- Email: [email protected]
Is anchovy (Engraulis encrasicolus, L.) overfished in the Adriatic Sea?
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Is anchovy (Engraulis encrasicolus, L.) overfished in the Adriatic Sea? ˇ cek ∗ , T. Legovi´c J. Klanjsˇ Ruder Boˇskovi´c Institute, Bijeniˇcka Cesta 54, 10002 Zagreb, Croatia
a r t i c l e
i n f o
Article history:
a b s t r a c t Based on Santojanni et al. [Santojanni, A., Arneri, E., Barry, C., Belardinelli, A., Cingolani, N.,
Received 22 August 2005
Giannetti, G., Kirkwood, G., 2003. Trends of anchovy (Engraulis encrasicolus, L.) biomass in the
Received in revised form
northern and central Adriatic Sea. Sci. Mar. 67(3), 327–340] stock size estimates for the period
20 September 2006
from 1975 to 1996, we constructed a model to investigate population dynamics of anchovies.
Accepted 22 September 2006
Using numeric simulations we calculate the maximum sustainable catch (MSC) as well as
Published on line 7 November 2006
the optimum level of spawning stock to maintain the MSC. By comparing computed levels with Santojanni et al. estimates, we find that the anchovy population is below the optimum
Keywords:
level, i.e. overfished since 1982. We find evidence of overfishing in 1982, 1985, 1986 and 1988.
Two stage model
We claim the large catch in 1985 was more responsible for the collapse of anchovy fisheries
Optimum fishery
in 1987 than low recruitment levels. We investigate possible ways of fishing using the two
Anchovy
stage model by considering three fishing scenarios: the whole stock is fished with equal
Stock estimates
effort, only mature individuals are fished, mature and immature individuals are fished with unequal effort. We show that the best strategy is to fish only the spawning stock. © 2006 Elsevier B.V. All rights reserved.
1.
Introduction
In the period between 1972 and 1997 overall landings in the Adriatic Sea of pelagic fisheries showed a 40% decrease (Massa and Mannini, 2000). Anchovy, as a very important commercial species, constituted a major part of catches and therefore ˇ c, ´ 2000; was a subject of numerous research papers (Sinovci Cingolani et al., 2001; Santojanni et al., 2001, 2003). Santojanni et al. (2003) demonstrated the trend of anchovy biomass in the Adriatic Sea from 1975 to 1996. They obtained the estimates of stock sizes for each age class using DeLurys model as well as Virtual Population Analysis (VPA). VPA enables to estimate the number of fishes by rewinding the historical number, starting with catches in 1996. We used the estimates to construct a production model of anchovy population.
∗
Corresponding author. Tel.: +385 1 4680230. ˇ E-mail address: [email protected] (J. Klanjˇscek). 0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2006.09.020
According to Haddon (2001) models commonly used in fishery fall into three categories: surplus-production models, age-structured models, and size-structured models. Surplusproduction models such as Schaefer’s, Fox’s and Pella and Tomlison’s (Haddon, 2001, and references therein) are simple and consider stock as undifferentiated biomass. These models ignore age, sex, size and other differences between individuals and are not frequently used in recent literature. Unlike surplus-production models, age-structured models distinguish between individuals by classifying them according to their age and assigning different fecundity, survival probability and fishing mortality to each age class. Age structured models are widely used (Aubone, 2004; Dew, 2001; Allen and Miranda, 1998; Jensen, 1996), even though they require lots of data. Size-structured models, on the other hand, distinguish individuals according to their size, rather than age (e.g. Pet
313
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
et al., 1996). These models are usually used when modeling tropic fishery because of difficulties in fish age determination (Sparre and Venema, 1998). To parameterize our model we use Santojanni et al. (2003) estimates, which are age-structured. However, due to constant age-class mortality which Santojanni et al. (2003) assumed when obtaining the estimates, and the fact that contribution of each age class to recruitment is difficult to evaluate (Aubone, 2004), we separate individuals according to their reproductive status and create a stage-structured model. The individuals in our model are grouped into two stages—immature individuals (recruits) and mature individuals (spawning stock). Reproduction of anchovy is pulsed, so the model is based on the postbreeding census. We suggest the relationship between the number of mature individuals of one generation and the number of immature individuals of the next generation. After the individuals enter the system they are tracked by the relation designed to uphold the basic assumption of the VPA method. We constructed the model in an attempt to answer the following three questions: (i) why did the pelagic fishery suffer the decrease of 40% in landings over the last decades, (ii) can the collapse in 1987 be explained by overfishing rather than low recruitment levels as suggested by Santojanni et al. (2003) and (iii) what is the optimal strategy of fishing the anchovies in the Adriatic Sea.
