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ICES SGRF REPORT 2013
1 Executive summary ........................................................................................................ 1
2 A framework for NSS herring recruitment modelling; Incorporating abundance indices and environmental drivers ........................................................ 2
2.1
Ecological considerations .................................................................................... 2
2.2
Recruitment projections ....................................................................................... 3
2.3
Spiked recruitment ............................................................................................... 4
2.4
Stock considerations ............................................................................................. 6
3 Data Description and Analysis ................................................................................... 8
4 Modelling NSS herring recruitment ........................................................................ 10
4.1
Potential model descriptions ............................................................................. 10
4.2
Dealing with multiple recruitment predictions .............................................. 11
4.3
Source information for recruitment forecasting modelling .......................... 11
5 Conclusions .................................................................................................................. 13
Appendix A: Review of Methodology for recruitment prediction applied for Northeast cod ........................................................................................... 14
6 References ..................................................................................................................... 20
Annex 1: List of participants ................................................................................ 25
| i

ICES SGRF REPORT 2013 | 1
The Study Group on Recruitment Forecasting (SGRF) met at the Instituto Português do Mar e da Atmosfera (IPIMA) in Lisbon, Portugal from November 18–22, 2013, with five participants and Dr Sam Subbey (Norway) as Chair.
The formal mandate for this SG meeting was established in 2011/2/ACOM26 under
Action Plan No: 1.2, 1.10, and 2.5. The objectives of the SG are to decide on guidelines and standards with regards to (1) How to develop models for recruitment projections which incorporate both abundance indices and environmental drivers, and (2)
Criteria for validating models and for choosing the ‘best’ or a set of the best models.
The ToRs for the 2013 meeting included: a ) Application of a stock–recruitment framework (developed in previous reports of the group) to the following stocks: i ) North Sea cod (NS cod); ii ) Norwegian spring-spawning herring (NSS herring); iii ) North Sea Autumn Spawning herring (NSAS herring).
There was also a special request from AFWG, which is designated as ToR B: b ) The methodology for recruitment prediction applied for northeast Arctic cod should be reviewed by SGRF.
The constitution and limited number of attendees for the 2013 meeting meant that the
SG could only focus on addressing some of the 2013 ToRs. The revised ToRs addressed and reported in this report include: a ) Application of a stock–recruitment framework (developed in previous reports of the group) to Norwegian spring-spawning herring (NSS herring); b ) Review of the methodology for recruitment prediction for northeast Arctic cod.
This report summarizes work by the SG on the above revised ToRs. It deals with using biotic and abiotic time-series information to understand the ecological underpinning to NSS herring recruitment, and to aid in the development of appropriate models, which link recruitment to relevant process drivers. The SG recognizes that a good understanding of such drivers is necessary e.g. for predicting spikes in NSS herring recruitment.
The report reviews also discusses how to deal with multiple model recruitment forecasts and presents an illustrative example using recruitment models for Northeast Arctic Cod (NEAc). In particular, the SG reviews the methodology of combining recruitment forecasts from several candidate models, rather than forecasts from an individual ‘best’ model. The variance across a number of models is related to the risk of selecting among these models. Hence the goal of combining individual forecasts will be to reduce the variance of the performance across the combinations relative to the variance across the individual methods, for various measures of variance. It is demonstrated how this can be implemented for a suite of models for forecasting
NEAc recruitment.

