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ICES CM 2007/C:11

Interactions between cod, herring and sprat in the Baltic Sea, simulated with a robust dynamic model

Outi Heikinheimo

Abstract

The interactions between cod (Gadus morhua), herring (Clupea harengus) and sprat (Sprattus sprattus) in the Baltic Sea were examined by simulation with a robust dynamic model, an alternative to more complicated and data-demanding multispecies models. The main targets of the study were to find out structural uncertainties of the system and sensitivity of the model output to key parameter values. The results were then compared to the predictions made with the forward calculating multispecies model used by ICES for fish stock assessment in the Baltic Sea. The model output was sensitive to the functional response in predation by cod on herring and sprat. The type II functional response led to a collapse of the clupeid stocks when cod was abundant, while the type III response produced more plausible stock dynamics. According to the simulation, an abundant cod stock was able to keep the sprat stock at a low level. Herring was less affected. The functional response was the most important source of differences in the results obtained with the dynamic model compared to the ICES multispecies model.

Keywords: Cod, sprat, Baltic herring, interactions, dynamic model, Baltic Sea

Contact author: Outi Heikinheimo, Finnish Game and Fisheries Research Institute, Viikinkaari 4, P.O. Box 2, FI-00791 Helsinki, Finland [tel: +358 205 751 254, mobile phone: +358 40 745 2421, fax: +358 205 751 201, e-mail: [email protected]]

1. Introduction, material and methods

In the Baltic Sea, the interacting fish community in the open sea areas is dominated by three species: cod, herring, and sprat. Large changes in the abundance of cod and sprat have been typical in the Baltic Sea during the past three decades (Fig 1). Both environmental changes and interactions between the fish species are involved, which complicates fisheries management and prediction of the effect of management measures. The abundance of cod stock is currently low, herring stocks are decreasing, and the sprat stock is at high level (ICES 2005).

450000 3500

t 400000 a

3000 ) r 350000 s p ) n

s 2500 s o

300000 i n d l l o n 2000 i i 250000 l a l

m i ( g

200000 1500 m n d i ( r 150000 o

r 1000 C

e 100000 H 50000 500 0 0 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 7 7 7 8 8 8 8 8 9 9 9 9 9 0 0 0 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 Year Herring Sprat Cod

Fig. 1. Development of the stock sizes of cod, herring and sprat (ages ≥ 1) in the Baltic Sea from 1974--2004. Note the different scale for the cod stock.

Multispecies virtual population analysis (MSVPA) has been used in the fish stock assessment of the Baltic with both a hind-cast VPA type mode and a forecast catch prediction mode MSFOR (e.g. Sparre 1991, Magnusson 1995). Complicated multispecies models are sensitive to structural uncertainty (ICES 2005). One target of the BECAUSE project (EU FP6) was to develope more robust and less data demanding models that increase understanding of the interactions of the fish species in the Baltic.

A dynamic model on interactions between cod, sprat and Baltic herring was constructed using parameter values from multispecies assessment key run for the Baltic (Study Group on Multispecies Assessment in the Baltic, SGMAB) and literature, with the software Powersim Constructor. The main interactions that are assumed to affect the dynamics of the species are predation by cod on herring and sprat, predation by the clupeids on the early stages of cod, and cannibalism in cod (Köster et al. 2005). The model includes two options, good and bad environmental conditions for cod reproduction, as in the SGMAB scenarios. The model is suitable for examining the feasibility and effects of different model structures on the dynamics of cod and the clupeids, and the sensitivity of the system to the parameter values. The results were compared to the predictions made using MSFOR.

Stock/recruitment equations (Ricker) were used for sprat and herring but the recruitment of cod was drawn from lognormal distributions, based on the data from “good” and “bad” periods.

Good/ Bad S/R- Spawning stock Herring relationship biomass stock

Herring Herring Herring 0+ 1-year-old Ad. catch Sprat stock Herring taken by cod Fishing mortality Herring stock Other Predation natural mortality Predation mortality mortality Functional response Cod stock

Fig. 2: Structure of the herring submodel. Squares are level variables (numbers of fish); ovals are auxiliary variables; diamonds are auxiliary variables with constant values; arrows between the level variables indicate flows (in numbers of fish), with faucets that regulate the flows; thin arrows indicate effects on variables or flows; and “clouds” represent the borders of the system. The variables with double outline are duplicates of variables elsewhere in the model or in other submodels.

