When I wrote this, back in the before times (when graduate school seemed more like the Elysian Fields than it did a ravine full of a pile of dead Sisyphus impersonators), I honestly thought it was a somewhat strained analogy. Bacterial genomes were, I knew, somewhat prone to self-stabilizing. That seemed sort of like the right thing to map onto a matrix, with the eigenvectors being forces that act on it. But there's no really snappy way to refer to, specifically, a matrix that is part of a system with a set of eigenvectors and eigenvalues, so I twisted the metaphor, slapped the nice eigenvector label on it, and sort of let it go, like the shower thought it was.

But now, having long-since fled the ravine and all its boulders, I'm not so sure I was wrong. The piece missing, I think, from my understanding of the model was the supraorganism—not the extreme Gaia hypothesis one, but rather the notion that every bacterial community is also an economic community. Within it, undirected evolution plays games with itself: Red Queen (constant adaptation is required to retain balance), Black Queen (growth is maximized by outsourcing burdens, thereby encouraging cheating in symbiosis), and even some amount of border control and protectionism (niche-specific antibiotic + antibiotic resistance genes). The community is, simply, the matrix, and the eigenvectors—the genomes of the organisms that live within it—are imperfect.

At each time step, these pseudo-eigenvectors nudge the whole table in slightly different directions, and coerce other members of the community: they must either mutate into a compatible form closer to being true eigenvectors of the new matrix state (to restore the matrix's stability), or let the community destabilize for a time until something happens to restore order.

The actual eigenvalues are almost pathetically obvious, and are not two, as I'd previously assumed: if the eigenvector is perfectly aligned with the matrix (which should be essentially impossible) it would give an eigenvalue either exactly 1 or slightly more than 1, representing the real population growth that would result from the steady-state maintenance of the community. You might see 2 under ideal growth conditions.

But there you have it: approximate eigen-population-genetics. I'm probably re-inventing the wheel at this point, but as I am no longer burdened by boulders of expectation, I have to admit I'm not terribly motivated to do the reading necessary to confirm or disprove that...

...However, it would be exceptionally fascinating if it were possible to assess a strain's compatibility with its community based on this sort of math.

But now, having long-since fled the ravine and all its boulders, I'm not so sure I was wrong. The piece missing, I think, from my understanding of the model was the supraorganism—not the extreme Gaia hypothesis one, but rather the notion that every bacterial community is also an economic community. Within it, undirected evolution plays games with itself: Red Queen (constant adaptation is required to retain balance), Black Queen (growth is maximized by outsourcing burdens, thereby encouraging cheating in symbiosis), and even some amount of border control and protectionism (niche-specific antibiotic + antibiotic resistance genes). The community is, simply, the matrix, and the eigenvectors—the genomes of the organisms that live within it—are imperfect.

At each time step, these pseudo-eigenvectors nudge the whole table in slightly different directions, and coerce other members of the community: they must either mutate into a compatible form closer to being true eigenvectors of the new matrix state (to restore the matrix's stability), or let the community destabilize for a time until something happens to restore order.

The actual eigenvalues are almost pathetically obvious, and are not two, as I'd previously assumed: if the eigenvector is perfectly aligned with the matrix (which should be essentially impossible) it would give an eigenvalue either exactly 1 or slightly more than 1, representing the real population growth that would result from the steady-state maintenance of the community. You might see 2 under ideal growth conditions.

But there you have it: approximate eigen-population-genetics. I'm probably re-inventing the wheel at this point, but as I am no longer burdened by boulders of expectation, I have to admit I'm not terribly motivated to do the reading necessary to confirm or disprove that...

...However, it would be exceptionally fascinating if it were possible to assess a strain's compatibility with its community based on this sort of math.