2.
Model description
We separate the anchovy population in two classes, according to their reproductive status: immature (recruits) and mature (the spawning stock). Denoting the number of recruits with N0 and the number of mature individuals with Nsp , the total number of individuals in the population, Ntotal , is: Ntotal = N0 + Nsp
(1)
We estimate coefficients a and b using the least square method and the number of individuals that Santojanni et al. (2003) obtained using Virtual Population Analysis (VPA). Also, we use Jackknife method as suggested by Haddon (2001) to obtain upper and lower bounds of the recruitment function. The number of dead and fished individuals is expressed according to the basic assumptions of the VPA method. VPA distinguishes between the stage-independent mortality (coefficient x), not related to fishing and the stage-dependent fishing mortality (coefficients z and y) for immatures and matures, respectively. The coefficient x is equivalent to the mortality coefficient used by Santojanni et al. (2003) and accounts for all deaths other than deaths caused by fishing (e.g. starvation, predation, diseases, old age, etc.). Note that the number of dead fish depends on the fish stock size. Ndead(t) + Nfished(t) = N0(t) (1 − xz) + Nsp(t) (1 − xy)
(4)
Note that z = y = 1 means there is no fishing at all. In addition, we define fishing effort as ez = 1 − z and ey = 1 − y, i.e. the effort grows with fishing intensity. To calculate the number of caught individuals we use √ √ catch(t) = Nsp(t) x(1 − y) + N0(t) x(1 − z)
(5)
which is based on reversing the Pope’s formula (Sparre and Venema, 1998) that approximates VPA results. Recursive equation for tracking the numbers of mature and immature individuals separately are: Nsp(t+1) = N0(t) xz + Nsp(t) xy
N0(t+1) = aNsp(t)
1−
Nsp(t)
(6)
b
We consider three possible scenarios for fishing practice and for each we calculate the maximum sustainable catch: (a) Fishing mortality is equal for all individuals (z = y):
Since the reproduction is pulsed we replace it with a discrete process. The model is based on the postbreeding census of this birth pulse population (Caswell, 2001). The total number of individuals at time t + 1 is equal to the number of individuals at time t, increased by the number of new recruits at time t + 1 and decreased by the number of dead (Ndead ) and fished (Nfished ) individuals between t and t + 1. Ntotal(t+1) = Ntotal(t) + N0(t+1) − Ndead(t) − Nfished(t)
N0(t+1) = aNsp(t)
1−
Nsp(t) b
Ntotal(t+1) = Ntotal(t) xy + aNsp(t)
1−
Nsp(t)
.
b
(7)
(b) Only the spawning stock is fished (z = 1):
Ntotal(t+1) = N0(t) x + Nsp(t) xy + aNsp(t)
1−
Nsp(t)
b
.
(8)
(2)
The number of new recruits as a function of number of adults is a very important step in creating a model. There are several different functions that describe this relationship, e.g. Beverton–Holt, Rickers and Deriso-Schnute recruitment functions (Haddon, 2001). We assumed that the number of recruits depends on the size of the spawning stock, but that the increase in the spawning stock is density dependent.
(3)
(c) The spawning stock is fished heavier then recruits, with a constant ratio of fishing mortalities (y < z).
Ntotal(t+1) = N0(t) xz + Nsp(t) xy + aNsp(t)
3.
Results
3.1.
Coefficients a and b
1−
Nsp(t) b
.
(9)
We obtained values for a and b coefficients, a = 1.792 and b = 33.03 × 109 , using the least square method on Santojanni et
314
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
Given the values of the coefficients in the model: a = 1.792, b = 33.03 × 109 , and the stage independent mortality coefficient x = 0.55 we searched for y which gives the maximum catch. The MSC is 3.24 × 109 individuals, and y = 0.789 (ey = 0.211). The total number of individuals in the steady state is 20.71 × 109 and it consists of 11.72 × 109 immature and 8.99 × 109 mature individuals.
3.2.2.