2 | ICES SGRF REPORT 2013
2.1
Ecological considerations
The Norwegian spring-spawning (NSS) herring ( Clupea harengus ) stock is considered a widely distributed stock, occurring in both the Norwegian and Barents Sea (Holst et al ., 2004). This stock has undergone very large fluctuation in abundance (ICES
WGWIDE, 2013). In addition to the changes in overall abundance there have also been related major shifts in migration patterns and the locations of overwintering and summer feeding areas (Holst et al ., 2004). The population dynamics of the stock are characterized by periods of low recruitments with occasional strong year classes that ultimately come to dominate the stock. There has been very little success at forecasting the very high recruitments.
NSS herring spawn on the Norwegian continental shelf between 0 and 250 m depth and on hard substrata (gravel, stones) (Slotte, 2001). Spawning times vary annually, very often linked to the ambient thermal regimes and gonad development times
(Kennedy et al ., 2010). The spawning times are also partially dependent on the proportion of recruit spawners in the stock, the younger individuals tending to spawn later (Husebø et al ., 2009). The benthic eggs are potentially subject to an annually varying mortality either through ‘suffocation’ due to a lack of oxygen in the layers of eggs or predation (Morrison et al ., 1991; Toresen, 1991). The south and more recently northward usage of suitable spawning grounds have varied annually. The hatching times also vary annually depending on the spawning times and the ambient thermal regime which determines the development rates of the eggs (e.g. Blaxter and Hempel,
1963). Data from the larvae surveys suggests that the 50% hatch dates can vary over a
30 day period (R.D.M. Nash IMR Bergen, Norway, unpublished data). In general, after hatch, the larvae drift northwards with the Norwegian Coastal Current towards the Barents Sea nursery areas, however, a relatively small proportion end up in fjords along the coast (Holst and Slotte, 1998).
The drift paths between the spawning grounds and the nurseries are relatively well documented (e.g. Vikebø et al ., 2010; Stenevik et al ., 2012). Whilst travelling along the west coast of Norway the larvae are subjected to annually varying thermal regimes which will affect growth, prey levels which will affect growth and survival and predation levels from a diverse group of predators e.g. birds (Durant et al ., 2003), young saithe (Husebø et al ., 2009) and possibly more recently Atlantic mackerel. This highlights the point that there are ecological considerations and the dynamics of NSSH are not isolated from the dynamics of both the predators and the prey.
In general NSS herring juveniles spend up to 3–4 years on the nursery grounds (either the Barents Sea or in fjords) before joining the adult stock in the Norwegian Sea feeding grounds. The young herring are usually located in the southern Barents Sea where there is spatial overlap with young cod and capelin (e.g. Barros et al ., 1998;
Dingsør et al ., 2007). Mortality on the nursery grounds may partially be a function of the abundance of the predatory cod and offset by the abundance of the alternate prey, capelin (Barros et al ., 1998). Juvenile herring are also probably subject to predation by numerous other predators, including large mammals such as minke whales
(Lindstrøm et al ., 2002). The varying levels of mortality will have an influence on the resulting year-class strength.

ICES SGRF REPORT 2013 | 3
In general it is thought that the proportion entering the fjords is inversely related to the total abundance of 0-group herring, the strong year classes primarily growing up in the Barents Sea (Dragesund, 1970). Recent studies on the exceptionally strong 2002 year class suggests that much of these 0-groups were actually on the western boundary of the Barents Sea and may be considered as being in the Norwegian Sea at a much earlier age than most other year classes.
The numbers of individuals that survive through to recruitment or join the adult stock starts from the number of eggs produce and after a stage dependent mortalities results in an annually varying number of survivors. This in essence constitutes a onestep SRR from e.g. SSB to recruitment. One factor that hasn’t been raised as yet, in relation to the NSS herring stock is the potential for variable egg production through variations in fecundity (Seliverstova, 1990; Serebryakov, 1990; Krysov et al ., 1995;
Belikov et al ., 1996; Ma et al ., 1998; Óskarsson et al ., 2002; Kurita et al ., 2003; González-
Vasallo, 2006; Kennedy et al ., 2011a) and/or skipped spawning ((Engelhard and
Heino, 2005; 2006). On the question of skipped spawning, Kennedy et al . (2006) did not find evidence of this phenomenon in recent times; however, there is not enough evidence to suggest that this may not have been prevalent in the past. The resulting numbers at recruitment are therefore a result of factors affecting different parts of the life history, as illustrated in the ‘Paulik diagrams’ given by Nash (1998) and Payne et al . (2009).
In a number of the Northeast Atlantic herring populations, where recruitment indices are estimated, the year-class strength can be detected at a quite early stage in the life cycle i.e. post-winter in North Sea Autumn spawners (Nash and Dickey-Collas, 2005) or by 20 mm length in western Baltic Spring Spawners (WBSS) (Oeberst et al ., 2009).
The reasons why year-class strength is determined at these stages are still equivocal.
2.2
Recruitment projections
There have been numerous papers which have examined the relationships between recruitment and potential drivers or explanatory variables that determine the number of recruits. For the purposes of this report we will focus on two papers as examples, the first of which considers the effect of predator effects in the Barents Sea on 0-group survival (Barros et al ., 1998) and the second the hatch date on the survival of larvae between the spawning grounds and the nurseries in the Barents Sea (Husebø et al .,
2009). In both cases models were presented which could be parameterised and used for prediction of recruitment. Whilst these are not necessarily the best or most appropriate predictors of recruitment they are used here to illustrate how a forecasting framework can be utilised.
In the past a recruitment model based on a combination of a stock parameter (0group herring abundance in the Barents Sea) and environmental conditions (in this case the sea surface temperature) (Stiansen et al ., 2005) was suggested as a reasonable predictor of recruitment. Essentially this predictor used the survey estimate of abundance, modified by the thermal regime at the time, to predict the recruitment three years in to the future. Whilst this was never used in assessments it does provide another model for evaluating the processes of incorporating forecasting models in to the assessment process.
A more traditional approach to forecasting recruitment is by using a Stock–
Recruitment Relationship (SRR). A variety of models can be fitted to these data (ranging from hockey-sticks to Beverton–Holt or Ricker type functions) (Needle, 2002). An alternate to SSB is the use of Total Egg Production (TEP); however, this has shown to

