on vampires and stochastic processes
Posted by Laura McLay on March 26, 2009
Welcome vampire enthusiasts! See the response posted on March 31.
The movie Twilight came out on DVD came out earlier in the week. This movie about teenage vampires made a lot of money at the box office, and I have to admit that I’m a little curious to see what all the fuss is about. But I can’t get into the whole vampire thing. I have a great deal of skepticism about vampires.
Here’s my problem with vampires. I have a hard time believing that there would be just a few vampires out there and that the existence of vampires would be such a well-kept secret. After all, they reproduce rather easily (a single vampire could create thousands of offspring, whereas there are limits to human reproduction) and vampires don’t die easily. If there were vampires, they would almost certainly outnumber humans (but then vampires would run out of food).
This argument becomes even more overwhelming if you model a vampire population as a branching process or birth-death process and assume that each vampire in the population has probability Pj of producing j offspring (with j=0,1,2,… ). 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!
I have yet to see a vampire movie that implicitly assumes that there is a reasonable model for vampire population dynamics (using a stochastic process framework or something else). And frankly, I’m pretty disappointed. Until I am offered a reasonable explanation for why there aren’t more vampires, I won’t be able to jump on the vampire bandwagon. If I had free time, maybe I would write a mathematically consistent vampire novel.