To model the predation on sprat and herring by cod, the clupeids are considered here as one group of prey, because their individual size and behaviour are similar (e.g. Rindorf & Gislason 2005). The total consumption then breaks down in proportion to abundance of the prey species (see below). Other food was not taken into account, which means that the clupeids were assumed to be the most preferable food so that the abundance of other food would not affect their proportion in the diet. The value for maximum consumption of clupeids was the number of clupeids taken per cod versus clupeid density, obtained from the results of SGMAB key run; so it is not the bioenergetic maximum energy intake.

n n n Pi = Ci (Nh+s) /[(Nh+s) +(Dh+s) ]

P = functional response, i.e. number of herring + sprat eaten by one cod in one year

C = maximum consumption by cod of herring + sprat (in numbers), i.e. the number of herring and sprat together eaten by one cod/ year when the abundance of the clupeids was at a maximum level during the study period

i = age classes of cod (age 1, age 2, adults)

Nh+s = size of herring + sprat stock in numbers (all age groups)

Dh+s = half saturation constant (size of herring + sprat stock when the consumption was half of the maximum) n = constant that determines the type of the functional response (n = 1 for type II response, n ≥2 for type III response)

r g a 160 e n i y r

r 140 r e e h p 120 /

t

d n=1 a r o 100 c p

n=2 s

e 80

f n n=3 o o

60

r y

e n=4

b 40 b

n n=5 m 20 e u k N a 0 t 0 500 000 1 000 000 1 500 000 Sprat+herring stock (millions)

Fig. 3. Functional response curves for cod predation on sprat/herring with different values of n; n = 1 is the type II response, others type III. Half-saturation constant D = 260 000 millions. (Sprat+herring stock level in millions during bad conditions for cod approximately 4-7*105, good conditions 2-2.5*105).

d e

s 0.0006 u a

c 0.0005

s y d t i o l 0.0004 n=1 c a

t r 0 n=2 0 o 0.0003 0

m n=3 1

n 0.0002 y

o n=4 b i t

a 0.0001 n=5 d e

r 0 P 0 500 000 1 000 000 1 500 000 Sprat+herring stock (millions)

Fig. 4. Predation mortality for different functional response curves

According to the SGMAB results, the annual proportions of sprat and herring in the diet of cod correspond to their abundances in the sea but sprat seems to be “preferred” to herring. Sprat was taken about twice the proportion that the relative abundance compared to herring would suggest. To take this into account in the FR calculation, the abundance of sprat was weighted by 2.

The most important difference between the types of functional responses is in the form of the mortality curve: with the type II response the mortality rises with decreasing prey density (depensatory mortality) (Figs. 3 and 4).

2. Results

The effects of different types of functional responses and values of the half-saturation constant (D) were first studied. The type III functional response with the value 2 for n and D = 260 000 millions were the assumed nominal values.

The simulations with the model showed that the type III functional response in cod predation on the clupeids produces moderately feasible stock sizes and fluctuations in each species, but the type II response leads to collapse of sprat and herring during good conditions for cod. Sprat collapses also with low half saturation constants. During bad conditions for cod, the clupeid stocks are only little affected by cod predation.

Simulation results with current fishing and type III response (stock sizes in millions), Figs. 5 and 6:

) 5000 n o i l

l 4000 i m (

3000 e

z Cod i s

2000 k c

o 1000 t S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1 0 5 6 7 8 9 2 1 1 1 1 1 1 1 1 1 1

)

n 300000 o i l

l 250000 i m

( 200000 Herring e

z 150000 i

s Sprat

k 100000 c o

t 50000 S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 5 6 7 8 9 2 3 4 5 6 7 8 9 0 1 1 1 1 1 1 1 1 1 1 2 Time in years

Fig. 5: Simulation: Stock sizes of herring, sprat and cod (age ≥1) during good conditions for cod reproduction with type III functional response.

)

n 800 o i l l i 600 m (

e 400 Cod z i s

k 200 c o t 0 S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 8 7 6 5 4 3 2 1 0 5 6 7 8 9 2 1 1 1 1 1 1 1 1 1 1 Time in years )

n 600000 o i l

l 500000 i m

( 400000 Herring e

z 300000 i

s Sprat 200000 k c

o 100000 t

S 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 1 1 1 1 1 1 1 1 1 2 Time in years

Fig. 6: Simulation: Stock sizes of herring, sprat and cod (age ≥1) during bad conditions for cod reproduction, with type III functional response.