4 | ICES SGRF REPORT 2013 only be marginally different from a traditional SRR using SSB in NSS herring (see
Ndjuala et al ., 2010). Whilst this may be a valuable variation for some stocks, in the case of NSS herring it does not substantially increase the predictive power of a SRR for predicting recruitment. In fact, the predictive power of the fitted SRR is relatively poor. This is a common feature of many SRR.
The current practice for the Working Group dealing with the assessment of the Norwegian Spring-spawning herring for forecasting 0-group abundance in the short-term forecast is to use a geometric mean of 0-group abundance from the years 1988–2009
(ICES WGWIDE, 2013). Also, the abundance of recent year classes were not estimated separately because the available information of these year classes from surveys had already be included in the VPA.
2.3
Spiked recruitment
As defined in the previous report (ICES SGRF, 2012), spiked recruitment is defined as, sporadic, exceedingly strong (or poor) recruitment pulses, which characterize periods of exceptionally high (or low) survival for the early life stages. Here, we will only consider strong, relatively short-term pulses. Norwegian spring-spawning herring is often presented as a good illustration of this phenomenon (shown in Figure X,
Y). Spiked recruitment requires a certain level of biomass, which differs by stock, and low biomass does not rule out the possibility of such dynamics, as shown by NSSH with the 1985 year class (see also Figure Yb). In general, as long as the stock is not in the density-independent phase of stock–recruitment, a spike may occur.
Spiked recruitment is an indication that something has happened within the system outwith the effects of the spawning stock, providing an indication that conditions should be closely monitored. Temperature conditions have been linked to these pulses for species that inhabit water near the edge of their thermal optimums (O'Brien et al ., 2000; Planque and Frédou, 1999), but this is not the sole factor driving such dynamics (Petitgas et al ., 2011). Shifts in productivity, measured through multiple parameters, often underlie such outbursts (Munch and Kottas, 2009); shifts in productivity can be viewed by the relationship between SSB and recruitment, split into different environmental situations/regimes (Olsen et al ., 2011). When conditions align spatial-temporally (e.g. temperature, match with prey, low cannibalism), there is an appropriate response in recruitment. The very large recruitments can raise the population to a new state or abundance level (Solari et al ., 1997). Under these circumstances, the stock–recruitment relationship can be complex. Furthermore, dynamics within the stock are often driven for years afterwards by these strong pulses
(Skjoldal, 2004), particularly when they result in strong density-dependent responses, where recruitment of subsequent year classes (at the appropriate lag) is depressed
(Caley et al ., 1996) or when they change the behaviour of the stock (e.g. Huse et al .,
2010).

ICES SGRF REPORT 2013 | 5
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Figure X. Recruitment patterns of 0-group Norwegian Spring-spawning herring (NSSH), data from ICES WGWIDE (2013). A. Recruitment time-series, solid red line = geometric mean recruitment, dashed green line = arithmetic mean recruitment. b. Recruit per spawner (RPS, R/kg SSB) time-series, c. Log RPS time-series, solid red line = average.

6 | ICES SGRF REPORT 2013
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Figure Y. Stock and recruitment data for Norwegian Spring-spawning herring (NSSH). A. Relationship between SSB and recruits for 1988 to 2012 (data from ICES WGWIDE, 2013). B. Extended
SSB and recruitment data (1950 to 2012) (data for 1950–1988 from ICES WGWIDE, 2006 and 1988–
2012 ICES WGWIDE, 2013).
2.4
Stock considerations
In the past decade or so the NSSH stock has been increasing in size, however, a lack of a large recruitment in the period since 2000 has led to a decline in the SSB. During this time period the productivity of the stock has been declining (see Log R/SSB; Figure Xc) suggesting either a downward shift in the individual fecundity and thus egg production and/or a reduction in survival from egg to adults (increased mortality rates). Additionally, there appears to have been an increase in the mean condition factor of sexually mature fish in the population (Nash et al . IMR, Bergen unpublished data). The causes or potential interlinking of these changes are at present unknown. It is known that there are changes in the ecosystem e.g. an increase in abundance and spatial extent of the predatory and competitive mackerel for instance and there are substantial changes in the abundance of e.g. cod on the nursery grounds. How these are impinging on the NSSH dynamics is unknown but do highlight the point that

ICES SGRF REPORT 2013 | 7 recruitment dynamics in NSSH must take the ecosystem state and dynamics in to consideration.

