Using the MSVPA/MSFOR model to estimate the right ...

ICES J. mar. Sci., 52: 819–826. 1995

Using the MSVPA/MSFOR model to estimate the right-hand side of the Ricker curve for Baltic cod Henrik Sparholt Sparholt, H. 1995. Using the MSVPA/MSFOR model to estimate the right-hand side of the Ricker curve for Baltic cod. – ICES J. mar. Sci., 52: 819–826.

? 1995 International Council for the Exploration of the Sea

Key words: Ricker curve, MSVPA model, Baltic cod, cannibalism, stock-recruitment, fisheries management. Received 12 May 1994; accepted 10 May 1995. H. Sparholt: International Council for the Exploration of the Sea, Palægade 2–4, DK-1261, Copenhagen, Denmark.

Introduction The lack of knowledge of the relationship between recruitment (R) and the spawning stock biomass (SSB) of a fish species is a major source of uncertainty in fisheries management. Often, this lack of knowledge results in the assumption that recruitment is independent of SSB, although in some cases a minimum SSB has been defined below which recruitment will be negatively affected (Anon., 1992). Despite this uncertainty, it has still been possible to give advice on rational management because it can be claimed that, in spite of the unexplainable variation in recruitment, maximum yield would be obtained at a fishing level of Fmax (see Beverton and Holt, 1957), or F0.1 if some economical aspects are taken into account (see e.g. Jakobsen, 1992). In multi-species based assessments, it has been shown that Fmax usually does not exist and that F0.1 is so high that fishing at that level will result in very low SSB values (Pope, 1991; Anon., 1994a). Multi-species based assessment has shown to be superior to single-species based assessment in many cases, for most stocks in the North Sea (Andersen and Ursin, 1977; Pope, 1991) and for cod, 1054–3139/95/050819+08 $12.00/0

herring, and sprat in the Baltic (Sparholt, 1995), and so it has become of even greater importance to use a reasonable SSB-recruitment relationship. Research efforts have been intensified lately to identify SSB-R relationships (e.g. Anon., 1993; Hilborn and Walters, 1992) and to obtain an understanding of the mechanisms governing recruitment (e.g. Blaxter, 1990). To date, SSB-R relationships have yet to be resolved for any one stock dealt with by the International Council for the Exploration of the Sea (ICES). Several models for the SSB-R relationship have been suggested in the past (e.g. Beverton and Holt, 1957; Hilborn and Walters, 1992). The Ricker model (Ricker, 1954, 1975) is one of the most often mentioned. Ricker suggested that recruitment increases with increasing SSB until a certain level where it decreases due to cannibalism. He expressed this as: R=A*SSB*exp("B*SSB)

(1)

where A and B are parameters to be estimated. It can easily be shown that this model has a maximum level of recruitment of A/(e*B) at an SSB value equal to 1/B. ? 1995 International Council for the Exploration of the Sea

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Cod cannibalism in the central Baltic is estimated by the Multi-Species VPA (MSVPA) Model. By using the corresponding Multi-Species Forward (MSFOR) Projection Model, Ricker curve relationships were found for the relationship between cod spawning stock biomass (SSB) and recruitment of 1-, 2-, and 3-year-old cod, assuming that recruitment of 0-year-old cod was proportional to the SSB. It is argued that a proportional relationship between 0-year-old cod and SSB was the most simple and biological reasonable assumption for central Baltic cod, unless the SSB was extremely large. The SSB level that gave the highest number of recruits at age three was 500 000 t, and this value was independent of the assumed proportionality factor between recruitment of 0-year old cod and SSB. The proportionality factor changed from year to year and this was postulated to be environmentally driven. Independent of the environmental conditions in a given year, the maximum recruitment of age three cod was obtained at SSB values of 500 000 t. This finding has important fisheries management implications. Cannibalism is an important self-regulatory mechanism in the central Baltic cod stock.

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H. Sparholt dependent on hydrographical conditions, especially salinity and oxygen concentrations, than on SSB (e.g. Anon., 1992). This paper is an attempt to improve our understanding of the SSB-R relationship for the central Baltic cod stock.

Material The MSVPA/MSFOR model for the central Baltic with the input data as described by Sparholt (1994) was used, with the exception of the following input data for cod: —the recruitment of 0-groups for 1993; —fishing mortalities for 1993–2001; —stock numbers at the beginning of 1993. How these input data deviate from Sparholt (1994) is described below.

