Ecological Archives E085-020-A3

Brian R. MacKenzie and Friedrich W. Köster. 2004. Fish production and climate: sprat in the Baltic Sea. Ecology 85:784–794.

Appendix C. Effects of temperature and exploitation on projected abundance trends of the Baltic sprat population, including background text, methods, computational details regarding recruitment–environment–spawner biomass relationship, Table C1, and Figs. C1 and C2.


ICES (ICES 2001) routinely produces for management authorities 10-year projections of population abundance for a large number of fish populations, including sprat in the Baltic Sea.  These projections are produced during annual assessments of stock status and use existing knowledge of fish biology (e.g., growth, mortality, maturation rates, recruitment) and fishing mortality rates as inputs to the calculations.  Because variations in fish biology in the future are unknown and cannot presently be predicted, the biological inputs assume mean values with random variation based on historical data.   As a result the biological inputs represent the overall biological response to average environmental conditions observed in the recent past.  The projections therefore represent stock development under environmental conditions observed during the period represented by the biological variables.  In the case of sprat, the projections assume no functional relationships between any of the key biological variables and abiotic factors; hence the effects of climate variability on stock development cannot be simulated.  Nevertheless major changes in ecosystem structure and functioning occur and are known as “regime shifts” (Beamish et al. 2000) .  In such instances it is useful to know how a fish population will react (e.g., increase vs. decrease, or whether the population might fall below predefined critical levels) during a different regime and under different levels of exploitation.

Notably one of the major uncertainties in projections of fish population development (especially for sprat in the Baltic Sea) is a functional relationship between recruitment and any other variable, including spawner biomass and environmental factors.  In the absence of a functional relationship, assessment working groups often must assume a mean recruitment with random variability, or a highly uncertain relationship (i.e., one that explains little variation) between spawner biomass and recruitment.  As a result, projections based on these inputs are also highly uncertain.

We have observed that recruitment for sprat in the Baltic Sea has co-varied with temperature for at least 45 years.  We incorporated our temperature–recruitment relationship into a population-projection model used by the assessment working group (ICES 2001) and calculated the expected spawner biomass trend for the next 10 years.  In addition, we estimated the probability for different temperature and exploitation scenarios that the spawning biomass would fall below the level that would require ICES to recommend major reductions in fishing quotas.  This level of biomass is known as the “precautionary-approach biomass” (BPA; ICES 1998 ).


The projections used the same assumptions of sprat biology (e. g., growth, maturity, natural mortality rates) and exploitation as used by ICES when making stock projections as part of its routine stock assessment procedures.  The only modifications we made involved the functions used to generate recruitment estimates (see below).  Natural mortality rates were age-specific and derived from a multi-species virtual population analysis (MSVPA) that calculates sprat mortality rates due to predation by cod.  These rates were assumed constant throughout the projection period to be consistent with ICES assessment practice (ICES 2001) .  The applied exploitation pattern used age-specific fishing mortality rates for the years 1998-2000 (ICES 2001) .  The projections assumed random variation associated with initial estimates of age-specific sprat abundance as derived from virtual population analyses (VPA; ICES 2001) .  Calculations also assumed that growth rates were variable by allowing weights-at-age to vary randomly within ranges observed in historical data (ICES 2001) . The ICES projection used a Beverton-Holt stock-recruitment model to derive recruitment estimates; the model does not explain significant variation and no environmental forcing was included in this projection (ICES 2001) . We conducted six series of projections to explore how stock development might react to changes in temperature (three levels; cold, average and warm) and exploitation (i.e., status quo and 1.2 × status quo).  The higher exploitation rate corresponds to the “precautionary fishing mortality” (FPA; ICES 2001) and enables us to evaluate whether a sustainable stock development is possible under different environmental scenarios. The simulations of stock development for all scenarios were repeated 200 times to generate distributions of spawner biomass, recruitment and fishing yield.  These distributions used the random variations associated with the temperature–recruitment–spawner biomass functions (see below) and other inputs (e.g., growth) to generate realistic levels of recruitment variability.  Based on the computed spawner biomass distributions we estimated several percentiles to examine the probability that spawner biomass would fall below BPA for different temperature and exploitation scenarios.  These probabilities were visualized by producing time-dependent contour plots of spawner biomass. 