Scenario (b)
Only the spawning stock is fished (z = 1): ∗ ) and immature (N∗ ) individuals The number of mature (Nsp 0 in the steady state are:
Fig. 1 – Spawning stock vs. recruitment. The least square fit of the recruitment function to the Santojanni et al. (2003) estimates.
al. (2003) estimates (Fig. 1). Fitting the Eq. (3) we obtain a statistically significant (p < 0.05) correlation coefficient between spawning stock at time t (Nsp(t) ) and recruitment at time t + 1 (N0(t+1) ), r = 0.6126. Resampling the data by removing one stock–recruitment pair (Nsp(t), N0(t+1) ) from the data set, we calculated that all the pairs of coefficients a and b are statistically significant (p < 0.05, 0.5449 ≤ r ≤ 0.6793). We used Jackknife method as suggested by Haddon (2001) to calculate MSC in order to get confidence intervals for the average value of the whole sample for three different scenarios.
3.2.
The maximum sustainable catch
According to Eq. (6) we can track the numbers of individuals for each stage given the fishing efforts. If other environmental conditions that act on the anchovy population stay the same, the number of individuals will reach certain steady state. To each pair of efforts there corresponds one steady state of number of fish and one pair of steady catches (mature and immature). By applying the Eq. (5) in numeric simulation of fishing effort, we can find the maximum sustainable catch (MSC). Since there is a fishing effort applied to both stages (ey and ez ) there is a broad range of fishing strategies. Our scenarios cover the three most important cases in practice. They were calculated for whole sample, as well as for the resampled data. The lowest and the highest MSC value of resampled data are presented as upper and lower bounds of the MSC.
3.2.1.
Scenario (a)
Fishing mortality is equal for all individuals (z = y) ∗ ) and immature (N∗ ) individuals The number of mature (Nsp 0 in the steady state are:
1 − xy axy 1 − xy 1 − xy ∗ 1− N0 = b xy axy ∗ =b 1− Nsp
(10)
1 − xy ax 1 − xy . 1 − xy N0∗ = b 1− x ax ∗ =b 1− Nsp
(11)
Given the values a = 1.792, b = 33.03 × 109 and x = 0.55, we searched for y which gives the maximum catch. This fishing scenario allows for MSC of 3.24 × 109 individuals when y = 0.513 (ey = 0.487). The total number of individuals in steady state is 20.68 × 109 and it consists of 11.71 × 109 immature and 8.97 × 109 mature individuals.
3.2.3.
Scenario (c)
The spawning stock is fished heavier then recruits (y < z): ∗ ) and immature (N∗ ) individuals The number of mature (Nsp 0 in the steady state are:
1 − xy 1 − xyaxz . 1 − xy ∗ N0 = b 1− xz axz ∗ =b 1− Nsp
(12)
Given the values a = 1.792, b = 33.03 × 109 and x = 0.55 we searched for y and z which gives the maximum catch. This fishing scenario allows for MSC of 3.24 × 109 individuals whenever: z = −0.766y + 1.393.
(13)
The total number of individuals in steady state is 20.68 × 109 and it consists of 11.71 × 109 immature and 8.97 × 109 mature individuals.
4.
Discussion
4.1.
Choosing the optimum fishing strategy
Our three scenarios show that the MSC stays the same regardless of how the stock is fished. If there is no fishing, the number of mature individuals in the steady state is 17.95 × 109 , and if there is optimum fishing then it is around 8.97 × 109 . That figure is approximately half of the value that would be in the steady state without fishing. Since the mature individuals are the ones that produce new organisms, it is their number that limits the total population size. So, regardless of the fishing scenarios, it is necessary to have the same amount of mature individuals to ensure the optimum recruitment.
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
Fig. 2 – Santojanni et al. (2003) estimates of spawning stock levels for the period from 1975 to 1996 compared to the optimum spawning stock for maintaining the MSC.
ˇ c´ (2000) the average weight of immaAccording to Sinovci ture individuals is 3.3 g, while mature individuals weight from 12.08 g for 1 year olds up to 31.03 g for 4 year olds. Hence, if one limits the number of fish caught, it is more advantageous to fish only the spawning stock to maximize biomass caught, because mature individuals are heavier.
4.2.
