Educational Model: Bergmann’s Rule

This model is a component of the IUMC (Innovative Educational and Methodological Complex) "Ecology: Constructing the Biosphere", developed in 2008 by D. A. Shabanov, A. G. Kozlenko, and M. A. Kravchenko by order of the NTFP (National Training Foundation) of the Russian Federation (more about this project is in the article "Innovation and Reality"; reasons why this complex is not used are briefly described in the column "Textbooks: Straight into the Day After Tomorrow"). This model is posted here for educational use. The model explains the zoogeographic Bergmann’s rule. The theoretical material related to the model is in the section "Clinal Variability and Some Ecological Rules" of the manual "Ecology: Biology of Interactions." A similar model covers Allen’s rule. Bergmann’s rule shows the relationship between habitat conditions and body size in homeothermic animals. The mathematical model allows estimation of the ratio between heat production (proportional to body volume) and heat loss (proportional to body surface area). The higher this ratio, the easier it is for an animal to maintain constant body temperature in a cold environment. Instructions for working with the model are located at the bottom of its window; if they do not fit, they can be scrolled using the arrows on the right. The first page explains the essence of Bergmann’s rule. The second page contains a calculator for computations. Selection of compared animal sizes is done by checking the corresponding boxes. After completing the calculations, indicate which animal can maintain constant body temperature more easily. Study the mathematical model by choosing two model animals for comparison. Enter values of surface area and volume for both selected animals into the corresponding cells. To calculate area and volume, use the gridded figures shown next to the calculation table. If you enter the correct area and volume values, a computation appears showing the ratio of these parameters for that animal. Note: if the model considered a cubic animal with linear dimension 2a, its surface area would be 24a² (a cube has 6 faces, each with area 4a²; 6×4=24), and its volume would be 8a³. Based on the volume-to-surface-area ratio (proportional to the heat-production/heat-loss ratio), choose which organism is better adapted to low-temperature conditions.