Expected economic value of the information provided by fishery research surveys

Fisheries Research 190 (2017) 95–102

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Expected economic value of the information provided by fishery research surveys Raúl Prellezo AZTI, Txatxarramendi Ugartea z/g, 48395 Sukarrieta, Spain

a r t i c l e

i n f o

Article history: Received 7 October 2016 Received in revised form 6 February 2017 Accepted 7 February 2017 Handled by A.E. Punt Keywords: Expected value of information Signals of information Anchovy Bay of Biscay

a b s t r a c t Information gathering can reduce critical uncertainties and, consequently, lead to better decisions on conservation and exploitation of fisheries. Such decisions might improve the fishing opportunities or lower their variability. However, information gathering comes at a cost. The concept of the expected value of information is based on the idea that decisions will be more accurate if the decision maker has more information. The objective of this work is to use this concept to measure and understand the economic value of fishery research surveys using the mathematical theory of the expected value of information. The Bay of Biscay anchovy fishery is used as an example, given the importance of the surveys in the assessment and management in this fishery. The paper provides a measure of the value of information obtained by research surveys. It also analyses the properties of these values, considering the methodology used, and examines the circumstances under which such calculations are adequate. The sources of subjectivity inherent to this methodology and to the general concept of information signals in the fishery assessment and management are explored. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Uncertainty is unavoidable in the stock assessment, advice and management of fish stocks. Even though this issue is acknowledged in management strategy evaluation (Punt, 2015), information gathering can help to reduce critical uncertainties and, consequently, improve management decisions. Reducing uncertainty should help the managers to make more accurate management decisions or at least form a clearer picture of expected outcomes. In the stock advisory process, it can improve fishing opportunities without increasing risk or, at the very least, reduce the variability of the future fishing opportunities. Information gathering can include fundamental research, assessment, monitoring and analytical processing of gathered data. However, such information gain comes at a cost, and it is essential to measure the economic value of the information. The concept of the expected value of information (EVI) is pivotal in the economics of information (Stigler, 1961; Howard, 1966). The idea is simple: the accuracy of the decisions will improve if the decision maker (DM) receives more information. The EVI has been used in many scientific areas, such as health decision-making (Doug and Jeremy, 2008; Fenwick et al., 2000;

E-mail addresses: [email protected], [email protected] http://dx.doi.org/10.1016/j.fishres.2017.02.004 0165-7836/© 2017 Elsevier B.V. All rights reserved.

Rachael, 2007; Welton et al., 2008) and agriculture (Pannell, 1994; Wuyang et al., 2005), among others. However, it has not often been used in the scientific evaluation of fisheries. Mäntyniemi et al. (2009) discussed the value of hypothetically perfect knowledge of the type of stock-recruitment function for the North Sea herring, Punt and Smith (1999) analysed the value of collecting new data to improve the management of one stock, and Peterman (1990) examined the value of fishery research. This last study showed that a statistical power analysis can help in interpret available results and improve the design of future experiments. There are only a few scientific studies of the economic value of fishery research surveys. Dennis et al. (2015) assessed the relative value of different combinations of fishery survey methods, using a modelling approach, while Zimmermann and Enberg (2016) present an analysis of the required frequency of surveys and assessments. These authors found that the frequency of assessments can be reduced and still provide similar stock estimates, decreasing the overall costs in the case of two Northeast Atlantic stocks, blue whiting and Norwegian spring-spawning herring, Here, a different approach was taken. The value of the research survey itself was assessed, but not the frequency of research surveys. Furthermore, in contrast to Dennis et al. (2015), the subjectivity of the management DM was considered. The objective was to provide a methodology to measure and understand the economic

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value of the fishery research surveys and information gathering in general, to improve the management decisions of a DM. The mathematical theory of the EVI was applied here to the Bay of Biscay anchovy fishery where independent research surveys play an important role in the stock assessment process and in the management advice provided by the associated scientific body.

• The PELGAS spring acoustic survey (PELGAS hereafter). The time series for this index is available from 1989 to 2015 (22 observations, indices for some years missing). • The JUVENA autumn acoustic survey of juveniles (JUVENA hereafter). The data for this index are available from 2003 to 2015 (13 observations, no missing observations).

