•.,

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Not to be cited without prior reference to the authors

International Council for theExploration of the Sea

CM 1997N:7Applying the PrecautionaryApproach in Fisheries andEnvironmental Mapping

1'1_ ... ~ ..... -........

•

THE APPLICATION OF A SUSTAINABILITY CRITERION TO DEMERSALSTOCKS IN THE ICES AREA

R M Cook

FRS Marine LaboratoryPO Box 101, Victoria Road

Aberdeen, AB11 9DB. Scotland, UK

SUMMARY

Applying replacement line theory to observed stock recruitment scatter plots, a reference valueGtoss is defined which corresponds to the replacement line at the lowest observed spawning stockbiomass. The probability that demersal fish stocks in the ICES have been fished above this levelover the last decade,"and ttierefore likely to decline still further, is estimated using a bootstrap

.procedure. About 60% of the stocks have been fished with probabilities greaterthan 10% and25% with a probability greater than 30%. This is consistent with the observation that most stockshave declined for many years. For a number of stocks, the lowest SSB corresponds to a regionwhere recruitment is reduced. This combined witti replacement lines above G 10SS means thatthere is an increased risk of stock collapse. It is possible using the replacement line approachto identify fishing rriortality rates which produce low probabilities of exceeding Gtoss ' At presentabout half the stocks examined fail to meet the criterion of a 10% or less probability of exceedingG10SS'

INTRODUCTION

ACFM conventionally c1assifies stocks in relationto "Safe Biological Limits". This term has noformal definition but generally attempts are made measure the state of the stock against criteriasuch as the direction of change of the biomass, the magnitude of fishing mortality rate in relationto Fmed (Sissenwine and Shepherd, 1987), the occurrence of good year classes and currentbiomass in relation to MBAL, the "Minimum Acceptable Biological Level" ( ICES, 1991). Thelatter is usually interpreted as either the spawning stock biomass below which the probability ofpoor recruitment increases er the lowest observed spawning stock biomass if the stock­recruitment data show no relationship. This somewhat informal approach does not lead to aconsistent jUdgement about the state of the numerous stocks for which ICES gives advice andgenerally fails to address the uncertainties in assessments.

In recent years there has been growing interest in ttie Precautionary Approach as applied tofisheries (eg FAO, 1995). Underlying much of the thinking behind this is the concept of"sustainability" whicti, while easily understood, is not simple to define operationally. Arecent

1

study group (ICES, 1997a) began work on the implementation of the Precautionary Approachwithin the ICES advisory framework. Central to this is the nemd to define reference points whichembrace the problems of sustainability and uncertainty. In this paper 30 ICES demersal stocksare examined by comparing the present exploitation rate of the stock with rates which are Iikelyto be sustainable. A new reference point is (jeveloped which considers the probability of stockdecline below observed values. This overcomes some of the weakness of the traditionalreference points used to classify Safe Biological Limits by sin1Ultaneously considering bothbiomass and exploitation rate. An essential element of the analysis is the assumption Hiat thereis a relationship between stock and recruitment even though this may not be adequatelyestimable. Increasingly this assumption is accepted as the appropi-iate null hypothesis whenexamining stock-recruit data (Rosenberg and Restrepo, 1996).

THEORY

The sustainability of harvesting is largely determined by two factors, the relationship betweenthe size of spawning stock (SSB) and the annual number,of offspring (the recruits) produced,and the subsequent survival of the recruits on entering the fishery. This is iIIustrated in Figure 1awhich shows a theoretical stock-recruitment curve and a recruit survivorship line. Where the twoIines intersect is an equilibrium point to which the population is attracted (Beverton and Holt,1957). If the survivorship line lies above the stock recruitment curve there is no non-zeroequilibrium point and the population is attracted to the origin. The slope of the survivorship lineis affected by the fishing mortality rate, F. The more heavily the stock is exploited, the steeperthe slope. This line is also called areplacement line since it defines the survivorship needed toreplace the spawning stock in the future. It is important to note the distinction between areplacement line and fishing mortality. Areplacement tine (referred to as G), while dependenton F, is also dependent on a number of biological parameters including growth, maturity andnatural mortality.. Thus a unique value of F ean give a variety of replacement lines if thebiological parameters vary.

With perfect information of the type in Figure 1a itis easy to define conditions of sustainabilityand eollapse but this ignores estimation errors and the Iimitations of real data. Gonsider thestock recruitment data iIIustrated in Figure 1b. This shows the typieal problem wtiere data arescattered and are inadequate to define the left hand part of the stock-recruitment curve (thebroken !ine). If we knew the stock recruitme~t curve we could define the slope of the line, G crash ;

the replacement line for the fishing mortality which results in stock collapse. However, the bestwe ean do is to define G10SS' the replacement line which corresponds to the 10west Qbserved§.pawning §.tock (LOSS). Although this is not the replacement line we seek it has certain valuebecause;

a) G,oss is a minimum estimate of Gcrash'

b) any fishing mortality which corresponds to areplacement line to the right of G10ss shouldbe sustainable and,

c) any fishing mortality which corresponds to areplacement line to the left of G10SS shouldresult in an equilibrium stock size below the lowest observed value or stock eollapse.

Clearly we wish to establish a fishing mortality rate which is below Gcrash with some degree ofconfidence. If it ean be established that F gives areplacement line below G10ss then thiscondition is satisfied.

2

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(1 )

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METHODS

a) Distribution of G,oss

The replacement (ine, G,oss' can be defined as the line joining ttie origin of the stock-recruitmentplot to the point given by the expected recruitment value, ~oss, at the lowest observed spawningstock biomass, SIOSS' The slope of this line is then simply calculated trom:

G = Rlosslass S

lass

In order to calculate ~oss it is necessary to describe a stock-recruitment relationship in the regionof Slo55' There are many parametrie stock recruitment models which can be used to summarisethe data (Deriso, 1980; Shepherd, 1982, Schnute, 1985). Although these are quite flexible inshape the choice of tunetion to use is usually stock-dependent. Ta avoid the need to choosea particular function a non-parametric approach has been used here. Non-parametric methodshave been used before (Evans and Rice, 1988) and have the advantage that the data determinethe shape of the curve. The particular method used here is to tit a lowess curve (Cleveland,1981) assuming log-normal errors and use the smoothed value at SIOSS as an estimate of R,oss'It was found that the best results were obtained with the ·stiftest" smoother, so all the data pointswere used for each of the local regression estimates.

These calculations take no account of the uncertainties in the data. Of particular concern is theuncertainty in G10ss replacement line. Uncertainty in G loss can be considered by calculating afrequency distribution of the estimate in equation (1). This can be achieved by bootstrapping thelowess fit to the stock recruitment data. It has been done here by re-sampling with replacementusing a similar approach to Gabriel (1994). For n observations, n stock recruitment pairs weredrawn at random and the lowess curve fitted. For each of five hundred realisations, G,oss wascalculated using equation (1). This allowed a distribution for G,oss to be calculated.

b) Equilibrium curves

The equilibrium yield, Ye, and equilibrium spawning stock, Se' can be easily calculated if anadequate description of the stock-recruitment function is available. Such curves can be usefulin understanding the likely spawning stock and yield associated with a given exploitation regime.Given the lowess estimated values of recruitment these equilibrium curves can be obtainedsimply by multiplying the fitted recruitment value, R, by the appropriate yield per recruit value,y(8), or spawning stock biomass per recruit valuo, b(8) (Table 1) ie:

(2)

(3)

The parameters, 8, are the standard vital quantities of weight at age, w, proportion mature atago, Pt fishing mortality rate, Fand natural mortality rate, M.

3

c) Distribution of GF

The position of the G10SS is determined directly fram the stock-recruitment data. The calculationof replacement Iines for given fishing mortality rates can be made fram the standard "per recruit"formulae (Table 1). The slope, GF, of the replacement line for a particular value of fishingmortality rate, F, is simply 1/b(8) ie:

,

1G =-F b(8)

(4)

The parameters, 8, are generally measured with error or are by their nature variable quantities.Growth, for example would be expected to vary fram year to year leading to different annualmean weights at age. These sources of error need to be considered when calculating afrequency distribution of Gp The calculation of such a frequency distribution has been achievedhere by simulation. A mean and coefficient of variation (CV) for each parameter was specifiedwith an associated distribution. The quantity GF was then calculated repeatedly by drawingparameter values at random fram the specified distributions. The methods for estimating theparameters,8, and their CVs are given in (f) below.

d) Probability that GF>Gloss

Given the estimated distributions of the replacement Iines it is simple to calculate the prababilitythat the present fishing mortality rate, F has areplacement line above G10SS' This probability isgiven by considering the distribution of the ratio G10S/Gp The ratio will be centred on one ifG10SS=GF• If G1OSS<GF, then the ratio will be less than one. Hence the prabability we seek is simplythe prabability that this ratio is less than or equal to one, ie:

(5)

(6)

It can be calculated by drawing at random values of Gloss and GF as described above, formingthe ratio and then accumulating the proportion of the total sampie which is less than or equal toone.

e) Floss distribution

For a unique value of G,oss and a unique set of parameters, 8, it is possible to calculate amultiplier, floss, on the exploitation pattern, s, which satisfies the equation:

1G =-loss b(8)

This multiplier leads to the fishing mortality rate, Floss, above which the stock would be expectedto decline to an equilibrium spawning stock below the lowest observed value. A distribution ofFloss, can be obtained by combining the pracedures described in (a) and (c). For eachbootstrapped valuQ of GlosS ' a set of parameters e is selected at random fram their givendistributions and equation (6) is solved. This gives a distribution of fishing mortality rates whichare Iikely to lead to stock decline below th~ lowest observed spawning stock.

4

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f) Parameter estimates and CVs

The input values required to estimate GF are fishing mortality rate at age , natural mortality rateat age, weight at age and maturity at age. In order to obtain a distribution of GF , it is necessaryto estimate these values and their variances. Nominal values for these quantities have beenobtained from standard ICES assessments (see Data) and the required parameter values andCVs were calculated as folIows:

Fishing mortality: In the examples presented in this paper, fishing mortality is estimated fromXSA (Darby and Flatman, 1994) which gives annual estimates byage. It is assumed that fishingmortality can be decomposed into an age specific selectivity effect, sa' and a year effect fy:

Fay = S/y (7)

Values of fy were estimated as the mean F over the standard age range in each year. Thesampie variance of the fys in the last 10 years was taken as the required variance for calculatingthe parameter CV. This variance expresses the annual year on year variability of F caused byboth process and measurement error.

Values of sa were calculated by dividing the age specific Fs by the fys each year and then takinga mean across the most recent 10 years. The sampIe variance for each sa was then used tocalculate the appropriate CV for selectivity. This will approximate the variability in selectivitywhen year effects are removed.

Natural mortality: A similar approach to that for fishing mortality was adopted. The naturalmortality, M, was decomposed into an age effect, ma, and year effect ky such that:

May = maky (8)

The values. for m were taken as the conventional values of NI used in the assessment. Anarbitra.y value for the CV was set to 0.1. For the year effect, k, a nominal value of one was'used, also with an arbitrary CV of 0.1.

Weight at age: This quantity was taken as the mean over a range of the 10 recent years. Thesampie variance was used as an estimate of the variability in weight. This variance will notadequately describe longer term systematic changes in growth rate but should serve as anestimate of cohort specific growth rate changes assuming an overall stationary mean over time.

Maturity: For each stock the most recent maturity ogive is used. The CV for maturity was takento be 0.1 for those age classes which were partially mature.

For fishing and natural mortality, the parameter distributions were assumed to be normal. Forweight the distribution was assumed log-normal. In the case of proportion mature, this wastaken to be. normally distributed after a logit transformation.

DATA

Data used were taken from the assessments undertaken by ICES in 1996 and reported by theArctic Fisheries Working Group (ICES, 1997b), the Northwestern Working Group, (ICES,1996a), the Working Group on the Assessment of demersal Stocks in the North Sea and

5

Skagerrak (ICES, 1997c), the Working Group on the Assessment of Southern Shelf Demersalstocks (ICES. 1997d) and the Working Group on the Assessment of Northern Shelf Demersalstocks (ICES, 1997e). In the case of North East Arctic cod a new assessment was run becausethe working group assessment uses an inconsistent series of natural mortality and maturity ogivedata which makes the stock-recruitment data problematic to interpret. The assessment was re­run using standard ICES assessment methodology with a constant maturity ogive and naturalmortality value.

RESULTS

Summary results for each stock from the G10ss analysis are given in Figures 2-31. These figuresshow:

a) The stock-recruitment data with the G10sS (vertical shading) and GF (horizontal shading)distributions. These are the 5-95 percentiles.

b) The equilibrium spawning stock biomass (solid line) expected at a range of fishingmortalities. The time series of observed data is superimposed on the graph.

c) The equilibrium yield (solid line) expected at a range of fishing mortalities. The timeseries of observed data is superimposed on the graph.

d) The cumulative distribution of Floss'

Table 2 summarises the principal results for all 30 stocks. It shows the probability that the meanfishing mortality over the last 10 years exceeds G10SS' Figure 32 shows a plot of this probabilityfor each stock ranked in order of magnitude. The values range from close to zero to very highvalues in excess of 0.7. There does not appear to be any pattern either by species orgeographical area.

Figure 33 shows the proportion of stocks examined which have a probability of exceeding G,osswith any given value. About 60% of stocks have been fished with a probability of 0.1 or moreof exceeding G10ss in the last 10 years. About a quarter of stocks have been fished with thisprobability exceeding 0.3.

In Figure 34 the fishing mortality in 1995 (F95) estimated by ICES is compared with the fishingmortality which would produce a 10% probability of exceeding G1oss' The diagonal line is theboundary above which F95 exceeds this 10% probability. About half the stocks examined Iieabove the boundary.

The position of the prevailing exploitation rate on the sustainable yield curve is often consideredto be important in relation to the precautionary approach. In particular fishing below Fmsy issometimes considerd to be safe. Figure 35 summarises the shape of the equilibrium yieldcurves for all 30 stocks. The majority of stocks do not have a maximum within the range ofobserved data. About one third of the stocks are exploited on the descending Iimb of the yieldcurve while the single largest category, about half, are exploited on the rising Iimb of the yieldcurve.

6

DISCUSSION AND CONCLUSIONS

Exploitatiory rates whichgive replacement lines above G,oss have a high probability of resultingin stock sizes below the lowest observed value. For the majority of the main ICES demersalstocks the probabilitY of exceeding this threshold is at least 10% and in about a quarter of stocksabove 30%. More work is required to judgethe probabilitylevel which might be.considereddangerous, but if 10% is taken as the conventional value then most stocks risk further declineif there exploitation rates ramain comparable to those of the last decade.

When the·most recently estimated fishing mortality rates are compared wlth the F required toproduce a1 0% probability of exceedirig G,oss' about half the stocks fair to satisfy the criterion(Fig.34). Perhaps unexpectedly, it is stocks which are exploited at lower absolute values of Fwhich are more likely to fall into this category. Whatever the reasons for this, it appears thatmany stocks require reduction in fishing mortality of about 20% to satisfy the criterion.

The analysis in this paper is limited by the range of the observed stock-recruitment data. Thisrestricts the range of ttie estimated equilibrium yield and SSB curves. When the observedannual data are superimposed on the equilibrium curves, there is a tendency for these data totrack the equilibrium trajectorY..This would be expected if fishing mortality rates evolve slowlyover time and thera are sufficient age groups in the stock to damp out the effects of recruitmentvadability. U implies that for a number of stocks the annual SSB observations are consistent withthe equilibrium analysis.

The equilibrium SSB curves also provide a basis for judging Iikely future stock trajectories. Forexample, if the most recent SSB lies above the equilibrium curve then for the same fishingmortality the stock would be expected to decline in the long term.. This property has implicationsfor ttie interpretation of MBAL. It is quite possible for the SSB to lie, above MBAL (and byimplication "safe") but for the expected stock trajectory to be downward toward and equilibdumvalue below MBAL. A stock in such a condition could not reasonably be judged to be within safebiological limits if the expected time course to the new equilibrium state was short.