Computational details regarding recruitment–environment–spawner biomass relationship

We chose to include in our stock projections a functional relationship among recruitment, spawner biomass, and environmental variability, even though our statistical analyses indicated only a small and usually insignificant effect of spawner biomass on recruitment for our data.  The type of relationship we used (see below) can represent stock dynamics at low spawner biomass levels, should certain combinations of exploitation and environmental variability cause the simulated population to fall to low levels.  We emphasize that our environmentally based models of recruitment (Fig. 2 of the article; Table B1) may not apply in situations where spawner biomass (S) is lower than that observed in our time series.

We assumed a piecewise spawner biomass–recruitment relationship in which recruitment for S > Scrit. and S < Scrit. had two different functions (see also ICES 2003a, b).  Simulation studies with real spawner biomass–recruitment data for several fish populations show that implementation of a piecewise model (“hockey stick”) is acceptable or even preferable to traditional models in cases where stock dynamics at low S are unknown or highly uncertain (Barrowman and Myers 2000) . 

When S > Scrit., we assumed that recruitment was more strongly influenced by environmental variables than by variations in spawner biomass.  This assumption is supported by our statistical analyses (e.g., Fig. 2 of the article; Table B1). 

When S < Scrit., the relationship between recruitment and spawner biomass is poorly known because there are few data points in this range.  We assumed for S < Scrit. that recruitment was more strongly influenced by spawner biomass than by environmental variables and that the relationship between the variables is linear.  We assumed that recruitment increased from 0 to the long-term geometric mean (here labelled Rmax) for the range S < Scrit.

Since no recruits can be produced if S = 0, the slope A of a line from the origin to Rmax over the range of SScrit. is assumed to be Rmax/Scrit. and 

Ri = Rmax/Scrit. × Si                            for Si < Scrit.

We chose Scrit. = BPA = 275 × 108 kg (ICES 2001) .  Other values could be determined using least-squares (Barrowman and Myers 2000) ; however BPA is a reasonable choice for our purpose as it assumes impaired recruitment due to low spawning stock size.

Recruitment predictions derived from these functions were configured to include realistic levels of variability.  This variability was defined on the basis of historical recruitment variability observed under three different levels of temperature (i.e., cold, average, and warm).  Observations indicate that cold and warm periods do occur in the Baltic Sea (Fig. 1 of the article): for example, mean temperatures during 1976–1987 and 1989–1999 were, respectively, 2.6 ± 1.0 °C and 4.4 ± 0.9 °C (mean ± 1 SD).

We ranked our temperature data from coldest to warmest and then grouped the data into three categories whose means approximated the (1) overall mean temperature (3.7 °C), (2) overall mean temperature – 1 SD (2.4 °C), and (3) overall mean temperature + 1 SD (5.0 °C).  We assigned temperatures to only one category to ensure that each category had a unique set of recruitment-temperature observations.  For each of the three subgroups, we estimated the mean and standard deviation of log recruitment.  The subgroup standard deviations were then used to estimate the variation in recruitment (R) expected at different temperatures (Table C1). 

For example, for S > Scrit. and for the mean temperature situation (category 2):

R(109) = exp(4.02 ± 0.761)
For S < Scrit. and the mean temperature situation (category 2):
R = exp(log Rmax)/275 × S 
= exp(4.02)/275 × S              (mean log Rmax = 4.02)
= 0.202 × S                           (109).