8 | ICES SGRF REPORT 2013
A number of datasets are available on the early life-history stages of Norwegian
Spring-spawning herring which cover the stock and the prerecruits, potential predators and competitors of the prerecruits and the physical conditions which can affect the survival of individuals through the prerecruit phase. For the purposes of this report the data are divided in to these three groups; 1. Stock specific 2. biological mediators of survival and 3. Physical mediators and indicators of survival.
1 ) Stock specific.
The surveys that hold relevant biological information on NSS herring (see ICES
AFWG 2013; northeast Arctic cod and Stock Annex) are:
A. Norwegian acoustic survey on spawning grounds in February/March (NASF).
This survey covers the years 1994–2005 and provides information on the abundance of young (1–3 year old fish) that are sexually mature and are found on the spawning grounds. This is an indication of the dynamics of recruitment in relation to maturity and spawning migration.
B. Norwegian acoustic survey in November/December (NASN).
This survey covers the years 1992–2001 and provides information on the dynamics of young herring in relation to overwintering dynamics and recruitment processes.
C. Norwegian acoustic survey in January (NASJ).
This survey covers the years 1991–
1999 and provides additional information on the dynamics of young herring in relation to overwintering dynamics and recruitment processes.
D. International ecosystem survey in the Nordic Seas (IESNS). The international ecosystem survey in the Nordic Seas explores the pelagic ecosystem, with a special focus on herring, blue whiting, zooplankton and hydrography. The herring stock is currently dominated by nine year old herring (2004 year class) in numbers but 7, 8, 10 and 11 year old herring (the 2006, 2005, 2003 and 2002 year classes) are also numerous. The 2009 year class appears to be the largest of the younger age groups even if it is relatively small in historical perspective. However, this year class is almost absent in the Barents Sea Survey, suggesting it might have been growing up in the fjords. In the Barents Sea the investigations of herring covered the area from 33°E to the
20°30´E.
E. Ecosystem survey in the Barents Sea (Eco-NoRu-Q3 (Aco)).
This survey covers the period 2003–2012 and age groups 1 to 3.
F. Norwegian herring larvae survey on the Norwegian shelf (NHLS). This survey covers the period 1981 to 2013 and gives the number of larvae and this is deemed indicative of the Spawning-stock biomass with the exception of 2003 and 2009 due to incomplete cover-age in these years. A Larvae Production Estimate (LPE) has also been estimated which attempts to correct for losses due to the timing of the survey relative to the main spawning time.
This survey also provides an estimate of the 50% hatching date for NSSH based on the back-calculated time of hatching.
G. International ecosystem survey in the Norwegian Sea in July–August (IESSNS).
The survey (formerly called “Norwegian ecosystem survey and SALSEA salmon project in the Norwegian Sea in July–August”) has been carried out on the Norwegian shelf since 2004 for the exception 2007 but was extended to the whole Norwe-

ICES SGRF REPORT 2013 | 9 gian Sea, Icelandic waters, and Faroese waters in 2009. The objectives of the survey are to obtain estimates of abundance, spatio-temporal distribution, aggregation and feeding ecology of Northeast Atlantic mackerel, Norwegian spring-spawning herring, blue whiting and Atlantic salmon in relation to oceanographic conditions, prey communities and marine mammals.
2 ) Biological mediators of survival
There are many biological mediators of survival in the prerecruit phase of fishes ranging from maternal and paternal effects through predation, competition, physiological and environmental mediated effects. In the case of NSS the parameters were restricted to those considered in the papers presented by Barros et al . (1998) and
Husebø et al . (2009) as these were two of the examples to be used in this report.
In the case of Barros et al . (1998) survival was deemed to be a function of young cod and capelin abundance as either predator or prey. The abundance data were obtained from ICES AFW (2013). Indicators of survival were estimated from the losses in abundance between the Larvae Production Estimate (LPE) and Larvae Abundance
Index (LAI) for the drift period along the western Norwegian coast (data from ICES
WGWIDE, 2013). Survival rates from the Norwegian coast and in the Barents Sea up until October were taken as the differences in abundance between the larvae (LAI) and the 0-group index.
In the case of the Husebø et al . (2009) model that examined the effect of hatching time and temperature on survival of 0-groups, the 50% hatch dates were calculated from the larvae survey data on the west coast of Norway (Fossum and Nash, IMR Bergen,
Norway unpublished data) and the temperature data were from 20 m depth at the fixed hydrographic station Bud (IMR data). In this case the survival was estimated as the RPS (recruits per spawner; 0 groups/SSB). This model also incorporated the proportion of repeat spawners (a proxy for both spawning time, younger and first time spawners tend to spawn later and for egg and larvae quality, the assumption that offspring from repeat spawners have a better survival). These data were not readily available for the WG and so were not included in the model. This paper also suggests a link between survival and potential predation by young saithe exiting the fjordic nursery areas. In this study catches from the purse-seine fishery from the second half of the year, north of 67 o N, were used. Here we have used the abundance of 1 and 2 year old Northeast Arctic saithe (ICES AFWG, 2013) as a proxy for the potential predation pressure by saithe on the young herring.
3 ) Physical mediators and indicators of survival
There are a number of physical factors which can mediate survival or could be used as proxies. In this study the only one used is the sea surface temperature. In the Stiansen et al . (2005) publication the ‘skin temperature’ was used. However, to extend this analysis in to the present the temperature series used was the sea surface temperature from the International Comprehensive Ocean-Atmosphere Data Set. (ICOADS).

