How Fast is Fast?

A recent finding by a group of undergraduate biologists received a great deal of media attention.   The  authors of the paper claimed that  a mite, Paratarsotomus macropalpis, is the fastest animal because it can move the fastest in terms of body lengths per second. The article was published  as a supplement  to The  Federation  of American  Societies for Experi- mental Biology Journal, Samuel Rubin, Jonathan Wright, Maria Young, Dwight  Whitaker, and Anna Ahn, Exceptional locomotory performance in Paratarsotomus macropalpis mites (878.1), April 2014 (28).

This one measure of speed may not be the best way to compare animals of vastly different sizes. For example, if you were to scale a mite up to a larger size, its mass will  not change in the same proportion as  its length.  The same is true for its area as well as its energy requirements.  Because of these considerations  we ask you to consider other ways to compare the  relative speeds of different animals. In particular construct comparisons between the aforementioned mite, a cheetah,  a person, and at least one other animal whose length is between that of a mite and a cheetah.

Your comparisons should include three parts. First, using the approach adopted in the paper cited above construct a model that  can be used to compare the relative speeds of different animals. The model should take any animal, scale the animal to a common  size, and then predict the speed of the animal if it were scaled to the predetermined,  common size. Use the four animals described above to make comparisons.

Secondly, extend the modeling in the first part to determine the relation- ships between physical quantities such as mass, area, and any other quantity you think is important with respect to a single length scale.  Use the model to determine another way to compare the relative speeds between  the four animals that provides a better comparison. You should make a case as to why your model is better than what was used in the paper.

Finally, once you have established a method to compare top speeds be- tween  animals extend your model to compare the long distance migration patterns of various animals. Use your model to compare pacific humpback whales, monarch butterflies, wildebeest, and at least one other animal species.

Problem written by Kelly Black, an associate professor in the department of mathematics at Clarkson University.