Overfishing
We distinguish two terms connected to overfishing: state of stock and the fishing practice. State of stock is the level of spawning stock in a certain year compared to the optimum level needed to maintain MSC. If the stock level is below the optimum level we consider the stock overfished. On the other hand we can talk about overfishing as a process. It happens when the fishing effort on the stock is greater than the optimum effort. The optimum effort is the effort on the mature (ey ) and immature (ez ) individuals that leads to MSC in the steady state. As mentioned in the results section, the required spawning stock level that ensures MSC is 8.97 × 109 individuals. By comparing that level to the actual stock levels we find that the spawning stock is overfished since 1982 (Fig. 2). To distinguish between affirmative and destructive fishing practice we compare historical efforts that were calculated from Santojanni et al. (2003) estimates and optimum efforts (Fig. 3). Different pairs of optimum efforts (ey , ez ) can be chosen to give MSC. Hence, it is appropriate to select the pair that retains the actual ratio between efforts for each particular year. Overfishing for the immature as well as mature individuals was found in the 1982, 1985, 1986 and 1988. However, the extent of overfishing, measured as a difference between optimum and historical efforts that were calculated from Santojanni et al. (2003) estimates, was not equal for all years. It was relatively small in 1982 and 1988 while high in 1985 and 1986. The anchovy stock was heavily overfished in 1985. From only 43% of the spawning stock required for the full MSC, 90% of the MSC was taken. We believe this overfishing induced the crash of anchovy fisheries in 1987, rather than the
315
Fig. 3 – Efforts calculated from Santojanni et al. (2003) estimates compared to the optimum efforts for the period from 1975 to 1996.
lower recruitment levels several years earlier as suggested by Santojanni et al. (2003). Indeed, the recruitment levels in those years were really low. However, even if the recruitment were at expected levels (Eq. (3)) and the fishing effort ey and ez stayed the same as they were in 1985, the stock would collapse. Our simulations shows that the stock would reach the level of 1987 2 years later. So, we conclude that the lower recruitment levels only speeded up the process.
4.3.
Applicability
The capability of the presented model to reproduce the stock assessment by Santojanni et al. (2003) is best seen on the Fig. 4. Clearly, the main reason for existing differences is in the recruitment variations (Fig. 1) which are unaccounted for in the stock–recruitment relationship. Other, more complex functions may have led to a better fit to the available data, but that would create an empirical model with no predictive capability. Differences between actual recruitment and proposed stock–recruitment function may be connected to the changes
Fig. 4 – Comparison of model prediction with Santojanni et al. (2003) estimates.
316
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
in the environmental parameters (Shannon et al., 2004, Roy et al., 2004). Biotic and abiotic factors could be modelled by incorporating several additional parameters, which then may reproduce the history better and increase predictive capability. The present model highlights the effects of fishing effort on the population, which enabled us to find the best fishing strategy and to detect the overfishing period. Further refinement is necessary to obtain more precise MSC levels as well as required spawning stock levels. Improvement toward that goal may be possible when considerably longer data record becomes available. Therefore, monitoring should continue and in the meantime all available tools should be used to preserve the anchovy stock.
Acknowledgements This research has been supported by the Croatian Ministry for science, education and sport, EU-FP6 project on Ecosystem approach to sustainable aquaculture and the NorwegianCroatian PSSA project. We wish to thank M. Jusup for discusˇ for comments on the paper. T.L. is gratesions and T. Klanjˇscek ˇ c´ for discussions on the fate of anchovies ful to Dr. G. Sinovci in the Adriatic Sea. We are also wish to thank to the editor and reviewers for constructive suggestions and comments.
references
Allen, M.S., Miranda, L.E., 1998. An age-structured model for erratic crappie fisheries. Ecol. Model. 107, 289–303. Aubone, A., 2004. Threshold for sustainable exploitation of an age-structured fishery stock. Ecol. Model. 173, 95–107. Caswell, H., 2001. Matrix Population Models. Sinauer Associates, Sunderland, MA, USA. Cingolani, N., Arneri, E., Giannetti, G., Santojanni, A., Belardinelli, A., Colella, S., Donato, F., 2001. The small pelagic fisheries on the Western coast of the Adriatic Sea: monitoring and
