Tuesday, September 27, 2011

Columbia workshop, pre-pre-post

Note: a prelude to writing about two and a half days of math.

Much of ecology and evolutionary biology lives firmly in the world of small data[1] and the field has done quite well (thank you very much) with regression and [AN,MAN,AMO,ANC]OVA[2].  There's a pretty strong tradition of teaching good frequentist statistics and my own introduction to that, by Bill Bradshaw, was fairly complete (if a little brutal).  Bill's approach was to go step by step, and thoroughly cover the mechanics of each technique he presented. 

Bill's course had to be a little brutal because the mathematics requirements for biology are generally pretty low.  We biologists act as though algebra is frightening to students, linear algebra should only be brought up in passing and quickly swept under the rug, and calculus is beyond the pale.  Anyone who would like to avoid that general attitude is faced with the problem that most biology students are unprepared for moderately mathematical subjects.  Bill's solution was to go at it like his was the only course students had signed up for and expect everyone to keep up.  Much of the class looked something like this:
                               Figure 1: Bill Bradshaw leads the charge against the axis of evil (ANCOVA, ANOVA, and regression).
The general attitude Bill maintained was that you needed a solid statistical background to do ecology and there was no reason to doubt that a biologist could "get it".  Besides, as mathematically inclined[3] types are likely to tell you, the math you need to get into for the purposes of understanding basic statistics (in the mathematical sense), hardly counts as math. 
Figure 2: Peter Pappas says, "you see this?", "This is _NOT_ math."
The real barrier to introducing more advanced math to biology courses (you know, beyond spreadsheets) is that math builds on itself. As a biologist I might encounter it first in a population ecology book as matrix multiplication and my eyes would just conveniently glaze over until the little "eq. 1" on the right margin passes.  The fact is that a linear algebra class devotes significant time to simple mechanics and its not surprising that an untrained person will not just "get it" on the spot.  That means either raising the bar for course requirements or building the time for math into biology courses.  Unless your whole department is excited about raising standards, the second route is probably the only one that's open the an instructor.  You just have to go it alone.
Figure 3: The author, about to pwn calculus in front of an ecology class (without departmental support).

All this is to say that there's a gulf between biology and mathematics/statistics which is damaging to the quality of work in biology.  I think it also shows up in published work, but that's for another day (XKCD #303 only holds for so long).  I'm interested in advances in mathematics and statistics, and how they are relevant broadly to biology research (as well as my own work).  This led me to spend two and a half lovely days in NYC this past weekend attending a workshop at Columbia University which I intend to write about, once I've had the opportunity to digest the lectures a little more.

[1] Yes, I know, NEON will change everything, as will Data Dryad, etc...
[2] You know, it's robust to stuff.
[3] The word "inclined" should have been linked to Peter Pappas, Vassar College professor of mathematics who enjoyed referring to calculus/linear algebra/multivariate calculus as "trivial" and "not math", much to the dismay of his captives students.  Can't find him right now though.

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