Written by Brian Thomas, a PhD candidate in ecology at Stanford University, "Vampire Population Ecology" is a wacky little theoretical study of possible predator population dynamics in a population of vampires (predators) and humans (prey), specifically that in Buffy the Vampire Slayer’s fictional home town of Sunnydale.
Thomas takes several standard differential equations that are used construct mathematical models approximating the behavior of a predator/prey population, and then attempts to find the equilibrium population, where the humans and vampires co-exist. These equations end up being:
H = (s-m)/(ba)
V = r/a * [1 + (m-s)/(baK)]
- r growth rate of the human population
- K is the human carrying capacity of the habitat
- a is a the number of human-vampire encounters that result in actual feedings
- b is the vampire creation rate
- m is the net rate of vampire migration into Sunnydale
- s is the rate at which the Scoobies stake vampires
Thomas also makes the following assumptions:
- The carrying capacity of the Sunnydale area is 100,000 (the population of Berkeley, California.)
- Sunnydale’s human population growth rate is 10% annually (high end for a budding California community.)
- There is a vampire migration rate of 10% also. (hey, it is the Hellmouth)
- A vampire feeds every three days, and encounters about one hundred potential victims in the course of a day, meaning that 1 out of every 300 encounters results in a feeding
- An individual vampire sires a victim every other year, or once per 240 feedings.
- Buffy and the Scoobs annually stake about 1/3 of the vampires plaguing Sunnydale.
This 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!
I’ll let Mr. Thomas sum it up:
Obviously, this is a very simplified model, and it is very vulnerable to flawed assumptions. For example, our guesses as to how often vampires feed and sire could be well off the mark. And to be fair, I’ll tell you that my first order guesses, while probably not too far off, were chosen at least partly to obtain a reasonable result on our first try. In addition to our parameter assumptions being vulnerable, we may have made mistakes in the overall structure of the model. For example, we know that vampires can live (albeit miserably) on non-human prey. We’ve also heard from Spike that while vampires can starve, they don’t actually starve to death. Incorporating these facts into the model might give some very different results.
Although the creators and writers of Buffy the Vampire Slayer are probably not theoretical ecologists, and although we are consistently amazed by the depth and sophistication of their fabricated milieu’s continuity, it is downright nifty that the show appears to make ecological sense.
I say, give this man a PhD!
The paper is available at http://www.geocities.com/blairarmeau/Vampire_Ecology/vampire_ecology.html