos administrative
region. Primary data required for such an ap-
proach rely on monitoring fishery and biological
data regularly, depending on how the fishers
operate within territorial, social, economic, and
cultural aspects. As in most artisanal fisheries,
monitoring the Los Lagos sea silverside fishery is
complex due to dispersion and access to multiple
fishing coves and fishing grounds in species
widely distributed in a complex territory.
Biological data collected here were limited in
sample size and spatially but covered all the
seasons during 2019. Nevertheless, samples re-
vealed a length structure for males and females
supported by adults, matching results of Pavez et
al. (2008) in 2007. These authors found sea
silverside specimens ranging between 10 and 32
cm, with an average total length of 23.6 cm and
average weight of 98.8 g. Although, not rigor-
ously compared, our results suggest a reduction
in the average length and average weight of sea
silverside compared with Pavez et al. (2008).
Fishers operated mainly with standardized gill-
nets (SUBPESCA 2003), and the average length
comparison with data of Pavez et al. (2008) could
288 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
be correct. In addition, larger specimens collected
in autumn and winter could be associated with the
pre-reproductive and beginning of the reproduce-
tive cycle (Plaza et al. 2011). Besides, length-
weight relationships were similar between males
and females, but the expected body weight was
lowest in autumn and the highest in summer,
coinciding with better conditions for feeding
(Iriarte et al. 2007 al. 2011) and with results
reported by Gómez-Alfaro et al. (2006) in Pisco,
Perú. Regarding to the condition factor (CF) of
sea silverside, it did not change among seasons,
but the wider CF occurred in females during
spring, which coincided with the reproductive
cycle and the transition to higher concentrations
of phytoplank-ton biomass in the coastal waters
(Iriarte et al. 2007).
As mentioned, length-frequency data are one
of the primary data to determine the fish popula-
tion status (Hordyk et al. 2014a, 2014b). Thus,
the annual length frequency of sea silverside
obtained here is fundamental to estimate the
spawning potential ratio (SPR), resulting in 58 %
with confident intervals between 50 and 70 %.
These results mean that the sea silverside would
be fully exploited in Los Lagos administrative
region. The fishing gear utilized by fishers varies,
but in Los Lagos, the gillnet is the main fishing
gear used by fishers (SUBPESCA 2003),
followed by beach seine pulled by hand to the
beach (personal observations). The length at first
capture estimated here was 19.7 cm, i.e., the
length at 50 % selectivity. Thus, the length at first
capture was higher than maturity length (lm = 15.8
cm, Pavez et al. 2008). Furthermore, the selectivity
curve obtained with LBSPR allows a significant
fraction of sea silverside to spawn prior to be
captured. Therefore, although sea silverside
aggregates close to the coast to spawning, raising
its vulnerability to fish activity, there is no
evidence that the fishery affects the reproductive
potential, as suggested by Pavez et al. (2008).
Nevertheless, the reduction in average total
length from 23.6 in 2007 to ca. 20 cm in 2019
would indicate a sensible reduction in fecundity
due to the repetitive removal of larger female
individuals in the past. Partial fecundity as a
function of total length was demonstrated for sea
silverside in the study area by Plaza et al. (2011),
and for the sea silverside in Peru (Gómez Alfaro
et al. 2006). However, the reduction in the SPR to
58 % (IC: 50 - 70 %) obtained by applying the
LBSPR method should consider the caveat of this
data-limited stock assessment model. Indeed, the
LBSPR is a steady-state or equilibrium model, and
therefore the length-frequency data must be
representative of average conditions. Further-
more, although sea silverside is a small pelagic
fish with a short life cycle, the recruitment
variability should be influencing the abundance
and length structure like in the summertime.
However, the fishery is supported by larger
adults, and hence, the length structure is not
influenced by fluctuations in recruitment. In
addition, the fishing effects in the length structure
are represented in the descending arm of the
length-frequency histogram. That is the reason
why the LBSPR estimated a ratio F/M = 3.1 (IC:
1.9 to 4.3).
In terms of the catch history, the Only-Catch
Optimized Method (OCOM) (Zhou et al. 2017a;
Free 2018) revealed a different status for the sea
silverside artisanal fishery in Los Lagos region.
