
October 30th, 2006
01:29 am I ran across this interesting tidbit while reading old postings in alt.fan.mikejittlov:
From: the October 1993 issue of _MIX_ Magazine, Audio Village ad
Industry Fact  When Elvis Presley died in 1977 there were
37 Elvis impersonators in the world.
 Today there are 48,000.
 If the current trend continues, by the year
2010, one out of every three people in the
world will be an Elvis impersonator.
Naturally, this intrigued me, there's two points given, so it's trivial to solve for a linear equation.
Using a script I wrote to calculate differences in time and convert it to standard average sidereal years:
# timescript f 1977816000 t 1993101000
16 years, 1 month, 15 days, 11 hours, 1 minute, and 34 seconds.
Alternatively, 16.1256589371767 years.
This yields an E (Elvis impersonators per year) of around 2974.32806850604397291147 per year and the subsequent linear regression: 2974.32806850604397291147*t+37 where t is the number of years since Elvis's death. 2010 was 33 years away, so that implies:
(2974.32806850604397291147) * (33) + 37 = 98189.82626069945110607851 Elvis Impersonators. Far short of their calculation. In researching more information, I found the Wikipedia article on Elvis Impersonators which gives this quote:
"There are now at least 85,000 Elvis’s around the world, compared to only 170 in 1977 when Elvis died. At this rate of growth, experts predict that by 2019 Elvis impersonators will make up a third of the world population."  The Naked Scientists, 3rd December, 2000.
Using that information:
# timescript f 1977816000 t 2000123000
23 years, 3 months, 17 days, 12 hours, 55 minutes, and 33 seconds.
Alternatively, 23.298018020482 years.
From which we find E equivalent to 3641.08225538427145370131 and the resulting equation: (3641.08225538427145370131) * (42) + 170 = 153095.45472613940105545502 Elvis Impersonators. Somewhat more respectable, but still a fraction of the 2,000,000,000 expected.
It's worth noting that these articles quote experts. Furthermore, it's known that populations tend to grow as exponential functions of e (the natural number  2.71828182846 is a good approximation). Since my equations prove that the projected rate of growth is superlinear, it's reasonable to bow to Biology and expert opinion.
In doing all this, I've come to the logical conclusion that the growth of the population of Elvis Impersonators is in fact a natural function.
Natural functions follow the form e^(t/k) + P0. Given that equation, we find from the later article: e^(42/k)+170 = 2000000000 e^(42/k) = 1999999830 ln 1999999830 = 42/k k * ln 1999999830 = 42 k = 42/ln(1999999830) k = 1.96111272846496985794
The older data gives a k of 1.08785808443098960307, incidentally.
The k portion of the equation usually provides a measure of population loss due to predation, old age, illness, and other environmental pressures with the amount of time until an Elvis Impersonator matures to recruitment age (where they can reproduce) and how frequently the reproduce. In short, the higher the k, the greater the obstacles to continued population growth. k is normally broken down into other functions representing these factors individually. I lack expertise in the area of Elvis Impersonator study, so I'm drawing my conclusions from data provided to me by peerreviewed experts.
The older k estimates a much lower k than the new data. It's unlikely that recruitment age has changed, so it suggests that times have grown ever tougher for Elvis Impersonators. One can assume this is due to limited income from a relatively constant number of clubs willing to accept an Elvis Impersonator act.
Note as well that older Elvises seem to require increased amounts of food to support their increased girth, thus as the population of Elvis Impersonators grows, the food consumed grows not merely with the size of the population, but additionally with the relative age. This has the effect of creating a shortage of sustenance for Elvis Impersonators.
Furthermore, it's unclear how Elvis Impersonators reproduce. Some research suggests the presence of socalled Elviras  Female Elvis. Consider this female impersonator and the Hitchhiker's Guide to the Galaxy entry. Assuming that Elvis Impersonators reproduce only with females of their own kind (or, possibly, some members of the genetically similar species of Homo sapiens sapiens), it's possible the number of breeding opportunities has gone down.
