Educational Model: Dependence of Animal Body Proportions on Body Size
The model makes it possible to understand allometric-growth patterns.
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 helps to understand patterns of allometric growth. The theoretical material related to the model is in the section "Size-Related Features of Organisms" of the manual "Ecology: Biology of Interactions". To begin working with the model, click the "Next" button. Instructions for working with the model are located at the very bottom of its window; if these instructions do not fit in the small box, they can be scrolled up and down with the arrows on the right. The model proposes studying the presence of a mathematical relationship between body length and body mass, as well as femur diameter, within one animal group: theropods (bipedal predatory dinosaurs). The model illustrates the use of mathematical operations to detect relationships: if a relationship is insufficiently clear on a regular scale, then after switching to a logarithmic scale, a simple linear relationship between variables becomes visible. Analysis of this linear function allows one to obtain a mathematical model used to solve the task of the exercise: estimating body mass and body length of fossil reptiles from a recovered femur. The theoretical information necessary for the study, as well as the work procedure, are described in detail in the corresponding sections of the model (opened by pressing the "Theory" button). In the left part of the working area there is a place to plot a graph; in the right part there is a table of known parameters of representatives of the studied group. Clicking the name of a dinosaur in the table displays its brief description and reconstructed appearance (to hide this description, click on it with the mouse). While holding the right mouse button on a table column, drag it to the graph-plotting area. Changing the graph scale from regular to logarithmic is done by checking the corresponding box. Some tasks that can be solved while working with the model: 1. To identify dependence between body length and mass, as well as femur diameter in theropods, build the necessary graphs and examine their character on regular and logarithmic scales. In the reference area of the screen, examine the obtained relationships. 2. Based on measurements of an unknown theropod femur, determine its mass and length. After performing mathematical calculations, determine the size of the dinosaur to which this bone belonged. While doing the work, strictly follow the instructions in the information area and the work procedure. 3. Apply the obtained relationship to any other bipedal dinosaur bone by entering its diameter values and performing calculations. You can verify calculation accuracy using parameters of known dinosaurs from the table. 4. Are similar relationships characteristic of other animal groups? Are the parameters linking body size and femur diameter identical for other animal groups?