assessment. AdriaMed technical documents 3. http://www.faoadriamed.org/pdf/td3/web-td-3-C D.pdf (last visited July 10, 2005). Dew, I.M., 2001. Theoretical model of a new fishery under a simple quota management system. Ecol. Model. 143, 59–70. Haddon, M., 2001. Modelling and Quantitative Methods in Fisheries. Chapman & Hall/CRC, Boca Raton, FL, USA. Jensen, A.L., 1996. Density-dependent matrix yield equation for optimal harvest of age-structured wildlife populations. Ecol. Model. 88, 125–132. Massa, F., Mannini, P. (Eds.), 2000. Report of the First Meeting of the Adriamed Coordination Committee. FAO-MiPAF Scientific Cooperation to Support Responsible Fisheries in the Adriatic Sea. GCP/RER/010/ITA/TD-01, 64 pp. http://www.faoadriamed.org/pdf/web-td-1.pdf (last visited July 10, 2005). Pet, J.S., Machiels, M.A.M., Van Densen, W.L.T., 1996. A size-structured simulation model for evaluating management strategies in gillnet fisheries exploiting spatially differentiated populations. Ecol. Model. 88, 195–214. Roy, D., Haffner, G.D., Brandt, S.B., 2004. Estimating fish production potentials using temporally explicit model. Ecol. Model. 173, 241–257. Santojanni, A., Arneri, E., Barry, C., Belardinelli, A., Cingolani, N., Giannetti, G., Kirkwood, G., 2003. Trends of anchovy (Engraulis encrasicolus, L.) biomass in the northern and central Adriatic Sea. Sci. Mar. 67 (3), 327–340. Santojanni, A., Arneri, E., Belardinelli, A., Cingoalni, N., Giannetti, G., 2001. Small pelagic fish in the Adriatic: stock fluctuations and environmental factors. Arch. Oceanogr. Limnol. 22, 133–138. Shannon, L.J., Field, J.G., Moloney, C.L., 2004. Simulating anchovy-sardine regime shifts in the southern Benguela ecosystem. Ecol. Model. 172, 269–281. ˇ c, ´ G., 2000. Anchovy, Engraulis encrasicolus (Linnaeus, 1758): Sinovci biology, population dynamics and fisheries case study. Acta Adriatica 41 (1), 3–53. Sparre, P., Venema, S.C., 1998. Introduction to Tropical Fish Stock Assessment I: Manual. FAO Fisheries technical paper 306/1 Rev.2. Rome, Italy. http://www.fao.org/documents/show cdr.asp?url file=/docrep/w5449e/w5449e00.htm (last visited July 10, 2005).
available at www.sciencedirect.com
journal homepage: www.elsevier.com/locate/ecolmodel
Is anchovy (Engraulis encrasicolus, L.) overfished in the Adriatic Sea? ˇ cek ∗ , T. Legovi´c J. Klanjsˇ Ruder Boˇskovi´c Institute, Bijeniˇcka Cesta 54, 10002 Zagreb, Croatia
a r t i c l e
i n f o
Article history:
a b s t r a c t Based on Santojanni et al. [Santojanni, A., Arneri, E., Barry, C., Belardinelli, A., Cingolani, N.,
Received 22 August 2005
Giannetti, G., Kirkwood, G., 2003. Trends of anchovy (Engraulis encrasicolus, L.) biomass in the
Received in revised form
northern and central Adriatic Sea. Sci. Mar. 67(3), 327–340] stock size estimates for the period
20 September 2006
from 1975 to 1996, we constructed a model to investigate population dynamics of anchovies.
Accepted 22 September 2006
Using numeric simulations we calculate the maximum sustainable catch (MSC) as well as
Published on line 7 November 2006
the optimum level of spawning stock to maintain the MSC. By comparing computed levels with Santojanni et al. estimates, we find that the anchovy population is below the optimum
Keywords:
level, i.e. overfished since 1982. We find evidence of overfishing in 1982, 1985, 1986 and 1988.
Two stage model
We claim the large catch in 1985 was more responsible for the collapse of anchovy fisheries
Optimum fishery
in 1987 than low recruitment levels. We investigate possible ways of fishing using the two
Anchovy
stage model by considering three fishing scenarios: the whole stock is fished with equal
Stock estimates
effort, only mature individuals are fished, mature and immature individuals are fished with unequal effort. We show that the best strategy is to fish only the spawning stock. © 2006 Elsevier B.V. All rights reserved.
1.
Introduction
In the period between 1972 and 1997 overall landings in the Adriatic Sea of pelagic fisheries showed a 40% decrease (Massa and Mannini, 2000). Anchovy, as a very important commercial species, constituted a major part of catches and therefore ˇ c, ´ 2000; was a subject of numerous research papers (Sinovci Cingolani et al., 2001; Santojanni et al., 2001, 2003). Santojanni et al. (2003) demonstrated the trend of anchovy biomass in the Adriatic Sea from 1975 to 1996. They obtained the estimates of stock sizes for each age class using DeLurys model as well as Virtual Population Analysis (VPA). VPA enables to estimate the number of fishes by rewinding the historical number, starting with catches in 1996. We used the estimates to construct a production model of anchovy population.
