To begin, Allometry is the growth of portions of the body at different rates. In order to have a negative allometry, one body part should continue to increase, while another part of the body begins to decrease. To have positive allometry there should be two body parts that increase over time together.
After completing the Desmos activity there is an example for both negative and positive allometry. The example of a positive allometry is the fiddler crab claw size was compared to its body growth over time. Which was positive being that the claw and body both increase in size as it matures? The example for negative allometry is a human’s head and body growth. Given that the head of a baby’s head is bigger than it’s body, as the baby matures the head shrinks and the body grows.
An example of a power function used to depict allometry is the power function formula f(x)=kx^p. An example of this formula working in an allometry scenario is the growth of a body and its metabolism. For this creature, the formula used to figure if it is a negative or positive allometry is 4.14(x)^0.66= M(b) (for the growth of the metabolism) and M(b)/x= y (for the growth of the creature’s body). This creature is an example of negative allometry. Because of the metabolism increases, while the body decreases over time. Here is the formula plugged in with numbers 2 &3 below…
4.14(2)^0.66 = 6.54154206223
6.54154206223/2 = 3.27077103111
4.14(3)^0.66 = 8.54870575972
8.54870575972/3 = 2.84956858657
What other examples can you find for allometry? Is the example a negative or positive example of allometry?