2945: Broken Model

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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 HELPLESS GRASS. Do NOT delete this tag too soon. Otherwise, the KILLER SKINWALKER RABBIT may come for you. If you can address this issue, please edit the page! Thanks.

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 pulls nutrients from air and soil and 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 '...' ellipses 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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Discussion

If only Randall had included a cabbage somewhere... 172.68.64.241 05:03, 13 June 2024 (UTC)

He included grass... --Kynde (talk) 06:50, 13 June 2024 (UTC)

The cabbage would consume nothing & nothing would consume the cabbage; it's a null value, so the mathematician left it out.

ProphetZarquon (talk) 16:55, 13 June 2024 (UTC)

The cabbages are too busy eating the goats in the universe next door. Mathmannix (talk) 07:43, 15 June 2024 (UTC)

They're probably also eating the boats if anything. Eelitee (talk) 00:41, 17 June 2024 (UTC)

This "terrifying alternate universe" thing goes all the way back to the 5th century before the Common Era:

The lion shall lie down with the lamb, and they shall eat grass. Alas for the lion! He cannot eat grass, he shall be no more, unless he become a lamb. Alas for the grass! There are too many lambs, it cannot grow, it shall be no more, unless it become thorns. Alas for the lambs! They cannot eat thorns, they shall be no more, unless they eat each other - yea, unless some become lions, and they eat enough lambs so that the grass may grow again.

Ergo, Heaven is Hell. QED. 172.68.22.177 06:09, 13 June 2024 (UTC)

Yep predators are important, but only if they are the 20 and the prey are the 400. Else it is extermination for the prey. And if the predators only eat those kinds of animals also the end for them. Luckily the rabbits could eat grass. But what should the grass eat now there are no more foxes? ;-) --Kynde (talk) 06:50, 13 June 2024 (UTC)

I wonder if the term hell is a reference to the paper A slow life in hell or a fast life in heaven: Demographic analyses of contrasting roe deer populations (2009). I couldn't find any earlier mention in this context. 172.71.130.199 07:51, 13 June 2024 (UTC)

It's probably a reference to the realm mentioned in most religions where eternal punishment is dished out to uncool individuals based on their bad deeds. "Hell" is the reference here, not an article on deer populations, lol. Psychoticpotato (talk) 17:58, 13 June 2024 (UTC)

Anyone else with a sudden urge of writing a Zootopia fanfic ("No, Judy, NOOOOO!")? (Oh yes, the relevant pic exists. This is teh Internet.) 198.41.242.174 08:44, 13 June 2024 (UTC)

That last paragraph is completely incomprehensible at time of writing. --Mushrooms (talk) 11:37, 13 June 2024 (UTC)

Apparently, AI doesn't have a problem with redundant content - for example, the double mention of "Fox Hell" in the Title Text with two separate paragraphs. The AI generator also seems intent on commenting excessively on typical xkcd humor patterns. I feel like some of this extra AI content needs to be trimmed down just a bit, as it doesn't add value and just makes it look like a school essay instead of a human-readable explanation. Ianrbibtitlht (talk) 16:44, 13 June 2024 (UTC)

Agreed.

ProphetZarquon (talk) 16:58, 13 June 2024 (UTC)

It's rather obvious LLM was used here, especially the part where it only mentions the teacher saying "If this were an ecology class, I would have to fix that." 162.158.146.32

Are AI-generated additions to the explanations allowed here? I immediately came here after reading the "explanation" and noticing how redundant and inaccurate it was and was hoping it would be removed. 162.158.62.217 22:07, 13 June 2024 (UTC)

I don't believe anyone has ever come out and said "don't use AI-generated text in explanations" at this point, but I'm finding it annoying that at least one person feels the need to do it. I find it disruptive to some degree, as it probably takes almost as much work to clean up the extra garbage included as it would to write the explanations from scratch. I fear it may discourage editors from contributing to explanations when they end up just cleaning up someone's AI additions. Just my 2 cents worth. Ianrbibtitlht (talk) 22:48, 13 June 2024 (UTC)

I think it's a net positive because cleaning up an AI explanation takes less time than writing one from scratch. I do think we should have a rule that AI explanations need to be marked as such in the edit summary, which was done in this case. 162.158.41.22 19:09, 14 June 2024 (UTC)

Maybe a 2nd rule that when someone adds an AI explanation, they themselves should remove the redundant content and gushing endorsements for the comic strip from the explanation text. Ianrbibtitlht (talk) 12:57, 18 June 2024 (UTC)

Carnivorous grass?

I feel like this grass exists, even though I've never seen it named. Looks like grass, but puts out thorns tough enough to penetrate bike tires, & can sometimes be found as a patch growing extra thick around a snared animal carcass?

A quick search suggests that "carnivorous grass" with features like this is a trope in world-building games. However, you may be thinking of this real-world South American bromeliad. 172.71.150.128 17:45, 13 June 2024 (UTC)

Naw, this literally just looks like grass, until it seeds, & then the seeds are these horrific burrs. I don't think the plant is specifically carnivorous, though. I just know the burrs can injure, smallish critters can get snagged in stands of it, & I've taken to calling it "hell grass" because I imagine hell would have huge tracts of suburban lawns full of the impassable stuff. Re: carnivorous, almost any plant seems to like some carcass mixed into its soil now & then? So, I go more by how deadly they seem to be... & I mentioned this stuff mostly because I don't know what to call it & so have been calling it Hell Grass. WTF is this impostor-grass?

