NetLogo User Community Models

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## WHAT IS IT?

This model explores the stability of a dynamic open access fishery.

## HOW IT WORKS

Fish grow based on the classic growth function. Fish are discrete. With discrete fish,
the number of new fish are randomly spawned from existing fish, where the number of fish
that have offspring is

growth * count(fish) * (1 - count(fish) / carrying capacity)

with the maximum number of spawned fish being the number of existing fish. Thus, this is a fish species that has one offspring per season. The fish live for a number of periods
and then die. They also die if they are caught.

Boats catch fish, with the number of fish caught being

catchability * count(fish) * count(boats) / carrying capacity

with the maximum being the total number of fish. The fish caught are randomly selected,
and caught by the nearest boat. That boat earns the income from the sale of the fish,
which is added to the savings for the boat.

Each season, the boat pays its financing cost, which is the value of the boat multiplied by the finance cost. This is analogous to interest paid on the loan to purchase the boat. This payment reduces savings. The savings retained earn interest at a rate that
can be adjusted separately from the boat financing cost.

## HOW TO USE IT

1. Adjust the slider parameters (see below), or use the default settings.
2. Press the SETUP button.
2. Press the GO button to begin the simulation.
5. Look at the monitors to see the current number of fish and boats
6. Look at the Fish and Boats plot to see how the size of the fish stock and the
number of boats in the fishing fleet fluctuate over time

Parameters:
FISH-INITIAL-NUMBER-SHEEP: The initial size of fish stock
FISH-CARRYING-CAPACITY: The carrying capacity of the fish stock
FISH-GROWTH: The scaling parameter for the fish growth function
FISH-LIFESPAN: Number of periods fish live, if not caught
FISH-PRICE: The revenue a boat earns from catching a fish
BOATS-INITIAL-NUMBER: The initial size of the fishing fleet
BOAT-CATCHABILITY: The scaling parameter for the harvest function
BOAT-VALUE: The value of the boat, and cost of a new boat
BOAT-FINANCE-COST: The cost per season for financing the boat
BOATS-LAUNCH-THRESHOLD: The threshold multiplier for the amount of savings needed before a boat is launched

## THINGS TO NOTICE

The system, from its initial values enters limit cycles. Given that the fish and boats are discrete units, it would be very lucky if the system could converge onto a precise steady state.

## THINGS TO TRY

Explore the impacts of changing the model parameters. It is possible to find arrangements where the fish population goes extinct, and where there is insufficient profit earned and the fishing fleet goes to zero.

## EXTENDING THE MODEL

1. Schooling fish. If fish school, then boats closest to the school will catch the most fish. Will schools form, be fished down, and new schools emerge elsewhere? Will it be easier to drive the fish to extinction if they school?
2. Fish finding by fleet. Let the boats move in the direction of the highest concentration of fish. What happens if this is combined with fish schooling.
3. The opposite of these. Fish dispersal and/or fleet dispersal.
4. Add an underlying resource that the fish eat. This resource could be impacted by fishing pressure. Something like bottom trawling. If it takes time for the fish food to recover, then it will take time for the fish to recover. What sort of limit cycle behavior will emerge?
5. Don't wrap the world. Have the fish in a pond, confined by the boundaries of the pond.

## NETLOGO FEATURES

In contrast to the typical bioeconomic models, this is an experiment with discrete fish and boats.

## RELATED MODELS

The basic design is similar to the Wolf and Sheep model and its variants, a system defined by two interacting dynamic processes.

## CREDITS AND REFERENCES

Based loosely on the ideas in Bjørndal, Trond, and Jon M. Conrad. "The dynamics of an open access fishery." Canadian Journal of Economics (1987): 74-85.

## HOW TO CITE

Janmaat, J. (2022) Netlogo Open Access Fishery Model.

## COPYRIGHT AND LICENSE

Copyright 2022 John Janmaat.