Very few of the estimated yield curves exhibit a maximum. For some of these, the position ofthe maximum may He very close to precipitous decline with any further increase in F resultingin stock collapse (eg Fig. 29). Clearly those stocks for which the. yield cUrVe has a negativeslope must have a maximum somewhere belowthe lowest observed F.. However, the positionof the maximum cannot be located with any useful precision. Nearly half the stocks have yieldcurves with observations only in the region where yield increases with fishing mortality rate.These stocks mayhave no MSY point, and again, if it does exist it cannot be determined withany precision. It should also be noted that even stocks exploited around a positive yield slope,often considered a "safe" position may still show a high probability of exceeding G10ss (eg Fig. 26).This would lead the stock toward SSB values at which expected recruitment is unknown. Allthese difficulties suggest that using MSY asthe basis of a precautionary reference point asimplied in the UN agreement on straddling and highly migratory stocks is urirealistic.

REFERENCES

Beverton, R.J.H. arid Holt, S. 1957. On the dynamics of exploited fish populations. FisheriesInvestigations, Sero 2, vol 19. London, 533pp

Cleveland, W.S. 1981. LOWESS: A program for smoothing scatterplots by robust locallyweighted regression. The American Statistician, 35, 54.

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Darby, C.D. and Flatman, S. 1994. Virtual Population Analysis: version 3.1 (windows/Dos) userguide. MAFF Information Technology Series No. 1. Directorate of Fisheries Research,Lowestoft, 85pp.

Deriso, R.ß. 1980. Harvesting strategies and parameter estimation for an age-structuredmodel. Canadian Journal of Fisheries and Aquatic Sciences, 37, 268-282.

Evans, G.T. and Rice, J.C. 1988. Predicting recruitment from stock size without the mediationof a functional relation. Journal du Conseil pour f'.Exploration de la Mer, 44,111-122.

FAD. 1995. Precautionary Approach to Fisheries. FAD Fisheries Technical Paper 350/1.

Gabriel, W.L. 1994. A simple method for estimating uncertainty associated with Fmed' ICES CM1994/0:5.

ICES. 1991. Report of the ICES Advisory Committee on Fishery Management, 1991. ICESCooperative research Report no:179.

ICES. 1996a. Report of the Northwestern Working Group. ICES CM 1996/Assess:15.

ICES. 1997a. Report of the study group on the precautionary approach to fisheriesmanagement. ICES CM 1997/Assess:7.

ICES. 1997b. Report of the Arctic Fisheries Working Group. ICES CM 1997/Assess:4.

ICES. 1997c. Report of the working group on the assessment of demersal stocks in the NorthSea and Skagerrak. ICES CM 1997/Assess:6.

ICES. 1997d. Report of the Working Group on the Assessment of Southern Shelf Demersalstocks. ICES CM 1997/Assess:5.

ICES. 1997e. Report of the Working Group on the Assessment of Northern Shelf Demersalstocks. ICES CM 1997/Assess:2.

Rosenberg, A.A. and Restrepo, V.R. 1996. Precautionary Management Reference Points andManagement Strategies. pp129-140. In: Precautionary Approach to Fisheries, Part 2:Scientific Papers, FAD Fisheries Technical Paper 350/2.

Schnute, J.T. 1985. A general.framework for developing sequential fisheries models.Canadian Journal of Fisheries and Aquatic Sciences, 42, 414-429.

Shepherd, J.G. 1982. A versatile new stock-recruitment relationship for fisheries and theconstruction of sustainable yield curves. Journal du Conseil pour I' Exploration de laMer, 40, 67-75.

Sissenwine, M.P. and Shepherd, J.G. 1987. An alternative perspective on recruitmentoverfishing and biological reference points. Canadian Journal of Fisheries and AquaticSciences, 44, 913-918.

8

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Not to be cited without prior reference to the authors

International Council for theExploration of the Sea

CM 1997N:7Applying the PrecautionaryApproach in Fisheries andEnvironmental Mapping

~ , .THE APPLICATION OF A SUSTAINABILITY CRITERION TO DEMERSAL

STOCKS IN THE ICES AREA

R M Cook

FRS Marine LaboratoryPO Box 101, Victoria Road

Aberdeen, AB11 90BScotland, UK

SUMMARY

Applying replacement line theory to observed stock recruitment scatter plots, a reference valueGtoss is defined which corresponds to the replacement line at the lowest observed spawning stockbiomass. The probability that demersal fish stocks in the ICES have been fished above this levelover the last decade, and therefore likely to decline still further, is estimated using a bootstrapprocedure. About 60% of the stocks have been fished with probabilities greater than 10% and25% with a probability greater than 30%. This is consistent with the observation that most stockshave declined for many years. For a number of stocks, the lowest SSB corresponds to a regionwhere recruitment is reduced. This combined with replacement lines above G10ss means thatthere is an increased risk of stock collapse. It is possible using the replacement line approachto identify fishing mortality rates which produce low probabilities of exceeding G1oss' At presentabout half the stocks examined fail to meet the criterion of a 10% or less probability of exceedingG1oSS'

INTROOUCTION

ACFM conventionally classifies stocks in relation to ·Safe Biological Limits". This term has noformal definition but generally attempts are made measure the state of the stock against criteriasuch as the direction of change of the biomass, the magnitude of fishing mortality rate in relationto Fmed (Sissenwine and Shepherd, 1987), the occurrence of good year c1asses and currentbiomass in relation to MBAL, the "Minimum Acceptable Biological Level" ( ICES, 1991). Thelatter is usually interpreted as either the spawning stock biomass below which the probability ofpoor recruitment increases or the lowest observed spawning stock biomass if the stock­recruitment data show no relationship. This somewhat informal approach does not lead to aconsistent jUdgement about the state of the numerous stocks for which ICES gives advice andgenerally fails to address the uncertainties in assessments.

In recent years there has been growing interest in the Precautionary Approach as applied tofisheries (eg FAO, 1995). Underlying much of the thinking behind this is the concept of"sustainability" which, while easily understood, is not simple to define operationally. Arecent

1

study group (ICES, 1997a) began work on the implementation of the Precautionary Approachwithin the ICES advisory framowork. Central to this is the noed to dofine reforonce points whichembrace the problems of sustainability and Lincertainty. In this paper 30 ICES demersal stocksare examined by comparing the present exploitation rate of the stock with rates which are Iikelyto be sustainable. A new reference point is developed which considers the probability of stockdecline below observed values. This overcomes some of the weakness of the traditionalreference points used to classify Safe Biological Limits by simultaneously considering bothbiomass and exploitation rate. An essential element of the. analysis is the assumption that thereis .a relationship between stock and recruitment even though this may not be adequatelyestimable. Increasingly this assumption is accepted as the appropriate null hypothesis whenexamining stock-recruit data (Rosenberg arid Restrepo, 1996).

THEORY

The sustainability of harvesting is largely determined by !Wo factors, the relationship betWeenthe size of spawning stock (SSB) and the armual number of offspring (the recruits) produced,and tho subsequont survival of the recruits on entering the fishery. This is iIIustrated in Figure 1awhich shows a theoretical stock-recruitment curve and a recruit survivorship line. Where the two elines intersect is an equilibrium point to which the population is attracted (Beverton and Holt,1957). If the survivorship line lies above the stock recruitment curve there is no non-zeroequilibrium point and the population is attracted to the origin. The slope of the survivorship lineis affected by the fishing mortality rate, F. The more heavily ttie stock is exploited, the steeperthe slope. This line is also called areplacement line since it defines the survivorship needed toreplace the spawning stock in the future. It is important to note the distinction between areplacement line and fishing mortality. Areplacement Iino (referred to as G), while dependenton F, is also dependent on a number of biological parameters iricluding growth, maturity andnatural mortality. Thus a unique value of F can give a variety of replacement Iines if thebiological parameters vary.

With perfoct information of the type in Figure 1a it is easy to define conditions of sustairiabilityand collapso but this ignores estimation errors and the Iimitations of real data. Consider thestock recruitment data i1lustrated in Figure 1b. This shows the typical problem where data arescattered and are inadequate to define the left hand part of the stock-recruitnient curve (thebroken line). If we knew thestock recruitment curve we could define the slope of the line, Gcrash '

the replacement line for the fishing mortality which results in stock collapse. However, the bestwe can do is to defino G1oss' the replacement line which corresponds to the !owest ,Qbserved§pawning §tock (LOSS). Although this is not the replacement line we seek it has certain valuebecause;

a) G 10SS is a minimum estimate of Gcrash' . .

b) any fishing mortality which corresponds to areplacement line to the right of G,oss shouldbe sustainable and, . ,

c) any fishing mortality which corresponds to areplacement line to the left of G10ss shouldresult in an equilibrium stock size below the lowest observed value or stock collapse.

Clearly we wish to establish a fishing mortality rate which is below G crash with some degree ofconfidence. If it can be established that F gives areplacement line below G,oss then thiscondition is satisfied.

2

3

(1 )

(3)

(2)

G = R,oss1055 S

1055

The parameters, 8, are the standard vital quantities of weight at age, w, proportion mature atage, p, fishing mortality rate, Fand natural mortality rate, M.

METHODS

The replacement line, G1oss' can be defined as the line joining the origin of the stock-recruitmentplot to the point given by the expected recruitment value, ~oss, at the lowest observed spawningstock biomass, SIOSS' The slope of this line is then simply calculated from:

In order to calculate ~oss it is necessary to describe a stock-recruitment relationship in the regionof S,oss' There are many parametric stock recruitment models which can be used to summarisethe data (Deriso, 1980; Shepherd, 1982, Schnute, 1985). Although these are quite flexible inshape the choice of function to use is usually stock-dependent. To avoid the need to choosea particular function a non-parametric approach has been used here. Non-parametric methodshave been used before (Evans and Rice, 1988) and have the advantage that the data determinethe shape of the curve. The particular method used here is to fit a lowess curve (Cleveland,1981) assuming log-normal errors and use the smoothed value at Sloss as an estimate of R ,oss'It was found that the best results were obtained with the "stiftest" smoother, so all the data pointswere used for each of the local regression estimates.

b) Equilibrium curves

a) Distribution of G,oss

These calculations take no account of the uncertainties in the data. Of particular concern is theuncertainty in Gloss replacement line. Uncertainty in G loss can be considered by calculating afrequency distribution of the estimate in equation (1). This can be achieved by bootstrapping thelowess fit to the stock recruitment data. It has been done here by re-sampling with replacementusing a similar approach to Gabriel (1994). For n observations, n stock recruitment pairs weredrawn at random and the lowess curve fitted. For each of five hundred realisations, G10SSwascalculated using equation (1). This allowed a distribution for G10sSto be calculated.

The equilibrium yield, Ye, and equilibrium spawning stock, Se' can be easily calculated if anadequate description of the stock-recruitment function is available. Such curves can be usefulin i..mderstanding the likely spawning stock and yield associated with a given exploitation regime.Given the lowess estimated values of recruitment these equilibrium curves can be obtainedsimply by multiplying the fitted recruitment value, R, by the appropriate yield per recruit value,y(8), or spawning stock biomass per recruit value, b(8) (Table 1) ie:

c) Distribution of GF

The position of the G10ss is determined directly from the stock-recruitment data. The calculationof replacement Iines for given fishing mortality rates can be made from the standard "per recruit·formulae (Table 1). The slope, GF, of the replacement line for a particular value of fishingmortality rate, F, is simply 1/b(8) ie:

1G =-F b(8)

(4)

The parameters, 8, are generally measured with error or are by their nature variable quantities.Growth, for example would be expected to vary from year to year leading to different annualmean weights at age. These sources of error need to be considered when calculating afrequency distribution of Gp The calculation of such a frequency distribution has been achievedhere by simulation. A mean and coefficient of variation (CV) for each parameter was specifiedwith an associated distribution. The quantity GFwas then calculated repeatedly by drawingparameter values at random from the specified distributions. The methods for estimating theparameters,8, and their CVs are given in (f) below.

d) Probability that GF>G,oss

Given the estimated distributions of the replacement Iines it is simple to calculate the probabilitythat the present fishing mortality rate, F has areplacement line above Gtoss' This probability isgiven by considering the distribution of the ratio G1os/GF. The ratio will be centred on one ifGloss=GF. If G'oss<GF.then the ratio will be less than one. Hence the probability we seek is simplythe probability that this ratio is less than or equal to one, ie: .

(5)

(6)

It can be calculated by drawing at random values of GlosSand GFas described above, formingthe ratio and then accumulating the proportion of the total sampie which is less than or equal toone.

e) FlOSS distribution

For a unique value of G10ss and a unique set of parameters, 8, it is possible to calculate amultiplier, floss, on the exploitation pattern, s, which satisfies the equation:

1G =-loss b(8)

This multiplier leads to the fishing mortality rate, FlOSS' above which the stock would be expectedto decline to an equilibrium spawning stock below the lowest observed value. A distribution ofFlOSS' can be obtained by combining the procedures described in (a) and (c). For eachbootstrapped value of G10SS' a set of parameters e is selected at random from their givendistributions and equation (6) is solved. This gives a distribution of fishing mortality rates whichare Iikely to lead to stock decline below the lowest observed spawning stock.

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f) Parameter estimates and CVs

The input values required to estimate GF are fishirig mortality rate at age , natural mortality rateat age, weight at age and maturity at age. In order to obtain a distribution of GF , it is necessaryto estimate these values and their variances. Nominal values for these quantities have beenobtained from standard ICES assessments (see Data) and the required parameter values andCVs wen3 calculated as folIows:

Fishing mortality: In the examples presented in this paper, fishing mortality is estimated fromXSA (Darby and Flatman, 1994) which give~ annual estimates byage. It is assumed that fishingmortality can be decomposed into an age specific selectivity effect, sa' and a year eHect fy:

Fay = S/y (7)

Values offy were estimated as nie meari F over the standard age rarige in each year. Thesampie variance of the fys in the last 10 years was taken as the required variance for calculatingthe parameter CV. This variance expresses the annual year on year variability of F caused byboth process and measurement error.

Values of sa werecalculated by dividing the age specific F,s by the fys each year and then takinga mean across the most recent 10 years. The sampie variance for each sa was then used tocalculate the appropriate CV for selectivity. This will approximate the variability in selectivitywhen year effects are removed.

Natural mortality: A similar approach to that for fishing mortality was adopted. The naturalmortality, M, was decomposed into an age effect, ma, and year eHect ky such that:

May = maky (8)

The values for m were taken as the conventional values of M used in the assessment. Anarbitrary value for the CV was set to 0.1. For the year sHect, k, a nominal value of one was·used, also with an arbitrary CV of 0.1.

Weight at age: This quantity was taken as the mean over a range of the 10 recent years. Thesampie variance was used as an estimate of the variability in weight. This variance will notadequately describe longer term systematic changes in growth rate but should serve as anestimate of cohort specific growth rate changes assuming an overall stationary mean over time.

Maturity: For each stock the most recent maturity ogive Is used. The CV for maturity was takento be 0.1 for those age c1asses which were partially mature.

For fishing and mitural mortaiity, the parameter distributions were assumed to be normal. Forweight the distribution was assunied log-normal. In the case ot proportion mature, this wastaken to be. normally distributed after a logit transformation.

DATA

Data used were taken trom the assessments undertaken by ICES in 1996 and reported by theArctic Fisheries Workirig Group (ICES, 1997b), the Northwestern Working Group, (ICES,1996a), the Working Group on the Assessment of demersal Stocks in the North Sea and

5

Skagerrak (ICES, 1997C), the Working Group on the Assessment of Southern Shelf Demersalstocks (ICES, 1997d ) and the Working Group on the Assessment of Northern Shelf Demersalstocks (ICES, 1997e). In the case of North East Arctic cod a new assessment was run becausethe working group assessment uses an incorisistent series of natural moitality and maturity ogivedata which makes the stock-recruitment data problematic to interpret. The assessment was re~

run using standard ICES assessment methodology with a constant maturity ogive and naturalmortality value.