The effect of different fishing strategies was examined by simulation. The results were compared with the results of MSFOR (forward-calculating multispecies VPA), according to ICES (2005), for different scenarios (Figs. 7-8): F (status quo) = current fishing F (pa) = fishing mortality when precautionary approach is implied F (0.5pa) = fishing mortality is half of F(pa)

Good environment Cod Herring Sprat )

n 4 000 80 000 200 000 o i l l i 3 000 60 000 150 000 m (

e 2 000 40 000 100 000 z i s

k 1 000 20 000 50 000 c o t

S 0 0 0 Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa)

Bad environment Cod Herring Sprat )

n 600 120 000 500 000 o i l l i 500 100 000 400 000 m

( 400 80 000 300 000 e 300 60 000 z i 200 000 s

200 40 000 k

c 100 20 000 100 000 o t

S 0 0 0 Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa)

Fig. 7. Average stock sizes in numbers of cod, herring and sprat, with standard deviations, according to simulations of three scenarios: Current fishing (Status quo), fishing effort according to the precautionary approach (F(pa)), and fishing with an effort half of that (F(0.5pa)).

Good environment Cod Herring Sprat )

n 4 000 80 000 200 000 o i l l i 3 000 60 000 150 000 m (

e 2 000 40 000 100 000 z i s

k 1 000 20 000 50 000 c o t

S 0 0 0 Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa)

Bad environment Cod Herring Sprat )

n 600 120 000 500 000 o i l l i 500 100 000 400 000 m

( 400 80 000 300 000 e 300 60 000 z i 200 000 s

200 40 000 k

c 100 20 000 100 000 o t

S 0 0 0 Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa) Status quo F(pa) F(0.5 pa)

Fig. 8. Average stock sizes in numbers of cod, herring and sprat according to simulations with MSFOR (SGMAB, unpublished), three scenarios: Current fishing (Status quo), fishing effort according to the precautionary approach (F(pa)), and fishing with an effort half of that (F(0.5pa)). In good environmental conditions herring and sprat collapsed to zero.

The results of MSFOR are presented as biomasses of fish stocks in the report (ICES 2005), but here the average numbers from about one hundred runs (Morten Vinther, unpublished) were used.

The most marked differences were found in good environmental conditions (Fig. 7). Both herring and sprat collapsed in all fishing scenarios in good environmental conditions according to MSFOR simulations. In the MSFOR simulation the stock size of cod in numbers declined with decreasing fishing effort, which is the opposite response compared to the dynamic model. However, the biomass of the cod stock increased with decreasing effort (ICES 2005), which means that there were fewer but on the average larger individuals. This indicates at increased mortality of small individuals in the simulation.

In bad conditions, the MSFOR stock sizes for herring and sprat were very similar to those produced with the dynamic model, but the cod stock size in numbers decreased with fishing effort, although only slightly compared to the good conditions.

3. Conclusions

• Type III functional response in cod predation produces feasible stock sizes and fluctuations in the simulations of cod-herring-sprat interactions • The most significant difference in the results of this dynamic model and MSFOR is the collapse of sprat and herring in the MSFOR predictions in “good” environmental conditions (abundant cod stock). This is apparently due to the type II functional response in MSFOR. • The S/R equation for sprat in the ”good” period works also for ”bad” period. This indicates that sprat recruitment not essentially regulated by environmental factors. • Cod is able to control the abundance of sprat during good period but not vice versa.

Acknowledgements

This study was a contribution to EU FP6, TP 8.8 Specific Targeted Research Project 502482 (BECAUSE). I wish to thank the participants of Baltic Case Study group and the ICES Study Group on the Multispecies Assessment in the Baltic (SGMAB), especially Eero Aro and Morten Vinther for the MSVPA assessment results.

References

ICES 2005. Report of the Study Group on Multispecies Assessment in the Baltic (SGMAB), 13—17 June 2005, Riga, Latvia. ICES CM 2005/H:06. 100 pp.

Köster F.W., Möllmann C., Hinrichsen H.-H., Wieland K., Tomkiewicz J., Kraus G., Voss R., Makarchouk A., MacKenzie B.R., St. John M.A., Schnack D., Rohlf N., Linkowski T. & Beyer J.E. 2005. Baltic cod recruitment --- the impact of climate variability on key processes. ICES J. Mar. Sci. 62: 1408--1425.

Magnusson, K.G. 1995. An overview of the multispecies VPA –theory and applications. Rev. Fish Biol. Fish. 5: 195–212.

Rindorf, A. & Gislason, H. 2005. Functional and aggregative response of North Sea whiting. Journal of Experimental Marine Biology and Ecology 324: 1-19.

Sparre, P. 1991. Introduction to multispecies virtual population analysis. ICES Mar. Sci. Symp. 193: 12–21.