
Costa et al.: Length-based analysis of Micropogonias furnieri 511
net sheries within RESEXMAR-Itaipu during a
48-month sampling period from January 2001 to
December 2004. All hauls occurred over a 200-m
beach stretch. Boats were monitored by teams of
2-3 observers at the landing site on the sampling
day. Total length (TL, in cm) and total weight (TW,
in g) of sh were taken whenever possible. Once
a month, one full beach seine haul was conducted
to collect scientic information, including the TL
and TW of M. furnieri.
Data analysis
Stock assessment was conducted using individ-
ual TLs and the TropFishR package (Mildenberger
et al. 2017a) to calculate population growth param-
eters. The TropFishR includes enhanced versions
of all functions of the FAO-ICLARM Stock As-
sessment Tool II (FISAT II) (Gayanilo et al. 2005).
We applied an optimized bootstrapped ELEFAN_
GA (Mildenberger et al. 2017b; Schwamborn et al.
2019) to the length-frequency distributions (LFD)
to assess uncertainties around growth estimates.
The length data were grouped into 2-cm size class-
es to obtain approximately 20-25 length classes,
as suggested by Gayanilo et al. (2002). Data from
corresponding months across dierent years (e.g.
January 2001, January 2002, January 2003, and
January 2004) were merged monthly and treated as
a single theoretical year to minimize adjustment er-
rors in population parameters. The selectivity curve
was used to correct the length-frequency data for
gear selection in small sh (Sparre and Venema
1997). The Bhattacharya method is a statistical ap-
proach used to separate length-frequency distribu-
tions into distinct cohorts by decomposing data into
overlapping normal distributions, each represent-
ing a group of individuals of similar size and age.
The relative growth-weight/length relationship
was calculated using the equation W = a.Lb (Pauly
and Munro 1984), and logarithmically transformed
into log W = log a + b log L, where W is the weight
(g), L is the total length (cm) of the sh, a is the in-
tercept of the regression curve (related to sh body
form), and b is the regression coecient (exponent
indicating growth) (Froese 2006). This coecient
was compared with and tested against the value
of 3 (t test, Zar 1984) to determine deviation from
isometric growth. Growth parameters were inves-
tigated by tting a seasonally oscillating von Ber-
talany growth function (VBGF) (Somers 1988):
where L∞ is the asymptotic length, K is the von
Bertalany growth coecient, Lt is the length at
age t, C is the amplitude of growth oscillations (typ-
ically between 0-1; values > 1 imply rare periods of
length shrinkage), t0 is the theoretical age of the sh
when Lt is equal to zero, and ts is the fraction of a
year (relative to the age of recruitment, t = 0) where
the sine wave oscillation begins (i.e. turns posi-
tive). One additional output of ELEFAN_GA run in
TropFishR is the parameter tanchor, which represents
the fraction of the year in which yearly repeating
growth curves cross the length equal to zero.
The VBGF parameters were adjusted using the
TropFishR ELEFAN_GA function. The genetic al-
gorithm uses the idea of natural selection to nd
the best-scoring parameter combinations. These pa-
rameters were treated as genes carried by individ-
uals in the population. Individuals with the highest
tness (i.e. Rn score) reproduced and recombined
their parameter values in subsequent generations.
Over time, the population becomes dominated by
individuals with an ever-increasing tness. The
growth parameter seed values were obtained from
FISAT II routines (Maximum Length Estimation
and K-Scan) (Gayanilo et al. 2005) and applied to
the LFDs. For the more complex genetic algorithm
(ELEFAN_GA), some key settings were ne-tuned
for precision, allowing for assessment of uncer-
tainties around the growth estimates (Mildenberger
et al. 2017b; Schwamborn et al. 2019). The ELE-
FAN_GA settings were ne-tuned for precision as
follows: MA = 5, maxiter = 50, run = 10, pmutation