∗
Corresponding author. Tel.: +385 1 4680230. ˇ E-mail address: [email protected] (J. Klanjˇscek). 0304-3800/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2006.09.020
According to Haddon (2001) models commonly used in fishery fall into three categories: surplus-production models, age-structured models, and size-structured models. Surplusproduction models such as Schaefer’s, Fox’s and Pella and Tomlison’s (Haddon, 2001, and references therein) are simple and consider stock as undifferentiated biomass. These models ignore age, sex, size and other differences between individuals and are not frequently used in recent literature. Unlike surplus-production models, age-structured models distinguish between individuals by classifying them according to their age and assigning different fecundity, survival probability and fishing mortality to each age class. Age structured models are widely used (Aubone, 2004; Dew, 2001; Allen and Miranda, 1998; Jensen, 1996), even though they require lots of data. Size-structured models, on the other hand, distinguish individuals according to their size, rather than age (e.g. Pet
313
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
et al., 1996). These models are usually used when modeling tropic fishery because of difficulties in fish age determination (Sparre and Venema, 1998). To parameterize our model we use Santojanni et al. (2003) estimates, which are age-structured. However, due to constant age-class mortality which Santojanni et al. (2003) assumed when obtaining the estimates, and the fact that contribution of each age class to recruitment is difficult to evaluate (Aubone, 2004), we separate individuals according to their reproductive status and create a stage-structured model. The individuals in our model are grouped into two stages—immature individuals (recruits) and mature individuals (spawning stock). Reproduction of anchovy is pulsed, so the model is based on the postbreeding census. We suggest the relationship between the number of mature individuals of one generation and the number of immature individuals of the next generation. After the individuals enter the system they are tracked by the relation designed to uphold the basic assumption of the VPA method. We constructed the model in an attempt to answer the following three questions: (i) why did the pelagic fishery suffer the decrease of 40% in landings over the last decades, (ii) can the collapse in 1987 be explained by overfishing rather than low recruitment levels as suggested by Santojanni et al. (2003) and (iii) what is the optimal strategy of fishing the anchovies in the Adriatic Sea.
2.
Model description
We separate the anchovy population in two classes, according to their reproductive status: immature (recruits) and mature (the spawning stock). Denoting the number of recruits with N0 and the number of mature individuals with Nsp , the total number of individuals in the population, Ntotal , is: Ntotal = N0 + Nsp
(1)
We estimate coefficients a and b using the least square method and the number of individuals that Santojanni et al. (2003) obtained using Virtual Population Analysis (VPA). Also, we use Jackknife method as suggested by Haddon (2001) to obtain upper and lower bounds of the recruitment function. The number of dead and fished individuals is expressed according to the basic assumptions of the VPA method. VPA distinguishes between the stage-independent mortality (coefficient x), not related to fishing and the stage-dependent fishing mortality (coefficients z and y) for immatures and matures, respectively. The coefficient x is equivalent to the mortality coefficient used by Santojanni et al. (2003) and accounts for all deaths other than deaths caused by fishing (e.g. starvation, predation, diseases, old age, etc.). Note that the number of dead fish depends on the fish stock size. Ndead(t) + Nfished(t) = N0(t) (1 − xz) + Nsp(t) (1 − xy)
(4)
Note that z = y = 1 means there is no fishing at all. In addition, we define fishing effort as ez = 1 − z and ey = 1 − y, i.e. the effort grows with fishing intensity. To calculate the number of caught individuals we use √ √ catch(t) = Nsp(t) x(1 − y) + N0(t) x(1 − z)
(5)
which is based on reversing the Pope’s formula (Sparre and Venema, 1998) that approximates VPA results. Recursive equation for tracking the numbers of mature and immature individuals separately are: Nsp(t+1) = N0(t) xz + Nsp(t) xy
N0(t+1) = aNsp(t)
1−
Nsp(t)
(6)
b
We consider three possible scenarios for fishing practice and for each we calculate the maximum sustainable catch: (a) Fishing mortality is equal for all individuals (z = y):
Since the reproduction is pulsed we replace it with a discrete process. The model is based on the postbreeding census of this birth pulse population (Caswell, 2001). The total number of individuals at time t + 1 is equal to the number of individuals at time t, increased by the number of new recruits at time t + 1 and decreased by the number of dead (Ndead ) and fished (Nfished ) individuals between t and t + 1. Ntotal(t+1) = Ntotal(t) + N0(t+1) − Ndead(t) − Nfished(t)
N0(t+1) = aNsp(t)
1−
Nsp(t) b
Ntotal(t+1) = Ntotal(t) xy + aNsp(t)
1−
Nsp(t)
.
b
(7)
(b) Only the spawning stock is fished (z = 1):
Ntotal(t+1) = N0(t) x + Nsp(t) xy + aNsp(t)
1−
Nsp(t)
b
.