RESULTS

Summary results for each stock from the Gloss analysis are given in Figures 2-31. These figuresshow:

a) The stock-recruitment data with the G10sS (vertical shading) and GF (horizontal shading)distributions. These are the 5-95 percentiles.

b) The equilibrium spawning stock biomass (solid Iirie) expected at a range of fishirigmortalities. The time series of observed data is superimposed on the graph.

c) The equilibrium yield (solid line) expected at a range of fishing mortalities. The timeseries of observed data is superimposed on the graph.

d) The cumulative distribution of Floss'

Table 2 summarises the principal results for all 30 stocks. It shows the probability that the meanfishing mortality over the last 10 years exceeds G1osS' Figure 32 shows a plot of this probabilityfor each stock ranked in order of magnitude. The values range from close to zero to very highvalues in excess of 0.7. There does not appear to be any pattern either by species orgeographical area.

Figure 33 shows the proportion of stocks examined which have a probability ofexceeding G10SSwith any given value. About 60% of stocks have been fished with a probability of 0.1 or moreof exceeding G10sS in the last 10 years. About a quarter of stocks have been fished with thisprobability exceeding 0.3.

In Figure 34 the fishing niortality in 1995 (F95) estimated by ICES is compared with the fishingmortality which would produce a 10% probability of exceeding G1oss' The diagonal line is theboundary above which F95 exceeds this 10% probability. About half the stocks examined Heabove the boundary.

The position of the prevailing exploitation rate on the sustainable yield curve is often consideredto be important in relation to the precautionary approach. In particular fishing below Fmsy issometimes considerd to be safe. Figure 35 summarises the shape of the equilibrium yieldcurves for all 30 stocks. The majority of stocks do not have a maximum within the rarige ofobserved data. About one third of the stocks are exploited on ttie descending Iimb of the yieldcurve while the single largest category, about half, are exploited on the rising limb of the yieldcurve.

6

DISCUSSION AND CONCLUSIONS

Exploitation rates which give replacement Iines above G,oss have a high probability of resultingin stock sizes below the lowest observed value. For the majority of the main ICES demersal

• stocks the probability of exceeding this threshold is at least 10% and in ab6ut a quarter of stocksabove 30%. More work is required to judge the probability level which might be considereddangerous, but if 10% is taken as the conventional value then most stocks risk further declineif there exploitation rates remain comparable to those of the last decade.

When ttie most recently estimated fishing mortality rates are compared with the F required toproduce ci 10% probability of exceeding G1055 ' about half the stocks fai! to satisfY the criterion(Fig. 34). Perhaps unexpectedly, it is stocks which are exploited at lower absolute values of Fwhich are more likely to fall into this category. Whatever the reasons for this, it appears thatmany stocks require reduction in fishing mortality of about 20% to satisfy the criterion.

The analysis in this paper is Iimited by the range of the observed stock-recruitment data. Thisrestricts the range of the estimated equilibrium yield arid SSB curves. When the observedannual data are superimposed on the equilibrium curves, there is a tendency for these data totrack the equilibrium trajectory. This would be expected if fishing mortality rates evolve slowlyover time and there are sufficient age groups in the stock to damp out the effects of recruitmentvariability..It implies that for a number of stocks the annual SSB observations are consistent withthe equilibrium analysis.

The equilibrium SSB curves also provide a basis for judging likely future stock trajectories. Forexample, if the most recent SSB lies above the equilibrium curve then for the same fishingmortality the stock would be expected to decline in the long term. This pr6perty has iniplicationsfor the interpretation of MBAL. It is quite possible for the SSB to lie. above MBAL (and byimplication "safe") but for the expected stock trajedory to be downward toward and equilibriumvalue below MBAL. A stock in such a condition could not reasonably be judged to be within safebiologicallimits if the expected time course to the new equilibrium state was short.

Very few of the estimated yield curves exhibit a maximum. For soms of these, the position ofthe maximum may lie very close to precipitous decline with any further increase in F resultingin stock collapse (eg Fig. 29). Clearly those stocks for which the yield curve has a negativeslope must have a maximum somewhere belowthe lowest observed F. However, the positionof the maximum cannot be located with any useful precision. Nearly half the stocks have yieldcurves with observations only in the region where yield increases with fishing mortality rate.These stocks may have no MSY point, arid again, if it does exist it cannot be determined withany precision. It should also be noted that even stocks exploited around a positive yield slope,often considered a "safe" position maystill show a high probabilityof exceeding G,oss (eg Fig. 26).This would lead the stock toward SSB values at which expected recruitment is unknown. Allthese difficulties sLiggest that using MSY as the basis of a precautionary reference point asimplied in the UN agreement on straddling and highly migratory stocks is unrealistic.

REFERENCES

Bevertori, R.J.H. and Holt, S. 1957. On the dynamics of exploited fish populations. FisheriesIrwestigations, Sero 2, vol 19. London, 533pp

Cleveland, W.S. 1981. LOWESS: A program for smoothing scatterpiots by robust locallyweighted regression. The American Statistician, 35, 54.

7

Darby, CD. and Flatman, S. 1994. Virtual Population Analysis: version 3.1 (windows/Dos) userguide. MAFF Information Technology Series No. 1. Directorate of Fisheri~s Research,Lowestoft, 85pp.

Deriso, R.B. 1980. Harvesting strategies and parameter estimation for an age-structured •model. Canadian Journal of Fisheries and Aquatic Sciences, 37, 268-282.

Evans, G.T. and Rice, J.C. 1988. Predicting recruitment from stock size without the mediationof a functional relation. Journal du Conseil pour I' Exploration de la Mer, 44, 111-122.

FAO. 1995. Precautionary Approach to Fisheries. FAO Fisheries Technical Paper 350/1.

Gabriel, W.L. 1994. A simple method for estimating uncertainty associated with Fmed' ICES CM1994/0:5.

ICES. 1991. Report of the ICES Advisory Committee on Fishery Management, 1991. ICESCooperative research Report no:179.

ICES. 1996a. Report of the Northwestern Working Group. ICES CM 1996/Assess:15.

ICES. 1997a. Report of the study group on the precautionary approach to fisheriesmanagement. ICES CM 1997/Assess:7.

ICES. 1997b. Report of the Arctic Fisheries Working Group. ICES CM 1997/Assess:4.

ICES. 1997c. Report of the working group on the assessment of demersal stocks in the NorthSea and Skagerrak. ICES CM 1997/Assess:6.

ICES. 1997d. Report of the Working Group on the Assessment of Southern Shelf Demersalstocks. ICES CM 1997/Assess:5.

ICES. 1997e. Report of the Working Group on the Assessment of Northern Shelf Demersalstocks. ICES CM 1997/Assess:2.

Rosenberg, A.A. and Restrepo, V.R. 1996. Precautionary Management Reference Points andManagement Strategies. pp129-140. In: Precautionary Approach to Fisheries, Part 2:Scientific Papers, FAO Fisheries Technical Paper 350/2. _ .

Schnute, J.T. 1985. A general framework for developing sequential fisheries models.Canadian Journal of Fisheries and Aquatic Sciences, 42, 414-429.

Shepherd, J.G. 1982. A versatile new stock-recruitment relationship for fisheries and theconstruction of sustainable yield curves. Journal du Conseil pour I' Exploration de laMer, 40, 67-75.

Sissenwine, M.P. and Shepherd, J.G. 1987. An alternative perspective on recruitmentoverfishing and biological reference points. Canadian Journal of Fisheries and AquaticSciences, 44, 913-918.

8

TABLE 1

Standard "per recruit" formulae referred to inequations (2) and (3) of the main text used in thecaclulation of the replacement line slope, equilibrium SSB and equilibrium yield. Z is the totalmortality and is the sum of Fand M.

Ay(B) = L Fawae -cumza[1_e -za]/Za

a=1

Ab(8) = L waPae -cumZa

a=1

wherea-1

cumZa=L (Fj+M)j=1

TABLE 2

Summary of the results of G10ss analysis on 30 ICES demersal stocks. The second column refersto the figure which summarises the individual stock analysis. Column 3 gives the probability thatG(F) is greater than G1oSS ' Column 4 gives the fishing mortality where this pobability is 0.1.Column 5 gives the reference F in 1995 as estimated from the 1996 ICES assessment. ,Thefinal column gives the sign of the slope of the equilibrium yield eurve or the fishing mortalitycorresponding to maximum sustainable yield (Fmsy) where this exists.

Stock F p{G(F»G(gloss)} Fishing mortality at F95 Sign of gradient ofIgure tor Mean F 86-95 p{G(F»G(gloss)}=0.1 yield eurve or Fmsy

Cod Are 2 0.00 0.84 0.59 -ve.......................................................................................................................................................................................................................Had Arc 3 0.14 0.39 0.58 -ve.............................................................................................................................................................................................................Sai Are 4 0.32 0.45 0.49 -ve..................................................................................................................................................................................................................................................................................Cod Va 5 0.56 0.56 0.48 -ve..............................................................................................................................................................................................................................................................................................................Sai Va 6 0.02 0.42 0.30 +ve........................................................................................................................................................................................................................................Cod Vb 7 0.02 0.87 0.56 0.50...............................................................................................................................................................................................................................................................Had Vb 8 0.37 0.00 0.21 +ve...................................................................................................................................................................................................................................................................................................Sai Vb 9 0.74 0.23 0.42 +ve..................................................................................................................................................................................................................................................Cod IV 10 0.36 0.79 0.81 -ve........................................................................................................................................................................................................................................................................HadlV 11 0.17 0.71 0.74 -ve.....................................................................................................................................................................................................................................................Whi IV 12 0.26 0.24 0.51 +ve.........................................................................................................................................................................................................................................................Sai IV 13 0.39 0.56 0.43 -ve...............................................................................................................................................................................................................................................Sol IV 14 0.02 0.68 0.51 +ve..................................................................................................................................................................................................................................................Pla IV 15 0.26 0.35 0.46 +ve................................................................................................................................................................................................................................................................Cod Via 16 0.26 0.78 1.10 +ve..........................................................................................................................................................................................................................................................Had Via 17 0.01 0.90 0.52 +ve.......................................................................................................................................................................................................................................................

) Whi Via 18 0.09 0.72 0.66 0.00,,I .

Sai Via 19 0.70 0.42 0.43 0.30......................................................................................................................................................................................................................................Cod Vlla 20 0.18 1.03 0.69 0.97.................................................................................................................................................................................................................................................................Whi Vlla 21 0.10 1.43 1.25 +ve.................................................................................................................................................................................................................................................................Sol Vlla 22 0.16 0.37 0.45 +ve...................................................................................................................................................................................................................................................Pla Vlla 23 0.05 0.68 0.37 +ve...................................................................................................................................................................................................................................................Cod Celt 24 0.58 0.63 0.86 -ve..................................................................................................................................................................................................................................Whi Celt 25 0.02 1.30 0.86 1.70.................................................................................................................................................................................................................................................................Sol Celt 26 0.43 0.37 0.51 +ve................................................................................................................................................................................................................................................Pla Celt 27 0.02 0.82 0.59 +ve...................................................................................................................................................................................................................................................Sol WCh 28 0.58 0.23 0.26 -ve.........................................................................................................................................................................................................Pla WCh 29 0.49 0.41 0.68 0.58

Sol ECh

Pla ECh

30

31

0.05

0.27

0.54

0.40

0.49

0.46

+ve

0.52

Figure 1

FIGURE LEGENDS

(a) Theoretical stock-recruitment relationship for a fish stock. The curve predictsrecruitment given stock size, while the straight lines are the replacement lines.These lines predict expected spawning stock fram recruitment for two levels ofexploitation. At a low exploitation rate (A), the dotted line indicates the populationtrajectory expected which cycles towards an equilibrium point. For highexploitation (8) the dotted line shows the expected population trajectorycollapsing towards the origin. (b) An example of typical stock recruit data wherethere is insufficient information to define the recruitment function near the origin(dotted line). GcraSh is the slope of the stock-recruitment function at the origin andis the replacement line which would lead to stock collapse. G10ss is thereplacement line which gives an equilibrium at the lowest observed spawningstock biomass.

Figures 2-31 These figures show for each stock, as tabulated in Table 2; (a) The stock­recruitment data with the G10ss (vertical shading) and GF (horizontal shading)distributions. These are the 5-95 percentiles.(b) The equilibrium spawning stockbiomass (solid line) expected at a range of fishing mortalities. The time seriesof observed data superimposed on the graph. (c) The equilibrium yield (solidline) expected at a range of fishing mortalities. The time series of observed datasuperimposed on the graph. (d) The cumulative distribution of Floss'

Figure 32

Figure 33

Figure 34

Figure 35

The prabability that fishing mortality in the last decade has exceeded Glossfor 30ICES demersal stocks. Sai=saithe, Sol=sole, Pla=plaice, Had=haddock,Whi=whiting.

The proportion of stocks which exceed a given prabability that mean fishingmortality over the last decade has exceeded G,oss'

Fishing mortality in 1995 plotted against the fishing mortality required to have a10% probability of exceeding G1oSS' The diagonal line is the line for which F in1995 equals this prabability. About half the stocks have Fs abave this line aretherefore have a higher prabability of exceeding G1osS'

A summary of the slope of the sustainable yield curve for all 30 stocks. Moststocks have a monotonaus positive slope. Few stocks show a curve which amaximum.

cn:!:::::::J....oQ)

0::

Fig. 1

Spawning Stock Biomass

A

( a)

• •• •• •

( b)

Spawning Stock Biomass

,70 .BO .90 1.00 1.10 1.20FJ Shin9 mo rt a I i t Y

Equi I i br i um y i eid

.60.50

60

....90........ ......

70 69..' .........::.. .,-

7t.······ .. '.. ..'........ ..... ·St·.. ·· ..'

92 6.~:::· •... :· ...~·· .....~3 '. . ::.. :lll!

~,... .... :.jj. . ::...·· .. ·..17• 6ß' 9 1.& •• U .• 83

• • ·' ..r: • .. • .

.... 65 75 ":;"-:;:28....J.~ 4 ..••• ....JJ:: .....,....... .... .

79 ..:.. 80 82 81

. ·······0 ::::"",.,.....·.. ··...:1...... 84

.J~;::::::::.~:.;~, .....

.40

200

100

O..l--.-----,--..,...---r--,.---r----r--~--.---.l

1100

1000

Equi I ibrium SSB

rn

~ 900E.~ BOO..c,.".,; 700u

..e 600rn

=500c.~ 400;s

:5.,300U')

70•

69•

-Cod,NE ArcticProb G(F»G(loss)= .00

2.

100 200 300 400 .500 6tO0 k70 Q 800 90 D1DDD11 0D

Spawnlng s oe bromass

Cumulative F(loss) Distribution

FigureStock-reeruit

200-r--------------------,

180 /:./J~160 ..; : ::

.~": : ::140 &{ ~ ~ ~ ~ ~

,.: : : : ::~120 .....~::~::~

:'~~~ ~ :' ~ ~~ 100 83 .'.:: : :

~ ::o(f1[rrIoI!::!o~~~~'::::::Ji:1 ~:'20 .':' a 79 808 .~7.

..);:):.:.;/:,,::::::::::~::.:::"'" - .o+,"-,~---.--,.---r-...,.----,---r-.----r-....--r---Jo

.60 ,70. .BO .90 1.00 1.10 1.20FIshing mortality

.50

69.. ::..Jts ......... .'

\......... 821~<: ". ". 76 .•••;~.•:'. ..':75::' .... :-••.. 7Jal ..••.. ':".: ~. .... 94 ·...::· ~3:.··::w.o::::· 78

611. ······ ": .•.•:.::.•.::.. •••• '...... ........:.....

•. 9}..··:a "'::::. 729~ .......-... 87

•. . 68' .' . ..•." -" 65 6~··· ~~., 86 ··8'8··.... • J~ 8.2 "" .

