The paper chase

“So what exactly are you doing?”

It seemed like nothing. Last week, it was reading papers, all of them about biology, some of them also about math. When I finished reading a paper, I wrote down a summary in a couple sentences of what I just read (usually I can’t do more than a handful of scattered points) and tried to relate the main points of the article back to my area of study, the mathematics of migration and selection. Then I would a break and drink some coffee. Then I would read another paper. I spent my first five days doing this in what computer coders call an “infinite loop”

Professor Lamar told me once that I should always have a bookmark folder on my browser for new papers to read. A really good paper will cite (or be cited by) other articles that relate to your topic, or at least pique your interest. These papers introduce you to the topic you are studying: why is it of interest? What does the problem look like? What tools are being used to study the problem? What limitations are there to studying the problem?

My long journey, at the end of one week, led me to the world of sources and sinks in a fragmented landscape. Imagine a bunch of ponds, and now imagine that frogs live in these ponds. Because some ponds are bigger than others and have more food and space (or fewer predators, maybe) some ponds will have more frogs in them than others. Maybe some ponds are too small to support any frog population. This “patchy” distribution of ponds makes a patchy distribution of frogs. Now imagine that the patches are close enough that frogs can move from patch to patch. Suddenly those ponds that are too small to support sustaining frog patches are receiving immigrants from nearby ponds; they are a “sink” for frogs. Similarly, the big patches with a lot of frogs, if they are close to other patches, may feed other patches when the frogs move out of the patch. These patches are “sources”

We can rewrite this story with grasses on mountaintops or ants in different rooms of my house or, most interestingly for me, birds in clumps of trees. Reading these papers about source-sink dynamics in the abstract or in the concrete has given me inspiration for a question: how does mercury affect the source-sink dynamics of the Shenandoah Valley birds? How do different dispersal behaviors and patterns affect these dynamics? If a source patch has some sort of toxic substance in it, it’s obviously bad news for the rest of the population, because there will be fewer migrants to inhabit the sink patches. There may be local extinction.

These can be modeled with matrices or partial differential equations. They can be simulated on computers or played with analytically. One can study a population with different age-classes. One can can study the effect of distance between patches on the health of the system, or the different configurations of patches on the landscape. But what nobody has done is study genetic changes on the network. This is what I will do, armed with tools that those before me have written about but with slight alterations to try to study a new problem. I’ve been spending this week actually putting pen-to-paper and doing maths to write down some greek letters and subscripts that actually make sense of this whole thing. If that can even be done. Because, I guess, that’s an option too.