(8)
(2)
The number of new recruits as a function of number of adults is a very important step in creating a model. There are several different functions that describe this relationship, e.g. Beverton–Holt, Rickers and Deriso-Schnute recruitment functions (Haddon, 2001). We assumed that the number of recruits depends on the size of the spawning stock, but that the increase in the spawning stock is density dependent.
(3)
(c) The spawning stock is fished heavier then recruits, with a constant ratio of fishing mortalities (y < z).
Ntotal(t+1) = N0(t) xz + Nsp(t) xy + aNsp(t)
3.
Results
3.1.
Coefficients a and b
1−
Nsp(t) b
.
(9)
We obtained values for a and b coefficients, a = 1.792 and b = 33.03 × 109 , using the least square method on Santojanni et
314
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
Given the values of the coefficients in the model: a = 1.792, b = 33.03 × 109 , and the stage independent mortality coefficient x = 0.55 we searched for y which gives the maximum catch. The MSC is 3.24 × 109 individuals, and y = 0.789 (ey = 0.211). The total number of individuals in the steady state is 20.71 × 109 and it consists of 11.72 × 109 immature and 8.99 × 109 mature individuals.
3.2.2.
Scenario (b)
Only the spawning stock is fished (z = 1): ∗ ) and immature (N∗ ) individuals The number of mature (Nsp 0 in the steady state are:
Fig. 1 – Spawning stock vs. recruitment. The least square fit of the recruitment function to the Santojanni et al. (2003) estimates.
al. (2003) estimates (Fig. 1). Fitting the Eq. (3) we obtain a statistically significant (p < 0.05) correlation coefficient between spawning stock at time t (Nsp(t) ) and recruitment at time t + 1 (N0(t+1) ), r = 0.6126. Resampling the data by removing one stock–recruitment pair (Nsp(t), N0(t+1) ) from the data set, we calculated that all the pairs of coefficients a and b are statistically significant (p < 0.05, 0.5449 ≤ r ≤ 0.6793). We used Jackknife method as suggested by Haddon (2001) to calculate MSC in order to get confidence intervals for the average value of the whole sample for three different scenarios.
3.2.
The maximum sustainable catch
According to Eq. (6) we can track the numbers of individuals for each stage given the fishing efforts. If other environmental conditions that act on the anchovy population stay the same, the number of individuals will reach certain steady state. To each pair of efforts there corresponds one steady state of number of fish and one pair of steady catches (mature and immature). By applying the Eq. (5) in numeric simulation of fishing effort, we can find the maximum sustainable catch (MSC). Since there is a fishing effort applied to both stages (ey and ez ) there is a broad range of fishing strategies. Our scenarios cover the three most important cases in practice. They were calculated for whole sample, as well as for the resampled data. The lowest and the highest MSC value of resampled data are presented as upper and lower bounds of the MSC.
3.2.1.
Scenario (a)
Fishing mortality is equal for all individuals (z = y) ∗ ) and immature (N∗ ) individuals The number of mature (Nsp 0 in the steady state are:
1 − xy axy 1 − xy 1 − xy ∗ 1− N0 = b xy axy ∗ =b 1− Nsp
(10)
1 − xy ax 1 − xy . 1 − xy N0∗ = b 1− x ax ∗ =b 1− Nsp
(11)
Given the values a = 1.792, b = 33.03 × 109 and x = 0.55, we searched for y which gives the maximum catch. This fishing scenario allows for MSC of 3.24 × 109 individuals when y = 0.513 (ey = 0.487). The total number of individuals in steady state is 20.68 × 109 and it consists of 11.71 × 109 immature and 8.97 × 109 mature individuals.
3.2.3.
Scenario (c)
The spawning stock is fished heavier then recruits (y < z): ∗ ) and immature (N∗ ) individuals The number of mature (Nsp 0 in the steady state are:
1 − xy 1 − xyaxz . 1 − xy ∗ N0 = b 1− xz axz ∗ =b 1− Nsp
(12)
Given the values a = 1.792, b = 33.03 × 109 and x = 0.55 we searched for y and z which gives the maximum catch. This fishing scenario allows for MSC of 3.24 × 109 individuals whenever: z = −0.766y + 1.393.
(13)
The total number of individuals in steady state is 20.68 × 109 and it consists of 11.71 × 109 immature and 8.97 × 109 mature individuals.
4.
Discussion
4.1.