91 .~8~::·--• • &ae: .' 84

····.90 • :~:::::::'I.',.•..........

.40

BOO

200

400

1200

1000

"'Cl

Q)

;;:: 600

1. 601. 501. 401.301.00 1.10.90.BO

· . . . . .................._ .· . . . . . .., . ..., . .., . ..., . ..· . . . . . . .·.. ·[·· .. ·.. ·.. ·-r· .. ···· .. ··r ..·..·..·.. r· ..·..·.. ··i· ..·..·..·..~ .. ·· )' '1' ..•••• : ';" •••••• 0 ••••;, ••••••••••• ! !. o. . .. ..•• ':•••.•••.•••• ';" .•••.• 0 ••• ~ ••••••••••••.. .· .· . ..· .. ..::1:::1:01::::::::r::::::1:::1::....[ : 1" ·..r· ..·..·.. ··1· ..·..·..·..[..·..·..·..;..· ·.. ·T..·..·..·......: -r ~. ····· .. ·.. :·· .. ·.. ·.. ··1· ..·..·..·..~···· ..·..·..r· ·..··r ..·.. ··· .. ··

[:1:1::1j:::01

•9

.8

....-. •7cncn0

.6.........l.L.

11 •5......l.L.

..c .40.... .3c...

.2

.1

0

Figure 3.Stock-recruit

eHaddock;North East ArcticProb G(F»G( loss)= .14 Equilibrium SSB

.60 .70 .BOmortal ity

Equi I i br i um yieid

.40 .50Fishing

.30

76~?::: :.::.::.:::.:.

89········· .. Jf ....70 '::::"~' 95 ..'

...... ·8.'. · ·· •. .....

71.. ' ::~: ~5 ".-'::

..... ....: 71' ".............. 51 72 62

7:~··.:.:::-:·.·.·.·.·.· ......······........:rr:J~·:;:::'·':··'~':~"··············f85' '. .....!.. ..... 94 GJ

1S····.. · ". .....91

92 J : : ::::::..,:.•................................. '................ 90 1" 79

.. 89 . .J~.::::-.8S r.. 84 ·--· ..

..· : "J5

0­e:::

50

300

CI>

~ 250Eo

O...L----r---,----.----,----,---,---J

; 100o0­

cn

.Q 200...><:uo-cn 150

300

75• 76

•7,"••

69•

70•87•

100 . 150 20.0 250Spawnlng stock blamass

F(loss) Distribution

90•

8J•

50

Cumulotive

110

100

90

80

70CI>-:::J 60....~ 50....

40

30

20

10o~~.:..:..=.:..:,:.:.:.~-...,.a.-~-r---=-~-r----r----.----'

o

•9

.8

- .7CI>CI>0

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11 •5Au....

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. 1

350-r-----------------------,

........ ................ 72.::.... '

...•. 74......:.

7J..:.:: .............. ....

. .

50

100

250

300

>- 150

-0200

· . . . . . . . .........................._ .· . . . . . . . .· . .. ....· . .. . .· . .. . ..· . .. . ..· . . . . ., . ........1' 1' ·'1'· ···:· ·..1.. ·.. ·..1"· .. ···;--··· .1' [ 1' ......... !, ~ ":' ~ " .,! !,. . ~ ,;, ~ ~ .· . . ., .· . . ., .· . . .. .· . . .. ........ ~ ~ t ~ ;.. . ~ ·1········ .~ ; ~ ... . ... .· . . . . . . .. .........................._ .· . . . . . . " .· . .. . " .· . . . .· . . . .· . . . '"· . . . . . . .. ........ : ~ , .. -; : ~ ~ -: ~ ~ .· . .., . .· . .., . .· . .., . .· .· . . . . . . .. ........ : ': : : : : : : : : .· . . . . . . .: : : : : : : " :....... : ~.. ';' ~ ! : .: ";" ?... .. .. . .: ..· . . . " .· . . . " .· . . . " .

... ....:. . . .:. ~ : :" ~ " .: ~ ; ..:: : ~· .

O-'----,------r---,------.------,,----...-----I.3 . ~ .5 .6 .7 .9 1.1 1.2 1.3 .30 .~O .50 .60 .70

Fishing mortal ity.BO

­Saithe,NE ArcticProb G(F»G(loss)= .32

Figure 4.Stock-recruit

". ···· J6.. '

.50 .60 .70 .BOmo r tal i ty

Equ i I i br i um y i eid

,.40 .FIshing

95...• ....~ .. ' Bg8 17-.... 84

BR.: _.8IW '.~·lIJ··91·9 9.~·~!/.'f~ii ·.lL ····J..Z·::::~, "~:::.•,.,, ........

.. '.. '

75... ······.. ,......".

'" '"

Equi I ibrium SSB

70 71...............J'qJ•...

".". ". ".'" .... ··· ..... J4...... '

. 30

700

600U)

U)

cog 500

...0

~ 400"".....U)

"'" 300cc

~ 200c..

U>

100

0.20700600

70•

71•

89• 72•

200 .300 400. 500Spawnlng stock blamass

F(loss) Oistribution

100

Cumu I at i ve

150

100

450

400

300

350

~200~

CI>

:::250:::J

.80.70.40. .50 .60Fishing mortal ity

n'95 79 J~,.:~ J2

J9 . ....• .u:~:::::: :::J4:.'~" .

". 89 •...B8 91·.. · ........·i! ....:,;:>,.- ...

.30.20O-'---,.---,----r-----r-------.---r---.,-J

50

250

200

100

>-

""CI

~ 150

.60

.......... ~

.......... ~

.......... \

.......... ~

.75.70.65.55F

.60.50.45.40.35

· . . . .· . . . ... , .· . . .. .· . . .. .· . . .. .· . . .. .· . . .. .· . . . . . ... ! ':' ..•....... : ':" ~ :' '; .

· .· .· ... j 'i ~ 'i... .. ... '1' '1' ~ .

· . . . .

'::1:':_::'::L:··j· .. ···· .. ··f· ..·..·.. ·:·· ·..·.. ·~· ..·..·.. ·i· ..·..·.. ·r···· ..·.. ·!· ..·..·..·.. ~ ~ ·! r ·1 ..·..· r..·..·.. ·! .. · .. · ..

::';.::1:'1'o..L.T--i----j---j---;.----T----i-----r------;.-----jJ

...,; .4o~ .3

.9

.6

.....-.. .7CI>CI>0

.6-u-11 .5......

u-

Figure 5.Stock-recruit

,-Cod,lcelandProb G(F»G( loss)= .56 Equi I ibrium SSB

Cumulative

o-'----,---,-_.,.-_---._--,;--_.-_-,-__,.--.l

.50 .60 .70 .80 .901.00Fishing mortal ity

Equi I ibrium yield

.~O.30

5556.'-

.:'" 57".~8•:.59..

...•. 80

•k 62........ 83 6970...• ..,..

~O"'" •.•• , 7~ 88...' ......::..,~,~.. .~...::.:........ 8?.···:,,::·:~··il5 .. ·::~:~JJ.•........J~...... • .

. · : ..,.~275··s'f·aU!.. 90·.,O~.l!tlll.•· .,,:.. 87 8895 .."",,,, .. ,. .

.......... 94 e·.92 93............................~:::::::" .....

1200

200

CI>CI>

El000o

0::::

~ ~OOc­

U>

.Q

...><: BOOCJo­CI>

600c­o::::

58•

1200

57•59•

400 .600 800. 1000Spawnlng stoc~ Dlomass

F(loss) Distribution

200o

400

450

350

....CJ

~200

300CI>-';;250

.90 1.00.5Q .. 60 .70 .BOFIs hin 9 mo r tal i t y

.~O.30

555&"-.: 58 70 71···· ..'7 60 ~ .

"59 .,. . 111 72

..:/ lIlll ~4... · ···~: 82.·.· ..· #. 88 ;'"_---.It,.:..:.:.......·... .····.::·&5.... ; ..... 82 87 88

• ..-:~······~71~."'..•:;~~·::.·:.·.·:.·;:.·:.·.·_.·..... 78 8&:.., ~.g.I1:.··;···.·.S7:: äb. . ..•.

............ ··~92..............,:3..................95 9~ ....... ···. .

400

200

100

500

600

O-'-----r---....----r---.,--~--_._-____r--__r_---l

-c::::o

Q>

;:: :300

1.101. 00.90.BOF

.70.60

· . . ........, ,. .

O-l------T----j-----j-----i----r-----j---'.50

.9 00 ••••• ••• 0 •• o •• ~ ••• 0 •••• o •••••• ~. 0 •• 0" o. 0 •• 0":0 .0' •• 0' • o ...... 0" 0" 0 •• o •• 0.. • o. 0 ••••• 0 •• o.

· .· .· .· . . .•8 : :............... 0" ~ o •••••••••••••••••••••••••••••

· .CI3 .7 ~ ;........ . ·:················f o •••••••• 0 ••• 0. • •••••••••••••

Cf) :: :o ..6 ; ; ~ ; .

· ..5 ~ ~ :················r '0'

· . .· . .· . .· . . ..Q • ~ -r- ·T · ·r..·..·.. ·· ~ ····· .o :::~ .0- .3 : ; : : .

· . . .· . . .· . . .•2 :.............. : i· ·· .. ·.. ·.~ ~ .

---­l.L.11

Al.L.

Equi I ibrium SSB

89 70................... 71

".-'::-....n····

7."".87 7~ ...····•

.- fs'." 90·· ~ Jlv:..·• 92

.... .' ..•. • 82····eJ~ ..-it~~·4·~81c~~.:.7 .•

....... 9!>'..

O...l...r--r--.------,---r--r-----,.---r--,.----,.---r--.,..----J.05 .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .60 .65

Fis hin 9 mo r tal i tY

Equi I ibrium yield

400350

~oo

CI'> 350CI'>.,!5 300.0

67 ..x 250• u0-66 CI'> 200• <::>"IC

.;;; 150~

72 71 6JO.,

74 • .- g-100•

50

eSa i t he, I'e eI andProb G(F»G(loss)= .02

50

Figure 6.Stock-recru i t

100 150. 200 250. 300Spawnlng stocK biomass

Cumulative F(loss) Distribution

120-r---------------------,84

110 • Trrrn100 82 /:~ :::

90 • .... :: ; 6& :... ' :.::80 ....( ~ ~ ~ .... ..

~ 70

~ 60u

~ 504030 ' , f 77 •

.,' : : ;::' ,.'.:: : ~,: 11~:j:f~:!:::':>··· · ~'O~-~-~--..__-~-~-~--..__-~---J

o

71

..........::.::::..69 70···· ..'

• ..... 7J72"...... ..······91

."" i4-'" J.q ....~....:' ~t:····76 /

68 ..." ",......raV'·.... 87 .:":.'. J

. .' 82... ~ 8'~'·1·r· 940" •

.' 6"' '- (. U lII· ....•w'" ...• ;" ·~:;,.·::'~,;1·3.··J~'" 61 7 ."'" 8~. .

.10 .15 .20 .-.25 ..30 .35 .~O .~5 .50 .55 .60 .65Fishing mortality

140

120

100

"080

Q)

>-60

~o

20

0.051. 00.90.80.70

F.60.50.~O

· . . . ... ,··········z··· : ~.. . : .· .· .· .· .· . ..............~ ~ ~.. . . : ~.............. . .· . . .· . . .: : : :· . . . ..............;. ( : } .

.. , ., ~ :...... .. . ~ :. ~ .

· . . . .......................................................................................................... ..· .· ..............: ~ :- : .... ... ... ... .· . . . .•••••••••.••. ,.......... . ! ~ : ,............... • ..· . . . .· . . . ... ... ... .••••••••••••• ; ••••••••••••• j •••••••••••••• \ •••••••••••••••:••••••••••••••• ; •••••••••••••••••••••••••••· . . . .· . . . .· . . . .· . . .· . . .· . . . ..,. .. ... .. .~ ~ ~ .· . . . .· . . .· . . .· . .· . .· . .

•9

.8

--- .7CI'>CI'>0

.6-L"...11 •5A

L"...

.0.~

0.....3c...

•2

•1

0

Figure 7.Stock-recruit

-Cod,Faroe PlateauProb G(F»G(loss)= .02 Equi I ibr i um SSB

140

120CI>CI>C

§ 100

..c

-"'= 80u0-V>

cn 60c::::c::::- ~oc

75 76 c-

• • V')

20

. 95..;~

.'. 8/li3··,.... '!62 6i··..

Q4 •• :e .•. ,'.

~93 Ja•... 9tY.....

.2 .~ .6 .8 I 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6FIshing mortal~ty

Equi I ibr ium yieid

140120

73•

40 .60 t BOb' 100Spawnlng s ock lomass

F(loss) Distribution

20

Cumu lot i ve

.2 .4 .6 .8 I 1.2 1.~ 1.6,1.8 2 2.2 2.~ 2.6FIshing mortal Ity

5

~o

10

30

15

35

-c 25

>- 20

7654F

32

· . . ......~ : ~ : ~ .· . .· . .· . .· .· . . . . . ......~ ~ ~. . ...,. ~ : ,. ..· . . . . .· . . . . .· . . . . .· . . . . .· ....

•••••; ••••••••••••••• j ••••••••••••••: •••••••••••••••• ;. ••••••••••••••• ; ••••••••••••••••:•• ··············i··.. ... ... ." ... .· . . . . . ......~ . ~ .· .. .. .· .. ...· '"· .... . .· .... ......................................................................................._ .· . . . . . .· .....· . '"· . '"· . '"· . . . . . ......" , , " .· . . . . . .· . . . . . .· . . . . . .· . . . . . .· . . . . . .· . . . . . ......; : ; ; : ; ; ..· .. .. .· .· .

.. ·.j···.···········j···.·.·········i·· .. ············j·· ·············i················:················; ..· . . . . . .· . . . . . .· . . . . . .· . . . . . .· . . . . . .· . . . . . ......, , .

•9

.8

CI'> .7CI'>0

.6.........u....

11 .5'"u....

-= .~

0

C- .3

.2

.1

0

Figure 8.Stock-recruit

eHaddock,Faroe PlateauProb G(F»G(loss)= .37 Equi I ibrium SSB

Cumulative

700

600

500CI')....

10 20 30 4Q 50 60. 70 BOSpawnlng stock biomass

F(loss) Distribution

76•

79•90

~•100

100

90CI')

CI')

800E0

...070

...><: 60...0-- 50CI')

""c ~oc,.,

300Cl..

c.n20

10

00 .10 .20 .30 .~o .50 .60 .70

Fis hin g mo r tal i tY

Equi I i br i um yi eid

.70

62 53

...::.::~::::...•.....

.60

.'67·····..

.20 .. 30. .~o .50FIshing mortal ity

'·91•95 92·······

?M....•t1i .

.10

20

25

10

30~------------------------,

Q) 15>-

1.81.61.4.1.21F

.8.6.~.2

· . ...... : ": : , ":' -: ~ :'.... . .· .. .· .. .· .. .· . .· . . .. ".....[ ·1 .. ·· .. ·.. ··f· ·..··r..·..·..·.~....... .r.. ···· .. ··:··· ~ 1.. ·...... '! '! ~ : ':' ~ ! ! ! .· . . . . . . . .

: : :: ::... . ...... ; ; ;. .; .;: ,; : ; ; .· . . . . . . . .· . . . . . . . .· . . . . . . . .· . . . . . . . .· .· . . . . . . . ............................................................................................................· . . . . . . . ... ... ... ... .· . . . . . . .... : : ~ : ':'" ~ ; : ; ... " . ... .. . .· . . .. . .· . . . . . . . ...... ~ ; ~ r······ ..·.; r··· ..·..··1······· .. ··:··· ..·..·..;.. ···

:::::t:::::::::::::::::::::::t:::::: ::::1:::::::::::~:::::::::: :1::::::::::1:::::::J::::::::: ::t:::::~: . :::· . . .· . .· . .· . .

•9

.8

CI') •7CI')

0•6...........

l.L..11 .5A

l.L..

