Biologists develop and use mathematical models in order to more fully understand observed phenomena and to predict outcomes under different scenarios. Models are derived from theory and/or empirical data, but all useful models must incorporate real-world data. Mathematical models are particularly useful in the field of population biology. They can be used to predict population size at a specific time in the future, and to analyze the influence of the various components that make up the model. For example, population growth models are particularly helpful in analyzing the effects of age of first reproduction, total fecundity, birth rates, and death rates on overall population growth and age structure.
Your first experience with population modeling will involve the derivation of the exponential model through use of fruit fly population data collected from flies reared under conditions with unlimited resources and no predators. Next, you will analyze a number of empirical data sets and describe the type of growth exhibited by each population. Your task will be much easier if you plot each of the following data sets and attempt to find the best fit function for each data set. For each model discuss your rationale for choosing the independent and dependent variables (e.g., which variable is plotted on the X-axis and which variable is plotted on the Y-axis.) Also, if you can fit a curve to the data, please describe the type of function which best fits the data. If you can't fit a function to the data, describe the apparent trends in the data. Finally, you should describe the biological meaning/implications of the graph/model. Use MS Excel for graphical analysis and computational analysis (or similar spreadsheet software) to plot the data and produce printed graphs for each data set to accompany your typed narrative.
Last updated 9/10/04