I was watching the show “Predator X” on the History Channel tonight. Apparently, they discovered this fossil of an enormous aquatic predator. It’s pretty awesome.

Here is a description of the bite force of this predator: (from here)
“At St Augustine Alligator Farm and Zoological Park in Florida , Dr. Hurum assisted evolutionary biologist Dr. Greg Erickson from Florida State University in calculating the bite force of this colossal creature. The jaws held in place a set of trihedral teeth, each measuring 12 inches, which clamped down on prey with an estimated 33,000lbs of bite force. The calculation is one of the largest bite forces ever calculated for any creature. Predator X would have had a bite a bite force was more than ten times the bite force of any animal alive today and four times the bite force of a T- Rex.”

(Here is a link of average bite forces for humans and a few selected animals.)

At this point you might be saying, “That IS awesome. But what does it have to do with this blog?” An astute observation. Well…

They estimated that the bite force of the predator was 33,000 pounds. The way they estimated this was by taking measurements of the bit force of different sized crocodiles (or alligators, I can never tell the difference.) Then they plotted the data in a scatter plot, weight of crocodile versus bite force. There was a clear postive relationship between bite force and size of the animal. Then they fit a simple regression line through the data and extrapolated how much bite force a 50 foot long animal that weighed an estimated 45 tons could pack in its bite force. That’s how I believe they came up with there estimated bite force. I’ll give them the benefit of the doubt and assume they did more than that to come up with the estimate but they didn’t want to show the details on the History channel. (If you have details on how they estimated the bite force, please send them my way.)

Let’s assume that all they did was extrapolate this simple regression line. What would be the problem with that? The problem is that they are extrapolating the linear trend outside of their domain. There is no guarantee that the bite force trend remains linear as the weight approaches the estimated 45 tons. They collected their data on animals with weight of crocodiles which can be up to 1.5 tons. It seems naive to assume that the linear trend will continue as you increase the weight of an animal.

Here is a simple example of why extrapolating outside of your domain is a bad idea.
Say you collected data of children’s heights and weights and you fit a regression line through the data. You’ll surely observe a postive relationship between age and height. As children get older, their heights generally increase. This increase can be approximated by a roughly linear trend say between the ages of 10-18. Also, say that we find that children grow on average of 1 inch per year between 10-18. If I were then to predict the height of a person by extrapolating out this trend I would assume that a 48 year old would be, on average, 30 inches taller than an 18 year old. Clearly, this is not true.

So just because a trend is linear over a certain domain does not mean that that linear trend continues outside of the tested domain.

Cheers.