Choosing the optimum fishing strategy
Our three scenarios show that the MSC stays the same regardless of how the stock is fished. If there is no fishing, the number of mature individuals in the steady state is 17.95 × 109 , and if there is optimum fishing then it is around 8.97 × 109 . That figure is approximately half of the value that would be in the steady state without fishing. Since the mature individuals are the ones that produce new organisms, it is their number that limits the total population size. So, regardless of the fishing scenarios, it is necessary to have the same amount of mature individuals to ensure the optimum recruitment.
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
Fig. 2 – Santojanni et al. (2003) estimates of spawning stock levels for the period from 1975 to 1996 compared to the optimum spawning stock for maintaining the MSC.
ˇ c´ (2000) the average weight of immaAccording to Sinovci ture individuals is 3.3 g, while mature individuals weight from 12.08 g for 1 year olds up to 31.03 g for 4 year olds. Hence, if one limits the number of fish caught, it is more advantageous to fish only the spawning stock to maximize biomass caught, because mature individuals are heavier.
4.2.
Overfishing
We distinguish two terms connected to overfishing: state of stock and the fishing practice. State of stock is the level of spawning stock in a certain year compared to the optimum level needed to maintain MSC. If the stock level is below the optimum level we consider the stock overfished. On the other hand we can talk about overfishing as a process. It happens when the fishing effort on the stock is greater than the optimum effort. The optimum effort is the effort on the mature (ey ) and immature (ez ) individuals that leads to MSC in the steady state. As mentioned in the results section, the required spawning stock level that ensures MSC is 8.97 × 109 individuals. By comparing that level to the actual stock levels we find that the spawning stock is overfished since 1982 (Fig. 2). To distinguish between affirmative and destructive fishing practice we compare historical efforts that were calculated from Santojanni et al. (2003) estimates and optimum efforts (Fig. 3). Different pairs of optimum efforts (ey , ez ) can be chosen to give MSC. Hence, it is appropriate to select the pair that retains the actual ratio between efforts for each particular year. Overfishing for the immature as well as mature individuals was found in the 1982, 1985, 1986 and 1988. However, the extent of overfishing, measured as a difference between optimum and historical efforts that were calculated from Santojanni et al. (2003) estimates, was not equal for all years. It was relatively small in 1982 and 1988 while high in 1985 and 1986. The anchovy stock was heavily overfished in 1985. From only 43% of the spawning stock required for the full MSC, 90% of the MSC was taken. We believe this overfishing induced the crash of anchovy fisheries in 1987, rather than the
315
Fig. 3 – Efforts calculated from Santojanni et al. (2003) estimates compared to the optimum efforts for the period from 1975 to 1996.
lower recruitment levels several years earlier as suggested by Santojanni et al. (2003). Indeed, the recruitment levels in those years were really low. However, even if the recruitment were at expected levels (Eq. (3)) and the fishing effort ey and ez stayed the same as they were in 1985, the stock would collapse. Our simulations shows that the stock would reach the level of 1987 2 years later. So, we conclude that the lower recruitment levels only speeded up the process.
4.3.
Applicability
The capability of the presented model to reproduce the stock assessment by Santojanni et al. (2003) is best seen on the Fig. 4. Clearly, the main reason for existing differences is in the recruitment variations (Fig. 1) which are unaccounted for in the stock–recruitment relationship. Other, more complex functions may have led to a better fit to the available data, but that would create an empirical model with no predictive capability. Differences between actual recruitment and proposed stock–recruitment function may be connected to the changes
Fig. 4 – Comparison of model prediction with Santojanni et al. (2003) estimates.
316
e c o l o g i c a l m o d e l l i n g 2 0 1 ( 2 0 0 7 ) 312–316
in the environmental parameters (Shannon et al., 2004, Roy et al., 2004). Biotic and abiotic factors could be modelled by incorporating several additional parameters, which then may reproduce the history better and increase predictive capability. The present model highlights the effects of fishing effort on the population, which enabled us to find the best fishing strategy and to detect the overfishing period. Further refinement is necessary to obtain more precise MSC levels as well as required spawning stock levels. Improvement toward that goal may be possible when considerably longer data record becomes available. Therefore, monitoring should continue and in the meantime all available tools should be used to preserve the anchovy stock.
Acknowledgements This research has been supported by the Croatian Ministry for science, education and sport, EU-FP6 project on Ecosystem approach to sustainable aquaculture and the NorwegianCroatian PSSA project. We wish to thank M. Jusup for discusˇ for comments on the paper. T.L. is gratesions and T. Klanjˇscek ˇ c´ for discussions on the fate of anchovies ful to Dr. G. Sinovci in the Adriatic Sea. We are also wish to thank to the editor and reviewers for constructive suggestions and comments.
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