10 | ICES SGRF REPORT 2013
4.1
Potential model descriptions
At the outset, it is not the intention of this SG to present definitive recruitment forecasting models for NSSH rather to illustrate a framework for selecting models and illustrate some of the potential pitfalls in the forecasting process. The WG should pick up these ideas and subsequently provide in depth advice on specific models that can be utilised.
The simplest models of recruitment, for the purposes of forecasting, are the average recruitment over a specified time period of time (see Figure X). The simplest is an average with a more conservative approach being a geometric mean. Within the suggested framework the SG suggests that this is the starting point and baseline from which any model(s) that are going to be used for forecasting should be an improvement. The choice of time span for the averaging needs to consider whether there have been shifts in the ‘productivity’ of the system e.g. changes in RPS (e.g. Figure Xc) or other ecosystem changes such as regime shifts for instance. There are a number of methods available in the literature for evaluating whether and when regime shift have occurred in the ecosystem but it is up to the researcher to determine if they are likely to have impacted on recruitment.
A second suite of recruitment forecasting models involve the estimation of stock and recruitment relationships. In the case of NSSH the current model is of the Beverton–
Holt type (ICES WGWIDE, WGBWNSSH, 2013). These models are on occasions more complex and incorporate environmental factors to try to account for non-stationarity in the SRR.
A third suite of models utilise stock-independent factors to forecast the recruitment.
These generally involve measurements in the current year that are indicative of events that will occur in the future e.g. temperatures in the Kola Section which indicate inflows in to the Barents Sea a number of years later that will lead to changing environmental conditions. In addition or alternatively there are current conditions that modify e.g. the 0-group abundance and hence indicative of the numbers of individuals that will recruit in the population at age 3. There are a number of these models, many of which have not been fully explored within a forecast framework.
Examples include Stiansen et al . (2005) which utilised temperature data to modify ages 1 and 2 to predict age 3 recruits. Whilst this model was a reasonably good predictor in the early 2000s the relationships are now not significant. The model of
Husebø et al . (2009), which utilised hatch dates and temperature conditions as the main drivers of survival, did not provide clear predictors of 0-group abundance or survivorship, however, a more thorough investigation should be undertaken. In the present investigation the exact sae datasets, extended to the present were not extracted. There also did not appear to be a connection with the juvenile saithe population size, however, the timing of exit from the fjords may actually be the definitive factor as highlighted by Husebø et al . (2009).
Barros et al . (1998) indicated that cod predation (especially when capelin was scarce) had a major effect of the survival of young herring in the Barents Sea. Using the concepts and model in this paper along with mortalities estimated from recent surveys ta mortality surface for herring based on cod and capelin abundances was constructed
(Figure XX). This simply illustrates that the response of survival may be very com-