..0.~

0~

.3Cl-

.2

•1

0

Figure 9.Stock-recruit

-Saithe,Faroe PlateauProb G(F»G(loss)= .74 Equi I ibr ium SS8

" ..... 91

......:.

.30 .4-0 .50 .60 .70Fis hin 9 mo r tal i t Y

Equi librium yield

.20

727.1.···········.l~. 7513~70 ••:;~ ••eg 7.i

J.8.... • 7119 90'. 6~ 66 ...••...::: .

63". 6it=- 85.. 88 " .•. '·64 7" .' ••.•..............,.. ....:

'. ... 80.' 83 8.7 ":::" 8-46182 ... "·79 8' ...... , :;;:;.11'6... ., ;~;.. 81 .

. "···9:jj 92 ..)i.+.. .

.10

160

14-0

'"'"c 120E0

...0 100

...><:(.)

0 80-'"t:nC 60c•c 4-0c..

U')

20

0160

74•75•

140

69•

78•91•

.... ;84 !•..: ;

... :': ~~/ .. u ·..:·!··)l6

83..

40 6Q BO 100 120Spawnlng stock biomass

F(loss) Distribution

20

Cumulotive

o~---r--,..----r---r-----r------,..-------r---r'o

100

200

600

500

~400

.70.60

•

90....•.....

.. e'4. :,......

89.•····8~-:::~{ ..: ....•I.;..:.::~ 88 .....

Q3·~?·... :::::::"z.·····..• ...•

,30. .40 .50FIshing mortality

.20

60

50

40-g

Cl)

>- 3D

20

10

0.10.80.70.60

· . . .......................................................· . . .· . . .· .· .· .

.50F

.40.30.20

....................................................· . .· . .· . .· . .· . . .· . . . . . .

......;.............•..:.....••••••.....:. .. . ....•....• ~ ••............. ~ ! .............•. ! •..· .. '"· .. ... ... .· . . . . . .......~ ~............. ··r········· .. ····f·· .. ···········!···············!···············;···· . .· . .· . .......; ;. '" :. ~ ~ ; : .· .· .· . . . . . ......- .· . . . . . .· . . . . . .· . . . . . .· . . . . . .· . . . . . .......; ~ ~ ; , ; ; .· . .· . .· . .· ....· . . . . . .......: ';" : :" ~ : ! ... . ." . ... . ... . .

••••••;•••••••••••••••;••••••••••••••••;. ••••••••••••••• ;. ••••••••••••••• j ••••••••••••••• ; ••••••••••••••• j •••· .· .· .· .. . . . .· . . . . ............................................., .· . . . . .· . . . . .: . : : : :· ....

•9

.8

'"•7

'"0 •6'--'.....

11 .5'".......c .4-0~ .3a..

.2

•1

0

".··· .... 72..........

.65 .70 .75 .80 .85 .90 .95 1.001.05Fis hin 9 mo r tal i tY

Equi I i br i um y i eid

70 71. .····J.~ D .

:.~.............. i 4

.... 65 '::;"737, ..•.... .. j6 ·:: .. ·8lt .... ·· ..... ~2. ..':.

7.Ln·· ....·.. 78 .••• ,,::::::: I' 11111". ',,83

84 ...... ·•····•85 .... '

•..:...... 868 "8:_.::.. 89

90 95..: .•···....":::: ..92. ..,, 4 9J..-~:...-.,'....•

.45 .50 .55 .60

Equi I ibrium SSB

50

300...r-----------------------,

""c::.;:; 100•C0­

Cf)

250CI)

CI)

oE

.~ 200

..c:>

...><:...

.e 150CI)

300250

70•76• 69•

81•65 n•

~rt2 72775 •\i

6~871• •

'e10. Cod,North Sea

Prob G(F»G(loss)= .36

100. 150 k b· 200Spawnlng stoc lomass

F(loss) Distribution

50

Cumu I at i ve

FigureStock-recruit

79.I.:;

84•(:~ ~ .

O~--___._---r__--__r_--_.---.___-----r

o

1000..,..---------------------,

900

800

700

~600

=500ucu.... 400

300

200

100

7271 111·""-;'·. ;: ...•,::.

6e.... ..:':" 80·7·8"····· ...~2•. 79 :.:: ..... :~.:.. ....•.

'./&7 ' '. 8J.-:::...... J:t'~ 8~ :.

66 .7.0" : .•.. • .........: 7.4-' \J2'" 8~.. ·· 87

'. ".8"9 0 86..... 85·· 8 .

......'. .. 95.. 9

63J4 90- , ··• 9J.' ..::::::: .. :::J~:::..,:~gJ~, •

.45 .50 .55 .60 .65 .70 .75 .80 .85 .90 .95 1.001.05Fishing mortol ity

100

-c

-.;; 200

>-

300

150

250

350

50

1. 301. 201.101. 00F

.90.80

· . ..:" ~ ;, -:.......... ..: ': '; .· . ..· . ..· . ..· . . . . . .·r·············!··············~·············· ~ 'f············ ..~ : ,'· .· .·~ ~ ~ ':' ':' :' :' ,· .. .· ., ..· .. ..· .. ...: : : .: ; :. :, ... ... '.· ..· "· "

.~ ~ ·············i··············i···············~········· ~ .

.. .· . . . . . .·r···· ..·..·..T· ..·.. ·· .. ·:·· .. ···· .... ·-r .. ···· .. ·· r····· .. ·· ..·..r..·..·.. ··· .. ·f·· ..·..· ..·r···· ..·..·.. ·r· .. ·· ..·.. ·]"· ..·.. ··· .. ·-r ..·..·.. ·· r ·· ..·.. ···r .. ···· ···r·..·..· ..·i····· .. ······ : ~ ; : : ~ .

· . ., .· . .. .· . .. .· . . . . ......... ; ; ~ : ;. :, .. .. .· . .· . .· . .O...l-j-----j---i----i----i-·__--j.__--,.;--_----J

.70

.9

.8

CI> .7CI>0

•6---L.L.11 . 5""L.L.

. .~..0

0.....3c...

.2

.1

FigureStock-recruit

e11. Haddock,North Sea +

Prob G(F»G(loss)= .17 " laEqui I ibrium SSB

.1.5 2 2.5 3FIS hin9 mo r tal i t Y

Equi librium yield

70-:' :.69

:.... :.-;' :'

900

'" 800'"<::>g 700.-...c 600-""

c.>

..e 500'"=400<::

;; 300<::>c..

Ul 200

100

0.5

70-69-800 900

67-

.:~ .• ':':8~'~'''''''''''''''': 65..+~:.~~':.;: ~.~J.~.~, 6.4 .. ,,: -O~o.....=;,:,::

o 100 ZOO 300 400 500 BQO 700Spawnlng stock biomass

Cumulative F(loss) Distribution

50

150

100

400

300

350

:::3

::;ZOOcu...

~Z50

32.5. 1. 5 2 .FIshing mortalrty

1000

900

800

700

600-0

.~ 500>-

400

300

200

100

0.5109875 6

F32

•9 ~ ~ ~ ~ ~ ~ ~ .· .

· . . .•B ..•. ~ ~ ...•.•....;.•..•..... : .· . .· . .· .. ..

CI1 • 7 ·0 •• ~ •••••••• o. ;, •••••••• '!,. 0' •••• ;' .0 •• '. o •• !,. '0' 0•••• ;' •• o •••• o.~. o ••••••••

(I'J :: : :

o : : ; : ; ; ; ...6: : : : : : :

" ." .· ..5 .... ;". o. •••• :, ••• 0 ••••• : ••••••• o' .; •••••••••• : •••••••••• :, ••••••••• ~ ••••••••••.. .... .... .... ....' . . . . . ...0 .,. ... -;- .. ...... ~ .. • ...... ·~ ...... • .. ·: .......... :· ........ ·~· ........·t..·....·

o : :: ::.... .c.... .3 : : : : : : : .· " ..· .. ..· " ..· .. .,•2 ! ~ : : ~ ~ ~ .· . .. ..· . .. ..· . " ..· . .. ..•1 ~ : ; j" j j j' .

· .. .· .. .· " .0...1.-;'-'--;.--i.r-----r-.---T---r.--i--i----i--...;..-J

.........l.L.

"Al.L.

FigureStock-recruit

e12. Whiting,North Sea and Vlld

Prob G(F»G(loss)= .26 Equi I ibrium SSB

.6 .8 1 1.2 1.4 1.6 1.8 2Fishing mortality

Eq ui I i br i um y i eid

600CI>CI>

E 5000

..0

.x ~oou0-CI>

300"'"0::

0::

~ 200c...

cn

100

0.~

89•

77 76• •

600

75• 79

•

200 .300 400. 500Spawnlng stock blamass

F(loss) Distribution

100

Cumulative

120 67

110100 ~4

90CI> 80....=> 70~ 60cu

.... 50

40 ..' f•.: ..: ..: ..: ..:..,,:.:Jl:~'1 : 65 6430 .. '.' ..~r 9n . • 81 80

~~ id~~l;~,.I~:·t:~E.2L::~··;:.~:.:J .J'. •O-t"'-'..........:..:..:..:.:.;-T---~--~--,.---~--,.-_--Jo

· . . .•••••••••:- j •••••••••••••••:••••••••••••••• ; •••••••••••••• -: ... .· .· .· .· .· . . . ......... ,~ .· . . . .· . . . ." .,

21.8

'.80•

.8 .1 1.2 1.4 1.6FIshing mortal ity

.6

7677 ~.

69 ..... .... 81

• •"'=:j;.. ~.~ .... :·J5f"':1~8 ...

79[·"67·.'·····... 66":" ..:·.·;···8ll" .. ·.. :,.,~,· J2

71-•.. ······\1 /:~.; .......~ ....: ..,. .e

O...........,--~--,----r--r----,----.----,--~-.l

50

~oo-r----------------------,

150

250

100

300

350

.~ 200>-

76532

· ..........:- : -: : -:: .· .· .· .· .· .. ..........:•.•.•••••••.••. ! ••.•••••••.•••.:••.••••.••.................. -; ...••••.••••••....•..•.••••••· .. .· . .· . .· . .· . . . ..........: ! : ! : .· .· .· .· . .· . . . ..........~ ,. . .· . .· . .· . .· . .· . .· . . . .......................................................................- .· . . . ." ..

" .." .." ..· . . . ... ~ ~ '" .· . . .· . . .· . . .· . . .· . . .· . . . .........: : : : ; .· . . .· . . .· . . .

•9

•8

--- .7CI>CI>0

.6..........u...

11 .5Au.... ·~..Q

0.....3a..

•2

•1

0

FigureStock-recru i t

e _13. Saithe,North Sea and Skagerrak

Prob G(F»G(loss)= .39 Equi I i br i um SSB700..r--------------------,

50

O...L...-----r---...,---~---,r-----r------r----r----r..l

1. 00

yield

.90..~o ..60 .70 .80t I s hin 9 mo r tal i ty

Equf I i br i um

···.70•

74~~ ::..

72 .....• 7.'f1·..

.40

....... 76.....:.

17 .81 79 8~8 .

.., ::.~.'j~~: ..'. "8.~·.· J.~ J4......J~ 88 87 85 86

.. · Ul •.••:.8.9 ,.., .._:.~ ..

.30

rn 400rno§ 350

~ 300~

u

~ 250rn

450

~200

;; 150oc..

c.n 100

73•

400 450

7211 •• 74•

75•

50 100 150 200 250 30D 350Spawnlng stock biomass

Cumulative F(loss) Distributfon

100

500

200

600

rn

~400::::J~

u

~300

. .· . . . . . .·":" ., ~ '" .':' ':' : -:-... . : .., . ..... .., . .... . ..· . . . . . .'~""""""!" 0 •••••••• ~ ••••••••••• ':' ••••••••••• ~...... • ••• -r'" ~ .: : : . : : :

••: j -: •••••••••••• jo ••••••••••• ; • ••••••••••:,. ; •••••••••••· . ., ..· . ., ..· . .. .· . . . . .· . . . . ..~.. 0 ? 0 ~ o •••••~. 0...... .:' ...•... o •••~ •••••• 0 : ... .,... '".. .,.· .. .,.· .. .. ................................................................_ .· . . . . . .· . . . . . .· . . . . . .· . . . . . . .· . . . . . .· . . . . . .·r· ..· ·..[ ·..·..T..· ·.. ·~ : 'j' [ .·-: "':" : :- : : : .· . . . . . .· . . . . . .· . . . . . .· . . . . . .· ':" ? .••••••.•• ~.. ...••...: ! : : .: : : : : . :· . . .. .· . . . . . ..........................................................................................., .., .· .· ..· ... .

350-r-----------------------,

O...L----,---....-----,....----,-----r----,---...,---..-J

78

...................:.::..7~ ·..14'... :..:::.

71 72 .. '.'::::::'~" 7~1fr"••• d 84 85.... . .

82 .... il~..... ····· 88.......... :::."..... 87 :.•

-----.c'...... 78 .... • ......81 . . :

.:::::: J:.~:: .. U 8B'···· ........ IlII. 92 ·...•. 89......................

1. 00.90.~O .60 .70 .80FIs hfn9 mo r tal i tY

.40.30

250

50

300

100

>- 150

"'0 200

.85.80.75.70.60.55.50.45

. 9

.8

- .7rnrn0

.6u....

11 .5Au....

~.4

0~

.3a...

.2

.1

0

FigureStock-recruit

e14. Sole,North

Prob G(F»G(loss)=Sea.02 Equilibrium SSB

1.2

1. 2.

.8mo r to I i ty

Equi 11brium yield

. ~ . .,6 ,8 .FIshing mortol Ity

9086 67 68 !t.. 91.. ....... t!. f ~ ~43

.... f 92·r... ,.~ 84• 83 .•, __---------:~ . '!is

.:; '1IIl

t' ....:1'8•J~':4l8

J~ 67

: ".i ..... 88 ~o

~ ~" ':'g.~~4'. dg•• •'.• ". R5

7()"'~ .....

~4 7i 71 "'J3_:5 'tQ 84

119'..····7·

qj-•

.2 . ~ . ..6FIshing

.2

82 ~ 83.. ....•61 :;

· V

15

25

O..l---..-----,...----r---....----,...---.....--_--.J

30

5

10

160

35

20

6112 63........140

""""E 120o

=<:: 60<::,.,;;... 40

cn

..0 100

....><:u

~ BO""

"'C

Q) 20>-

63•

....................

....... ~ ! .

....... ~ ! .

....................

....................

. ~ " .

•••.•.. ~ ••••••. ! ••••

....... ; j ••••

....................

2 2.2 2,~ 2.6 2.8 31.2 1.4 1.6 1.~,8,6

. .. ...i···· .. ·~····· .. ]"· ..··I ···~· ..· 1' 1' '1' : : ... ~ 1' 1" ''1'''' "'~"""T"'''' r'" ? ~ 1' .

..~·······~·· ..·.. r··· ·j" ..· 1..·..·T..·.. ··~·· ..·.. ·r ···1··· .. ·'1' .. ····

.. ~ , : .; :. ~ : ,: :. ; : .

..........: j _ l : ; .

..1····"';' 1" r· : 1' r'" .,. f"" .. ~ : .

..:.... ··1'· .. ·..r· ..·..r.. ·····i· ..·.. ·r ..·.. ·r···· .. ·r·······: ..·.. ·T .. ····

.. ·······1·· .. ···)"······j"· ··j·······)"··· .. ·r· ..·.. 'f'······: )" .

..;....... ~ .......:....... ·~ ·..i'"· ....(....T......r...... ·j ( ..

Cumulotive

.9

,B

"".7

""0, 6........

u..11 .5"u..

..c ' ~0...

.3a..