Indeed, the OCOM showed that the sea silverside
population was recovering from the lowest
depleted biomass (B/BMSY = 12.9 %) from 2010
to 2020 (B/BMSY = 57.5 %). In 2020, however, the
uncertainty represented by the confidence inter-
val was vast from a depleted to a fully exploited
status. In addition, the median value for r was
0.342, which according to the natural mortality
estimates the r value seemed to be lower than
expected. Indeed, the estimates of natural
mortality (M) ranged between 1.1 and 1.2, and
hence FMSY = 0.87M = 0.96 - 1.0 (Zhou et al.
2012), and r = 2FMSY2. Therefore, the OCOM
results seemed to be inconsistent with the sea
silverside biology and considered invalids. In
order to proceed to a more formal stock assess-
ment with surplus production models, it will be
necessary to collect fishery data and obtain catch
per unit effort as a relative abundance index.
Age-structured simulations showed that the
spawning stock biomass would be reduced to
approximately 75 % from the unexploited condi-
tion in 1960. The underexploited status reached a
probability close to 49.4 %, and the fully ex-
ploited status was 41.2 %. The underexploited
status could be a consequence of sampling re-
cruitment from a log-normal distribution. The
short life cycle of sea silverside could benefit
from the low frequency of higher recruitments.
Nevertheless, higher catches observed in 1990,
1999-2000 and 2003 affected the response of the
stock negatively and transitorily because these
higher catches were sporadic and acted as
outliers. Therefore, simulations conditioned to
the observed catch seemed more consistent with
the LBSPR method, i.e., the sea silverside is in a
fully exploited status in Los Lagos region. The
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 289
approach was based on the estimated life-history
parameters with FishLife rather than those known
for sea silverside (Pavez et al. 2008). Parameters
obtained by FishLife have the advantage that they
are consistent and estimated simultaneously
within a given model. Thus, the statistical uncer-
tainty contained in the covariance can be utilized
to improve the estimates when new and better
data become available. Besides, the life-history
parameters (mean and variance-covariance)
could be sampled at random to construct operat-
ing models and evaluate the data-limited stock
assessment models here utilized (e.g., Carruthers
and Agnew 2016).
In the meantime, it is necessary to start with
monitoring the sea silverside fishery in terms of
fishing effort and catch per unit effort, and
biological data. New data will facilitate
estimating the fishery's status and the implement-
tation of fishery management regulations.
Therefore, the framework for a data-limited
stock-assessment approach and the results
obtained here for the artisanal sea silverside
fishery is a starting and essential step.
AGRADECIMIENTOS
LAC thanks the support provided by COPAS
COASTAL (ANID FB210021). PM and PSO thank
the scholarship of the Dirección de Postgrado,
Universidad de Concepción, Chile. GFM thanks
the CONICYT-PFCHA/Magíster Nacional/
2020-22200247 scholarship.
REFERENCIAS
AKAIKE H. 1974. A new look at the statistical
model identification. IEEE T Automat Contr.
19 (6):716–723. doi:10.1109/tac.1974.1100705.
ARELLANO CE, SWARTZMAN G. 2010. The
Peruvian artisanal fishery: Changes in patterns
and distribution over time. Fish Res. 101 (3):
133-145. doi:10.1016/j.fishres.2009.08.007.
ARRIETA SB, GOICOCHEA CE, MOSTACERO JA.
2010. Edad y crecimiento del pejerrey
Odontesthes regia regia (Humboldt) en el mar
peruano. 2002. Inf Inst Mar Perú, Callao. 37
(3-4): 75-77.
BARROS SE, IWASZKIW JM. 2006. Fecundidad del
Pejerrey Odontesthes bonariensis (Cuvier y
Valenciennes, 1835) (Pisces: Atherinidae) en
el embalse Cabra Corral, Provincia de Salta,
Argentina. AquaTIC. 24: 42-49.
BRIAN S, DYER H. 2006. Systematic revision of the
south American silversides (Teleostei,
Atheriniformes). Biocell. 30 (1): 69–88.
CAMPOS LEÓN S, INCIO PÉREZ A, PINAZO K. 2020.
Aspectos biológicos y pesqueros del pejerrey
Odontesthes regia (Humboldt, 1821) en
Arequipa. Enero 2016-setiembre 2018. Bol
Inst Mar Perú, Callao. 35 (1): 88-95.
CARRUTHERS TR, AGNEW DJ. 2016. Using
simulation to determine standard requirements
for recovery rates of fish stocks. Mar Policy.
73: 146–153. doi:10.1016/j.marpol.2016.07.026.
