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mathematical population growth models

Message 335

From: raeky
Date: 2002-01-25 21:20:41


To determine the rate of change in population size, we must take into account the time interval involved, that is, the change in time.

\tchange in N/change in t = b - d

N = number of animals
t = time
b = number born
d = number died

This is called the growth rate (r). thus r is change in animals divided by change in time.

\tr = b - d

if r is a positive value that means that there are more animals being born then dieing, thus the population will increase, if its negative then more are dieing then being born, so the population will decrease.

What should be decided on is if you want to allow a species of animal to go extinct in majik. If not then you can bump up the birth rate to match the death rate when ever the population number (N) drops below some preset unacceptable level.

Then in contrast you also need to decide on what is the physical limit the area the animals are living in can support them, how many can be alive at once before they eat
all the available food and start dieing off.

Also migration and emigration needs to be discussed. can animals move from one area to another and if so that will effect the growth models, and available food.

\tr = (b - d) + (i - e)

r = growth rate, same as above
b = number born
d = number died
i = number immigrated
e = number emigrated

The maximum number of animals that can be supported in an area would need not to be species specific but food source specific, if 10 species all eat the same plants then the population of all 10 species will need to be limited. Possibly by bumping up the birth rate of predators that eat the plant eaters, or by just causing them to die off.

Kass Lloyd, AKA Raeky