Here’s an example about how maths is awesome, hard, but awesome!
Darwin’s finches have been a touchstone of evolutionary biology since, well, Darwin. These finches live on the Galapagos Islands off the coast of Ecuador and exhibit amazing variation in beak structure. The species of finches on the Galapagos have evolved to utilize a myriad of niches, from cracking hard seeds, to eating insects, to drinking blood (yes, this is creepy, and yes they are called vampire finches) and nectar. As you might imagine, a bird that needs to eat seeds will require different equipment than one that drinks blood. The variation in beak morphology mirrors the niches of these birds.
In PNAS this week (it’s really a cracker issue of PNAS, check it out) there is a paper that describes how all of these apparently wildly different beaks can be scaled into one basic beak type, and how these beaks are scaled relates to 1: their phylogeny (that is, their evolutionary relationship to one another) and 2: the expression of a particular gene during development (bmp4 or bone morphogenetic protein 4 for those of you who care).
Now there are a number of things that kickass about this paper. First, it’s the kind of paper that makes me wish I knew more maths. Second, it’s approachable enough that it allows me to maintain that tenuous hope that I can learn more maths and apply it to fantastic questions like this. Third, it bridges all kinds of stuff: theory, applied maths, genetics. Fourth, it has awesome figures. Finally, it offers some real insight into how these finches differ and how that could have changed. Now, here’s that pretty figure
It's a big figure, but be brave. It's worth it.