Methods Two different assumptions about the relationship between SSB and recruitment of 0-group cod at 1 July, R0, in a given year were explored. In the first assumption R0 was constant, that is, it was independent of SSB. R0 was taken as the mean stock numbers in 1977–1990, as estimated from the MSVPA model (1.371*109 0-group cod). Points for plotting recruitment of 0-, 1- (R1), 2- (R2), and 3-group (R3) cod against SSB were taken from MSFOR estimates of SSB for each of the years 1993–2001 and from an additional run where the fishing mortality (F) on cod in 1993–2001 was set to 0 in order to obtain high values for SSB. In the second assumption, R0 was proportional to SSB. The proportionality factor between SSB and R0 was obtained by dividing the average recruitment of 0-group cod in 1977–1990 with the average SSB in the same period as estimated by the MSVPA (652 000 t). The relationship was R0 =2.1 SSB where R0 is measured in 109 and SSB in thousands of t. Points for plotting recruitment of 0-, 1-, 2-, and 3-group cod against SSB were obtained by running MSFOR several times. In each case the cod stock numbers at age at 1 January 1993 were taken as a multiple of the values from Sparholt (1994) and the recruitment values for 0-group cod according to the above formula. The stock numbers estimated by the MSFOR of 1-, 2-, and 3-group cod at 1 January 1994, 1995, and 1996, respectively, were plotted against the SSB value used. Ricker curves were fitted to the plots by use of the SAS NLIN Procedure (Anon., 1988).

Results The recruitment of 0-, 1-, 2-, and 3-group cod was plotted against SSB under the assumption that

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The development of a comprehensive multi-species model for the central Baltic (e.g. Sparholt, 1993, 1994; Anon., 1994a) has shown that cod cannibalism in the central Baltic was significant and quantifiable. It is therefore possible to estimate the right-hand side of the Ricker curve for central Baltic cod and this is very important in order to be able to give biological advice on fisheries management, as will be shown later. The multispecies model is an application of the so-called MSVPA/ MSFOR programs (Multi-species VPA/Multi-species forward projection model) (e.g. Sparre, 1991). It is a VPA-type model (e.g. Gulland, 1965), where several VPAs (one for each fish stock considered) are run simultaneously with predation included. Predation is estimated based on predator consumption rates data and on food composition. Food composition is assumed to vary with the variation in relative abundance of prey items. Consumption rates are assumed constant. Different prey types are assumed to be eaten in proportion to their relative abundance, weighted by a specific suitability factor for each predator and prey combination. This assumption is used in the MSVPA/MSFOR model to extrapolate predation rates to years where no data were available on food composition. That is, the overall suitability of each species age group as prey for each predator age group is constant. The suitability factor can be thought of as integrating different aspects of vulnerability, such as prey size preference of the predator and degree of spatial overlap between predator and prey type. By assuming that suitability is constant, the model ignores the possibility of prey switching or of annual variation in spatial overlap. This inherent simplification has been subject to much debate, but comprehensive tests made by Rice et al. (1991), Larsen and Gislason (1992) and Anon. (1994b) for both the North Sea and the Baltic Sea show that it is a reasonable simplification. Cod, two herring stocks, and one sprat stock were included in the model for the central Baltic with cod as predator and cod, herring, and sprat as prey. Even though the proportion of cod in the food of cod is less than 5% (in weight) (Sparholt, 1993), the MSVPA/ MSFOR model for the central Baltic estimates high mortalities of 0- and 1-group cod due to cannibalism in most of the years covered by the model, i.e. 1977–1992 (Anon., 1994a; Sparholt, 1994). In the biological advice on the management of the central Baltic cod stock given by ICES it is assumed that recruitment of 2-group cod is independent of SSB. However, a Minimum Biological Acceptable Level (MBAL) of SSB is identified as the smallest historical level. The idea is that it is ‘‘dangerous’’ to exploit the stock to the extent that the SSB becomes lower than observed in the past. This is, of course, a pragmatic procedure and results from limited knowledge of the true relationship. Furthermore, recruitment of cod in the central Baltic has generally been believed to be more

Estimating the Ricker curve for Baltic cod

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Figure 1. Recruitment of 0- (/), 1- (.), 2- (-), and 3-group (,) cod plotted against SSB under the assumption that recruitment of 0-group cod is constant.

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SSB (000s t) Figure 2. Recruitment of 0- (/), 1- (.), 2- (-), and 3-group (,) cod plotted against SSB under the assumption that recruitment of 0-group cod is proportional to SSB. Ricker curves are fitted to the points for each age group.

recruitment of 0-group cod is constant (Fig. 1). The 0-group line is a straight line with a slope of 0 because of the assumptions used. The recruitment of the other age groups shows a strong negative relationship to SSB, and there was almost no cod surviving to age 3 when SSB was over about 1.5 million t. The recruitment of 0-, 1-, 2-, and 3-group cod was plotted against SSB under the assumption that recruitment of 0-group cod is proportional to SSB (Fig. 2). The 0-group line is a straight line with slope 2.1 because of the assumptions used. Ricker curves can be nicely fitted to the points for the older age groups and the estimated parameters are given in Table 1. These curves reach maximum values at SSB values around 1.15 million t for 1-group cod, around 600 thousand t for 2-groups, and around 550 thousand t for 3-groups.