2. Methods

Each of these three research surveys produces one index of biomass (ICES, 2016) for the Bay of Biscay anchovy. The study analyses the economic value of these surveys for the period starting in 1987 and ending in 2015.

2.1. Study system The anchovy fishery in the Bay of Biscay has often been described in the scientific literature (Uriarte et al., 1996; Lazkano et al., 2013; Andrés and Prellezo, 2012; Del Valle et al., 2001, 2003, 2008). Anchovy is evaluated, as are many other species, on a single stock basis, by the Working Group on Southern Horse Mackerel, Anchovy, and Sardine (ICES, 2016) of the International Council of the Exploration of the Sea (ICES). The data on catches, overall and by member state, were obtained from this source. Two member states are involved in this fishery: France and Spain. The management of this fishery involves a system of vessel entry licenses and a system of Total Allowable Catches (TACs) and quotas. The vessel entry licensing system is managed by the individual member states while the European Union (EU) decides on the TAC. Hence, three DMs are involved in the management of this stock. The TAC advice during 2015 and 2016 was produced using a harvest control rule (HCR) based on that the spawning stock biomass (SSB) does not fall below a lower limit reference point for SSB with a probability of 95%. According to this HCR, the TAC advised will be zero if the predicted SSB is below 24,000 t; 33,000 t ˆ (where SSB ˆ is the preif it is above 89,000 t and −2, 600 + 0.4SSB dicted value of the SSB) if it falls between these two limits (STECF, 2014). Neither of the fleets involved in this fishery is strictly economically dependent on anchovy. The vessels from the member states also fish other species, such as mackerel, tunas and hake. According to the bilateral Arcachon agreement, the Spanish fishery is active in the spring (April to June), and French vessels are at sea for the remaining months of the year. Approximately 85% of the catches occurs in the south-eastern corner of the Bay of Biscay, and almost 95% of the French landings are sold on the Basque markets (Pita et al., 2014). Therefore, the prices used in the analysis were obtained for the landings in these markets (source www.eustat.es). They have been adjusted to 2015 level using the Spanish inflation rate (see Supplementary data for time series of deflated revenue). Fig. 1 presents the evolution of the real revenue (inflated to 2015) for the two member states from 2003 to 2015. Three different periods can be distinguished. From 2003 to 2006, the trend of the real revenue was negative. From 2007 to 2009, the fishery was closed due to successive recruitment failures that ended in the collapse of the stock. In 2010, the fishery was re-opened and, from that point, the revenue has shown a positive trend. The assessment of the Bay of Biscay anchovy has been conducted using a two-stage, biomass-based state-space model with stochastic recruitment and deterministic dynamics. The model is fitted in a Bayesian context using a Markov chain Monte Carlo technique (see Ibaibarriaga et al. (2011) for further details). The required input data include commercial catches, fish numbers by age and the indices of biomass and recruitment produced by research independent of the commercial fishery. In 2016, three such independent sources of information were used in the assessment for the Bay of Biscay anchovy: • BIOMAN daily egg production survey conducted in the spring (BIOMAN hereafter). The data for this index are available from 1987 to 2015 (26 observations, indices for some years missing).

2.2. Analysis It was assumed that the goal of the DM is to evaluate the economic value of different signals of information. To achieve this goal, the expected value of perfect information (EVPI) was used (Raiffa and Schlaifer, 1961). It can be mathematically formulated as: EVPI =



(Ex [maxa [U (a, x)]] − maxa Ex [U (a, x)])

(1)

x

where a is the management decision taken by the DM and x is a hypothesis for the system. In the studied system, a is the TAC to be set by the DM and x is the SSB expectation formed by the DM for this stock, given the available information. U(a,x) is the utility associated with decision a under the system x. In this case, the utility is the value ascribed by the DM to the outcome, and is the measure of the management decision performance. Two possible management measures were considered: the real revenue and the landings obtained by all the fishing fleets involved in the fishery. E[maxa U(a,x)] is the expected value when all the uncertainties are resolved by the DM, who then takes the best management decision, while maxa Ex [U(a,x)] represents the expected value when the DM does not have or does not use any information to make the (best) management decision. The difference shown in Eq. (1) is, therefore, the expected utility gain from acquiring the perfect information or the opportunity cost of not using (acquiring) it. Information signals do not necessarily provide the perfect information and do not necessarily reduce the uncertainty to zero. In such cases, instead of calculating the value of perfect information, it is worth calculating the expected value of imperfect (or sample) information (EVII) (Yokota and Thompson, 2004; Raiffa and Schlaifer, 1961). Mathematically: EVII =



