MARS 4400-6400
MPA Exercise - Baseline
Fall 2015
Student Name: KEY
This exercise is worth 5 points out of 25 for project total. Email back to me by November 17.
Email to khyrenba@gmail.com using “MARS 6400 – MPA baseline” as the title.
1) Run one simulation for each species at a time, using the default settings and NO reserves.
For each simulation, report the trends in species abundance, yellow port total profits and blue
total profits as either: increase, decrease, remain stable. Illustrate each pattern, by pasting the
corresponding output figure below each of your answers.
Population size:
Yellow port total profits:
Blue port total profits:
Decrease (Fig. 1)
Decrease (Fig. 2)
Decrease (Fig. 3)
Species: Grouper (+1/2 point)
Fig. 1: Total population (Nt) of groupers in individuals over time of simulation (20 years).
NOTE: Because this simulation does not include reserves, no organisms are inside protected areas.
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MARS 4400-6400
MPA Exercise - Baseline
Fall 2015
Fig. 2: Total profit from grouper harvesting for yellow port in dollars over time of simulation (20 years)
Fig. 3: Total profit from grouper harvesting for blue port in dollars over time of simulation (20 years)
Species: Conch (+1/2 point)
Population size:
Yellow port total profits:
Blue port total profits:
Decrease (Fig. 5)
Decrease (Fig. 6)
Decrease (Fig. 7)
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MARS 4400-6400
MPA Exercise - Baseline
Fall 2015
Fig. 4: Total population (Nt) of conches in individuals over time of simulation (20 years).
NOTE: Because this simulation does not include reserves, no organisms are inside protected areas.
Fig. 5: Total profit from conch harvesting for yellow port in dollars over time of simulation (20 years)
Fig. 6: Time records of total profit from conch harvesting for blue port in dollars over time of simulation (20 years)
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MARS 4400-6400
MPA Exercise - Baseline
Fall 2015
Species: Lobster (+1/2 point)
Population size:
Yellow port total profits:
Blue port total profits:
Decrease (Fig. 7)
Decrease (Fig. 8)
Decrease (Fig. 9)
Fig.7: Total population (Nt) of lobsters in individuals over time of simulation (20 years)
Fig. 8: Total profit from lobster harvesting for yellow port in dollars over time of simulation (20 years)
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MARS 4400-6400
MPA Exercise - Baseline
Fall 2015
Fig. 9: Total profit from lobster harvesting for blue port in dollars over time of simulation (20 years)
2) Run the simulation again, and stop at these time steps to record the following data:
See the dataset created by combining the individual runs.
3) Read the Background document and respond to the following questions
(1/2 point each):
-
Briefly explain whether / how environmental variability is accounted for in this
model.
While there is no temporal environmental variability (e.g., demographic rates do not change,
there are no catastrophic events), there is spatial environmental variability which is apparent by
the heterogeneous landscape, with different habitats and suitabilities in the different cells.
The area is divided in sections (apparent when “suitability” is chosen for “base image of display”
with different types of habitats (coral reefs, seagrass beds, silt, mangroves) and unclassified cells
(land or deep water). Lobsters and groupers prefers coral reefs (i.e., cells of this type of habitat
harbor more individuals) and conches seagrass (i.e., cells of this type of habitat harbor more
individuals). Moreover, to add extra complexity to the model, these two general categories of
habitats are divided in more specific ones (e.g. coral reefs = dead coral and Microdictyon,
Montastraea reef; sea grass = sparse, dense) for a total of 16 types of habitat in the model.
All these specific habitats have been found to be inhabited by these species from the literature.
Mathematically the preference for each of these habitats is reflected by the parameter
“suitability” which ranges from 0 for unsuitable (no individuals of the species in that cell) to 1
for most suitable (highest number of individuals for the species in a cell). The suitability is
multiplied with fixed K (carrying capacity in a given cell) and thus modifies the carrying
capacity for each cell. Cells with 0 suitability have no individuals since carrying capacity is 0.
