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Broken Model

Title text: In addition to eating foxes, rabbits can eat grass. The grass also eats foxes. Our equations chart the contours of Fox Hell.

Explanation

This explanation may be incomplete or incorrect: Created by a KILLER RABBIT. Do NOT delete this tag too soon. Otherwise, the KILLER RABBIT may come for you.

This comic shows Miss Lenhart explaining a mathematical model of a predator-prey relationship. The model has the terms swapped, showing that 400 rabbits are preying on 20 foxes. The teacher realizes this mistake and says "If this were an ecology class, I would have to fix that." Instead of fixing the model, though, she instead begins to calculate using this flawed model, and notes that this model implies that rabbits are carnivores.

The equations start with N_rabbits(0)=400 and N_foxes(0)=20, the number of rabbits and foxes at time 0, followed by what looks like the Lotka–Volterra equations, a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact. One of the pair of equations describes the number of prey over time, the other the number of predators over time, differing only by a negative sign (and coefficients). It is easy to mix up which equation describes which species, leading to the inverted predator-prey relation described.

If this was indeed the case the rabbits would soon render the foxes extinct. The reason this doesn't happen in reality for rabbits is that they outnumber the foxes (20 foxes vs 400 rabbits) and thus can survive being preyed upon. Often the predator takes the old and sick animals first, thus keeping the rest of the animals more healthy. But following the math of the wrong formula would soon lead to zero foxes. As per the title text, the rabbits could survive without the foxes to prey on, since they still eat grass. However, this reality is terrifying for the foxes, because they are rendered as prey.

The title text extends the joke by looking at a even more flawed model. This model has grass as well, but instead of grass and foxes not interacting, grass eats foxes, creating a "Fox Hell." In the real world, grass doesn't hunt foxes^{[citation needed]}, but instead, grass synthesizes its energy through photosynthesis, and may use foxes that have already died from other causes as fertilizer. Foxes do occasionally eat grass, although not as food, but for other health reasons.

Transcript

[Miss Lenhart is holding a pointer to a whiteboard, indicating the last part of the last line of text.]

Miss Lenhart: Hmm, looks like I accidentally swapped the predation terms.

Miss Lenhart: If this were an ecology class, I would have to fix that.

Miss Lenhart: Unfortunately for those 20 poor foxes, this is calculus, and the math says these 400 rabbits are hungry for meat.

[There are three lines on the white board, where the '...' parts in the bottom line are illegible:]

N_rabbits(0) = 400

N_foxes(0) = 20

dN₀/dt = ... dN_.../... = ...

[Caption below the panel:]

Every broken mathematical model is just a glimpse into a terrifying alternate universe.

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