(Es [maxa Ex\s [U (a, x)]] − maxa Ex [U (a, x)])

(2)

x

where Es [maxa Ex\s U(a,x)] is the expected benefit derived from using the (imperfect) information provided by the signal (s) and then making the best management decision. Eqs. (1) and (2) are related, in the sense that EVII = EVPI when the signal is providing perfect information. EVPI is easier to calculate than EVII because the likelihood assessments and Bayesian calculations are trivial. In this particular example, the algorithm used to solve Eq. (1) was based on calculating the opportunity cost of not using or not acquiring information. The algorithm can be summarised in six steps (see Supplementary data for the R code): 1. Select the management measure (revenues or landings) and calculate its mean and standard deviation. 2. The mean value of the management measure was considered the maximum expectation of the DM for any possible hypothesis explaining how the system works (x), given the management

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Fig. 1. Evolution of revenue for the fishery of the anchovy in the Bay of Biscay. Values are in euros, inflated to 2015.

3.

4. 5.

6.

action (a) (E[maxa U(a,x)]) (see Section 4 for the discussion of this assumption). To calculate the term maxa E[U(a,x)], all the likely values of the standard deviation were considered (all the hypotheses explaining how the system might work (x)). In the studied system, this was done by multiplying the standard deviation by 1000 fractions from −5/100 to +5/100. The opportunity cost of the information was computed (E[maxa U(a,x)]- maxa E[U(a,x)]) for each hypothesis (x). A distribution (in this case, lognormal) was fitted to the 2015inflated revenue (and landings) time series. Using the probability density function of the fitted distribution, the probability of each hypothesis was calculated. To calculate the EVPI, all the products obtained in steps 4 and 5 were totalled.

The second relationship states that, when the correlation between the information signal and the value ascribed by the DM to the outcome can be determined, EVII is equal to EVPI, where the original standard deviation (step 1 in the algorithm) is multiplied by the correlation coefficient between the signal and the value ascribed to the outcome by the DM. It implies that to calculate the EVII, the algorithm for the EVPI (steps 2–6) can be followed, using this adjusted standard deviation. Lognormality in both the biomass indices and the revenue is commonly assumed for the biomass indices, landings and revenues in fisheries (Merino et al., 2007) and revenues in general (Battistin et al., 2009). 3. Results 3.1. Expected value of perfect information

The calculation of EVII is more complex because all possible outcomes and all alternatives have to be obtained. It requires a Bayesian pre-posterior analysis because the posterior distributions of x|s, for all possible values of the imperfect information, must be calculated before the signal of information is received by the DM. In other words, it is necessary to establish what the DM had in mind (Runge et al., 2011). Here, the methods of Fatti et al. (1987) and Bickel (2008) were used for solving the computational problem of the EVII. The results showed that under the conditions of risk neutrality of the DM and normality (and lognormality) in the distribution of the signals and the value ascribed to the utility (revenue or landings), several relationships between EVII and EVPI can be found. The first relationship is quite straightforward. The EVPI is an upper bound for the EVII. This implies that if the correlation between the information signal and the value ascribed by the DM to the outcome cannot be determined, the EVPI will be the maximum value of the information signal.