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MARS 4400-6400
-
MPA Exercise - Baseline
Fall 2015
Briefly explain whether / how stochastic variability is accounted for in this model.
Stochasticity is apparent in the model by the varying results when the same run is repeated using
the same parameter set. This stochasticity is achieved in two ways: (i) by using a searching
behavior of the predators (the fishing boats) based on probabilities and (ii) using dispersal rates
(% of individuals that move from one cell to another per day) that is also based on probabilities.
However, the logistic growth model applied to each cell does not incorporate environmental
stochasticity, since the parameters K, and r (lnλ) are constant over time. Furthermore,
demographic stochasticity is not accounted for either, since the probabilities of dying / surviving
are not varying probabilistically (i.e., a fixed proportion of the individuals in a given cell are
fished per unit time).
4) Read Appendix I (in Background) and respond to following questions
(1/2 point each):
-
Does fish population growth account for carrying capacity? Explain how this is
done.
Yes it does. The model treats every cell (x) individually due to the spatial variation in habitat
suitability. Therefore, the total population size at time t that we see in the graphs is Σpt(x) where
pt(x) is population size for cell x at time t (Σpt(x) = Nt). The logistic growth for cell x is shown
by the formula: gx(p) = -μ + r(1 – p/KH(x))
The content of the parenthesis is the equivalent of (1 – N/K) that we dealt with in our logistic
models so far. Here however carrying capacity is K*H(x) since it varies spatially as previously
mentioned with H(x) being suitability and ranging from 0 to 1 (K is the carrying capacity for the
best suitable habitats therefore). Also, despite intrinsic growth which is density-dependent in
logistic growth, some density-independent natural mortality is subtracted from the growth
(designated by letter μ) which is 1/lifespan, and therefore when p = K*H(x) => gx(KH(x)) = -μ,
showing a slight decrease and no stability as we have seen in our models (i.e. g(KH(x)) = 0).
-
Do fishing boats search randomly? Explain how their searching behavior is
modelled.
Randomness implies that each no-reserve cell has the same probability of being visited by a boat
in a day. However, this is not true for this model, since fishing boats follow a certain pattern
depending on the profit in one day from a cell x and according to certain probabilities: some cells
are more likely to be visited than others according to their profitability and their distance from
the starting cell (conditional probabilities). That allows for partial randomness since every noreserve cell has a chance (from lowest to highest) of being visited in a day.
The pattern is as follows: In a port (yellow or blue), if a boat’s profit in one day from cell x is
either negative (money loss) or less than 1/3 of the average profit from the other boats of that
port, then the next day this boat visits a random cell (the boats might change randomly cell
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MARS 4400-6400
MPA Exercise - Baseline
Fall 2015
independent of profit with a probability of 0.03, low chance of random behavior). If however the
profit is higher than 1/3 of the average, then the boat visits the same cell x the next day or one of
the non-reserve adjacent cells with the intent of maximizing profit (choice not random, the other
cell has to have high profit). The profit(x) therefore is a function of price of animal species
($/kg), average weight (kg), travel costs ($/km) and daily boat cost ($). That means the profit for
a boat can be higher if the boat chooses an adjacent cell with moderate catch than a distant cell
with high catch due to high travel costs as it goes from cell 1 to 2.
If profit in any non-reserve cells x is positive then the boat that day will choose among these
cells with a probability proportional to the profit, whereas if profit in all non-reserve cells is
negative it chooses a cell x with a probability proportional to exponential profit (eprofit(x) > 0).
Also, the total number of boats from one port is controlled during the simulation to prevent a
large loss of money due to negative profits and overfishing the population. Each boat has a
maximum number of boats. If during the simulation (at time t) at least two boats are working and
neither of those makes profit in that day, then one of these is removed from the simulation.
However, if the boats are not at maximum number, 1 boat is added when all the boats have at
least 50 $/day for at least 30 days. This way fishing effort is variable during the experiment.
The adjustment of the fishing effort of a port in this model allows for maximization and
perpetuation of potential profit, and prevents overfishing and depletion of the target population.
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