Assessing the risk of alternative management strategies in a Mediterranean fishery: protecting the younger vs reducing fishing effort

Figures & data

Table 1.  Growth, population, reproduction and numerical scheme parameters used for the base run scenario.

Symbol	Parameter	Value
Growth
L0^b	Length at birth	3.5 mm
Lmax^b	Maximum length	195 mm
ab	Age at birth	0
k^b	Curvature parameter	0.39 year^−1
aw^b	Parameter	0.00003
bw^b	Parameter	3.2144
Natural mortality
m1^a	0<age≤35 days	0.21 day^−1
m2^d	35<age≤182 days	0.10 day^−1
age−0^b	182<age≤365 days	1.50 year^−1
age−1^b	1<age≤2 year	0.96 year^−1
age−2^b	2<age≤3 year	0.69 year^−1
age−3^b	3<age≤4.5 year	0.61 year^−1
Fishing mortality
fy(t)^b	Interannual fishing mortality	0.40 year^−1(2003)
		0.66 year^−1(2004)
		0.84 year^−1(2005)
		0.66 year^−1(2006)
		0.55 year^−1(2007)
		0.55 year^−1(2008)
		0.61 year^−1(>2008)
fag(a)^a	Fishing-at-age	0.2 (age-0), 2.88 (age-1), 0.84 (age-2), 0.08 (age-3)
fs(t)^a	Seasonality of fishing mortality	0 (season-1), 1.2 (season-2) 1.6 (season-3), 1.2 (season-4)
Reproduction
	Batch fecundity	325 ()
R^c	Sex ratio	0.55
s1^c	Maximum spawning frequency fraction	0.09
s2^d	time-1	0.5
s3^d	time-2	1
s4^d	Curvature parameter	0.3
Numerical scheme
Δ a	Age step	0.056
Δ t	Time step	0.0051
amax	Maximum lifespan	4.5 years
Trun	Simulation period	18 years

^a[3].

^b[4,25].

^c[26].

^dThis study.

Table 2.  Notation of the population dynamics model.

Variable	Notation	Units
a	Age	Year
t	Time	Year
n(a, t)	Density of age a at time t	Fish number
n(0, t)	Density of newborns (a=0) at time t	Fish number
m(a)	Natural mortality rate	1/year
f(a, t)	Fishing mortality rate	1/year
Dsf(a, t)	Daily specific fecundity rate	Fish number/per fish gram
G(a)	Growth at age in terms of weight	Grams
n0(a)	Initial age distribution	Fish number
amax	Maximal age of the sardine species	Year
W(a, t)	Independent two-dimensional Brownian sheet	Dimensionless

Figure 1. Spawning frequency function S(t) during a year.

Table 3.  List of examined scenarios.

Scenario	Description
Sc-1.1	January–March closing period
Sc-1.2	October–December closing period
Sc-2.1	Fixed reduction of fishing mortality by 10%
Sc-2.2	Fixed reduction of fishing mortality by 20%
Sc-3.1	Gradual reduction of fishing mortality by 5% annually (5 years)
Sc-3.2	Gradual reduction of fishing mortality by 8% annually (5 years)

Figure 2. Initial distribution of the population. The initial values are derived from [4].

Figure 3. The black line shows the mean simulated sardine biomass from 500 runs, the dark grey shaded area covers the 25%–75%th percentile, while the light grey shaded area covers the 5–25%th and 75–95%th percentiles. The dot lines with the error bars represent the estimated biomass from acoustics with the corresponding 95% confidence intervals [4].

Figure 4. Box plots for modelled annual catches. The top and bottom of the boxes represent the interquantile range while black dots represent the annual reported landings during 2003–2008 period.

Figure 5. Empirical distribution of sardine biomass level at June 2013 for 500 sample paths.

Table 4.  Summary statistics of forecasted sardine biomass distribution.

Parameters	June 2013
Mean (m)	22,559.2
Median	21,666.4
Standard deviation (std)	6097.5
Skewness	0.93
Interquantile	7998.1
5% percentile	14,277.1
95% percentile	32,770.2
Fractional uncertainty (QSB)	0.25
Uncertainty interval (ISB)	[16,462.4, 28,657.3]
	0.67

Figure 6. Plots of median biomass for the base run (black line) and examined scenarios. Black vertical dot lines represent the reference dates (June 2014 and June 2020) to provide risk analysis.

Figure 7. Plots of median annual yields for the base run (black dots) and examined scenarios.

Table 5.  MWW non-parametric statistical test, comparison of the base run with the various scenarios over the 2009–2020 period.

Table 6.  Probability of sardine biomass (SB) to become greater than mean biomass of base run scenario with assigned standard uncertainty.

Year	2014	2020
Sc-1.1	0.41 (0.14)	0.35 (0.11)
Sc-1.2	0.54 (0.14)	0.62 (0.20)
Sc-2.1	0.62 (0.17)	0.62 (0.19)
Sc-2.2	0.72 (0.15)	0.80 (0.24)
Sc-3.1	0.69 (0.16)	0.84 (0.24)
Sc-3.2	0.67 (0.23)	0.94 (0.30)

Table A1.  Potential changes of n_j(t) for j>1 and n₁(t) during time Δ t.

Change	Probability
	1
	1
−1
Change (Δ n)1	Probability
1
	1

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