Vampire Ecology: Twilight vs. Buffy

It is a truth universally acknowledged that a hungry vampire must be in want of blood. It is also universally acknowledged that the sucking of said blood makes more little vamplings, whether by direct infection or by a Buffy-esque “whole sucking thing.” Vampires are top predators, and like lions and wolves, their population can’t outstrip their prey supply.

But since there are so many people, why aren’t we awash in vampires? That’s why Laura McLay at Punk Rock Operations Research is skeptical of vampires. Based on a mathematical model of their population dynamics, she calculates that:

The vampire population would either explode or die out, depending on the expected number of offspring per vampire. But if you take into account the fact that vampires live many, many generations (they’re virtually immortal) and may create thousands of offspring, the population explodes (if you assume that each vampire creates at least one vampire, on average, before it dies). With those numbers, vampires would not be living under the radar–they would be everywhere!

But basing her calculation off icky goopy Twilight, McLay makes a critical mistake. She left out human predation on vampires, fetchingly epitomized in Buffy the Vampire Slayer. Brian Thomas, a theoretical ecologist, calculated the vampire ecology and population dynamics of the Buffyverse and found:

This [Thomas’ assumptions] results in an equilibrium population of 36,346 humans and 18 vampires. Thomas then notes that interestingly enough the established population of Sunnydale on the show is 38,500 humans, pretty damn close to the equation result. Maybe Buffy needs to cut back on the slaying in order to let the vampires weed out that extra 2100 people, we wouldn’t want human overpopulation to lead to starvation.

But is this equilibrium stable? Will natural fluctuations in the vampire population prevent the equilibrium state from ever existing? Thomas then ran the model using several different initial population sizes and seeing whether they eventually moved to equilibrium, or spiraled off into an abyss where everybody died. Turns out the model is stable and the vampires and humans can co-exist forever! Hooray!

Check out Thomas’ original paper here (PDF).

So, because we are not neck-deep in starving vampires, clearly we are living in the Buffyverse. Down with mooshy sparkly vampires & limp, passive heroines! Up with snarly-faced evil vamps and ass-kicking Slayers! Now where’s my activated Slayer powers?

Punk Rock Operations link via Boing Boing, Buffyverse Ecology via JEByrnes a long time ago

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48 Responses to Vampire Ecology: Twilight vs. Buffy

  1. wow. just wow. What happens when you add werewolves to the equation?

  2. jebyrnes says:

    Forget werewolves – what about various species of demon, liches, zombies, and the odd random god or two. Fortunately, Huisman and Weissing more or less have answered this in their 1999 Nature paper.

    Chaos.

    But really, is anyone surprised?

  3. of course there’s also the possibility that buffyverse vampires cursed with the return of their human souls (hence afflicted with a conscience and condemned to an eternity of remorse for their vampiric predilections) can eek out an existence by scavenging the streets for rats…

    once you add those gypsy curses, it’s anyone’s guess as to vampire carrying capacity…
    :)

  4. Irradiatus says:

    I would be interested to figure out how the alternative Buffyverse brought forth by Anya, in which even Willow and Xander are vamps and Sunnydale seems to be 90% vampire, could even exist (note Willow vamp image above).

    Obviously, Anya may have just instantly created the alternate vampire universe, without it having had to go through population dynamics to reach the extraordinarily high vampire proportions. If this is the case, I guess we would expect the vampire population in the hellish version of Sunnydale to collapse on its own due to the lack of prey?

    However, it is equally plausible (and even implied) that the vampire-overrun alternate universe was already in existence, and Anya just swapped the Willows between dimensions. In this case, one must wonder how the hell the vamp population ever got to where it did without collapsing already.

    Intriguing ideas.

  5. Yoder says:

    Oddly enough, just last week I tried to talk a professor, for whom I TA, into putting a SIR model of zombie population dynamics on his next exam. I’m strongly tempted to bring this up in the next review session.

