#### Adaptation of the Drake Equation for determining probability of speciation in populations

A while back, I broke a personal rule of mine and got involved in a debate at work over a controversial subject. Evolution in particular. I wouldn’t let myself get involved except that it was after 5pm, and thus I was off the clock. I’ll add that I have a great deal of respect for the intelligence of the person I was debating. We went back and forth for about 45 minutes as I explained how DNA works, and how cells reproduce, etc etc. In the end I had convinced him that something like evolution does happen, but he was still not sold on the entire theory.

In particular, he was hung up on the notion of speciation. He was fine with a wolf evolving into a dog, or dogs coming to have many breeds. What he didn’t subscribe to was the notion that tiny little changes could carry a species all the way from an amphibian to a horse, or a snake, or a human. So that’s where I left the debate. It was actually the first day of summer and I was already at work an hour later than I needed to be. On the way home I tried to think if there was a way to demonstrate how small changes in a population could become significant over time. It was then that I recalled something vaguely similar from “Cosmos” by Carl Sagan.

In one chapter regarding extra-terrestrial life, he referred to the Drake Equation. This is a big but simple equation that tells you how many civilizations there are in the universe that can communicate with Earth. Now, of course it doesn’t *actually* tell you the answer to the question. The idea though, is that you feed the equation certain variables and play around with it. You can tell it your estimates for how many stars might have planets, and how likely a civilization is to try to communicate. You can feed in whatever crazy numbers you want, and see if there’s still a few planets out there.

I figured I could do something similar regarding the likelihood of speciation. Speciation is defined as the evolutionary process by which new species arise. After a number of failed attempts at doing it via computer programming, I remembered one of my own programming tips: “If at all possible, do it in Excel”.

So here’s my Equation. Perhaps it could be called the Darwin Equation. Mostly because Darwin is the name of a guy who, like Drake, has the letters D, A, and R in the first part of his last name.

N = [A / (B * V * W * X * Y)] * Z

(years per each new trait in population), times (the number of traits needed to be adopted)

N = years before speciation occurs

A = time between generations in years

B = number of new offspring per generation

V = chance of any mutation occurring in an individual

W = chance for any mutation to be beneficial

X = chance of beneficial mutation being passed to offspring

Y = chance of inherited beneficial mutation becoming prevalent in population

Z = number of mutations in population before speciation will have occurred

Here’s a link to a spreadsheet that lets you plug in values: Darwin Equation.xls

and if that doesn’t work, or you don’t have Excel, click here to see it in Google Doc’s (The text formatting’s a bit weird).

Perhaps you notice some weird flaws in my reasoning. There’s actually a number of them, but this equation is still useful. First it assumes that all these mutations happen one at a time. Also, it makes broad generalizations about things that aren’t known. It’s a vast oversimplification in all respects -But that’s the entire point.

The beauty of this equation is that one can simply plug in the numbers as desired and play around with the results. Ok, so one hundred new mutations isn’t speciation, then how about a *one hundred thousand* new mutations? Is that enough?

I’ve been playing around with it myself. Consider a species generating ten thousand offspring every 10 years, and 1/100 odds for each V, W, X, and Y variables, and requiring one hundred new mutations to occur. This works out to ten million years needed for speciation. Don’t like it? Plug your own values in. I don’t like it either. Ten million seems like a lot. Though if mammals first evolved about 200 million years ago, that leaves time for twenty speciation events to have occurred, each being a major step away from where that group started.

Now I know it didn’t really happen that way. This system is way too linear, it’s not meant to actually model how a species changes, it’s meant to model *the numbers* behind these changes. It allows one to give the most generous possible allowances in support of their own beliefs and see what’s comes of it. I’m a big fan of “upper bounds”. See my boat making notes, and my Whopper combinations. Upper bounds are relatively easy to determine, and are usually useful even with a good amount of error. As with the original Drake Equation, this algorithm smooshes together very large numbers and very small numbers. One in a million chances of a mutation, billions of members in the population. If a girl is one in a million, then there over a thousand of her in China. Some of whom may have beneficial mutations.