CARRUTHERS TR, HORDYK AR. 2018. The Data-
Limited Methods Toolkit (DLMtool): An R
package for informing management of data-
limited populations. Methods Ecol Evol. 9
(12): 2388-2395. doi:10.1111/2041-210x.13081.
CIFUENTES R, GONZALEZ J, MONTOYA G, JARA A,
ORTIZ N, PIEDRA P, HABIT E. 2012. Weight-
length relationships and condition factor of
native fish from San Pedro River (Valdivia
River basin, Chile). Gayana. 76: 101-110.
DEVILLE D, SANCHEZ G, BARAHONA SP, YAMASHIRO
C, ORÉ-CHÁVEZ D, BAZÁN RQ, UMINO T. 2021.
Spatio-temporal patterns of genetic variation
of the silverside Odontesthes regia in the
highly productive Humboldt Current System.
Fish Res. 244: 106127. doi:10.1016/j.fishres.
2021.106127.
DYER BS, GOSZTONYI AE. 1999. Phylogenetic
revision of the South American subgenus
Austromenidia Hubbs, 1918 (Teleostei,
Atherinopsidae, Odontesthes) and a study of
meristic variation. Rev Biol Mar Oceanogr. 34
(2): 211-232.
[FAO]. 2018. El estado mundial de la pesca y la
acuicultura 2018. Cumplir los objetivos de
desarrollo sostenible. Roma. https://www.fao.
org/state-of-fisheries-aquaculture/2018/es/.
FREE CM. 2018. datalimited2: More stock
assessment methods for data-limited fisheries.
R package version 0.1.0. https://github.com/
cfree14/datalimited2.
FREE CM, JENSEN OP, ANDERSON SC, GUTIERREZ
NL, KLEISNER KM, LONGO C, MINTO C, OSIO
GC, WALSH JC. 2020. Blood from a stone:
Performance of catch-only methods in
estimating stock biomass status. Fish Res. 223:
105452. doi:10.1016/j.fishres.2019.105452.
FROESE R, BINOHLAN C. 2000. Empirical
relationships to estimate asymptotic length,
length at first maturity and length at maximum
290 MARINE AND FISHERY SCIENCES 35 (2): 275-291 (2022)
yield per recruit in fishes, with a simple
method to evaluate length frequency data. J
Fish Biol. 56 (4): 758-773. doi:10.1111/
j.1095-8649.2000.tb00870.x.
FROESE R, BINOHLAN C. 2003. Simple methods to
obtain preliminary growth estimates for
fishes. J Appl Ichthyol. 19 (6): 376-379.
doi:10.1111/j.1439-0426.2003.00490.x.
FROESE R. 2006. Cube law, condition factor and
weight--length relationships: history, meta-
analysis and recommendations. J Appl
Ichthyol. 22 (4): 241–253. doi:10.1111/j.1439
-0426.2006.00805.x.
FROESE R, PAULY D, editors. 2022. FishBase.
World Wide Web electronic publication.
[accessed February 2022] https://www.
fishbase.org.
GÓMEZ ALFARO C, PEREA DE LA MATTA A,
WILLIAMS DE CASTRO M. 2006. Aspectos
reproductivos del pejerrey Odontesthes regia
regia (Humboldt 1821) en la zona de Pisco
durante el período 1996-97 y mayo-julio del
2002, relacionados con su conservación. Ecol
Apl. 5 (1-2): 141-147.
GULLAND JA. 1965. Estimation of mortality rates.
Annex to the Northeast Arctic working group
report. p. 231-241.
HARTING F. 2022. DHARMa - Diagnostics for
HierArchical Regression Models (R-package)
[accessed March 2022] http://florianhartig.
github.io/DHARMa/.
HAWKSHAW M, WALTERS C. 2015. Harvest control
rules for mixed-stock fisheries coping with
autocorrelated recruitment variation, conser-
vation of weak stocks, and economic well-
being. Can J Fish Aquat Sci. 72 (5): 759-766.
doi:10.1139/cjfas-2014-0212.
HORDYK A, ONO K, SAINSBURY K, LONERAGAN N,
PRINCE J. 2014a. Some explorations of the life
history ratios to describe length composition,
spawning-per-recruit, and the spawning
potential ratio. Ices J Mar Sci. 72 (1): 204-216.
doi:10.1093/icesjms/fst235.
