Transcript Skabelon

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
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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