In this activity, students develop a model of the mathematical nature of population growth. The investigation provides an excellent opportunity for consideration of the population growth of plant and animal species and the resultant stresses that contribute to natural selection. This activity will require two class periods and is appropriate for grades 5 through 12. The activity is based on an original activity from the Earth Science Curriculum Project. It is used with permission.14
This activity provides all students an opportunity to develop understandings about scientific inquiry and biological evolution as described in the National Science Education Standards. Specifically, it conveys the following concepts:
Mathematics is essential in scientific inquiry. Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations, and communicating results.
Species evolve over time. Evolution is the consequence of (1) the potential for a species to increase its numbers, (2) the genetic variability of offspring due to mutation and recombination of genes, (3) a finite supply of the resources required for life, and (4) the ensuing selection of those offspring better able to survive and leave offspring in a particular environment. (Item 1 is the primary content emphasis of this activity. Teachers can introduce the other factors as appropriate.)
Populations grow or decline through the combined effects of births and deaths and through emigration and immigration into specific areas. Populations can increase through linear or exponential growth, with effects on resource use and on environmental pollution.
Populations can reach limits to growth. Carrying capacity is the maximum number of organisms that can be supported by a given environment.
Living organisms have the capacity to produce populations of arbitrarily large size, but environments and resources are finite. This fundamental tension has profound effects on the interactions between organisms.
The tension between expanding populations and limited resources was a fundamental point that Darwin came to understand when he read Thomas Malthus.15 This understanding subsequently had an important influence on the formulation of his theory of natural selection.
This activity extends the general idea of population growth to humans. Here the important point is that human beings live within the world's ecosystems. Increasingly, humans modify ecosystems as a result of population growth, technology, and consumption. Human destruction of habitats through direct harvesting, pollution, atmospheric changes, and other factors is threatening current global stability, and, if not addressed, ecosystems will be irreversibly affected.
The increase in the size of a population (such as the human population) is an example of exponential growth. The human population grew at the slow rate of only about 0.002 percent a year for the first several million years of our existence. Since then the average annual rate of human population has increased to an all-time high of 2.06 percent in 1970. As the base number of people undergoing growth has increased, it has taken less and less time to add each new billion people. It took 2 million years to add the first billion people; 130 years to add the second billion; 30 years to add the third billion; 15 years to add the fourth billion; and only 12 years to add the fifth billion. We are now approaching the sixth billion.
Each group of three or four students will need: