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Species Interactions in the Baltic Sea -An age structured model approach PhD Student Thomas Talund Thøgersen Purpose - To assess the biological and economic effects of an age-structure model approach, compared to a “traditional” approach. - To see the effects of species interaction in a bio-economic management model. - To compare the biological and economic effects of including different stock-recruitment relationships in bioeconomic models. More specific, this is done by: 1. Including an age structured module in the bio-economic management model “FISHRENT” 2. Including salinity as a proxy for environmental factors affecting the stock-recruitment relationship for cod 3. Include stochasticity in the stock-recruitment functions. Purpose The inclusions is not a purpose in itself!! Applied: The models should be generally applicable to fisheries within the EU waters. The data requirements should therefore not be more detailed than DCF. Flexible The models should be flexible so that the assessments can easily be applied to different multi-fleet and multi-species fisheries. Overview of presentation • • • • • • • • • • Theoretical background….will be skipped Characteristics of the Eastern Baltic Sea Overview of the fleets fishing in the Eastern Baltic Sea FISHRENT – A bio-economic management model Stock-recruitment relationships The age structured model Species interaction in the model Conclusions Where to go next? If time…show the FISHRENT model The Baltic Sea Characteristics: - Semi-closed Sea - Low salinity level - High nutrient levels due to many adjoining countries - Species poor Sea, but highly productive - Main species is cod (Gadus morhua), herring (Clupea harengus) and sprat (Sprattus sprattus) The ICES subdivisions of the Baltic Sea The Fishing Fleets of the eastern Baltic Sea The fleet is dominated by two types of vessels - Vessels with active gears (trawl or seine fishing). - Vessels with passive gears (nets, traps or longline) The cost structure of the vessel is assumed to depend on whether it is uses ACTIVE or PASSIVE gears. The cost structure is furthermore assumed to be dependent on the SIZE of the vessel Net and longline Typical small vessels such as the one - long line is often used for salmon fishery 7 m vessel using net and longline Demersal trawlers Specialized in catching demersal species, such as cod and flatfish. Pelagic Trawlers Specialised in catching pelagic species, such as sprat and herring. Purse seiners/trawlers Purse seiners are vessels equipped with a net long enough to surround the fish stock. Purse seiners are specialized in the catch of pelagic species such as herring and sprat, used for fish meal These vessels are typically equipped with both seine and trawl gear. Purse seining are not allowed in the Baltic Sea. Fishing Segments in the Baltic - Segments are merged by countries, that is believed to have the same cost structure. - Demersal and pelagic trawlers are merged, since this segmentation can be arbitrary. - The 10 economically most important segments are chosen - These segments account for 96% of the total catch of cod, sprat and herring in the Baltic Sea. Segment Country Trawl and seine12-24m DEU/POL 10 3% Trawl and seine12-24m DNK /SWE 53 18% Trawl and seine12-24m EST/FIN 10 4% Trawl and seine 24-40m DEU/POL 26 9% Trawl and seine 24-40m DNK /SWE 60 21% Trawl and seine 24-40m EST/FIN 45 16% Trawl and seine 24-40m LTU/LVA 19 7% Trawl and seine >40m DNK /SWE 40 14% Passive gears < 12m DEU/POL 8 3% Passive gears < 12m DNK /SWE 15 5% 287 100% Total Value Value share The value of cod, sprat and herring Cod Trawl and seine12-24m Trawl and seine 24-40m Trawl and seine >40m Passive gears < 12m I alt DEU/POL 8.8 5.4 1.2 4.6 20.0 DNK /SWE 41.3 16.2 