A Model for Population Growth

initial population

y

0

0.1

growth rate r

0.15

carrying capacity M

4

This Demonstration models population growth over time given the initial population, the growth rate, and the carrying capacity in the biome. The carrying capacity depends on limiting factors that may involve, among other things, the amount of biomass available to the population, predation, and environmental stresses. The model can be represented by the equation

y

t

=M/(1+(M/

y

0

-1)exp(-rMt))

, where

y

is the size of the popuation,

t

is time,

M

is the carrying capacity, and

r

is the growth rate. In all cases, a constant, steady state population is eventually reached.

Details

This Demonstration was written in Making Math.

Special thanks to the Netmath Program at the University of Illinois at Urbana/Champaign and the Math Department at Schaumburg High School.

References

[1] N. Campbell, J. Reece, and L. Urry, Biology AP Edition, 8th ed., San Francisco: Cengage, 2008.

External Links

An Intra-Population Imitation Model in the Two-Population Hawk-Dove Game

Modeling World Student Populations

Continuous Exponential Growth

Permanent Citation

Samer Hassan, Joey Espino

"A Model for Population Growth" from the Wolfram Demonstrations Project http://demonstrations.wolfram.com/AModelForPopulationGrowth/
Published: June 13, 2014