The EVPI (Eq. (1)) for the fishery and each DM was obtained for the periods between 1987 and 2006 (before the closure of the fishery) and 2010–2015 (after the re-opening) (Table 1). This was done using two values ascribed by the DM to the outcome: the revenues and landings. The sum of the revenues (or landings) obtained by the member states and the corresponding mean and standard deviation were used to calculate the EVPI of the fishery. For the calculations at the individual member state level, the revenues (landings) of the fleets in each country were used, and their averages and standard deviations calculated. The results for the two values ascribed by the DM to the outcome (revenues and landings) are reported in Table 1. In the case of landings, the value obtained (in tonnes) was multiplied by the average price (inflated to 2015) of the period examined (3,283 D /t for the 1987–2006 period and 2,059 D /t for 2010–2015). After the closure of the Bay of Biscay anchovy fishery, the canning industry obtained the anchovy from markets outside the Bay of

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Table 1 Mean, standard deviation (st. dev.), coefficient of variation (var. coeff.), EVPI and the ratio of EVPI to the mean, for the three DM (EU, Spain and France) involved in the management of the Bay of Biscay anchovy fishery, for the two management measures (revenues and landings). Periods: 1987–2006, before the closure of the fishery and 2010–2015, after re-opening. Mean, standard deviation and EVPI are provided in euros, inflated to 2015. DM Management measure

Period

Variable

EU

Spain

France

Revenues

1987–2006

mean st. dev. var. coeff. EVPI EVPI/mean mean st. dev. var. coeff. EVPI EVPI/mean

62 232 002 25 636 780 41% 10 081 209 16% 34 946 392 6 728 721 19% 1 953 371 6%

38 063 225 15 705 672 41% 6 220 329 16% 25 041 419 9 717 780 39% 3 330 147 13%

36 115 473 20 133 032 56% 7 410 346 21% 8 986 243 3 235 222 36% 1 000 493 11%

mean st. dev. var. coeff. EVPI EVPI/mean mean st. dev. var. coeff. EVPI EVPI/mean

62 236 456 35 395 964 57% 13 405 437 22% 34 942 946 13 084 202 37% 4 228 085 12%

40 318 054 24 318 502 60% 9 186 949 23% 26 239 553 13 489 462 51% 4 400 127 17%

35 727 326 21 166 745 59% 7 892 132 22% 8 520 142 2 421 728 28% 893 216 10%

2010–2015

Landings

1987–2006

2010–2015

Biscay; this explains the 37%-reduction in the average real price between the two periods. Furthermore, the fish-processing plants entered long-term contracts with external suppliers as a result of uncertainty surrounding the opening of the fishery in 2010 and the expected (by the canning industry) low level of TAC (Pita et al., 2014). This depressed the average price in the post-closure period. When revenues were used as the DM management measure, the EVPI for the period 1987–2006 was approximately 16% of the average revenue. For the period 2010–2015, this value was 6%. The decrease in the standard variation (see Table 1) was responsible for the observed reduction in the ratio of EVPI to the mean revenue. In other words, the revenue was more stable during 2010–2015; hence, the EVPI decreased. The EVPIs obtained for these periods when the landings were used as the DM management measure were significantly different. The EVPI/mean revenue ratios were 22% and 12% for the two periods examined. When the revenues were considered, the standard deviation for the time series, as a result of the price changes, was smaller than when the landings were ascribed to the outcome. Thus, both the variability and the EVPI, were reduced. The EVPI for the member states participating in this fishery was also calculated (Table 1). The EVPI for 1987–2006 revenues in Spain was approximately 16% of the average revenue observed by the DM. For France, the value was 21%. The values were 13% and 11% for Spain and France, respectively, for 2010–2015. This implies that the increased stability between 2010 and 2015 was perceived by the two member states separately. The effect reported at the overall fishery level was also observed at the member state level; the variability was higher when the landings were considered the management measure. The differences between the EVPIs for the two member states were caused by the rise in variability (in France during 1987–1996, when the revenues were used as the value ascribed) or by the increased mean (Spain during 2010–2015). This implies that the value of information perceived by each DM individually is related to the size of their fishery (revenues or landings of their fleets), but also to the variability. The sum of the EVPIs of the two member states participating in this fishery was larger than the EVPI of the fishery overall for both periods, irrespective of the management measure used. As shown by Samson et al. (1989), the sum of the information values

Table 2 Correlation coefficients between the surveys and revenues or landings (overall and by member state) for the anchovy fishery of the Bay of Biscay for the periods 1987–2015 (BIOMAN) 1989–2015 (PELGAS) and 2003–2015 (JUVENA). DM Management measure

Survey

EU

Spain

France

Revenues

BIOMAN PELGAS JUVENA

0.14 0.19 0.39

0.20 0.15 0.65

0.11 0.14 0.35

Landings

BIOMAN PELGAS JUVENA

0.21 0.20 0.63

0.16 0.12 0.69

0.06 0.14 0.60

of two random variables might be greater (super-additive), smaller (sub-additive) or equal to the sum of the individual EVPIs of the member states. The consequences of this non-additivity property of the value of information will be examined in Section 4.