,2

•1

0

FigureStock-recru i t

e'15. Plaice,North Sea

Prob G(F»G(loss)= .26 Equi I i br i um SSB

.~O .. 35 .40 .45 .50 .55 .60 .65FIs hin 9 mo r tal i tY

Equi I i br i um y i eid

.25.20.15

50

o...L--.--------r--,.---,--.....--.---r---r---r-----,,----.J

500

450CI'>

~ 400ECl

~ 350

~ 300Cl

-:;; 250c>

.:: 200c::

~ 1500-

cn 1007•

450 500

83•

85•

81•

50 100 150 200 250 300b

.350 400Spawnlng stock lomass

Cumulative F(loss) Distribution

40

120

100

~ 80

.65.60.25 . ~O .35 .40 .45 .50 .55FIs hin 9 mo r tal i t y

.20

180

160

140

120

~ 100QJ

>- 80

60

40

20

0.75.70.65.60.50 .55

F.45.40.35

· . . . . . .......... , , .· . . . . . .· . . . . . .· . .. .· . .. ..· . .. ..· . . . . . .......... ~ ~ .•••••••••. !, •••.••• 0 •• ! ....•...... ~ !... . ! ................••..•.· . . . .· . . . .· .. .· . . . .· . . . . . .·.. ·······:···········i···········j···········i>··········i······· ···i···········j··········· .· .· .· .· .· .......... ~ ~ :.. , ;.......... .'" i········ j .· . ., ..· . .. ..· . .. ..· . .. ..· . .. ..· . . . . . ..........................................................................................................· . . . . . .· .. ..,· .. '"· . . . . . .· . . . . . .· . . . . . ......... '1' '1' 1' r ·.. ·: ·..r · T· · ...........; '1' 1' 1' 1' 1' [ .

......... , ·•••••• .. ··,····· .. • .. ·1·· • .. 1· .. • ·1· ·· .. 1·· .. •· .. · ..· "· "

· . . . . ......... .· . . . . . .· . . . . . .· . . . . . .· . . . . . .: : : : : : :

.9

.8

CI'> .7CI'>Cl

. 6---u..11 .5A

u..

..Q.4

Cl.....3Cl..

.2

.1

0

FigureStock-recruit

•16. eod,West of

Prob G(F»G(loss)=Scotland

.26 Equi I ibrium SSB

~,.,.'.i''''' 8169

".8·'?.•.•••• "1\\ 83

..' ····.·.80 84.' 76 "•.....•

..... 2.·':.- ···..ßI1.l8···· ..n.~:·.·.·... ". . 115 95•• ".7,7' <;.;·69 ··'•.•

• 93 .. · ....• . .

:.ll~. ,~~~:: :::::~>~;:::; ·.":917

.5 .6 .7 .8.9 1.1Fis hin 9 mo r tal i t y

Equi I ibr ium y i eid

.4-.3

55

50

rn 45rn0 40E0

...c::l 35

...><:<..> 300-CI> 25cn<:: 20<::.. 150Cl..

U)

10

5

0.2555045

81•67•

.6•

68•lIlO•

86•

15 20. 25 30 35 40Spawnlng stock blamass

F(loss) Distribution

105

Cumu lot i ve

o-fl'-=--,.----,-----,--r---r--,;-----,-----,--r---r----ro

50

100

250

300

~15o........

rn200-

........... ~ ,

............: .· .· .

. ~ .

.5 .,~ .7 .8.9 1.1FIshing mortolity

.4.3O...l..r-----r----,----,--.---.,.---.----r-----r----r--l

.2

5

25

10

20

....>-

-0 15

2.22

........... ~ ..

........... ~ .· .· .· .· .· .· .

.........................

........... ~ ,

1.81.61.2.8.6

· ., .............................................................· . . .· . . .· . . .· . . .· . . .· . . . . ..... °1'··· 0 •• 0 •••• ! 0" ••• "1" "':" "r" .. 4 ~ o •• 0' .0 •• o.

......: ! ;.. . . ! ~ ! .· . . . .· .. .· .. .· .. .

..... ,:. O' .0 ••••••• : ••••••••••• : ••••••••••• ; :. ••••••••••• ; •••••• 0 •• 0... ..,.. ..,.. "., ".. "· . . . . ........................... .· . . . . .· ., .,.. .,.. .... ..,· . . . . ..... -r ~ ·······r· .. ······T··········~···········~···········

.....1' ············:···········T.. ·········r···········)······ .

'i:::Il:::r::::L

•9

•8

-- .7CI>CI>0

. 6.......u..

11 . 5A-u..

...c::l•4-

0.... .3c-

.2

.1

0

FigureStock-recruit

•17. Haddock,West of Scotland

Prob G(F»G(loss)= .01 Equi I ibrium SSB

,~ ,6 ,.8. 1 1,2 1.4 1.6FIshing mortallty

Equi I ibrium yield

70

i.I..····•··•.........

' ........... .... 89....•

>" 72: ':.. •. f .....11 ···.G8 :....

". ~ 85 ..-['1l~ : · ..·1h' :.:: " 7 76. '!7. • .... lI:ll .

.... 95 e:... ;·tIll

~:'liö" '1":{{{Ij.'tI:":''':':~~'

160

~ 1400E.:= 120

...c::>

~ 1000-CI> 80c:nc

c 60•70 0

• c... 40c.n

71 20•

0140 160

89•72

• 82•o 20 40 60. 80 100. 120

Spawnlng stock biomass

Cumulative F(loss) Distribution

100

12067

I":"~"~":":":"""':"'":: :::: :.. .... . ' .

./ ~ ~: i; '":: : : ::: : : ~ ..

:-f . : : ..: :

~ 80 .: : : : : ::

~ 60 i{;~" . :!;)1~ 40 /I~:.:J:l.:~i:..:.'i:.:..:·}::t:..:.'~:.:..::);r;l;.:." _

20 A;: .Jll=r:····8tK·····::;;i.:::.. 'SKi ..:: : .:••., 7" ..•."~.••.7T D'll5 •

... :.,~~:·: 1O·68· 8111" •• •o ...~:........ •..

1.6.6 ,.8. 1 1,2 1.~FIshing mortal I ty

, ~

60

55

50

45

40"0 35Q)

>- 30

25

20

15

10

5

03.5

..............._ .

••••••••••••••• ,,0••••••••••

................: .

................: .

................: .

...........................

..............._ .

...........................

32 2.5F

1.5

· . ............ : , : ~. .. ... , :' .· . . .: : . :· . . .· . . .•••.•• •.••• ! ••.•••..•••••••. ~........... . ••. ~ ••••.•.••••.•... ~ ........•.•••.•· . .· . .· . .· . .· . ...·· .. ·····1· ....·..·· ..·.. '1'· ···· ·1·· ..·..·..·.. ···1 ..·.. ·..·..·..·

...........:.......... . ~ :, .· ..· ..· .· .· ............: : : : .· . .· .· .· .· . . ............ ~ . ., : ~ ~ .· . .· . .· . .· . .· . .... .': . : ~ : .

.......... ; ; ; .· .: :· .· .... . : ~ ~ ~ .. .. .

.9

•8

........ ,7CI>CI>0

.6.........l.L.

11 •5AL.J...

.0.~

0.... .3c-

.2

•1

0

FigureStoek-reeruit

e18. Whiting,West of Scotland

Prob G(F»G(loss)= .09 Equi I ibr i um SSB

88•800

700

600

cnSOO-:::0

~400cu~

300

200

100

. ." .. "l : : : ::

...« j' I!,'....~ . ~ ~

....: : I ::

75•70•

6081

Cf)

Cf) 50CIE0

~

~o......95 u• 0

93 -• 94 CI> 3074 • c-• c

c 20K78 c• c..

cnB5 10

• 82 BI• 59 ••

95

." 94.:. B9 7693..····• 65 .

•. , .... ..... lt ...::::.:....•...7...4.::>.........::.:.(". ~.( .. i/\:::·::·::···· .

\920

*:.:-;9. ,,: ..\...... B7 ..B .... ". - ...~

.. .:.... 4 7:'1'...71 B8 .

~/..... J(····:~..··B~r;;;;:·t~·:·:yi~?5 :::.:;J3•. 90 .. ' .. ". 72 ........... /" ....

..............Jf.

...& h,9 1 t1.1.1.2 1.3 1.~ 1.5 1.6r I s I n9 mo r alt y

Equi I i br i um y i eid

.7.6.5.46020 . 30 t k 40 50~pawnlng s oe ~Iomass

F(loss) Distribution

10

Cumulative

O-+"-"~--.-----.-----.-----.-----.-----.-----'

o

.& ,9 1 1.1 1.2 1.3 1.~ 1.5 1.6FIS hin 9 mo r tal i t y

.7.6

87

7···.

: 78

J,J' ~t::!:·~;:;;<.·i,.V . M.~...•7'J 87 ·:·: ..M · · :·.:·.,··,J3- 83 . ~'. ...::... r 72 ..

.5

~~ ··/.. ··•· ..1~::4f4.~.. i.·········· : ::» .....~:I ;./ ~.Q'J.f.!~:·::: ::.~ ~.:.::~:~.:~;.,..:> ...

Itl .' S.f• J.~ .

.~

50

~5

~O

35

-c 30

>- 25

20

15

10

5

O...l-r--'--"--~-.....---.--..----,.--r--..,---..----,.-.,J

2.2 2.4 2.62l.B1.2 1.~.B.6

· .· . . . . . . ................................................................._ .· . . . . . . .· . . . . . . .· .· ..· ..· . . . . . . . . .• 0" •• ~ •••••••• ~••••••••• ~ ••• o •••• ! .. 0••••••:•• '0' , ••• ~ 0•••• 0",0;' ••• o. ,!, ••••••• -:.••.•.••. ~ .••••• 0.· . . . ., .· . . . ., .· . . . ., .· . . . ., .· . . . . . . . . .•••••• ) •••••••• '! •••••••••) •••••••• ! :.•••..•....•••.•.: ) .; ) .· . . .. .· . . .. .· . . .. .· . . .. .· . . .. .· . . . . . . . . ..... .., "' , I···· ~.... . '.' , "' " .· . . . . . . . . .· .. . .· .. . .· " . .· " . .· . . . ., .. ..... .. ~ - ~ .· . . . . . . . . ... ... .· . . . . . . .· . . . . . . .· . . . . . . . . ................. ' .· . . . . . . . . .· . . . . . . . . .· . . . . . .. .· . . . . . .. .· . . . . . .. .· . . . . . . . . ....... : ~ , , : : : ';' ! : : .

· .· .· .· .•••••• j •••••••••: • •••••• :••••••••• , •••••••••;••••••••• j •••••••••;••••••• •• ; •••••••••; ••••••••• j ••••••••· .· .· ..· ..· . .· . . . . . . . . ........................, .· ., ... .· . .· . .· . .· . .

•9

•B

,......, •7cncn0

.6.........LL..

11 .5......LL..

~.~

0~

.3c...

•2

•1

0

FigureStock-recruit

e19. Saithe,West of

Prob G(F»G(loss)= .70

eScotland + Rockal I

Equilibrium SSB

.30 .4-0 .50 .60 .70 .80Fishing mortoli ty

Equi librium yield

74.,.':'.7J 76./' 78.·····~

.........J.:.::::.:~... ...7·~ ..' '.:

!~JP19" :i7.,.. ·~·1~ ~..... 88.' ....~fJ. l!:::::.'::··.

7. ...... 88•.... .•......

..... 89 •..•.....:. . .

~:~: J7 89......... 85 90 :.

84 ...•. '. 5'~"'ir fII·····53 '. · .. ··-Q2 .......... ...........

.201009080

100

90CI'J 80CI'J

73 c

• E700

.Q

74 ...>0: 6078 • u

0• - 50CI'J

7576 c:n 4-0• • c

c

• JOcc-

U') 20

10

0

83

10 20 30 {O 50 ksg. 70Spownlng sfoc lomass

Cumulative F(loss) Distribution

o

350

450

400

88 ~\7 77• • •f. ...../ .,e91. 9C· 89. .., ...

!....·.'~·:I1.-:.···r::z:r~ ...·;·'

1:: Mt"I.~·.·

o "

300CI'J--';;250.....u

~200

150

· . . . ....••..• ~ ...•...•....••••. ! ~............... .. . ~.•..............•· .· .

.80.4-0 .50 .60 .70Fishing mortality

.JO

75..~ 85

.... .' :::.'.

:::~;<..::~::/.~;.: ::J.~ ... ".~2'8J .•......•.. :' • .

• •. , "1 ".B~...• :· .... ". 7 .••...• ... . . • ". 89.::..' 8il2 ./ .....•

"( ~ " .. '

8~·.: • 7.9 90 ....··-71 .•85 85 ..

: 89 91

10.Q/~ .... ~?·· .. ~;.:.:::· .~~ ...............••. . ..- 95 .•wt.·····.. ' .

53.·········..

.20O...L-_-,---r---,----,---r---,----,-_-J

40

5

10

35

15

30

45

Q)

"'C 25

>- 20

.65.60F

.50 .55

· . .· . . .............................................................................· . .· . .· .

.45.4-0

········;·················i·················\··········· -: : .· . . . .· . .· . .· . .

........ : : ~ ~ .· . . .· . .· . .· . .

· . .· . . . .................................................................................................· . . . .· . . . .· "· .· .· .................................................................................................... .... .... .... ".. ..· . . . ......... ~ : ~ ~ ~ .· . . .· . . .· . . .· . . .· . . . .........: :........ . ~ : : .· .. .· ., .· .. .· . . . .

•••••••• j ••••••••••••••••• : •• ··············1·················r················1···· .

.9

.8

.....- .7CI'JCI'J0

.6----u-

11 . 5......u-

.Q.4-

0......J0...

.2

.1

0

FigureStock-recruit

e20. Cod,lrish Seo

Prob G(F»G(loss)= .18 Equilibrium SSB

.6 .7 .. B •• 9 1 1.1 1.21.3 1.4FIS hin 9 mo rt aI i t Y

Equi I i br i um yi eid

.........J:!::~:J:~.: :.'9 r:.'.. ::"::::::: J2J.~ ..

7J,. 82

......::.'.::/' J5....::::::·,·.' .. ' J~...."'" WJ-' .ilJ'"

72"' .~. ".. •..•...: 69. .. 7i' ....:. 89. J:.. . ~

......71 ..•/0:•.::.:....1-4.. 87 86 ..... ..

I a .,/" ~{ .

78 ··•·.. 7.~:~.: .

18000

J,6000CI)

c~OOO.-

4'2000..><:....:faooo

CI)

~OOO.-;6000c0..

U')~000

2000

0.~ .5

73•

74•

81 75• •

72•

2000 4000 6000 80001000012000140001600018000Spawnlng stocK Dlomass

Cumulative F(loss) Distribution

86

'iJH]. : .:I.7R.,..... il

:::I

~1 00CU

~ 80

60 .~:-·: ..: H ..: ..,: :: •.JI JJJ9

:~ ä~t:(n::irL~~}~::::,- l'

o..p::.:.:....--r---r---r--~----r----,----.,.----,.---,_---J

o

200

180

160

140

~12o

92......: 9391 .g~ ,".......u. :

88". .J~{•............... .... J9

..... I..' :

.7 .. 8 ..9 1 1.1 1.2 1.3 1.~FIs hIn 9 mo r tal i t Y

9-4~.~ .

.6

81~ .....

:' 7J: ..

88"}4":·.78 :

••.•: "" -7~ •••. 8672 . .. ...#.: .•.<~ : u~...". 19 ,. 69..::..:..<: :::::.•

7" .· .. ··.10 .. ··..~.. .. ..

16000

14000

12000

10000"'CI

.~8000>-

6000

~OOO

2000

0.~ .52.221.81.~ 1.6

F1.2.8

., ....· . . . . . . ..... )' ; ··T..·..· ·T··· ..·..·.. ·r· .. ···· .. ···1 ..·..· ·..;..·..·.. ·····1 ...... \ ·.···········,·············1· ·.·.·····1············.j j •••••••••••••jo •••· . . . . . . .· . .· . .· . .. '"...... ~ ; ; : ~ ~ ;. .,.· .. .· .. .· . .

