The fact that we are not over run with pachyderms means that something eventually puts the breaks on unrestrained growth. Taking our bacteria in a bottle as an example, sooner or later they are going to run out of nutrients; the availability of food becomes a limiting factor. Bacteria also produce waste products of their metabolism. These waste products are slightly toxic, and as more and more bacteria produce more and more wastes, the accumulation eventually reaches a level that inhibits the very bacteria that are producing them. Once again, growth must slow down and eventually stop.
The lack of food, or the production of waste can both stop a population growing. How much food is left, or how much waste is produced is, in turn, strongly influenced by the number of consumers and producers. The more bacteria we have growing in a bottle, the more food they will be consuming and the more waste they will be producing. These limiting factors are therefore directly related to the number of bacteria in the bottle at any one time. They are called density dependent factors, because they depend on the number and proximity of the individuals in any given population. One thousand bacteria in one thousand liters of nutrient don't have a density problem, but one thousand bacteria in only one liter of nutrient will soon run out of something.
In this next simulation, the growth of the bacteria is restrained by a density dependent factor (we don't know what). This limits the extent to which the population of bacteria can grow. As the bacterial growth slows down the population reaches a limiting size which it cannot exceed. This maximum size is called the carrying capacity of the population under these circumstances. Carrying capacity is a useful way of summarizing and visulizing the net effect of density dependent factors that limit population growth. In this simulation the user is able to set a carrying capacity for the population under study and the observe its effect on the growth of that population.
Once again the best way to see the effects of such denstiy dependent factors on unrestrained growth is to use the simulation to give numbers of individual bacteria over a range of time values and then plot the results on a graph. In this way it is possible to examine;