  6. whysharksmatter says:

    Miriam, you didn’t factor in the important “30 days of night” coefficient…when vampires in a small clan cut the heads off of people they “ate” so that they woudn’t turn into other vampires which would compete for food with the originals.

  7. […] some reason, I find this hilarious — it’s an exercise in applying the mathematics of population ecology to the dynamics of human-vampire interact…. It’s the real deal, the actual kinds of math used by those wacky evolution and ecology […]

  8. Ziwade says:

    This is awesome. However, I have to point out that the Twilight model is not so cut and dried, either. You forgot to factor in vampire infighting, and the vampire law enforcers that show up in the second book. Besides, not all vampire victims turn into vampires in either universe — in the Buffyverse because of the whole convoluted “sucking thing.” It’s actually never fully explained in the Twilight series….

  9. smartassskeptic says:

    An interesting paper, but I believe there is an error in the formula for stable vampire population size. The formula published includes the term, “1 + ((m-s)/baK)”. He then notes that if (m-s)/baK is greater than 1, the equilibrium vampire population size will be negative. That would only be true if the term were (1 – ((m-s)/baK)).

  10. There’s evidence that really pristine coral reefs have an “inverted biomass pyramid” – lots and lots of top predators and relatively few prey. It works because there’s incredibly high prey turnover. So maybe in the alternate vampire universe they’re just feeding really efficiently (sublethally, perhaps?).
    Maybe the Master’s blood extraction machine would increase the efficiency of shuttling energy from sun->plant->human->vamp?

  11. There is NO WAY I am subjecting my poor whimpering brain to any more Twilight. Even skimming the first book made me die a little inside.

    But true, vampire infighting and law enforcers would provide a density-dependent control on vampire populations. Of course, if vampires become legal citizens (as in the dreadful-yet-awesome Anita Blake series), these vampire populations would be released from those controls (i.e., killing a vamp = murder) and thus grow exponentially. Unfortunately the Anita Blake books descended into second-rate erotica and so failed to explore the important ecological effects of vamps “coming out of the coffin.”

  12. True, most victims don’t become vamps, whether via decapitation or lack of the “whole sucking thing.” The Buffy model accounts for this – he assumes that a vampire makes a new one every other year, or once per 240 feedings.

    Of course, this rate could be much lower if, for example, if extremely attractive gay/bi men were disproportionately likely to become vampires.

  13. lifedoesntimitate says:

    My wife linked this post to me, and I just wanted you to know that I quite liked it, and also I posted a link to it from Whedonesque.com. I suppose there’s no guarantee they’ll keep it up there, but it’s at least there right now, for what it’s worth.

  14. BonnieBelle says:

    Mixing science and fantasy makes me hot. Love this post. Also, hate Twilight with a vengeance. I am constantly amazed at the people who self-confess as fans, including the lady across the hall from me who runs a business and has two kids. I just expect more from my books. They don’t even have fangs! Apparently, they puncture skin through sheer force of bite? ouch.

  15. SemiGeekGirl says:

    In Anya’s alternative Buffyverse, the Master was also moving ahead with a “factory” that would drain human victims of their blood on an assembly-line model. As he would need a near-endless supply of humans to feed this factory, it’s entirely possible that he was planning to have human farms on which he bred his own supply.

  16. Irradiatus says:

    You are so right! I completely forgot that part. Mystery solved!

  17. Irradiatus says:

    Not to derail the population conversation, but to give my two cents on the whole Twilight series…

    First, I am a married thirty+ year old heterosexual male only slightly less masculine than the average Joe…well maybe moderately less anyway (just for reference). Despite the fact that Twilight is obviously intended for teen girls, I must say that the series get’s really really entertaining. I actually enjoyed it alot more once I got through the first book (all four of which were foisted upon me by my wife – in audiobook form).

    Yeah – the exaggerated romantic aspects are a bit nauseating at times, but the story-telling and character development (and the incredibly weird direction the plot takes, particularly in book 4) make it well worth the read (or listen).