In conclusion, the species of Elvis Impersonators seems to be on the rise. Large concentrations regularly appear at venues vying for supremacy, the popularity of Las Vegas clubs, and name recognition is strong. Furthermore, they seem to have advanced into other avenues of entertainment. Consider reports of the popular music band, the Red Elvises. They not only give frequent concerts, but have even been featured in a motion picture. Additionally, there is a troupe of skydiving Elvis Impersonators. Indeed, they've shown a remarkable ability to adapt despite a lack of new source material, crossing international boundaries. While pressures mount, it's likely that the population will be able to bear it and continue growing into a mature species, for better or worse.

I don't know about your model, I'm sure that there must be K of Elvis Impersonators, but it's hard to figure out witch models might be predictive on only two data points. (I'm a fan of the logistic because, we it's simple but many people think it's two simple) We need to know the size of the population at more points in time.
My model may very well be wrong. It clearly involved exponential growth, which thankfully is only a difference of a constant. When I modelled it, I hadn't been thinking of a Sigmoid function so much as a general solution on the order of the correct growth. I agree with many of the criticisms about logistic functions, but we have the Russian version of Cinderella here  if the equation fits, wear it! ; ) My simplified version only hopes to capture the general trend and is expected to be off by a constant factor.
Ultimately, what this study shows isn't a prediction of how the population of Elvis Impersonators will grow, but rather a general indication of the population's health and wellbeing. In having to show this lesser conclusion and disclaim its data, it's really shown the poor level of scholarship devoted to Elvis Impersonation and the lack of good statistics on the topic. Even the most popular Elvis Impersonator sites neglect to provide rigorous statistics!
I'm forced to reserve some doubt about the statistics I was able to find. There wasn't any explanation about how those figures were reached. The U.S. Bureau of Labor Statistics doesn't even recognize Elvis Impersonation as a profession. Even if it did, that would fail to capture an accurate idea of how many exist worldwide  this species has shown itself very capable of adapting to different cultures, after all.
Assuming the truth of my statistics and the validity of the expert opinions on the matter, I think it's reasonable to assume that k is somewhere between 1 and 2. It's a large range, but it's an increasing one, which I think is the important part.
It's my profound hope that my study will inspire better funded studies which can more accurately pin down an exact function and the biological factors which Elvis Impersonators face. I wonder how many of those 48,000 live in Las Vegas. According to Google, Las Vegas has 376,000 residents. That means that if there are any more than 3,760 of those 48,000 in Las Vegas, they comprise more than 1% of the Las Vegas population. Do Elvis Impersonators comprise a nondecimal percentage of the inhabitants of that city?
If Civilization II gives an accurate depiction of how Elvis Impersonators reproduce, then you can increase the number of Elvis Impersonators by clicking on villagers' heads. Perhaps a worthwhile experiment would be to find villagers, click on their heads and watch if they turn into Elvis Impersonators. If this was determined to be another vector of population growth, then you could calculate the predicted rate of Elvis Impersonator conversion and track it with respect to the rate of Elvis Impersonator reproduction through mating. Do Elvis Impersonators comprise a nondecimal percentage of the inhabitants of that city?
Would that make them an integral part of the city? ; )
If Civilization II gives an accurate depiction of how Elvis Impersonators reproduce, then you can increase the number of Elvis Impersonators by clicking on villagers' heads.
It's provable that clicking on a villager's head wouldn't do the trick  remember the mouse came along well after Elvis had. I also suspect that many Elvis Impersonators would say they were born to the part. Perhaps they'd say they were touched by his "blue suede shoes".
But, if findings on sexuality are confirmed and Elvis Impersonators prefer their own species to breed, then perhaps we'll find a second axis to sexuality. Perhaps instead of being straight, bi, or gay, people are also proElvis.
Of course, I can imagine the lawsuits now: "I was sexually harrassed when my boss came in singing 'Jailhouse Rock'!" 
