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Learning Goals
By the end of this reading you should be able to:
- Describe the conditions in which exponential growth might occur
- Calculate the intrinsic and maximum growth rate of a population
- Explain the relationship between logistic growth and carrying capacity
- Describe how intraspecific competition can impact population growth
- Predict the effect of changing environmental conditions on population growth
Introduction
Life histories describe the way many characteristics of a population (such as their age structure) change over time in a general way. However, there are other factors, including environmental conditions that impact the rate that a population can grow. When resources are unlimited (or in many cases just readily available) populations can often grow at very fast rates and in an exponential manner. When resources becoming limiting the rate of growth usually begins to slow and in some cases the population may actually begin to decline. Scientists have developed some models that help to predict the growth of populations based on the life histories of organisms and the environmental conditions. However, these models are only predictors and newer more complex models are constantly being built to take into account new or changing factors.
Exponential Growth
Charles Darwin, in his theory of natural selection, was greatly influenced by the English clergyman Thomas Malthus. Malthus published a book in 1798 stating that populations with unlimited natural resources grow very rapidly, and then population growth decreases as resources become depleted. This accelerating pattern of increasing population size is called exponential growth.
The best example of exponential growth is seen in bacteria. Bacteria are prokaryotes that reproduce by binary fission. In some species of bacteria the time between bouts of binary fission can be as short as 60 minutes, and in some species even as quickly as 20 minutes. Consider this, if 1000 bacteria can divide every 60 minutes are placed in a large flask with an unlimited supply of nutrients (so the nutrients will not become depleted), after an hour, assuming each individual divides, there will be 2000 organisms—an increase of 1000. In another hour, each of the 2000 organisms will divide, producing 4000, an increase of 2000 organisms. After the third hour, there should be 8000 bacteria in the flask, an increase of 4000 organisms. The important concept of exponential growth is that the population growth rate—the number of organisms added in each reproductive generation—is accelerating; that is, it is increasing at a greater and greater rate. After 1 day and 24 of these cycles, the population would have increased from 1000 to more than 16 billion. When the population size, N, is plotted over time, a J-shaped growth curve is produced.
The bacteria example is not representative of the real world where resources are limited. Furthermore, some bacteria will die during the experiment and thus not reproduce, l