: : :

· . . . .. .....- .· . . . . . . .· .... .., .., ... .· . . . . . . .• 0" '!, •••••••••••• ~ ••••••••••••• ~ •••• 0" o' 0 ••• ' •••••••••••• ! ~ oe ••••• ~ •••••••••••••:- •••· ., .· ., .· ., .· ., .· . . . . . . .• 0" ':' •••••••••••• ~••••••••••••• ~••••••••••••! ! ! 0 •• o ••••••••• ~ •••••••••••••~ .,... ... ... ... .•••• ~••••••••••••• ~••••••••• 0 ••• ; ; ••••••••••••• ; ••••••••••••• ; ••• 0" ••••••• ~ ;. •••· . . . . . . .· . . . . . . .· . . . . . . .· . . . . . . .· . . . . . . .· . . . . . . ............................................................................................................. ... ... ... ... .· . . . . . . ..... ~ ~ ~ : : ~ ~ ~ ..· . ..· . ..· . ..

.9

.8

--. .7CI>CI>0

.6----u...11 •5A

u...

..c .~0~

•3c....

.2

.1

FigureStock-recruit

e21. Whiting,lrish Sea

Prob G(F»G(loss)= .10 Equ i I ibr i um SSB

1 1.2 1.4 1.61oB 2Fishing mortel ity

Equi I ibr i um yieid

•B

24

22CI> 20(I)

0E 180

...0 16-""

14u0- 12(I)

c::n 10<::

<:: 8•0c. 6

U')

4

2

0.4 .6

1•

20 22 24

80

91•

91

2 4 6 B 1.0 12 14 16 18Spewnlng stock blomess

Cumuletive F(loss) Distribution

2402202001BO

CI> 160~140

:::0

~120cu

'-100BO604020o-f""-'---r-,.----,--.----,r---.--..------.-....--r-..,-----,----'o

............: :... : :- -: ~ ." .· .· .· ........... .. ; ; . ; : : ~ .: : : : : :· . . .· . . .· . . ............. ~ :. . ':" ':" ':' :' .· ..· ..· ..· . ... , : ~ :. :. ; ; .· . . . . .· . . . . .· . . . . .· . . . .· . . . .· . . . .......... . .· . . . . ." .,." ." .· . . . . .· . . . . .......,·····f···· ~ [ : -: "'1""· .. .· .. ............. ~ : ':" , ':' : ;' .

. .· .· .•••• •••• ..; • .. • ..i ; : : , .•••· . . . . .· .· .· .· . . . . .· " . . . ...............................................................................................................· . . . . .· . . . .· . . . .· ., .· ., .· ., .

2

BI.:.•......

.... 82 85J~ .~ .

~./ .e: B7 '.

88 j(········· ..:····:16 ::.\, ..D

.8 .1. 1.2 1.4 1.6 1.8FIshing mortel ity

22

20

18

16

14-0

12Q).-

>- 10

8

6

4

2

0.4 .63.5321.5

•9

.8

--- .7CI>CI>0

.6.......LJ....

11 .5'"LJ....

...0.~

0'- .3C--

.2

.1

0

300...,....--------------------,Equi I ibrium SSB

87

.::::::.::;;" ..ß·····8~:::::::::::·

~..

.. 179 ",-8!i·78 .~ .•.&"9- 80••·7!f1ln .

'. ~·.I.··iB ....

.3 .4- .5 .6 .7 .8 .9Fis hin g mo r tal i ty

Equi I i br i um yi eid

.2.1O+---,---y---,-----,--r--,.---,;---,----r--.---l

o

8000

1000

CI>CI>

E6000o

7000

..Q5000

..><:<.>o--;;;~ooo

0'>

.::JOOO<:,.~OOO

cn

7000 8000

e22. Sole,lrish Sea

Prob G(F»G(loss)= .16

84•

1000 2000 300.0 4000 kSgOO 6000Spawnlng stoc 10mass

Cumulotive F(loss) Distribution

FigureStock-recruit

200

250

100

;:150<.>CL>~

CI>-

.9

87",.

....::::::.::;"

.3 .,~ .5 .6 .7 .8FIs hin g mo r tal i tY

. 2

2500

1000

2000

3000

.~1500>-

.........:

2 2.2 2.~1.2 I.~ I. 6 1.8F

.8.6.~

· .••: •••••••••••••••••• -:•••••••••• : ••••••••• -: ••••••••••: ••••••••• : •••••••c:..;.•• =_.._._.;· . ..,· . ..· . ..· . ..· .,. . ...;- . .• . .. . .. . .•...... -; ! ...•..... ~. •• • .. .;.••••••.•. ~ ......•.•.:...••.•••. ~ .· . .., .· . .,.· . .., .· . .., ..-[ ~ ; ···· .. ·~··········}·········~··········1··········~···· ... . ... . ... . ... ::,. . .;.. . ~ .; :. : .: : .· .· .· . . . .· . . . .· . . . .· ...........................................................................- .· .· .· . . . .· . . . .· . . . .· ...................... ,. , .· .· .· .· .· .· .":'" : : ~ ~ ; ~ ~ .

.. .,.. .,.. .,........... ·········r·········1·········r.. ······r···· .. ·T········r····.. ··1·········..:. ~ ~ ~ ~ ; ~ ; .

. .: :::. ...

.9

•8

.--. •7CI>CI>0

.6----u....

" .5Au....

.Cl.~

0~

. 3c...

.2

. 1

0

FigureStock-recruit

e23. Plaice,lrish Sea

Prob G(F»G(loss)= .05 Equi I i br i um SSB

.6, ,7 .8.9 1.1 1.2 1.3FIs hin 9 mo r tal i ty

Equi I i br i um y i eid

.4 .5

87

.J~···l6.5"'9 72••• ••

. ~o··' -":'7'1',• •..8&. •• ".

~ :·::,'::J7...............~.

.... p lf...'.

.3

12000..,.------------------------,

11000

10000cn

G;9000E.~OOO

""",7000u

..e6000cn

o::::o:iOOO<::

'dOOOs:~OOO

U)

2000

1000

O-'--.,..--.,..---,----r-----r--,.----,--r--.---~-..,....

68•

88•89•

71•

84•

86•

JJ 70 72• • •

88•

240 n220 r ..:..i·T ..r·~;lr·:8ii-T.--r:·:j.' . J8 , ,200180160

cn

::::140:3

~120CL>

.... 10080

~: ,;{JJ~rg::::>·,.o-jl:---,r----.--...,.---,r----.---r----,----r--,.--,.----r----i

o 10002000300040005000600070g08oo0900rnOOOm100m2000Spawnlng stock lomass

Cumulative F(loss) Distribut~on

1.1 1.2 1.3.6. ,7 . B .9FIs hin 9 mo r tal i ty

.3 .4 .5

87

.....··:l87 6572 .. ······· ~

, ~8'···: ...... ·::,-IJ :.. ••••• :

~8~d 8~ J~' -\:;j' 175...... ··6l.····· 80 .

!S'zo" ······-.:·:···,·.. •..dI!l_j'r4::::...~~~-----• •......... :: 79:;...·• .' 76. gn~~ .....•_." ~~• ......o.....~ 78

J4 9,1:::::::.:·... ·::..:.:::::· .. ··.....Jv. .94 9,3.••••

~~ .1000

5000

2000

6000

>-3000

4000""'0

0-'---,--,...--,...--,...--,...--,...---,---,---,---.----.-11.81.61.4.8.6

· .· . . . . . .······r· ·· ..·.. ~ · ·· ..r· ..·..· ·r· ..·..·..·.. ·~·· .. ·· [ ]' .···· .. r· ..·..·..·.. ~ ·..·..·.. ·:··· ..·..· ·:·· ..· 1' [ 1' ....•• , i·· : :.. . .. . .. .. . .. . ; .. " '; " .....•..~.•.•.......

· .· .· ...... , ; : :..... . : : ~ .;: ".. .. .. . .· . ., ............................................................................................................· . . . . . .· . . . . . ... '"

: : : : : :...... : : :- ': : ; : .~ ; : . . ; ;

.. , .. , ~ !.. .. . : ~ ! ~ ~ .· . . . . . .· . . .. .· ... .· . . .. ...... ·i··········· ··;··············:··············i··············j······ ; : .· . . ... ... ... ... .... ... ' : :. ~ : ~ ~ .· .· . . .· . .· .· .· .

.9

•B

......... .7cncn0

•6lJ...

11 .5AlJ...

-= .40....

. 3a..

.2

•1

FigureStock-recruit

e24. Cod,celtic sea

Prob G(F»G(loss)= .58 Equi I ibrium SSB

89.,~.

. .

............. ·········.. 90

• •

.60 .70 .80 .90 1. 00Fis hing mo r tal i tY

Eq ui I i br i um y ieid

....

.50

20000

lBOOOU>

~5000

E.~OOO...Q

~20000

-;';0000

:;a000l::

~5000Q..

(/)4000

2000

0.40

89•

86•

93 ""'::;;~~:l79 91 Bfl':·;·-:,::Hi

...:..~;+·f:rt~:;::jlri.J8:"; .... i··: .. ;. .. ·: .. il

,;,d<;:[,~...H)~Jt:i!;:'•••": .",•. :.... • • 73 71

~.:::·:;I\I .. ' • •o~~-r--~--r----r----r---.-----.-----.--------,r-----,---'o 2000 4000 6000 80001 00001200Q14000160001800alOOOO

Spawnlng stocK bromass

Cumulative F(loss) Distribution

40

20

120

100

140

cn

- 80::::I.....U

~ 60

".90•

1. 00

89...........~....

.. '.. '

.50 .70 .BO .90Fishing mortal ity

lBOOO

15000

14000

12000

~OOO(I)

>-BOOO

5000

4000

2000

0.40 .501. 201.101. 00

F.70.60.50

·..t.' ".·1·"· ..·.. ·,,··~· ..·." .. "." ~ " "."[ "... . .... ~ •.••.•..•.•.•.:•••.••••..••.. !, •••..••••..•. ! :.•...........• ~ •••••.•••.••.•· .. .· .. .· .. .· .. .· .. ... '1'······· ~ ~ ;........ . 'f············· .~ ~ .

· .. .· .. .· " .... :, : : : :, ;. ; .· .· .· .· .· . . . . ....: ;, : : ~ ~ ~ .· . . . ... ... ... .· . . . . . .................................... , ••••••••••••• 1 ••••••••••••••• 1 ••••••••••••••· . . . . . .· . . . .· . . .· . . .· . . .· . . . . . ....: : : ! : ; : .

· . . .· .· .· . .. . ....;. : ··,··············1··············;.··············:······ · ···i··············· .· ..· ..· "· . . . . .· . . . . . ...., '.' , ~ ~ ..· .· .. ..· .. ..· . .,· '". ..

•9

.8

.......... •7cncn0

. 6---L..L.11 . 5A

L..L.

. .~..0

0......3c....

.2

.1

FigureStock-recruit

e25. Whiting,Celtic

Prob G(F»G(loss)= .02Sea

Equilibrium SSB

·······J.i:·· · ." 91:71J1::::.tI~'ilii"'1I4......::..,J3

94ar.t!.... 89'. '. 95 •...... '11 r....

: ".88: .

5000

~OOO

35000

<::

•%p000U)

'"~OOOEo

4';000...>0:

c.>

.:l0000'"

94•

.... . .

91

/,·1lJ·,·····'·· .,; .: ~ 1~ ~o ~ ~,..

: :

~500u

~400

300

200

100

900

800

700

",600

1.5 2 2.5 3 3.5 4- 4-.5 5 5.5 6 6.5 7F

O.l-----r---,----r----,------r------.J.5 1 1.5 2 2.5 3

Fishing mo r ta I i ty

Equi I i br i um yield18000

95

16000 H.··!t'

89•HOOO ;3 !"'··.8

• 9''':':' ..Jl12000 .... '. 87··.. 9.2.···· .:. 83

~OOO• 82 •.;: .•.•.;.

Q)M;'; &••,.- .......

>-8000

6000

4-000

2000

0.5 1 1.5 2 2.5 3

Fishing mo r tal i t Y

350005000 10000 150.00 20000 25000 30000Spawnlng stock Dlomass

Cumulative F(loss) Distribution

.... .;. : ; ; ; ; : :.._.,i,..:..= ::-:':~::":'±.:.~~~· . . . . .. ... .. ... . . ... ... .· . . . . . . . . . .

...• -:....•... ~..•....• ~ .•.•.... ! ...•..•.~. . : -;..•..... !, •••.••. ~ ••••••• ,! ••.••••.~ ...•••... . . ... . . .· . .. . . .· . .. . . .· .. .. ....·..·r···· .. ·r· ..·.. ·r· ..·.. ·~ ·..·..T..·.. ··[· ..·..·r··..··r· .. ····1·· ..·.. ·~········i···· ..·

.....:. : ; :. :. .: ,: ; ; ; .· . . . . . . . . . .· . . . . . . . . . .· . . . . . . .· . . . . . . .· . . . . . . .· . . . . . . . . . ....._ .· . . . . . . . . . .· . . . . . . . . . .· . . . . . . . . .. . . . . . . . .· : : : : : : : : : :·····r····· .;- ; ~""""f'" T' ; ~ ; ; ~ .· . . . . .. .· . . . . .. .· . . . . . . . . . ..... ':" r······· r······· ~ ····~········f······ .r" r ~ f···· ~ .· .. .... t ~ ~ ; ; ; y ~ ~ ';' ; .· .· ..... ·~ ..·....r..·.. r·· ....T ·; .. ··· .. ·t ·..r T..·..r ·"(··· .. ·t· ......

o~:'-'--,----r---r---r---,----r---,-------'o

.9

.8

- .7'"'"0

. 6........l.L.

11 .5Al.L.

...0.4-

0~

.3C-

.2

.1

0

FigureStock-recruit

e26. Sole,Celtic sea

Prob G(F»G(loss)= .43 Equi I i br i um SS81000

900B9• 6000

71..

.. JO .40 .50 .60 .70FIs hin 9 mo r tal i t Y

Equi I i br i um yi eid

_14 7.2 ...../.....•7.5' BO.........

77'; '.: i!2- .. B4 I67B .7.8.. .a.:<·.4115 83 B8

.''':'.:.. ". ·1I1 :··.· .. ·....... ".92 93 ···.s. 94 95.

.......J! ::.~:::: ~. ~:"" JO

.20.10

1000

'"~5000o

O...l...---r----r----,-----r-----,----,---,.J

...Q

..:.:4000uo-"'JOOO0­e:

6000

7B-e5•

2000 .3000 400.0 5000Spcwnlng stock blomcss

F(loss) Distribution

1000

Cumu let i ve

800

700

~600

~500(.)

cu..... 400

300

200

100 /(~\";,:,,

O....,:..----r-----,----,----,----,-----,-----'o

.70

71

......../... J'

..........73 •••.• 8~ .8'3'

, .... B'7{ a+",,;''-: ~.:" BI .•·.:·· ··.B7 90~7i ·:·~·:····91 J~..~ ::,..' 1 1 "

1'. • •••••••••••••;:.... • •••••....li:.··· 92'" ~i-" 8~ ... ·····

75: ':.' •. .7P•.:'f:;~ ..•.•..

.20 .. JO. .40 .50 .60FIshing mortal ity

.10

200

O..l.---,------r------,.-------r----r---,---...,.J

600

400

2000

lBOO

1600

1400

1200"'C

.~1000>­

BOO

.90.BO.70

. ........ -: ~ : .. . .

F.60.50.~O

· . . .......................................................· . . ... ... .· . . . . . .r···· ..·..·.. :······ ..·.. ····[····· ..·.. ··'1' ..·..·..·.. ···r .. ······· ..·..[··· ..·.... ·.. ·r···· ..·....·

~······ ..·....·r·· .. ···· ..·..T· ·..·....··r ..·..·..·.. ··:r ..·..·.... ·· ..f··· ..·.. ··· .. ·1····· ..·..·..

