mathematical probability of evolution¿

I don’t mean to try and prove or disprove anything, I was just wondering from a mathematical standpoint, what the probability of one step of evolution (meaning one species fully mutating into another) is.

I’d say it’s pretty well established to be 1, given that it’s already happened.

That said, it’s a very complicated calculation, but the transition from one species to another is way more than one step–more like several hundred or thousand, depending on the complexity of the original species.

I’ll let the resident biologists handle this one in more detail.

You left out the crucial variable of time. The probability of it (however you define ``it’’) happening tomorrow (or this year, or in our lifetime, or whatever) is nearly nil. However, the probability of it happening sometime over the course of several million years starts getting towards being a sure thing…

Sorta like the probability that I’ll win the lottery is vanishingly small, but the probability that someone, somewhere will win is pretty good.

I guess I didn’t really use very clear wording in my original post. I ment it more on the terms of approximately how many births (or equivilant) would it take and/or about how much time it would take for one species to mutate into another. I realize this is a rather broad question and is probably unanswerable because of that, but I thought I’d ask anyways.

I seem to recall reading once (maybe in something by Dawkins) that a mouse could evolve into an elephant in about 10,000 years. I’ll see if I can dig that up. I think it was in The Blind Watchmaker.

I was just wondering from a mathematical standpoint, what the probability of one step of evolution (meaning one species fully mutating into another) is.

If you think of the classic example of evolution (Darwin’s finches in the Galapagos Islands), we’re not really talking about one step. It’s possible, for example, that there was a certain time when the Galapagos finches would have been rather unappealing to mainland finches. A bit later, they might have been extremely unappealing. Would that make them separate species? Perhaps not, but they’d be well on their way to diverging.

When I think of evolution, I don’t think of a single mutation creating a new species. I think of it as a series of steps that moves one gene line away from another one.

Without entereing into a huge debate over the definition of “species”, theoretically you could see evolution of a population of a vertebrate species (i.e, speciation, or the forming of two disctinct species from one) on a very short geological time scale- perhaps < few thousand years- given optimal environmental conditions.

The botanist George Ledyard Stebbins first came up with this thought experiment. He calculated that a mouse-sized animal species, subjected to an extremely weak but constant selection pressure favoring an increase in body size (by an amount too small to detect from one generation to the next), could become elephant-sized within as few as 12,000 generations. Even if the “average generation time” is assumed to be five years, this would work out to a surprisingly short 60,000 years.

It is meaningless to talk about the probability of one species evolving into another without taking into account the timescale and environmental conditions.
If environmental conditions fluctuate between two extremes, drought and flood, for example, a species might rapidly evolve over a short timescale, while little net change is observed over a longer peiod. Drought might select for, say a smaller bird, due to the lack of food, while flood might select for larger birds, due to an abundance of food.
This was adequately demonstrated in the case of Darwin’s finches, and IIRC, is one of the ideas behind Gould’s Punctuated Equilibrium theory.
That is that the separation of species often occurs vary quickly under specific constant environmental conditions - for example, the worldwide dust storm following a meteor strike might create a constant selective pressure in a single direction, as opposed to the oscillating selective pressures observed in the case of Darwin’s finches.

Well, a good example would be to look at wild species of plants compared to domesticated ones. We have a reasonably good idea when they were domesticated and the evolutionary pressures are very strong. In particular, look at wild corn vs domesticated corn.

I have to reach back to my “Speciation” class so I’m going to miss the mark a bit but,

Using the “biological” definition of species (the ability of two organisms to produce a sexually viable offspring). Speciation in one step (one mutation?) has happened in a few documented cases within recent times.

The one I remember the most is a wasp (i think) that laid its eggs in one fruit tree. It was imported to America and the imports lay their eggs in a different fruit tree at a different time of the year. So now the two populations do not mate and produce viable offspring.

Also, there are two tree frog species, one of which is a polyploid (two times the number of chromosomes) of the other. Yet clearly they are two different species (they have different calls, and don’t mate to produce viable offspring)
This polyploid event is thought to be environmentally induced (cold shock) and has been attempted (I don’t know if it succeeded) in the lab.

Dammit where’s my collection of Nature from the last 30 years.

Anyway, in spite of my lack of details, I’m sure speciation has, does, and will occur as single spontaneous events, and we have a few documented cases of it (more will come as biologists continue the work)

Not that long.

Observed Instances of Speciation

Some more

It’s more meaningful to talk about number of generations rather than number of years. Singel cell organisms reproduce in days, humans reproduce in decades. If you’re talking about humans, look at this rough timescale. Humans and chimps shared a common ancestor somewhere about 6M yrs ago. While it’s arguable how many human ancestor species there are, I think we can pretty credibly say there were at least 4, and as many as 8 or 10. Let’s say it’s 6 (easy to do the math). That makes an average of about 1M yrs per species.

But earlier posters werre correct in that evolution can be sped up when environments change rapidly or slowed down when environments are stable and populations do not get isolated.

The mathematical probabilty of evolution? 0.9189367 of course.

By askng for a “probability”, you are assuming that the process is completely random. It isn’t.

There is also the problem of determining when speciation has acctually occurred. If you are asking about an entire population transforming over time (a scenario which Darwin believed to be the major mode of speciation, but which has since been shown to not be the case), then you must consider such variables as population size (large populations tend to be more stable than smaller ones), environmental conditions, mutation rates, etc. All of which will vary from species to species.

If you are asking about a more typical mode of speciation - that of peripheral isolates, or “daughter populations”, diverging from the parent population - then variables which must be accounted for are population size, environmental conditions, mutation rates, the degree to which both populations continue to interact (if at all), etc. Note that in this scenario, both populations continue to evolve, but at different rates.

And, in both scenarios, one must consider the time frame. Given an infinite amount of time, one could safely say that the “probability” of speciation is 1. Given less time, one must consider the aforementioned variables. In one generation, the probability is probably close to 0.

Or, to put it bluntly: you’re right, your question is unanswerable as stated.

That pretty much trumps me! Though I did see in the text that I was at least on the right track. Not too bad for a 15 year old memory.