HORDYK A, ONO K, VALENCIA S, LONERAGAN N,
PRINCE J. 2014b. A novel length-based
empirical estimation method of spawning
potential ratio (SPR), and tests of its
performance, for small-scale, data-poor
fisheries. ICES J Mar Sci. 72 (1): 217-231.
doi:10.1093/icesjms/fsu004.
HORDYK AR, ONO K, PRINCE JD, WALTERS CJ.
2016. A simple length-structured model based
on life history ratios and incorporating size-
dependent selectivity: application to spawning
potential ratios for data-poor stocks. Can J
Fish Aquat Sci. 73 (12): 1787-1799.
IRIARTE JL, GONZÁLEZ HE, LIU KK, RIVAS C,
VALENZUELA C. 2007. Spatial and temporal
variability of chlorophyll and primary
productivity in surface waters of southern
Chile (41.5-43° S). Estuar Coast Shelf Sci. 74
(3): 471-480. doi:10.1016/j.ecss.2007.05.015.
LAI H-L, HELSER T. 2004. Linear mixed-effects
models for weight-length relationships. Fish
Res. 70: 377-387.
LE CREN E. 1951. The length-weight relationship
and seasonal cycle in gonad weight and
condition in the perch (Perca fluviatilis).
Journal of Animal Ecology 20 (2): 201-19.
MANGIAFICO S. 2015. An R Companion for the
Handbook of Biological Statistics. North
Brunswick Township, NJ. Rutgers Coop. Ext.
MORESCO A, BEMVENUTI M DE A. 2006.
Reproductive biology of silverside
Odontesthes argentinensis (Valenciennes)
(Atherinopsidae) of coastal sea region of the
South of Brazil. Rev Bras Zool. 23 (4): 1168-
1174.
NAGELKERKE NJD. 1991. A note on a general
definition of the coefficient of determination.
Biometrika 78: 691-692.
NAHDI AAL, GARCIA DE LEANIZ C, KING AJ. 2016.
Spatio-temporal variation in length-weight
relationships and condition of the ribbonfish
Trichiurus lepturus (Linneaus, 1758):
implications for fisheries management. PloS
ONE. 11 (8): e0161989.
OGLE DH. 2016. Introductory Fisheries Analyses
with R. CRC Press, Taylor and Francis Group.
OVANDO D, FREE CM, JENSEN OP, HILBORN R.
2022. A history and evaluation of catch-only
stock assessment models. Fish Fish. 23: 616-
630. doi:10.1111/faf.12637.
PAJUELO JG, LORENZO JM. 2000. Biology of the
sand smelt, Atherina presbyter (Teleostei:
Atherinidae), off the Canary Islands (central-
east Atlantic). Environ Biol Fish. 59 (1): 91-
97. doi:10.1023/a:1007643732673.
PAULY D. 1983. Some simple methods for the
assessment of tropical fish stocks. FAO Fish
Tech Pap. 234: 1-52.
PAVEZ P, PLAZA G, ESPEJO V, DYER B, CERISOLA H,
SAAVEDRA J, ALMANZA V, MATAMALA M. 2008.
Estudio Biológico-Pesquero del pejerrey de
mar X Región (Proyecto FIP Nº 2006- 58).
Informe Final. Estud Doc. Pont Univ Católica
Valparaíso. 132 p.
PAY I, CANALES C, BUCAREY D, CANALES M,
CONTRERAS F, LEAL E, TASCHERI R, YEZ A,
ZIGA MJ. 2014. Proyecto 2.16: Revisin de
MORA ET AL.: DATA-LIMITED STATUS OF SEA SILVERSIDE IN SOUTHERN CHILE 291
los puntos biolgicos de referencia (Rendi-
miento Mximo Sostenible) en las pesqueras
nacionales. Convenio II: Estatus y posibili-
dades de explotacin biolgicamente sustenta-
bles de los principales recursos pesqueros
nacionales ao 2014. Informe Final. Instituto
de Fomento Pesquero, Valparaíso. 51 p.
PITA C, VILLASANTE S, PASCUAL-FERNÁNDEZ JJ.
2019. Managing small-scale fisheries under
data poor scenarios: lessons from around the
world. Mar Policy. 101: 154-157. doi:10.
1016/j.marpol.2019.02.008.
PLAZA G, ESPEJO V, ALMANZA V, CLARAMUNT G.
2011. Female reproductive biology of the
silverside Odontesthes regia. Fish Res. 111
(1): 31-39. doi:10.1016/j.fishres.2011.06.009.
