Living Graph: Exploring the effects of scale

In this exercise we imagine a scaling relationship among two aspects of an organism using the equation $y = {b x}^{a}$ We will let $x$ be the linear dimension of the organism and $y$ be some aspect such as metabolic rate, length of a limb, or surface area. You can vary the allometric relationship between these variables from negative allometry $(a << /mo>1)$ to positive allometry $(a > 1)$ . For each value you choose for $a$ , the graph will depict the relationship between $x$ and $y$ as well as the relationship under isometry $(a = 1.0)$ . You may also choose the value of the constant $(b)$ .

Choose a value of a less than 1.0. Examine the effect on the graph.
Choose a value of a greater than 1.0. Examine the effect on the graph.
Set $a = 1.0$ and examine the graph.

Range of x :

Value of constant (b) #1

Allometric relationship #1

Value of constant (b) #2

Allometric relationship #2

To compare two populations over the same range of X, please enter values above. Click the items in the legend to hide or display the corresponding plotted points. Explore the plotted points by hovering over them with your cursor; you can zoom in on a section of the graph by clicking and dragging. When zoomed-in, you may explore the timeline by dragging the scroll bar at the top of the graph. Reset the graph by clicking "Show all".