ProphetZarquon (talk) 22:43, 13 June 2024 (UTC)

Got it. Sounds like one of the 107 species in the genus Cenchrus, which is a bona fide member of the grass family (Poaceae). 172.71.146.53 23:58, 13 June 2024 (UTC)

That's it! The hell-grass cenchrus longispinus, grows all over southern NewMexico, & it's primary thorns get a lot longer & stouter than shown in most photos. Awful stuff; snares small beasts, makes dogs cry & cats angry, & it creeps in flat to the ground right through friendlier grasses. Even a few strands deploying seeds one year, can turn a lovely lawn into a lie.

ProphetZarquon (talk) 18:11, 14 June 2024 (UTC)

Couldn't fungi be classified as carnivorous "grass"? Psychoticpotato (talk) 18:00, 13 June 2024 (UTC)

I would say it would be stretch considering fungi is neither grass nor carnivorous. -- Hkmaly (talk) 21:34, 13 June 2024 (UTC)

I mean, it can "chew" (decompose) stuff by growing on it. Aren't fungi plants? What does their gene tree look like? Psychoticpotato (talk) 21:38, 13 June 2024 (UTC)

Fungi were originally in the plant kingdom, but they're actually more closely related to animals than plants. In 2007 the Fungi kingdom was created for them. Barmar (talk) 22:23, 13 June 2024 (UTC)

Actually, Fungi were first recognized as a lineage at the "kingdom" level by Robert Whittaker in 1969. Recognition that Fungi and Animalia are sister lineages came later. Remember that old line about how your boss must think you're a mushroom, 'cause dey keeps you in the dark and feeds you bullmanure? Your boss may have had more of a clue than you thought. 172.71.146.53 23:58, 13 June 2024 (UTC)

Today I learned. Psychoticpotato (talk) 12:47, 14 June 2024 (UTC)

True: no fungus is a grass. False: No fungus is a carnivore. Oh, you were lying in a field of mushrooms contemplating picking some and having them for dinner, were you? You better watch out ... 162.158.41.120 01:01, 15 June 2024 (UTC)

Uhhhh the explanation is wrong saying that the 400 rabbits will drive the foxes extinct. This is one of the unphysical parts of the lotka volterra equations actually, no matter what the start values are, if they are non zero they will remain nonzero forever. (This is called the atto fox problem)172.70.211.83 17:07, 14 June 2024 (UTC)

That's correct if there's any migration, but more generally less than half a fox is zero foxes. 172.69.34.16 00:46, 16 June 2024 (UTC)

In fact, less than two foxes (excepting "one 'widowed' fox that's already pregnant") is effectively zero foxes, in a closed-system.

But depends upon how quantized or probability-based you deal with each amalgamation of the differential/integral calculus figues... Or interpreting them correctly as the implied one. 162.158.49.18 13:48, 16 June 2024 (UTC)

In the basic "obligate vulpivoric leporid" model, the drastic reduction of the (already few) foxes would be catastrophic for the rabbits, leading to a crash in their population and (so long as at least one breeding pair of foxes survived, for long enough) re-establish a new dynamic equilibreum that might look somewhat similar (but the memberships flipped) to the starting condition that was supposed to be many prey and few predators. (Not exactly the same, probably, as breeding cycles would still be geated towards their respective original roles, so it'd probably settle at very few rabbits needing a truly huge population of foxes to support them. If it didn't end in mutual extinction first.)
The title-text's addition (or restatement) of rabbits being vulpo-vegetarian omnivores is not only hell for the foxes due to carniverous gramineae (which at least can nominally be avoided, by sticking to bare earth/rock or becoming arboreal/aquatic in pursuit of whatever now sustains them in leiu of any traditional lagomorphic food-source) but because their "hungry for meat" predators are not actually restricted by the plunging fox population. Foxes that evade their twin enemies will still have a large grass-sustained population of hoppy predators after their hides (or at least selective innards) whenever they become careless enough to show themselves (or their hide-out dens happen to get tunneled into by the even more capable burrowers). It is not explained what sustains the grass that would sustain the rabbits in this way (beyond the odd unwary renard), perhaps it's also significantly dual-diet with its original source of energy (i.e. photo-carninverous), but even if it's also subject to a population dive (unable to hunt foxes, being nibbled at by slightly frustrated bunnies), the fox-eating-rabbits will survive (and initially thrive) long enough to make it next to impossible for a stable revival of foxes to occur.
Though, depending upon whether foxes have any dietary requirements, via the miswrit equations, they might just get through to a "no grasses, no rabbits" situation where foxes are now mathematically unconstrained and potentially breeding like... well... their former foes. Hard times to get there, but now no longer hell. (At least until you add disease-burdening terms or other rates of mortality that scale up by population and/or population density.) 172.70.160.249 11:34, 18 August 2024 (UTC)