The amount of variation in R associated with this prediction cannot be directly estimated from observed data because there are too few observations of S < Scrit. (N = 4 of 25).  In this case we assumed that the amount of variation in R scales with spawner biomass and can be estimated from the observed variation in log R at each temperature category:

For example, consider temperature category 2, S = 100 and Scrit. = BPA = 275 × 108 kg: 

1 SD of log Rs = (SD of log R for temperature categoryi ) × S/Scrit.

= 0.761 * S/Scrit 
= 0.277.


R(109) = [(exp(4.02 ± 0.761×S/Scrit.)) / Scrit. ] × S
= [(exp(4.02 ± 0.761×100/275)) / 275] × 100
= [(exp(4.02 ± 0.277)) / 275] × 100
= 15.4; 20.2; 26.7  (respectively for mean - 1 SD, mean, mean + 1 SD)

These approximations allow us to estimate the combined effects of temperature and spawning stock biomass on recruitment in sprat for a wide range of temperatures and spawner biomasses, including the special case S < Scrit. where observations are lacking. 

The output from the simulations is summarized in Fig. 4 (article), and Figs. C1 and C2 (below). Biomass is highest in the warmest scenario after 10 years, even if exploitation rates increase 20%. The stock is expected to remain at current levels only in the warm environment scenario.  Note that the population has a 15% chance of falling below BPA (275 × 108 kg) in the low-temperature, high-exploitation scenario.  If temperatures remain near the long-term mean, the population has a high probability (> 95%) of remaining above BPA, even if exploitation rates increase by 20%.  As might be expected the projection for the mean temperature and status quo exploitation is nearly identical to that produced by the assessment working group (ICES 2001), which excluded environmental variability.

Table C1.  Temperature categories and recruitment means ± SD for input to medium term projections of sprat stock development in the Baltic Sea.

Temperature Category

Mean Temperature (°C)

Mean log R


1 SD log R

Exp(mean log R)

















   Notes: The temperature categories were derived from the overall mean (3.7° C) and standard deviation (1.3° C) for the entire time series.  Category means are derived from subsets of temperature data containing observations whose means equate to the overall mean or overall mean ± 1 SD. (N = 10, 7, and 8 years per category.)


   FIG. C1.  Percentiles of simulated distributions of projected sprat spawner biomass (SSB; 106 kg) under different temperature scenarios and assuming a hockey stick (Barrowman and Myers 2000) relationship between recruitment and spawner biomass with a break at 275 × 108 kg (BPA).  Exploitation rates are those observed in 1998–2000 (status quo). 


   FIG. C2.  Percentiles of simulated distributions of projected sprat spawner biomass (SSB; 106 kg) under different temperature scenarios with exploitation rates 20% higher than those observed in 1998–2000 (i.e., 1.2 × status quo).  Calculations assume a hockey-stick (Barrowman and Myers 2000) relationship between recruitment and spawner biomass with a break at 275 × 108 kg (BPA).   


Literature Cited

Barrowman, N. J., and R. A. Myers. 2000. Still more spawner-recruitment curves: the hockey stick and its generalizations. Canadian Journal of Fisheries and Aquatic Sciences 57:665–676.

Beamish, R. J., D. J. Noakes, G. A. McFarlane, W. Pinnix, R. Sweeting, and J. King. 2000. Trends in coho marine survival in relation to the regime concept. Fisheries Oceanography 9:114–119.

ICES [International Council for Exploration of the Sea]. 1998. Report of the Study Group on Management Strategies for Baltic Fish Stocks. ICES CM 1998/ACFM:11.

ICES [International Council for Exploration of the Sea]. 2001. Report of the Baltic Fisheries Assessment Working Group. ICES CM 2001/ACFM:18.

ICES [International Council for Exploration of the Sea]. 2003a.  Report of the Study Group on the Further Development of the Precautionary approach to fishery management.  ICES CM 2003/ACFM: 9.

ICES [International Council for Exploration of the Sea]. 2003b.  Report of the Study Group on Precautionary Reference Points for Advice in Fishery Management.  ICES CM 2003/ACFM: 15

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