  18. amphiox says:

    Regarding the alternate Buffyverse with all the vamps, it has never been definitely established exactly how often a vampire needs to feed to stay alive. We never actually see any vampires starving to death, and as far as I can tell, much of vampire feeding is done just for fun.

    And if the average yearly feeding rate given actually represents the volume of blood a vampire actually needs to survive, then how many rats did Angel have to go through?

  19. aiusepsi says:

    Can’t believe he lazed out on working out the eigenvalues of the Jacobian matrices. I mean sure, it’s tedious, but…

  20. Irradiatus says:

    A related point:

    The actual volume of blood usually consumed in the Buffyverse always seems minuscule.

    Usually the vamps bite for only like 5 seconds tops, after which their preys falls dead.

    I always wondered whether the vamps have super-sucking abilities allowing them to near-instantly drain a victim (in defiance of physics as far as I can tell) or whether they drink for such a short time due to the cinematographic inconvenience of filming vamps sucking for several minutes. That would certainly be alot of wasted air-time.

  21. […] On vampire ecology…or why the vampires need Buffy. […]

  22. Loa says:

    What top level preditor is going to tolerate the create of direct compertion every time it feeds. Surely a vampire would just wait for it’s victim to ‘rise again’ before staking it to get rid of almost all evidence of it’s activities. The model where a vamp has to chose if its going to infect a victim or not is better, it allows the selection of only those individuals who are going to make effective vamps while the weak just die. That’s more akin to natural selection and evolution anyway. The World of Darkness and Anne Rice’s idea versions are much better, at least their vampires are actually scary.

  23. […] 8. What is the equilibrium level of vampirism in the population? […]

  24. […] sum-up and summary post on a funny science aggregater […]

  25. Peter Mc says:

    And did the study take into account handwashing as a source of potential vampire mortality? I mean those coffins have got to be dirty.

  26. Don’t understand – do vampires (like Wicked Witches) melt in soapy water?

  27. […] Twilight and Buffy vampire ecology models were not the first to plumb the mysteries of vampire population dynamics – mathematicians and […]

  28. MM says:

    One flaw in this theory of Buffy-verse vs. Twilight-verse. The theory depends on vampire reproduction. However, in Twilight, vampires cannot reproduce together, and while male vampires can procreate with human women, the women do not survive the birthing process, unless made vampires themselves.
    Also, it would appear in Twilight that most vampires do not create other vampires often, and instead drink all of the blood of their victims.
    Thus, in a universe based on Twilight’s rules, the vampire population would not increase exponentially as suggested.

  29. VampireKat says:

    I know the debate is between the vampires of Buffy and those of twilight. But one must consider other vampire stories as well. Did anyone think about the Underworld vampires? To me, this is a more logical explanation of the whole vampire/human coexistance. And what about Blade? I still think Twilight was not a good representation of what vampires are.

  30. starcitsura says:

    They are not talking about sexual reproduction, they are talking about reproduction threw transmission, or “biting”

  31. […] written papers about this dilemma.   A good friend recently pointed me to a post which references this article and, of course, the original paper by Brian Thomas.  The most impressive part of the whole thing […]

  32. Buffybot says:

    Now i love Buffy way more than twilight, but i did however read the books, and you are wrong that they did not explain why all the vamp victims became vamps. They explain that you only have to bite a human, however when you taste that blood it is next to impossible to just suck them dry, and also the law claims to keep there existence a secret, and it would be pretty hard to do so if they were making vamps left and right.

  33. Buffybot says:

    amphiox this is true but they do need a good amount of blood once and a while, they wont die but they will get very week and just like shrivel up, we know this because in angel when Connor (angels son) got tricked by that crazy chick and locked up angel in that steal box and sent him to the bottom of the ocean, he was down there for like 3 months and when they pulled him up he could barley talk, he needed a large amount of blood before he could function again. however in twilight this is not the case, they just get very very thirsty and are more attuned to the smell of human blood, therefore wanting them more, but there strength is not affected much if at all.

