ICES CM 2013/H:20
The effects of multispecies and environmental factors on MSY reference points for
Baltic sprat.
Jan Horbowy and Anna Luzeńczyk
National Marine Fisheries Research Institute
Contact author: Jan Horbowy, National Marine Fisheries Research Institute, Kołłątaja 1, 81-332 Gdynia,
Poland, [email protected]
Summary
In the paper MSY reference points of sprat are estimated in relation to pressure from cod (predation)
and density dependence in sprat growth. The analysis is based on long-term stochastic simulations, in
which density dependent growth and density dependent predation mortality of sprat are considered.
The analysis indicates that estimates of MSY parameters and the equilibrium biomass and yield curves
strongly depend on the way growth and natural mortality are considered in the analysis.
Introduction
Sustainable harvesting is important subject of many jurisdictions, for example, the World Summit on
Sustainable Development and the Common Fisheries Policy of the EU. In the case of the Baltic Sea, the
procedure for implementation of the MSY (maximum sustainable yield) approach is quite advanced.
However, all MSY reference points that are used in management of the Baltic stocks were estimated
by applying single-species models. The work to include multispecies interactions in estimation of MSY
reference points in the Baltic is in progress in a few laboratories but that issue still requires a lot of
further investigation. One of the most intensively harvested species in the Baltic Sea, sprat, is heavily
influenced by the cod stock through predator-prey relations. In addition, sprat individual growth
undergoes huge variation, in which density dependent effects may play an important role.
Method
The analysis is based on long-term stochastic simulations and classical stock-dynamics equations
(Beverton & Holt stock-recruitment relationship, exponential decay of cohort numbers, Baranov catch
equation). The uncertainties are added as log-normal errors to recruitment, weight at age, and
maturity. The sprat density dependent effects are simulated in growth and predation mortality as
hyperbolic functions.
0.8
avM2 Model
avM2
1.0
0.6
0.8
M2
Relative weight at age
1.2
0.6
0.4
0.4
relative weight
0.2
relative weight Model
0.2
0.0
0.0
0
100000
200000
stock numbers
300000
0
1000
2000
biomass
3000
4000
Figure 1 The average weight of sprat (relative values,
Figure 2 The average predation mortality M2 of sprat as
weight in 1991 taken as 1) as dependent on stock numbers dependent on sprat biomass in 1974-2012.
(sum of age 2 and older) in 1974-2012.
Weight at age is corrected for density by
=
+
while predation mortality M2 is corrected by
2=
+
where corrW and corrM2 are correction factors (weight and M2 multipliers), sumN is total number of
sprats, sumB is total biomass of sprat and a, b, aM, bM are parameters. The stock numbers and
biomass explain 61% and 41% of mean weight and of mean M2 variance, respectively (Figure 1 and
Figure 2). Stock numbers, weight, maturity, and mortality data were taken from ICES (2013).
Results and Discussion
The simulations performed indicate that estimates of MSY parameters and the equilibrium biomass
and yield curves strongly depend on the way growth and natural mortality are considered in the
analysis. When density dependent growth is considered, the FMSY is higher than in case of constant
growth. On the contrary, inclusion of density dependent mortality in the simulations leads to lower
FMSY than in the case of constant predation mortality. When both (growth and mortality) density
dependent effects are included, they compensate to some extent (Figure 3).
(A)
4000
3500
biomass
3000
2500
2000
1500
1000
500
0
0
0.2
0.4
0.6
fishing mortality
0
0.2
0.4
0.6
fishing mortality
0.8
1
1.2
(B)
250
200
yield
150
100
50
0
0.8
1
1.2
Figure 3 The median biomass (A) and yield (B) versus fishing mortality from long-term stochastic simulations for
constant as well as density dependent weight and natural mortality.