POMEROY SA, NEIL A. 2011. Small-scale fisheries
management: frameworks and approaches for
the developing world. CABI. Cambridge
PRINCE J, VICTOR S, KLOULCHAD V, HORDYK A.
2015. Length based SPR assessment of eleven
Indo-Pacific coral reef fish populations in
Palau. Fish Res. 171: 42-58. doi:10.1016/
j.fishres.2015.06.008.
PUNT AE, COPE JM. 2019. Extending integrated
stock assessment models to use non-
depensatory three-parameter stock-
recruitment relationships. Fish Res. 217: 46-
57. doi:10.1016/j.fishres.2017.07.007.
QUINN TJ, DERISO RB. 1999. Quantitative Fish
Dynamics, New York: Oxford Univ.
RAMÍREZ JG, LLEONART J, COLL M, REYES F,
PUENTES GM. 2017. Improving stock
assessment and management advice for data-
poor small-scale fisheries through participa-
tory monitoring. Fish Res. 190: 71-83.
doi:10.1016/j.fishres.2017.01.015.
RICARD D, MINTO C, JENSEN OP, BAUM JK. 2012.
Examining the knowledge base and status of
commercially exploited marine species with
the RAM Legacy Stock Assessment Database.
Fish Fish. 13 (4): 380-398. doi:10.1111/j.1467
-2979.2011.00435.x.
SALAS S, CHUENPAGDEE R, SEIJO JC, CHARLES A.
2007. Challenges in the assessment and
management of small-scale fisheries in Latin
America and the Caribbean. Fish Res. 87 (1):
5-16. doi:10.1016/j.fishres.2007.06.015.
[SERNAPESCA]. 2020. Anuarios estadísticos de
pesca 2020. Servicio Nacional de Pesca y
Acuicultura, Chile. http://www.sernapesca.cl/
informacion-utilidad/anuarios-estadisticos-
de-pesca-y-acuicultura.
[SUBPESCA]. 2003. Red de Enmalle (GNS).
Departamento de Pesquerías. [accesed 25
April 2022] https://www.subpesca.cl/portal/
616/articles-9191_documento.pdf.
SHARMA R, WINKER H, LEVONTIN P, KELL L,
OVANDO D, PALOMARES MLD, PINTO C, YE Y.
2021. Assessing the potential of catch-only
models to inform on the state of global
fisheries and the UN’s SDGs. Sustainability.
13 (11): 6101. doi:10.3390/su13116101.
THORSON JT, JENSEN OP, ZIPKIN EF. 2014. How
variable is recruitment for exploited marine
fishes? A hierarchical model for testing life
history theory. Canadian Journal of Fisheries
and Aquatic Sciences. 71 (7): 973-983.
doi:10.1139/cjfas-2013-0645.
THORSON JT, MUNCH SB, COPE JM, GAO J. 2017.
Predicting life history parameters for all fishes
worldwide. Ecol Appl. 27 (8): 2262-2276.
doi:10.1002/eap.1606.
THORSON JT. 2020. Predicting recruitment density
dependence and intrinsic growth rate for all
fishes worldwide using a data-integrated life-
history model. Fish Fish. 21( 2): 237-251.
doi:10.1111/faf.12427.
VENABLES WN, RIPLEY BD. 2002. Modern
Applied Statistics with S. Fourth edition.
Springer.
VILLAVICENCIO Z, MUCK P. 1984. Estudio de
otolitos de Odontesthes regia r., pejerrey:
determinación de edad. Bol Inst Mar Perú.
Callao. 8 (3): 73-100.
ZHOU S, PUNT AE, SMITH ADM, YE Y, HADDON M,
DICHMONT CM, SMITH DC. 2017a. An
optimized catch-only assessment method for
data poor fisheries. ICES J Mar Sci. 75 (3):
964-976. doi:10.1093/icesjms/fsx226.
ZHOU S, PUNT AE, YE Y, ELLIS N, DICHMONT CM,
HADDON M, SMITH DC, SMITH AD. 2017b.
Estimating stock depletion level from patterns
of catch history. Fish Fish. 18 (4): 742-751.
doi:10.1111/faf.12201.
ZHOU S, YIN S, THORSON JT, SMITH ADM, FULLER
M. 2012. Linking fishing mortality reference
points to life history traits: an empirical study.
Can J Fish Aquat Sci. 69(8):1292–1301.
doi:10.1139/f2012-060.