3.2. Expected value of imperfect information As explained in Section 2, the EVPI provides an upper bound of the annual economic value of research and management. However, this is based on the assumption that the uncertainty will be reduced to zero. This is unrealistic because of the natural variability of the stock (changes in the natural patterns, trophic alterations, etc.), changes in prices (when revenues are the management measure) and the limitations of existing assessment and management. Furthermore, it does not allow the assessment of the individual values provided by the signals of information (research surveys). For the purpose of this study, the EVII is a more useful tool. To utilise it, the relationship between signals of information and the value ascribed by the DM to the outcome is considered. In other words, the predictive capacity of the information signal should be computed. The coefficients of correlation between the signals and the variables are given in Table 2, for revenues and landings. Table 3 shows that additivity was not preserved. For the two periods examined (1987–2006 and 2010–2015), the EVII of the three research surveys for the overall fishery was lower than the sum of the values of the information provided for the two member states.

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Table 3 Annual EVII of the anchovy research surveys in the Bay of Biscay for the two management measures (revenues and landings). The values are in euros inflated to the 2015 level. DM Management measure

Period

Survey

EU

Spain

France

Revenues

1987–2006

BIOMAN PELGAS JUVENA BIOMAN PELGAS JUVENA

1 437 457 1 903 441 4 015 806 377 280 499 585 1 040 330

1 238 134 957 834 4 071 188 766 087 592 653 2 438 352

881 616 1 123 817 2 788 006 141 688 180 588 447 058

BIOMAN PELGAS JUVENA BIOMAN PELGAS JUVENA

2 927 800 2 767 011 8 876 286 1 594 756 1 507 175 4 607 397

1 596 239 1 122 197 6 641 608 1 304 713 925 420 5 111 837

540 000 1 200 400 5 071 220 91 038 202 374 853 598

2010–2015

Landings

1987–2006

2010–2015

In the case of EVII, three variables affect the final differences observed, the mean (the “size” of the fishery), the standard deviation (the variability) and the correlation between the variable and the biomass index (the predictive power). 3.3. Value of current and future information

DM

Log(b)

Table 2 shows that, in some cases, the predictive capacity of the signals for revenue is low. Furthermore, it is questionable whether the correlation coefficient captures all the predictive capacity of a signal. There are several possible explanations for this. Firstly, the research surveys are not designed to predict the revenue but to provide information for stock assessment. Secondly, the market demand alters the relationship between the information signal and the revenue (even though this effect is mitigated when landings are the management measure). Thirdly, the signals were available for different periods, although the analysis of the 2003–2015 time series (a period common to the three signals) resulted in similar general conclusions. Fourthly, the advisory process and final management decisions are different and separate processes. The advice provided by ICES and the agreed TAC were based on the history of advice, catches and management provided by ICES (2015) in the period from 1987 to 2005. The TAC was always around 32,000 t (average), and the advice provided using the information signals fluctuated from 33,000 t (in 2002) to none (closure of the fishery, the year 2006). Thus, in the period from 1987 to 2005, the advice has not been followed by the DM formulating the final management decision (the TAC). Finally, the research surveys are not the only signal utilised in the assessment; the commercial catches and the fish numbers by age are also used. However, the methods described here might help a DM to determine the relationship between the expected economic value and the cost of the signals of information. Fig. 2 shows the EVII for different possible correlation factors. The EVII was computed using a percentage reduction in the standard deviation that a signal or signals might create. This was only done for illustrative proposes for the period after re-opening of the fishery and for the revenue as the management measure of the DM. The expected value curve follows an increasing trend: the more informative the signal, the higher the value. This curve allows fitting of a power function (Eq. (3)). EVII(I) = bI ˛ ,

Table 4 The results of fitting a power function (EVII(I) = bI˛ ) to the 2010–2015 revenue data. I is the relative reduction in standard deviation for the revenue time series.

