These fish live in a world of fish bowls. Each bowl Fish

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BLUE FISH AND GREEN FISH
This is a model of some features of a society of fish.
in a world of fish bowls. Each bowl is connected by a
holding tank, but the bowls are not connected directly
The fish go through life choosing mates, choosing fish
food, eating, and reproducing more fish.
Fish:
These fish live
fishway to a
to each other.
bowls, producing
Each fish has three (relevant) attributes that do not depend
on any action taken. (1) Age.. Each fish is born with an age of
zero and ages one day each day until death. (2) Cleverness. Each
fish is born with a certain cleverness (the initial population has
cleverness normally distributed with a mean of 100 and a standard
deviation of 10). (3) Color. Each fish is either blue or green.
Some of the blue fish are dark blue; some of the green fish are dark
green.
Couples:
Fish sometimes form couples. Each couple involves one blue
fish and one green fish. A couple is formed only if such an action
increases the food intake of both fishes; a couple is broken only
if breaking it increases the food intake of both fishes. Coupling
changes fish life in three ways: (1) The couple shares equally all
of the food obtained by either fish. (2) Being in a couple provides
a food bonus of 20% for blue fish, a food tax of 20% for green fish.
(3) Only fish who are coupled can reproduce.
Fish Bowls: There are a number of fish bowls and a holding tank connected to each of them. Fish that are in the holding tank can
swim into any of the fish bowls. Fish in any fish bowl can swim
into the holding tank. (Note: Fish that are coupled do not have
to be in the same pool.) The rules fish use to swim into bowls
or the holding tank depend on whether their colors are dark or
light: Dark blue and dark green fish always swim to (or stay in)
the available bowl (or tank) that has the highest proportion of
fish of the same color (i.e., blue or green). Light blue and light
green fish always swim to (or stay in) the available bowl (or tank)
in which the average amount of food obtained by fish of the same
color (before couple sharing, bonuses, or taxes) is greatest
currently.
Food Production:
The food in a fish bowl is produced by the fish in
that bowl. In the holding pool each blue fish produces 6 units of
food per day; each green fish produces 5 units. In the fish bowls
each blue fish produces 10 units a day; each green fish produces
7 units. Food produced in this way is deposited on the floor of
the bowl in a common supply for the bowl (or tank).
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Blue Fish and Green Fish. Page 2
Eating; The fish in each fish bowl (and the holding tank) divide the
food produced among themselves. In the holding tank the food is
divided equally among all fish in the tank. In each fish bowl,
however, the divisions are unequal. Each fish has seniority
depending on the number of consecutive days it has been in the bowl.
The food is divided among the fish so that each fish receives an
amount that depends positively on both its seniority and its
cleverness.
Once the food in each bowl and in the holding tank has been
divided, each blue fish that is in a couple receives a 20% addition (self-produced); and each green fish that is in a couple
receives a 20% reduction ( self -destroyed ) Then each fish that
is in a couple gives one-half of its food to its mate.
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Reproduction:
Only couples reproduce. Each couple produces one new
fish for the holding tank each day, provided neither the blue fish
nor the green fish is more than five days old. Each new fish has
an age, cleverness, and color. The age for each is zero. The
cleverness is either equal to the cleverness of the blue parent or
the cleverness of the green parent (with equal probability). The
color is either the same as the blue parent (including the degree
of darkness) or the same as the green parent (with equal probability).
The two probabilities are independent; thus it is possible for the
new fish to have the cleverness of one parent and the color of the
other.
Mortality: Fish die. Death rates are a joint function of age and food
intake. The older the fish the higher the chance of death (holding
constant food intake). The less the food intake the higher the
chance of death (holding constant the age). Age is, however, the
more significant factor; and the probability of a fish living
beyond the tenth day of life is zero. There are no differences in
mortality due directly to color, cleverness, or location.
In order to start the model a population of fish with particular attributes,
locations, combinations into couples, and food intake must be established.
The following suggestions are given to simplify life, but it might be well
to explore the extent to which the results depend on the initial conditions.
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Blue Fish and Green Fish, Page 3
(a) 100 fish allocated to four bowls and one holding tank with
20 fish in each.
(b) Fish atrributes (independent):
age
distribution over
-- rectangular
0 to 9 days
cleverness
color
the range from
distribution with mean = 100 and
— normal
standard deviation = 10
dark blue = 30
-- light
blue = 20
dark green = 10
light green = 40
location
— random
coupling
-- pair
(randomly) 40 of the blue with 40 green