Discussion The assumption about a constant R0 value independent of SSB gives SSB-R1, SSB-R2, SSB-R3 correlations which are clearly negative. This is in obvious contrast to the observed relationship (Figs 3b–d). From a biological

Table 1. The estimated Ricker parameters (&1 s.d.) for SSB-R relationships for 1-, 2-, and 3-group cod as recruiting ages. Cod age

A&1 s.d.

B&1 s.d.

1 2 3

2.09&0.07 1.89&0.16 1.43&0.14

0.00088&0.00002 0.00163&0.00010 0.00183&0.00012

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SSB (000s t)

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Recruitment in millions

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(a) R = 0.40

6000 5000 4000 3000 2000 1000 0 2000 (b) R2 = 0.37 1800 1600 1400 1200 1000 800 600 400 200 0 800 (c) R2 = 0.35 700

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SSB (000s t) Figure 3. Recruitment of (a) 0-group, (b) 1-group, (c) 2-group, and (d) 3-group cod against SSB, based on estimates from the MSVPA as described in Sparholt (1994). Correlation given as R2 values.

point of view it is unlikely that R0 is independent of SSB especially at very low SSB values. The only biologically plausible relation would be that R0 suddenly drops to

lower SSB levels than those observed here, as R0 has to be zero when SSB is zero. This, however, means that the SSB-R0 relationship is rather complicated and thus

Estimating the Ricker curve for Baltic cod

the prey (Sparre, 1991). Thus, it can be stated that, independent of the SSB-R0 slope, the maximum number of 3-group cod surviving will occur at an SSB value of 550 000 t. Of course, the maximal values of the Ricker curves will vary. A related problem is whether or not the stock will have the potential to rebuild the SSB or maintain it at 550 000 t in periods of poor environmental conditions, i.e. a low slope of the SSB-R0 line. Sparholt (1994) showed that, even in the case of the worst period observed, 1986–1990, it would be possible to rebuild the SSB to the above level if F was reduced to 0.4 or less; at present F is about 1.0. An assumption used for the catch and biomass projections in the ICES routine assessment of this cod stock is that recruitment of 2-group cod is constant. This is to some extent an arbitrary choice based on the fact that, in the VPA used, age group 2 is the youngest age. Based on the above results this corresponds to a rather strange assumption about the recruitment of 0-group cod. This assumption cannot be maintained in the MSVPA/ MSFOR context if standard scientific principles are followed. There were significant positive correlations between SSB and recruitment of cod in the central Baltic cod stock (Figs 3a–d). The correlation was highest for 0-groups, intermediate for 1- and 2-groups and lowest for 3-groups. However, there is a clear time trend in recruitment which cannot be attributed to SSB levels (Figs 4a–d). Table 2 shows the production of 0-group cod per unit biomass of SSB and a very clear decrese in production per unit biomass of SSB can be seen. Thus, the above correlations are, to a large extent, due to the general decrease in the survival of cod from the egg and larvae stage to age 0, which subsequently resulted in a decrease in SSB. The decrease in survival cannot be due to cod predation because no cod eggs or larvae were found in the cod stomachs (Sparholt, 1994). This is in line with the fact that cod eggs and larvae are pelagic and not spatially overlapping with older cod. In addition, eggs and larvae are probably too small to be suitable for most cod according to the food size preference of cod (Bundgaard and Sparholt, 1992). The observed relationships between SSB and R0, R1, R2, and R3 (Figs 3a–d) are in better agreement with the assumption of R0 being proportional to SSB than the assumption of R0 being independent of SSB. The time trend in the production of recruits per unit biomass of SSB might be due to environmental conditions. Among several attempts to find hydrographical parameters to correlate with cod recruitment, Bagge (1993) has been the most convincing. He found a slight correlation to the vertical size of suitable water masses for spawning as defined and estimated by Wieland (pers. comm.). Obviously, however, the vertical size of the suitable water masses is not the most important factor as

