Scaling laws in biology

I should be asleep now, but I've been working on a statistics problem set, and the program is going to take a couple hours to run my power analysis. So plenty of time por bloguear.

As a graduate student on an NSF Education Fellowship, I work two days a week in a middle and high school in rural Michigan, trying to "integrate ecological literacy into the school curriculum" and generally offer support to science teachers. Sometimes I teach lessons, and sometimes I support teachers by spurring class discussion, team-teaching and so forth. I had a good time a few weeks ago teaching ninth-graders about osmosis by dunking potato slices into salt water of various concentrations, and seeing if they increased or decreased in mass. The kids liked that activity although they were kind of distracted and amused by the fact that the potato cores looked like French fries- some of them tried to eat them. If any of you are school teachers and want to share suggestions for science activities, write me.

Another activity that I did the week afterward was quite interesting. It was in a high school Ecology class (the high school offers ecology as a high school science elective, which is pretty cool for such a small rural high school). I was talking about survival vs. reproduction tradeoffs, R vs. K selection and so forth (which is kind of nice because it ties directly into my research, and I had a couple slides about my research). This is an "inquiry based" class so I needed an activity to go along with it, so what I did was have the kids see if there was a relationship between an animal's life span and its average yearly number of offspring. I picked seven mammals that I thought they would find interesting (to reduce taxonomic variability)- shrews, dolphins, elephants, gorillas, porcupines, black bears, and white-tailed deer, picking somewhat randomly off the top of my head. The lifespans I got from the all-powerful Wikipedia oracle, and the birth rate data from actual scientific papers to the extent possible. I had the kids calculate birth rates from the data (number of offspring, number of adult females, number of years in the study) and then get the average.

I didn't have them graph the results, but just for my own private interest, I made an Excel chart plotting the common log of annual birth rate over the common log of life span. As a side note, I use natural logs as much as the next man for anything involving the slightest bit of calculus, and for solving differential equations and that sort of thing. But for simple graphs, regressions, and transformation of variables, I much prefer common logs (base 10) or binary logs (base 2), or even logs in a rather arbitrary base 1.5. Maybe this is just me being contrarian and reactionary. But I find it much easier to do mental calculations, and to interpret results, when I know that a difference of one unit means an increase of a factor of 10, or a doubling, or a 50% increase. A difference of two unit resulting in a 739% increase is just not intuitive to me. Binary logs, all the way.

Anyway.....I got a perfect line with an R-squared of 0.99....that means almost perfect fit. With seven points, it's very impressive. Physiological theory suggests that life span and birth rate should be inversely related- and they are, almost perfectly, even for seven species I chose pretty much at random. The slope wasn't perfect- it was -1.5 instead of -1. Still, that's pretty amazing....it shows how powerful some very simple scientific theories can be, even in a field as messy as mammalian biology. You can look at some truly outlandish examples of what life does in response to its environment.....but some basic but inexpicable and ubiquitous patterns bind them all together.

Enough for tonight. I'll post more tomorrow.