3.8 14.0 75.4 EST/FIN 0.0 2.1 1.6 0.0 3.7 LTU/LVA 0.0 2.6 3.3 0.0 5.8 I alt 50.2 26.4 9.8 18.6 104.9 Sprat Trawl and seine12-24m Trawl and seine 24-40m Trawl and seine >40m Passive gears < 12m I alt DEU/POL 0.0 15.1 0.0 0.0 15.1 DNK /SWE 5.6 20.5 21.3 0.0 47.4 EST/FIN 1.9 14.9 0.0 0.0 16.9 LTU/LVA 0.5 11.8 1.1 0.0 13.4 I alt 8.1 62.2 22.4 0.0 92.7 Herring Trawl and seine12-24m Trawl and seine 24-40m Trawl and seine >40m Passive gears < 12m I alt DEU/POL 1.0 5.7 0.0 3.4 10.2 DNK /SWE 6.1 23.7 15.4 0.8 46.0 EST/FIN 8.5 28.3 0.0 2.4 39.2 LTU/LVA 1.7 4.4 0.2 0.0 6.4 I alt 17.4 62.2 15.6 6.6 101.8 All Three Species Trawl and seine12-24m Trawl and seine 24-40m Trawl and seine >40m Passive gears < 12m I alt DEU/POL 9.9 26.2 1.2 8.0 45.2 DNK /SWE 53.1 60.5 40.5 14.8 168.8 EST/FIN 10.4 45.4 1.6 2.4 59.8 LTU/LVA 2.3 18.7 4.6 0.0 25.6 I alt 75.7 150.8 47.8 25.2 299.4 FISHRENT MODEL The catches of species s taken by fleet f in year y is given by the following Cobb Douglas function: 𝐶𝑦,𝑓,𝑠 = 𝛼0𝑓,𝑠 ∗ (𝐸𝑦,𝑓 )𝛼1𝑓,𝑠 ∗ (𝐵𝑦,𝑠 )𝛼2𝑓,𝑠 ∗ (1 + 𝑡𝑃𝑓,𝑠 )𝑦−𝑦0 Where E=effort, B=biomass, tP=technical progress The effort can be determined in 3 different way, dependent on assumptions about fishermen behaviour management policy. Policy module: 1. Species quota limitations 2. Effort limitations 3. Free access. Quota limitations When quota limitations are used as a policy option, then the fleet quota share is: 𝑄𝑦,𝑓,𝑠 = 𝑇𝐴𝐶𝑦,𝑓,𝑠 ∗ 𝑇𝐴𝐶𝑠ℎ𝑓,𝑠 The effort needed by fleet f to catch this quota is given by (the inverse of the Cobb Douglas production function): 𝑞 𝐸𝑦,𝑓,𝑠 =( 𝛼0 𝑞𝑦,𝑓,𝑠 𝑓,𝑠 ∗(𝐵𝑦,𝑠 𝛼2 ) 𝑓,𝑠 ∗(1+𝑡𝑃 𝑦−𝑦0 𝑓,𝑠 ) )1/𝛼1𝑓,𝑠 Should the fisherman use the effort that catches all quotas fully or should he stop, when the the quota of the limiting species is caught?? Effort limitations In case of effort limitations, the effort needed to catch each target species s by fleet f in year y is, by the manager, set to: 0 𝐹 𝑠 𝐸 𝐸𝑦,𝑓,𝑠 = 𝐸𝑦−1,𝑓 ∗ 𝐹𝑦−1,𝑓 The same question: Should the manager choose to restrict the effort in a way that all quotas are caught (and some overfished!!) or should he limit the effort thereby preventing (mitigating) overfishing? Open Access The last policy option (or lack of it): Open Access 𝐸 𝑀𝐴𝑋 = 𝐷𝐴𝑆𝑓𝑀𝐴𝑋 ∗ 𝑁𝑉𝑦,𝑓 The number of vessels (NV) is given in the first year, but is allowed to change over time due to investment or disinvestment. This is applicaple regardless of the policy option It is assumed that the vessel will invest 10% of its expected profit over time or disinvest 10% of its loss over time. Summary Policy Options 1. 2. 3. 4. 5. Minimum effort to catch the quotas (fishermen decision) Maximum effort to catch the quotas (fishermen decision) Minimum effort limitations based on F (manager decision) Maximum effort limitations based on F (manager decision) Open access (effort is maximized in order to catch the most) Net Present Value Some quick and dirty economic considerations - Landings value is calculated as landings times fish price - Fish prices change as the landings changes - Fuel cost and other variable costs is a function of effort - Crew share depends on the landings value as well as the fuel costs - Fixed and capital costs depends on the amount of vessels - The number of fleets depends on the investments - The investments depends on the profit - The profit is landings value – (variable costs, fixed costs and capital costs) - NPV = sum of discounted profits over time Stock-recruitment models Ricker 𝑅 = 𝑆𝑆𝐵 ∗ 𝑒 𝑎−𝑏∗𝑆𝑆𝐵 Ricker with stochastic recruitment 𝑅 = 𝑆𝑆𝐵 ∗ 𝑒 𝑎−𝑏∗𝑆𝑆𝐵 ∗𝑟 Ricker with salinity as an environmental proxy 𝑅 = 𝑆𝑆𝐵 ∗ 𝑒 𝑎−𝑏∗𝑆𝑆𝐵+𝑐 (𝐸−𝐸) Beverton Holt R= a * SSB/(b + SSB) Berverton Holt with stochastic recruitment R= a * SSB/(b + SSB)*r Where r is a random number between 0.5 and 1.5 reflecting the stochastic recruitment variation