Question

Could someone please explain the logistic growth equation. and how you would include a second species to it. Please provide an example of it.

Thanks in advance!

Answer 1

In logistic growth, per capita growth rate of a population gets smaller as the size of population approaches maximum, imposed by fewer and limited resources in the environment, that is known as the carrying capacity (K). Logistic growth produces an S-shaped curve.

Logistic growth equation:

During a population's growth, at any time the expression K−N denotes how many more individuals could be added to the population before they hit the carrying capacity. (K−N)/K is the fraction of the carrying capacity which has not been “used up" yet. More the carrying capacity which has been used up, more (K−N)/K will reduce the growth rate. In a small population, N is very small compared to K. Then (K−N)/K will become (K/K) = 1, similar as exponential equation. This fits with our graph, where population growth is exponential at first but it levels off continuously as it approaches K.

Ex: When grown in a test tube, Yeast can produce a classic S-shaped curve. Look at the graph below, where population hits the limit of the available nutrients, and yeast growth levels of. As the test tube is a closed system, that is fuel sources would run out eventually and wastes might reach toxic levels, yeast population would likely crash, if we follow the population for longer.

Addition of a second species may not affect populations which are below their carrying capacity, that is when resources are plentiful and every individual is capable to obtain what they need. But, if population size increases, intraspecific competition intensifies.