A population is a group of individuals of the same species. In our earlier discussions, we have focused on one characteristic of populations - their tendency to change genetically over time. Now, we would like to look at the other main feature of populations - their tendency to increase in size. Biological populations grow in a way that can be described by the equation on page 630 of your text: G = rN, where N is the number of individuals in the population, r is the net rate of increase in new individuals per existing individual per unit time, and G is the net number of new individuals produced by that population over the time specified. In the absence of limiting factors, populations grow exponentially (see figure 35.2). This means that the population has a doubling time. In the example in your text, looking at the table of numbers shows that the doubling time is about two months.

Nevertheless, we know that no population can go on increasing is size indefinitely. Limiting factors always slow, stop, or reverse the rate of population increase. Limiting factors may be density dependent, like those that set a carrying capacity (amount of space or suitable habitat, availability of food or water, accumulation of waste) or other density dependent factors like disease and parasitism. Alternatively, limiting factors may be density independent, like unexpected weather or sudden environmental change. Some organisms, notably those that are well adapted to sense and respond to the environment (bacteria, for example) show logistic growth (figure 35.3). As resources are used up, these populations slow and finally stop their growth so that numbers of individuals are almost exactly at the carrying capacity.

Complex organisms tend to overshoot the carrying capacity and experience devastating crashes in numbers like the one shown in figure 35.4. Human population has or is about to overshoot the carrying capacity (figure 35.7). During the last 300 years, human population has entered a period of unrestricted growth. In the past, humans were limited by suitable habitat, carrying capacity imposed by natural systems, and density-dependent controls like disease. Since the beginning of the industrial revolution, almost all available space has been converted to human use, while advances in medicine and in the ability to use energy to increase agricultural production have temporarily removed restrictions on the size of the human population. We know this is a temporary situation because no population can continue to double forever. Currently at six billion individuals, the human population certainly cannot support even two more doublings (about 100 years at current rates of increase). In fact it is probable that the carrying capacity has already been exceeded, in view of the tendency of humans to increase their demands on resources.

Some countries, notably China, have begun to impose controls on fertility (number of children per family). Note that this is a long term solution - in a rapidly growing population, fertility controls take at least two generations to take full effect. Reducing the fertility rate is the only alternative to a dramatic increase in the number of deaths. Some populations are not able to reduce their fertility rate because of religious objection to birth control or other cultural reasons. These populations are the most at risk for a crash in numbers as population exceeds carrying capacity.