in the past, 𝐸_bar is the average salinity level and a, b, c is estimated coefficients using non-linear regression in a way that minimize the sum of squared residuals Stock-recruitment model The five recruitment is calculated using nonlinear regression in a way that they minimize the sum of squared residuals. Maximum likelihood estimation is an alternative, and has measures to indicate if the regression results are robust - Akaike Information Criterion (AIC) - Bayesian Information Criterion (BIC) Age structured model The s stock of age a+1 in year y+1 is now calculated using the pope equation: 𝑆𝑎+1,𝑠,𝑦+1 = 𝑆𝑎,𝑠,𝑦 ∗ 𝑒 −𝑀1𝑎,𝑠 −𝑀2𝑎,𝑠 − 𝐿𝑎,𝑠,y ∗ 𝑒 −(𝑀1𝑎,𝑠+𝑀2𝑎,𝑠 /2) where M1 is the natural mortality and M2 is the predation mortality Where the landings of each age group for fleet f landing the species s in year y is: 10 L𝑎,𝑠,𝑦 = L𝑓,𝑠,𝑦 ∗ l𝑠ℎ𝑎,𝑓,𝑠 𝑓=1 Age structured model The spawning stock biomass of species s in year y is now calculated as: 𝐴 SSB𝑠,𝑦 = Sa,𝑠,𝑦 𝑎=1 Which is used to determine the recruitment for year y+1 Species interaction First attempt: Include a matrix containing the coefficients between the predator species at age and the prey species at age and multiply that with the abundance of species at age. Problem: - It does not exist !! - It will assume a linear relationship between species abundance and predation Three types of functional responses Type 1: Linear relationship between prey density and predator food intake Type 2: Marginal decreasing relationship between prey density and predator food intake (assumes that the food processing time is of importance) Type 3: Assumes that the marginal relationship between prey density and predator food intake is increasing at low densities and decreasing at high densities. This is explained by marginal increasing learning time (hunting efficiency) at low densities. Functional Response The number of herring and sprat eaten by one cod in age group a in one year t (or the functional response) is: 𝐶𝑎 (𝑁ℎ+𝑠 𝑡 )𝑛 𝑃𝑎 𝑡 = (𝑁ℎ+𝑠 𝑡 )𝑛 + (𝐷ℎ+𝑠 )𝑛 𝐶𝑎 𝑡 = Maximum consumption of herring and sprat eaten by one cod at age a in one year when the abundance of clupeids was at a maximum level. 𝐷ℎ+𝑠 = Half saturation constant (size of herring and sprat stock when the consumption was half of the maximum consumption) 𝑁ℎ+𝑠 = Population size of herring and sprat (in numbers) Functional Response The functional responses, i.e. the number of herring and sprat respectively eaten by one cod in one year, are: 𝑃ℎ,𝑎 𝑡 = 𝑃𝑎 𝑡 𝑁ℎ 𝑡 𝑁ℎ 𝑡 +𝑤𝑁𝑠 (𝑡) and 𝑃𝑠,𝑎 𝑡 = 𝑃𝑎 (𝑡) 𝑤𝑁𝑠 𝑡 𝑁𝑠 𝑡 +𝑤𝑁𝑠 (𝑡) w=preference coefficient for sprat compared to herring. Now, the predation mortalities for herring and sprat can be calculated: 𝑀2ℎ 𝑡 = 𝑁𝑐,𝑎 𝑡 ∗𝑃ℎ,𝑎 (𝑡) 8 𝑎=1 𝑁ℎ (𝑡) and 𝑀2𝑠 𝑡 = 𝑁𝑐,𝑎 𝑡 ∗𝑃𝑠,𝑎 (𝑡) 8 𝑎=1 𝑁𝑠 (𝑡) Conclusions - An age structured bio-economic model is constructed - Stochasticity in stock-recruitment has been added - Salinity has been added to stock-recruitment model - Lack of data to include ALL species interactions - Predation mortality for cod has been included. - The model is not as flexible as intended. This is a result of many area-specific relationships. - Results of comparing age structured models and species interaction models with the baseline non-structured model has not been performed yet…to be continued Where to go next - The literature has to be searched to find useful info to include the effect of cod, when the abundance of herring and sprat changes. - Fish prices should depend on the size of the fish. Lack of ambiguous relationship between age and size complicates this. - Estimate Maximum likelihood of stock-recruitments relationships instead of minimizing “sum of least squares” - Calculate useful Information Criteria - Include the increased variation of predicted climate changes in the recruitment models