Simple Population Growth Equations

 

Density-independent growth - In some cases, populations may invade a new habitat which has abundant resources. For a while at least, these populations will grow rapidly because the initial number of individuals is small and there is no competition. This is called density-independent growth because the density of individuals does not have any effect on future growth. As you can imagine, this cannot continue indefinitely.

Take the equation below and run through 10 generations. Start with a population size (N) of 100, and use a constant growth rate (r) of 0.5 (A growth rate of 0 indicates no reproduction and no change in number so no population growth will occur). N is the change in number. Add N to the initial N and then run through the equation again. We will say that each time you run through the equation, a new generation is born but the old individuals continue to live. Graph your results below.

 

N=rN

 

Density-dependent growth - In a population that is already established, resources begin to become scarce, and competition starts to play a role. We refer to the maximum number of individuals that a habitat can sustain as the "carrying capacity" of that population.

 

N=[rN(K-N)]÷K

 

Take the equation above and again run through 10 generations. Start with a population size (N) of 100. Use a constant growth rate (r) of 0.5 (A growth rate of 0 indicates that no reproduction is occuring and therefore no population growth will occur). K is the carrying capacity of the population, which we will set at 130. N is the change in number. Add N to the initial N and then run through the equation again. We will say that each time you run through the equation, a new generation is born, and again, we are assuming no death of individuals. Graph your results below.