ICES SGRF REPORT 2013 | 11 plex and in this illustration there appear to be combinations where survival may be very high and could lead to occasional very high recruitments.
Figure XX. Response surface for young herring mortality at varying levels of herring to cod and capelin to cod ratios. Capelin is a preferred prey of cod.
ICES WKBWNSSH (2013) recognised the problem of modelling the very large recruitments due to their influence on the stock dynamics. The challenge in the recruitment forecasting for this stock is to find a technique to forecast the occasional very large recruitments. Currently, it is unclear where progress will be made in this field but it is probably necessary to look in to other disciplines e.g. meteorology and forecasting catastrophic events.
4.2
Dealing with multiple recruitment predictions
The principal is to have an objective way of deciding which model or suite of models are the most appropriate for forecasting recruitment. It is accepted that it may be necessary to also have a subjective input, especially when a potential model has no discernible direct or indirect link to the biology or ecology of the system.
4.3
Source information for recruitment forecasting modelling
In the exercises presented here survey data were used from the larvae surveys along the west coast of Norway and the 0-group index for August–October. In the assessment report age 0 is given as the recruitment and this is generated from the VPA
(TASACS, see ICES WGWIDE, 2013). The ICES WKBWNSSH (2013) report does highlight that the 0-group index does not cover the whole stock as not all individuals are in the Barents Sea, therefore there are expected to be differences between the survey and assessment values and possibly trends. This is in fact the case and is shown in
Figure Z. It is clear that there are very large differences between the datasets. The
VPA can make use of additional information on the relative abundance of the year class as seen either in surveys or when appearing in the fishery, from catch data.

12 | ICES SGRF REPORT 2013
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Figure Z. Trends in the abundance of 0-group NSSH from the Barents Sea survey and the VPA output.
The above highlights a potential problem with the recruitment data. The first problem to be addressed is which datasets are to be used for analysing trends in recruitment and then for the recruitment forecasting process. The survey indices need to be evaluated thoroughly and objectively with respect to their bias e.g. periodically encompassing only a part of the stock, etc. Similarly, the VPA data needs to be examined carefully with respect to the underlying assumptions in the model e.g. constant natural mortality in the back calculation from earlier age classes, the use of stock– recruit models, etc. In addition, where assessment models are changed the new model also needs to be examined carefully since many have different assumptions that can radically affect the perception of recruitment. Unfortunately many of these assumptions are not explicitly stated so the user of the recruitment data is not made aware of them.

ICES SGRF REPORT 2013 | 13
All perceptions of recruitment dynamics are based on the recruitment time-series that are avaialble for a stock. Often these consist of both survey indices and outputs from the assessments. In many cases the two types of time-series differ in their trends, often widely. Each time-series needs to be examined thoroughally for underlying bias, error and also the assumptions which are utilised in the construction of the indices. These assumptions range from percieved satial or temporal locations of inviduals in survey design to the model constraints within an assessment.
The work reported here indicates that frameworks can be constructed for forecasting recruitment; however, as with other diciplines e.g. meteorology, forecasting has a limited time horizon. In fact, there is merit in examining the methodologies used in meteorolgical forecasting. Likewise it would be advantageous to bring some of these researchers in to investigate the problems associated with forecasting recruitment in fish populations.
There is still a major problem with forecasting exceptionally high or low recruitments and this stems from a continued lack of understanding of what factors are really important for driving survival during early life-history stages. The Norwegian
Spring-spawning herring example is a clear illustration of the problem. It is apparent that simple modelling approaches are not sufficient and that a greater level of complexity is needed to generate the observed dynamics in recruitment. The modelling example which generated herring mortalities based on predator/prey relationships generated quite large variability in mortality levels and also indicated that the relationships can be quite complex.
There will most likely be more than one candidate model for predicting recruitment and methods needs to be refined for an objective choice between these models. This will not, however, preclude a certain amount of subjective decision-making based on reserchers perceptions of the ecosystem dynamics.

14 | ICES SGRF REPORT 2013
Abstract
This document is response to a request by AFWG for review of the methodology for forecasting northeast Arctic cod recruitment. It deals with predicting recruitment based on an ensemble of plausible model predictions.
Background
The SGRF 2012 report addressed the problem of combining several model predictions to obtain a recruitment estimate with minimum variance. The method (involving a weighted average of individual model predictions) was proposed as a replacement for the hybrid method of Subbey et al . (2008). One major issue not addressed in ICES
SGRF (2012) was how to choose the initial ensemble of models, whose weighted average is sought. There are practical constraints (with respect to time and personnel), which stipulates that not all plausible models can be included in the calculation of the hybrid recruitment value.
The request by AFWG (and also an objective of the SGRF) requires that we:
1 ) Establish a rigorous criterion for accessing the quality of models, which would be used in the weighting process;
2 ) Demonstrate how a representative recruitment estimate may be obtained using the pool of acceptable models.
Results from the above two tasks will form the basis for assessing the quality of forecasts of northeast Arctic cod recruitment.
Method
1 ) Cause–effect evaluation
The SGRF 2012 report emphasized the need for recruitment model to be based on cause–effect considerations, rather than just correlations, which can be spurious.
Methodologies exist for investigating causal links between potential independent variables (biotic and abiotic data), and the dependent model output (e.g. recruitment). Without exception, the candidate models are based on correlations. Given this background, the SGRF leaves the decision on whether a model is plausible to the stock assessment group. This decision could be based on the use of auxiliary information over a period of time, e.g. comparing model predictions of recruitment to empirical (survey) data. In the following, we assume that this has been conducted for the example models, since they all have been used in the AFWG earlier.
2 ) Diagnostics of the model
The diagnostics follow SGRF 2012.