  34. Buffybot says:

    no vampires don’t melt in soapy water, there not even related to withes in any way, in Buffy they even take showers, they do however melt in holy water in Buffy.

  35. Buffybot says:

    I have a question, in Buffy/Angel verse it is physically impossible to have babies, however Angel and Darla have a human son together, I no it was written in fate but still it does not make sense and is just impossible, so even if that could happen, why would the baby be human? And not a tiny little vamp, i mean even in twilight it explains why Bella had that baby.

  36. elainecleo says:

    Don’t forget in Buffy, humans paid vampires to bite them, good for the vamps, they get blood and don’t leave bodies behind. And as for Twilight, they killed off the only good looking vamp, James. Spike does not need to Sparkle.
    For a different take on vampires read The Strain by Guillermo Del Toro and Chuck Hogan, the first book in a trilogy..Totally new type of vamp, enjoyed the book, but kind of like my Blondie Bear/Spike, Angel/Angelus, and also Mick and Josef from Moonlight better.

  37. Jake says:

    I’d like to adhere t the world of darkness approach, in which a human has to be bled dry and then fed a portion of its creator in order to be turned. Makes more sense, fictionally. It also explains the hunger afterwards.

  38. J-Master-5 says:

    twilight is retarded, Buffy/Angel not retarded

  39. Robert says:

    I like the fact that someone decided to do this kind of analysis..

    But you guys seem to have forgotten one thing:
    NOT ALL VAMPIRE LORE/STORIES/MEDIA CONTEND THAT A VAMPIRE IS CREATED
    SIMPLY BY BEING BITTEN.. Most involved other manners of vampiric procreation,
    the most metaphysically accepted one being that the Vampire drains the victim
    of blood to the point of near-death, and then quickly feeds the victim it’s
    vampiric blood. Some time later, the person wakes up as a vampire, having gone through
    the transformation..

    This completely changes the rate at which Vampires would prospectively multiply. They would likely
    be quite picky about who they want to give the curse/gift to..

  40. Robert says:

    …and by the way; Twilight has its charms, being a unique take on the Vampire genre..

    But the vampires of Anne Rice’s Vampire Chronicles are by FAR
    the most well-rounded, evocative, and believable versions, in my opinion (assuming Vampires
    exist in modern society).
    For those of you who never read any Anne Rice books; read them, they are amazing pieces of art.
    “Interview with the Vampire”, the movie, was done very, very well, though it did not include everything from the book.. “Queen of the Damned” was a freakin travesty. A terrible adaptation of
    Anne Rice’s book of the same name.. The book is an epic story, spanning the world and many lifetimes of memories, feelings… The movie was so superficial and way way off. ONly the names and skeletal structure of the book-story can be found in the movie-story.

    Blab blablabla abbala lbabalbalablablab

  41. Anonymous says:

    THAT IS SO STUPIP

  42. NICK says:

    HNDMJFRKO K KFKJFKD HBBIR

  43. Catherine says:

    Vampires cannot have babies, but they still retain human physiology and so a human repoductive system, thus making a HUMAN baby. However, Connor, their baby, was doomed to die because technically he could not have lived within Darla or couldn’t have possibly been born because a vampire’s body is essentially dead. This left Darla with only one choice which was to stake herself. This dissolved her body around Connor, leaving Connor alive.

    An idea which occurs to me is exactly what was described in Twilight. It is possible that maybe Darla ‘died’ as a human when she was fertile and so she was stuck like that, but then why had she not had a baby before? or maybe she had but it died before the foetus could grow strong enough.

    Connor was a superhuman born from two very strong vampires, so maybe it’s more the genelogy, the combination of the parents than the baby itself that allowed Connor to survive and ultimately Darla’s sacrifice.

    I hope this has helped, although the reply has come two years late.

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