(3)

where b is a positive constant, ␣ is the elasticity and I reflects the extent of the information content (from 0 to 100). To give an example, if I = 10, the standard deviation will be reduced by 10% (not very informative) and if I = 100, the uncertainty will be completely removed.

Elasticity R-squared Adjusted R-squared

EU

Spain

France

10.59*** (0.127) 0.868*** (0.032) 0.989 0.987

10.74*** (0.069) 0.944*** (0.018) 0.997 0.997

9.772*** (0.127) 0.898*** (0.027) 0.992 0.991

Standard errors are shown in parentheses. *** indicates significance at the 99% level.

Table 4 shows that the function EVII(I) is twice differentiable. As can be seen in Fig. 3, EVII(I) > 0. Furthermore, given that the elasticity (␣) is lower than one, EVII(I) < 0. That is, the marginal EVII is a decreasing function of information. Fig. 3 presents these marginal utilities for each DM. Given that the marginal utility decreases with information, the marginal costs of new signals of information have to be lower than the original marginal costs. Thus, if the DM is to acquire a new signal providing the same amount of information as the existing signals, it has to be acquired at a lower cost than the previous signals. Furthermore, Fig. 3 allows the DM to make marginal value judgments. The DM is likely to be aware of the cost function for each research signal. Thus, the DM will know the cost of increasing the research intensity of a given signal (for example increasing in one the number of days of a survey) and the information gain achieved by this increase. Fig. 3 allows the DM to compare the value and the cost at the margin, and judge the efficiency of the information gain. The economic efficiency of decisions on gaining new information (by increasing the intensity of the existing signals or by acquiring a new one) can be evaluated by the DM using the data shown in Table 4. 4. The subjectivity of the outcome The method presented here makes it possible to compute the economic value of each information signal and evaluate the efficiency of future decisions on gaining new information. However, as Mäntyniemi et al. (2009) report, the calculation of such economic values is not necessarily objective. The choice of the value ascribed by the DM to the outcome will depend on how the value is perceived by a particular person or group. For example, Murillas et al. (2011) use the net value added as an indicator of ecosystem services. Other candidates such as gross profits, gross value added, employment or consumer surplus can also be considered. However, the revenue and the landings seem

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Fig. 2. EVPI for a range of signals of information. “25” on the x-axis means that the standard deviation is reduced by 25% (not very informative) and “100” that the uncertainty is completely removed. Values are in euros, inflated to 2015.

Fig. 3. The marginal value of perfect information for a range of signals of information. “25” on the x-axis means that the standard deviation is reduced by 25% (not very informative) and “100” that the uncertainty is completely removed. “All” stands for the multiple correlation coefficient for all the research surveys simultaneously and its corresponding marginal utility. Values are in euros, inflated to 2015.