ICES SGRF REPORT 2013 | 15
3 ) Definitions used
We introduce the following definitions:
P ARAMETER
R3
X i
~
X
D EFINITION
Recruitment-at-age 3
“True” (observed) recruitment datapoint i
X f n
S
Average recruitment observations (Longterm mean recruitment)
Forecast of X, based on simple metric of past observations, e.g. long-term average (i.e. the recruitment model to be tested)
Number of observations
The standard deviation of all X i from
~
X
(Square root of SSE)
The standard deviation of all X from i
X fi
R ELATED TO AFWG
Last VPA estimate of R3 time-series
The different recruitment models to be tested (e.g. RCT3, Titov1-4, JES 1-
2)
To be consistent, we define a model as a set of mathematical/statistical description of the recruitment process, expressed in terms of a set of model parameters and conditioned on a unique set of input data. Different sets of parameter values will therefore result in different model realizations, given the data. Alteration of either the parameter set or the conditioning data will however, be considered as resulting in a completely new and different model from the original.
4 ) Testing model errors against long-term mean recruitment prediction errors a ) Model periods
There are several periods to consider.
1 ) Stability of the VPA. In a retrospective perspective the last year(s) of a VPA has larger uncertainties than earlier years. We therefore suggest removing the ‘unstable’ years from the forecast period; a decision left to the Assessment groups in general. For AFWG however, we suggest that the last three years be excluded.
2 ) The learning period, which should be flexible, and from approximately 2 /
3 of the available time-series to the end of the forecast period. For AFWG we suggest this period to start in 1984.
3 ) The forecast period, which should be approximately 1 /
3
of the available time-series. For AFWG we suggest using the last ten years, after removal of the unstable years (see point 1 above).
In our example the VPA for age 3 from the AFWG 2013 assessment was used as R3.
The initial learning period was 1984–2001, and increasing year by year to cover the period 1984–2010. The corresponding one year ahead forecast period was 2002–2011.
The last two years of the VPA are omitted. b ) Model retrospective runs
For the AFWG models, the learning period was set to 1984–2001 for the R3, and the retrospective runs was made for the periods 1984–2001, 1984–2002, …,

16 | ICES SGRF REPORT 2013
1984–2010. This results in a one-year-ahead prognoses for the years 2002, 2003,
…, 2011. c ) Deriving model weight by error variance.
The model error was calculated as the average over a given number of years, of the difference between the model prediction and the “true” recruitment (i.e. R3 from VPA of the assessment year).
σ mod n ∑
= i
=
1
(
R
( VPA ) i n
−
R
(mod) i
2
) d ) Testing for performance against the long-term mean.
Determining a representative pool of plausible models (Nesterov, 2011) requires a tolerance interval or permissible limit of the prediction error for each individual model to be assessed. This is because the recruitment data are in themselves uncertain. The forecast accuracy can be determined by comparing the prediction error with the predefined (acceptable) error level. In general however, model forecasts are meaningful only if they are more accurate (in a statistical sense) than forecasts based on simple, long-term averaging.
We assume that the distribution of forecast errors and the distribution of deviations of the predicted values (from e.g. average long-term average) are close to the normal distribution or differ from it slightly.
We define
σ x n ∑
= i
=
1
( x i
−
)
2 n
, S x n ∑
= i
=
1
( x i
− x fi
2
) n
, t
=
S
σ x . x
Then (see Nesterov, 2011), each NEA cod recruitment model must be considered a valid candidate under two scenarios (I and II):
Scenario I: Forecasting recruitment for current year t
≤
0 .
8
Scenario II: Long-term forecasting of recruitment t
<
1 .
0
This will mean that a model that predicts recruitment the same year as the stock assessment will use the Scenario I criterion, while a model that predicts recruitment for a longer time period will be subject to the Scenario II criterion. For example, in the
AFWG 2014 assessment any model that predicts the 2014 recruitment will need to have t <0.8, while models that predicts recruitment in 2015, 2016, 2017 and 2018 will need to have t<1.
We consider models passing this criterion as qualifying to be part of the ensemble of models, whose weighted average give a representative recruitment prediction. Tables
1 and 2 show example analyses for 1-year ahead recruitment predictions.
The second column in Table 1 shows the VPA estimates for R3, column 3 (the mean) represents the mean recruitment from 1984 to a year prior to the forecast year. For instance, the mean R3 forecast in 2002 is the average R3 (from the VPA) from 1984 to
2001. The models designated by RCT3, JES1, JES 2, T1, T2, T3 and T4 are fully described in SGRF 2012. The Inertia model is based on the principle of approximating