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violates the scientific principle that a simple model should be preferred to a more complex model if the complex model cannot be shown to be better than the simple model. The assumption about a linear relationship is simpler than the model above and seems to give much more reasonable SSB-R plots. From a biological point of view, this assumption seems quite reasonable. There is no known mechanism for cod egg and larval stages in the Baltic that could explain an SSB dependent mortality, which must occur if R0 is not linearly related to SSB. The abundance of cod larvae was so low, even in years with good recruitment (Wieland and Zuzarte, 1991), that grazing down of food items seems unlikely. Switching of potential predators to cod larvae in cases of high recruitment is also unlikely because cod eggs and larvae are so few that they cannot be an important food item for any predator. Even if they were, switching would probably not occur. Observations made in relation to the development of the MSVPA/MSFOR models for the North Sea and the central Baltic has shown that switching is rare (e.g. Rice et al., 1991; Larsen and Gislason, 1992; Anon., 1994b). Myers and Cadigan (1993) observed densitydependent juvenile mortality in several cod stocks in the north Atlantic. However, they only considered cod from the stage when they are demersal and can be caught by bottom trawls. This stage is included in the MSVPA/ MSFOR for the Baltic. It can be questioned whether it was an actual density dependent mortality they have found or whether it was a spurious one. For North Sea cod, juvenile density was positively correlated with total cod stock size for the time period considered by Myers and Cadigan (1993) and Daan et al. (1994), and it is more likely that they observed cannibalism of large and old cod on small cod. That they observed a negative autocorrelation between adjacent cohorts supports the hypothesis that cannibalism was involved. Thus, what they observed might simply be a similar phenomenon to the cannibalism estimated by the MSVPA for the Baltic cod stock, and at least not simply density-dependent mortality. The data used to estimate the proportionality between SSB and R were taken from the period 1977–1990. The estimated Ricker curves would differ if another proportionality between SSB and R0 was used. Other proportionality factors could be interpreted as corresponding to periods with favourable or less favourable environmental conditions, giving higher or lower survival rates for cod eggs and larvae. Therefore, the unfavourable Ricker curves were also estimated based on other proportionality factors between SSB and R0. Mean values for other ranges of years were applied but the SSBs corresponding to the maximum recruitment for each age group did not change. The reason for this is that predation mortality is related mainly to the biomass of the predator and only very weakly to the abundance of

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Year Figure 4. SSB and R by year and year class, respectively; (a) 0-group, (b) 1-group, (c) 2-group, and (d) 3-group cod. Based on estimates from the MSVPA described by Sparholt (1994). /=SSB.

it captures only a small fraction of the variation in recruitment. Another explanation of the time trend observed is predation on cod eggs by sprat and herring

(Köster, 1992). In some years and in some areas this predation can be very high and potentially important for the success of a cod year-class. Although the data used

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Estimating the Ricker curve for Baltic cod Table 2. Spawning stock biomass, SSB, recruitment of 0-groups, R0, and production of 0-groups per unit biomass of the spawning stock, R0/SSB, for the central Baltic cod. Data are from the MSVPA of the central Baltic (Sparholt, 1994).

Year

530 684 961 1088 1015 1045 1069 1007 746 595 445 420 363 249 170 92

2339 2774 6583 5238 2801 1868 1469 1363 1393 569 303 246 96 94 239 114

the cod SSB is kept around the above mentioned 500 000 t, the predation on sprat will be high and, thus, the frequencies of large sprat stock sizes will be low.

Acknowledgements R0/SSB 4.41 4.06 6.85 4.81 2.76 1.79 1.37 1.35 1.87 0.96 0.68 0.59 0.26 0.38 1.41 1.24

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by Köster were quite substantial compared to other similar studies, the spatial and temporal coverage of the cod spawning season and area contains serious gaps. Therefore, a reasonably precise quantification of the effect of sprat and herring is not yet possible.

Conclusions and fisheries management implications It can be concluded that assuming proportionality between R0 and SSB is a more appropriate model than assuming no relationship. Furthermore, the Ricker curves fit well the calculated relationship between R1, R2, R3, and SSB. The level or height of the curves depend upon the proportionality factor between R0 and SSB but the SSB values corresponding to the maximum value of R1, R2, and R3 are constant for each age group. As the fishery starts on 3-group cod in the central Baltic the recruitment of 3-group cod is very important from the fishery’s point of view. Thus, the results given above indicate that the management of the cod stock in the Baltic should aim at a target SSB of about 550 000 t, if maximising yield is the goal. This can be the target SSB value both in cases with favourable or severe environmental conditions for cod eggs and larvae. In order to take account of sprat predation on cod eggs as an important factor in controlling the survival of cod eggs, managers should probably aim at preventing the sprat stock from becoming too large. This can either be achieved by fishing sprat intensively at large sprat stock sizes or by keeping the cod predation rate high. If

I thank the ICES General Secretary for permission to use information from ICES Working Groups Reports.

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Sparholt, H. 1994. Fish species interactions in the Baltic. Dana, 10: 131–162. Sparre, P. 1991. Introduction to multispecies virtual population analysis. ICES Marine Science Symposia, 193: 12–21. Wieland, K. and Zuzarte, F. 1991. Vertical distribution of cod and sprat eggs and larvae in the Bornholm Basin (Baltic Sea) 1987–1990. ICES CM 1991/J: 37.

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