':::u.:::i::L:L:'::· : : : . : :} ·r···· ~ '1'·············T, [ ~ ,.· . . . . . .· . . . . . .r····· ..·.. ····~ ·..·..·..·.. '['···· ..·.. ···'1' ..·.. ·..·.. ··'1'··· .. ···· .. ·..:··· .. ·.. ··· .. ·r ..\ ··r·· .. ···· ..·.. ·l·· .. · .. · ··r ..·..·..·..·..:· .. ···· ..·.. ···f· .. ··· ·.. ·1·· .. ···· .. ·..

·.. ··· .. ·r·· ..·..·..·.. ·;··· ·..·.. '1' .. ·.. ·.. ·.. ·..(·· .. ·.. ·.. ·..; ·· 1' .O...L.;---~---.;~--.j----;-----i-----T-----J

.30

•9

•B

CI] .7CI]

0.6..........

u-11 .5......

u-

..0.~

0..... .3c....

.2

•1

eFigure27. Plaice,Celtic Sea

Stock-recruit Prob G(F»G(loss)= .02 Equi I ibrium SSB

120

100

<n 80.....

40

20

,/"';'I'T'[.lJJ"i

.?~ : : :84 : ..?l 85

91•92•

86•

87•

89•

•88•

~OOO

3500<n<n

~3000o

..c2500-""

c..>o

-;;;20000>

.::1500c~

~OOOU"l

500

88r

f! 90aig.·.·N' .

~ /.. 92 g.(.J . .....

9:~~l.~··;::'·80

.•........ 79

~:~78•

l.B

yield

1.2 1.4 1.6mo r ta I i ty

Equi I i br i um

•B 1Fishing

.6.~

O...l.--..,.------.----r----,.---.---,.---.---..---J40003500500 1000 150.0 2000 k25QO 3000

~pawnlng stoc Dlomass

Cumulative F(loss) Distribution

0...j:L:.:.:...---,----r-----,r----....----,----r--,--,-Jo

l.B1.6.8 1 1.2. 1.~Fishing mortal Ity

.6.~

~ 90'" ..11 ....... :

J5 .... :J.t;.... ....

4;"/."l!'89~1~;::. 4•..•.. 95..• '.

;:f

2200

2000

1800

1600

1400-0

~1200

>-,000

BOa

600

~OO

200

O...L.-----,r----....-----r----r---r---,-------r--,......J32.2 2.~ 2.6 2.B1.2 1.4 ,. 6 1. B

F2.8

· . .. .... : ': : :' : ~ ': : ':' : ~ ': .· .. .. .· ~ ~: ~ ~ .. ~ ~ ~ ~

....... ~ -:: ~ : ~ ~ -:: ! -; ~ ~ ~ .· . .. .· . .. '".., ...· . .. '"· . . . . . . . . . . ....... '~"""':"'" .. ! ; : : : ! : ; : : .... . .. ..., . .. ".. . .. ..· .·······r······ r·······~········r·······~········~·······r·······1·······r·······r·······~·······~····

· . .. .. . . . . . . . . . ............................................................................................................· . . . . . . . . . . .· . . . . . . . . . . ... .. .., ., .... ., .,.. ., ..

· . . . . . . . .................................................................................. -....· . . . . . . . ... ... ... ... .· . . . . .. ........ ~ -: ~ ~ ~ '; ':..... .; : ~ '; ~ .., ... '". .. ....... '1' : ! ':' ~ i ..••• ':" •••... ! '; ! ~ ~ .

· .., .· .. .· .. .· .. ........ ~ .:: : :. : :' .. '" .. .; : :. : ~ ~ .: : : ::: :· . .· . .· . .

.9

•B

....- .7<n<n0

.6----l.L.11 .5A

l.L.

. .~.J::>0~ . 3a..

.2

.1

0

FigureStoek-reeruit

28. Sole,Western ChannelProb G(F»G(loss)= .58 Equi I ibr ium SSB

.45.40

82...•..

~~5 .30 .35tlshing mortality

Equi I ibrium yield

80... ::: ....··..J9..... 81 .....' ....•......

.20

.... 83

J} :: ~.8.: •·· · It.~'i....,J5

77--"~ ~ ~

'. 75 ." 95 ". 89'. 72 'l.::;'.... J~ 90'.•.:::~!:........ .. ,.."," .J9 ··.,:-U··:::::f.Jl.............. ::...13

.15

02500<::

'dOOO•~500

cn1000

500

o..L-...-----r-----r-----.----.------.-------rl

6000

5500

",5000

~500

·~ooo..Cl

...:0<3500u

23000'"

80•

82•

79•

81•

83•

500100015002000l50030t003

k50

bQ40004500500055006000

Spawnlng s oe lomass

Cumulative F(loss) Distribution

.45.40

83J~....·......·.. ·::··B5. !!lA....

..::...:.:~ ..87•• •••• . ". 89

• ..i~ ..""·"·"·:"..'.. '.. '..'.. '

.~5 .30 .35FIshing mortality

80.,.,::: .. 79····· ....J.l.···

::....92 ....•.••..•~J

9..... ::~5 .....,,,...................

.20

7]..... 78.........15' 73..... 72 74 Jl7 ---.u\·." .. H"; ....6i· "'· .. ·.... ·•

.15o..L-,.---,.---..,-----r-----r-----r------,-!

200

400

600

1400

1200

1600

1000

.~ 800>-

.45.40.30 .35F

.25.20

· .............. -: ~ : ~ -: ~ : .· .· .· .· .· .., •••.•..••••.:••.•.••..••..•. !, ....•••.•••.•. ! • .•. . :.......•••.•••. ~.••.•.......... ! .· .· .· '"· .· .••••••••••••••:••••••••••••••• { ••••••••••••••• •••••••••••••••:••••••••••••••• , ••••••••••••••• j •••••• •••••••· .· .· .· .· .· . . . . ..............................., , , , .· . . . . .· . . . . .· . . . . .· . . . . .

: : : : : :............................................................... _ .· . . . . .· . . . . .· .· .· .· . . . . .............. -: ~. . ~ :.. " ~ ~ .· . . . .. . . .· . . . .· . . . .· . . . . .............. -:..•....•••...• ~ ! ..........•....: ~ : .· . . . . .· . ..· . ..· . ..· . ................~ ~ ~ ~ ~ ; .

· ..· ..· "· . . . . ............................................................_ .· . . . . .· . . . . .· . .· . .· . .· . .

.9

.8

---- .7cncn0

.6--u-11 .5.......

u-. .4

...00....

.30...

.2

•1

Figure5toek-reeruit

e29. Plaice,Western

Prob G(F»G(loss)= .49Channel

Equ i I i br i um 55 B

....89 90. :..

....45 .50 .55 I~O .65 .70 .75 .80r ishin 9 mo rtal ty

Equi I ibr i um y ieid

J.~.: ..". ". 91"

". .-·lra· .WU .. ··ll3'·. "&7

81 -8.~ .:"::, ....:-...... ·... 92..::. ."....

····· .• 80

J:~ ..776 ......·....·.. ·J''Ilij

.40.35.30

500

O...l.---,r---,r---,r--,.--,.--r--,--,--..,.--..,.--..,..J

4500..-----------------------,

4000

~2500o.....(172000<:n<::

'~1500,.c~OOO

.9&•

4000 4500

88•

91•

86•

85•

500 100051500. 2000

t25

kOO

b.3000 3500

pawnlng s oe lomass

Cumulative F(loss) Distribution

100

140

120

40

:::J 80~

'-'

~ 60

In.....

.80.75.70

9~.. ···.:. 95'.

90

J,~::: JP ::::.::·:·'"

............... 87

Ba S{::::·~f lIi .

..;a. '" .. ~.~". ........JJ....

....~5 ,.50 .55 I~O .65r I shin 9 mo r tal t y

.." .....

'.···.. 80

~.78 .

··::'.J3s•

.40.35.30O...l.--,----,------r-----r---r--r--r---,----,----,---r'

500

2500

2000

1000

-c~1500

>-

1. 00.90.80.60.50.40

· . . . ........................... , ' ..· . . . .· . . . ... .... .... ..· . ., ............. :- -: ~ !........... .~ : : .· . . . . . .· . . . . . .· . . . . . .· . . . . . .· . . . . . ............~ ':' ~......... : ~ ':' ';, .· . . . . . .· . . . . .· . . . . .· . . . . .· . . . . . ............, , .· . .· . .· .· .· .· . . ., ........................................ .· . . . . . .· .. '"· . .· . .· . .· . . . . . ,..............................................................................................................· . . . . . .· . . . . . .· . .. "· . .. ..· . .. ..· . . . . . .

........... ,. .........•.........•.••..... ! .....••..•••.. ! , : :.•..... .· .· . . . .· . . . .· . . . ....••......?•••••.. ..•••:•••..•..•..•.. ~ .••.... " .•..• :.••.•...•.•.•. ~ •••.....•••.•.~ ...••••.••• ,. ':'" •••· . . . . . .· " .· .. .· ., .· . . . . . .............................................................................................................· . . . . .· . . . . .· . . . . .· . ., .· . ., .· . ., .

.9

.8

...-.. .7InIn0

•6---u....11 . 5A

u....

..0.4

0~

.3a...

.2

•1

0

O..jol!:.:--r---r--...---r---,--__,---r--.,.--~-_r___,,_____r_'

o 10002000300Q40005.00060D07190~8000900(J 00001 0002000Spawnlng sfoc~ ulomass

Cumulative F(loss) Distribution

Equi I ibr i um SSB

•. 50 .60 .70 .80 .90FIshing mortality

Equi I ibrium yield

.40

93 94...811'····

8·~·····::~:.:~~~::..:::::::::::::::::::: .. J7..,~ .

82'•

.30

12000

11000

J,OOOOcn

~OOOo~8000

~OOOo

--;;;6000

~OOO

'~OOO~

~OOOV>

2000

1000

o..L----,,__----,,__----,--__,,__--,__--.------,J

Channel

93•

86•

88•84 92• •

89

e30. Sole, Eastern

Prob G(F»G(loss)= .05Figure

Stock-recruit500~------------------"'"

450

400

350

~300

~250uCI.J

.... 200

150

100

50

........;- ~.. . •.........= ~..•........... = -; : .· .. .... .... .... ..

········r·············~········ ~ ~ ; ~ ~ ... ".. "....... ': ~. . : ~ ~ ~ : ... .· ..· ..· ..· ..

.90.80.50 .60 .70Fishing mortal ity

.40

93 94 .............. gJ .....,',' ..". 9 ~~i' ..' 89

85 Jrt.- ::;~H\I\lU"""""···...::: ' ..82,.···..

.30

1000

5000

6000

4000

2000

O..L----,,----~--_r_--..,._--.,.._--_r_-----,J

QJ

>=JOOO

1.61.41.21F

.8.6.4

· ., .. .·.. ·····[ .. ·· ..·.. ·.. '1' ........·· .. ·1· .. ··· ..· ··r· ....·....·..1·· ·.. ····~·· ..·..·.... ··1··· ···········f·············~············· 'f'" ':'·············r···· '1············· '1····· .

: : . .: :... ..: (........... .~ ~ "';' ';, '1'···· .. .. .

.. ·t · ·.. ·: .. ·· ..· ·1·· ·j· ·..·..·.. [· ..· ·1"· ~ ..

· .........~ ~ ; ~ ; ; ; ..· '" .· .· ......... :, . : ~ : ~ .; : ..· .· .

•9

.8

---. .7'"'"0

. 6..........L..o..

11 . 5"L..o..

.Cl.4

0.... .3a.

.2

.1

0

".

Equi I ibrium SSB

".". 91

•••. BB ':.•.,:. .' .. '

9J .' 94 .... ··•·· ... ,,::::::i::~·:·:···:···:·:·~:·:::·1·~··. . , _-:"

6·".....................

.30 .35 .~o .45 .50 .55 .60 .65 .70Fishing mo r ta li ty

Equi I ibr i um y i eid

11000 88•10000 .........'. 90

9000J~

...J'18 ....8000 ...... ....Jl

". ..'7000 B8 .. '

85..··· 9~1I4'..'

-c-;;;6000 ......:::~:: ..::..:.::::.: ':':':':':':~'".- 9J " ............ '95# ...••.. B4>-5000 ..... .,....:......... ::...•......

~OOO

....3000 8P.···•2000

1000

0.30 .35 . ~O . .45 .50 . ~5 .60 .65 .70

FIshing mo rta /1 ty

16000

1~000

InCf>

~OOO0

4'0000-><:u0

-;;;8000

= BO.::6000 •...<:::,.~OOO

U')

2000

0

Channel

87•

e31. Plaice,Eastern

Prob G(F»G(loss)= .27

.40 .~5 .50 .55 .60.65.70.75.80.85.90F

· . . . . . . . . . .....~. . .· . . . . . . . . . .· . . . . ., .· . . . . ., .· . ., ., ..,· . .. .. ...· . . . . . . . . . ..•. . :••....... ~.•.•.....~ ~...... . .:..•••...• ~ .••.•....~ •.•••••. !, •.••....:..•....•• ~ :..••••.· . .. ..· . .. ..· . .. .· . .. .· . . . . .. .····:·········i·········j········· ········;.········i·········:;········i···· .. ···:·········i·········:.······· . .· .· .· .· .....:. : :, : :. : :, : :. : :, .· . . . . . . . . . .· . . . . . . . . . .· .. .· .. ... ... .•••• _ •••••••• u .· . . . . . . . . . ... .· .. .· .. .· . .. .· . . . . . . . . . ............... , , , .· . . . . . . . . . .· . . . . .. .· . . . . .. .· .. ... .· .. .,. .· .. .,. .....: , ; : ; ; : : ; ; : ..· . .. .... ..., ..., .....;. , ;. , ;. , ;. .. ······,·········:.········i·········;.······· .. .· .. .· .. .· .. .· .. .· . . . . . . . . ........................, , , , .· .. .· .. ... . ., ..· . . ..· . . ..· . . ..

2000 4000 6000 BOOO k10bOOO 12000 14000 16000~pawnlng stoc lomass

Cumulative F(loss) Distribution

600

B5•

500

FigureStock-recruit

700.r-------------------,

100

200

~....u

~300

.9

.8

.-- .7CI'>Cf>0

.6----u....11 .5......

u..... .~..Q

0.....3c...

•2

.1

CI'>

::::400

Figure 32

SaiVbSaiVla

Sol WChCod CeltCodVa

Pla WCh..... Sol Celte SailV

HadVbCodlVSai Are

Pla EChCod Via

WhilVPlalV

Cod VllaHadlV

SolVllaHad AreWhi VllaWhiVlaPlaVllaSol EChCodVb. Sol IVPla Celt

.' SaiVaeWhi Celt

Had ViaCod Are

•..... , .....•

-

---:_lIllI::

-;-

o 0.2 0.4 0~6<. ' .." ',,- ~

Prob. G(F):>G(loss)0.8

,.-------- -- ---

Figure 33

0.2 0.3 0.4 0.5 0.6 0.7Prob. G(F»G(loss)

0.1

Il

:~I~

I~

I~

---..fI\..

"1a--I---I!1'---

~

--.........

~- r----r-------il- -oo

1

'+-oc.2 0.4toa.e 0.2a..

xe~ 0.8

ooCi) 0.6

Figure 34

1.5

Pla IV

Sai Via

PlaVlla

Sol-ßEJltArcPlaWCh

WhiVlla

Sol ECh

SailV

HadVb

Pla ECh

WhiCel1

0.5 1F required tor prob{G(F»G(loss)}=0.1

Sai Va Sol Vlla Cod Va PI~ ~ Had ViaCo~~d Vlla a re

Whi IV W· a Sai Are

1.6 ,------------------------:71

1.4

1.2

LO 10)0)

,.... 0.8c--u. 0.6

0.4

0.2 S

O~---t-----+-----+----+-----t----+-----'

o

Figure 35

positive.

maximumShape of Yield Curve

negative

4

2

o -+---

10 ------------------------------------------

8

14 ------------ --- ------------- -- ------------

_12