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a good choice. This is because the main objective of the EU Common Fisheries Policy, on a stock basis, is to obtain the Maximum Sustainable Yield (EU, 2013). The maximum yield is targeted; this yield, multiplied by price (real price in this case), gives the revenue. The differences between the results for revenues and landings, used as the DM management measure, are consistent with a general demand curve for the anchovy (ex-vessel price decreases when the landings increase). This price reduction decreases the variability and, hence, the EVPI of the DM when the revenues are used. Other financial indicators of a fishing firm (e.g. gross profits) cannot be calculated on a single stock basis in a multispecies fishery such as that studied here. In terms of the best expectations of the DM (without information), it should be noted that the HCR for anchovy is based on the estimated SSB, which is highly variable (López-López et al., 2012). This implies that the DM has to create the expected values of SSB on the basis of the past data. The mean was considered the maximum guess when uncertainty was resolved, but other values might also be used, such as the last observed value. However, the results are quite straightforward if this value varies: if the value used is higher than the mean, the EVPI will also be higher (and vice versa), ceteris paribus. The perception of the DMs is subjective; their risk perception and time preferences should be taken into account. The calculations presented in this work were based on the assumption of a riskneutral DM. As stated by Bickel (2008), there is no rule of thumb for evaluation of imperfect information as a fraction of perfect information without assuming risk neutrality. However, if the aim is to choose between two signals of information, the selection will critically depend on their relative economic values afforded to the DM. Changing the period analysed also alters the absolute value of the information. It creates another source of subjectivity. In the studied fishery, three periods can be clearly distinguished: a period with no relationship between scientific advice and management decisions, a period when the fishery was closed and a final period in which the scientific advice and management decisions were related. The absolute value of the information changes depending on the period chosen (the overall period, the first period or the last period). The final choice of the interval to be used for the calculations has to be made by the DM. However, it should be noted that the EVPI and EVII calculations are based on the DM expectations. The expectations of the DM become more realistic as the time of implementing the management action approaches. Super-additivity is another critical property related to the subjectivity of the calculations. It is a mathematical property; the sum of the individual EVPIs of two random variables can be larger, equal to or smaller than the EVPI of their sum (Howard, 1966). This property is relevant to the DMs. The surveys are simultaneously financed by a supra-national authority (the EU) and the member states. The EVII perceived by the EU is lower than the sum of the EVIIs perceived by member states. Furthermore, the ranking given to each survey by the individual member states might differ, causing even greater discrepancies between the amounts of money that the EU and each of the member states are prepared to spend. This creates some difficulties in establishing the upper spending bound for these surveys. A possible policy implication is that the supra-national authority, apart from defining the co-financing budget, has to enforce the spending limit (of no more than the 100% of the EVPI), reducing the co-financed amount, if necessary. Time is another subjective factor, not only in terms of the DM preferences but also regarding opportunity costs. Ignoring an information signal (for whatever reason) increases opportunity costs in a cumulative manner over time. This phenomenon poses a question (beyond the scope of this work) of appropriate use of financial resources to reduce the existing uncertainty in fish stock assessment. In this field, the global sensitivity analyses of simulation

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models (Morris et al., 2014) are of great interest. These methods can relate the uncertainty in the output of a model with different sources of uncertainty in its input parameters. Subjectivity also affects the ecosystem analysis. Research surveys provide information not just for a single stock but also for other stocks and other ecosystem services. ICES (2016) shows that the acoustic surveys provide information on the anchovy, sardine, sprat, horse mackerel and blue whiting. Such research surveys provide information (and value) for various fisheries. Furthermore, these surveys create the signals for other marine services related to the Marine Strategy Framework Directive (EC, 2008), supplying the DM with a signal of information and its value. Hansen and Jones (2008) concluded that the value of the assessments should be measured not only in terms of the information they provide but also in relation to other management actions that might replace them. 5. Conclusions The methodology presented here relates the concepts of the “size” of the problem (mean), its “variability” (standard deviation) and the information provided (signal). The main conclusion is that the value of the information provided by the signals depends on the size of the fishery (measured as the value of the landings), but also on the variability of the landings or revenues. This implies that the regimes in natural variability will change the value of information. For example, stocks that are highly variable in size (small pelagics) will have a higher EVI than those with lower natural variability (demersals), for the same fishery size (i.e. the value of landings). This methodology (and its application) can be considered a starting point for any kind of economic evaluation of data collection policies at the commercial fishery level. It can provide economic values for various research surveys and obtain their relative ranking. For the DM, the EVPI represents an average improvement in the base-optimal expected payoff commensurate with a hypothetical acquisition of perfect information before making a decision. It can provide the marginal gain of acquiring new information or (what should be) the maximum marginal cost (acceptable to the DM) of acquiring such information. Thus, the method can be used by the DM to evaluate the economic efficiency of increasing the accuracy of information. This might mean, for example, an increase in research-survey effort or evaluation of a new research survey in a stock advisory process. The methodology itself is not free of limitations. Time was not explicitly considered, and several assumptions of the risk attitudes of the DM were made. However, the analysis of the economic value of research activities will always be subjective to some extent. Fishery stock assessment and management are not exceptions to this rule; the methodology presented here expressly recognises these sources of subjectivity. Acknowledgements The author gratefully acknowledges two anonymous reviewers and the editor (André E. Punt) for their insightful comments and suggestions. This work has received funding from the Basque Government funded project MULTIPLAN. All errors are my own responsibility. This is the contribution 807 from the Marine Research Division (AZTI). Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.fishres.2017.02. 004.

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