Modeling Exponential Population Growth

Abstract

[ILLUSTRATION OMITTED] The concept of population growth patterns is a key component of understanding evolution by natural selection and population dynamics in ecosystems. The National Science Education Standards (NSES) include standards related to population growth in sections on biological evolution, interdependence of organisms, and science in personal and social perspectives (NRC, 1996). Organisms have the potential to achieve exponential growth under ideal conditions, yet sustained exponential growth is not found in nature. This observation is a cornerstone of the theory of evolution through natural selection (Mayr, 1982). Factors that limit growth can lead to evolutionary change in a population and can have profound effects on the interactions between organisms (NRC, 1996). To promote understanding of the concept of exponential growth, a set of activities was developed to engage students by integrating mathematical principles with the science concepts. Students explore the concepts of population growth by predicting the growth potential of a plant population. Understanding exponential growth in a population includes knowledge of population dynamics, the mathematical principles used to calculate growth over time, and the ability to interpret the graphical representations of population growth. To facilitate the calculation and representation of growth patterns, students use a graphing calculator. Graphing calculators allow the students to predict population growth trends when conditions change and to answer questions about the future growth potential of a population. Students then apply the concepts they have learned by predicting how human population will grow in the future if current population trends continue. Finally, students discuss limits to population growth in nature and consequences of these limits to population phenotypic structure. * Background The plant model used is the bell pepper plant (Capsicum annuum). Bell peppers are annual plants (Crockett, 1972) and the fruits are readily available in supermarkets. However, any annual fruit with multiple seeds can be used. Before beginning the activity, it may be necessary to briefly review plant growth and development. Include the fact that the seeds are the potential offspring and are found in fruits. Annual plants produce seeds that typically germinate the next year (or later), and the parent plant only survives one year. Some plants, including the bell pepper, can self-fertilize. Using an annual plant allows for simplifying assumptions to be made about the potential for population growth. Students can then develop their own equation to use in graphing the population potential over a number of years. In this model of plant growth, the assumptions are: 1. The peppers distributed to the class represent the fruits from one pepper plant. 2. The number of seeds in the peppers is the offspring of one pepper plant. 3. The number of seeds produced by every pepper plant in a population will be equal to the total number of seeds in the peppers counted by the class. 4. Conditions are ideal. There are unlimited space and unlimited nutrients to support growth. There is no plant predation or disease. Climate is stable and favorable for growth. 5. All the plants die at the end of the summer. 6. All seeds produced by the pepper plants will grow a plant the following year. 7. There is only one generation of pepper plants per year. 8. The number of plants at the inception of the population model is one. These assumptions allow the students to calculate and graph a simple population growth equation by eliminating survivorship of plants in the next generation. The death rate is assumed to be 100%. This activity has been used successfully in undergraduate biology courses for majors and non-majors, and graduate courses in science teacher preparation. …