ICES SGRF REPORT 2013 | 17 the R3 estimate in year Yj+1 by the R3 estimate in year Yj (i.e. the Inertia column is a unit positive time-lagged version of the VPA columns).
Table 2 is a table of squared deviation between individual model predictions and
VPA values, i.e. (Model prediction – VPA)2. This table is needed in order to generate the required model discrimination statistics that follows. We calculate the parameter
σ x
=
311 .
044 from the first column (Mean) of Table 2, and derive the t-statistic for each model, which is presented in Table 3. The results from Table 3, together with the constraint on the t-statistics for a 1-year ahead prognosis, show that the JES1 and Inertia models are disqualified as candidate members of the ensemble of hybrid models.
Both models have t>1.

18 | ICES SGRF REPORT 2013
Table 1. One year ahead forecasts by indicated models.
Y EARS VPA
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
457
711
319
586
581
1237
1170
722
426
642
M EAN
554
549
557
546
548
549
578
602
606
600
RCТ3 JES1
336
682
308
590
450
572
636
470
263
504
691
810
677
711
457
596
801
905
909
755
Т1
471
549
485
442
503
672
721
789
671
576
JES2
599
797
551
445
438
517
794
811
819
678
Т3
588
725
196
443
535
801
774
606
518
381
Т2
619
620
461
592
494
780
829
707
549
365
Т4
585
467
307
390
512
762
716
531
470
398
I NERTIA
522
457
711
319
586
581
1237
1170
722
426
Table 2. Squared deviation between model prediction and VPA value.
M EAN RCТ3 JES1 JES2 Т1 Т2 Т3 Т4 I NERT
9484,596 14641 54756 20164 196
26158,81 841 9801 7396
26244 17161 16384 4225
26244 8281 196 59536 64516
56810,72 121 128164 53824 27556 20164 15129 144 153664
1600 16 15625 19881 20736 36 20449 38416 71289
1101,033 17161 15376 20449 6084 7569 2116 4761 25
472985,1 442225 410881 518400 319225 208849 190096 225625 430336
350562,7 285156 136161 141376 201601 116281 156816 206116 4489
14496,16 63504 33489 7921 4489 225 13456 36481 200704
32483,13 26569 233289 154449 60025 15129 8464 1936 87616
1801,531 19044 12769 1296 4356 76729 68121 59536 46656
Table 3. The t-statistics for models in Table 2.
S
RCТ3 JES1 JES2 Т1 Т2 Т3 Т4 I NERTIA
294.84
0.948
324.09
1.042
307.43
0.988
258.94
0.832
218.98
0.704
221.81
0.713
254.74
0.819
326.12
1.048
A hybrid model forecast
The SGRF 2012 report presents a methodology for combining several model forecasts into a single hybrid recruitment forecast. SGRF 2013 considered an alternative and simpler hybrid forecast, based on inverse variance weighting. From Table 3, we generate Table 4, which gives the individual weights P n
, for each model. In Table 4, P is the inverse proportion of the variance contribution to the total variance, and P n
is the normalized value of P, such that P n sums up to unity.

ICES SGRF REPORT 2013 | 19
Table 4. Inverse variance model weights.
RCТ3 JES1 JES2 Т1 Т2 Т3 Т4 I NERTIA
S 294.84 324.09 307.43 258.94 218.98 221.81 254.74 326.12
S 2 86927.8 0 94515.6 67051.2 47950.7 49200.4 64893.5 0
P 4.722761 0 4.343613 6.122772 8.561694 8.344225 6.326353 0
P n
0.12292 0 0.113052 0.159358 0.222836 0.217176 0.164657 0
The hybrid model recruitment forecast HMF) is presented in Table 5.
Table 5. Hybrid model forecast (HMF) from inverse variance weighting.
Y
EARS
HMF
546 634 373 486 496 709 754 652 544 460

20 | ICES SGRF REPORT 2013
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ICES SGRF REPORT 2013
N
AME
Pavel
Gasyukov
Yuri Kovalev
Richard D.M.
Nash
Jan Erik
Stiansen
Samuel
Subbey
Chair
Oleg V. Titov
A
DDRESS
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Institute of Marine Research
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Norway
Institute of Marine Research
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Institute of Marine Research
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HONE
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| 25