Probabilistic thinking is pervasive in evolutionary theory. It’s not a bad thing, just something that needs to be acknowledged and appropriately handled.
Some go so far as to deny it, but in my experience these people are ideologues. These are critics of ID who complain about the lack of any numbers being attached to the probability arguments of ID proponents, and their denial is perhaps rooted in their fear of a tu quoque.
Where are their own probability calculations?
Another reason for their denial could be that they also love to accuse ID proponents of making arguments from incredulity, while being unwilling to face up to the fact that they are guilty of the same thing. Does evolutionary theory depend on arguments from incredulity? Almost certainly.
Take for example the idea that all extant life shares a common ancestor. It is based upon the idea that it is simply too implausible that life should arise more than once and yet share common features such as the genetic code.
We can be very sure there really is a single concestor of all surviving life forms on this planet. The evidence is that all that have ever been examined share (exactly in most cases, almost exactly in the rest) the same genetic code; and the genetic code is too detailed, in arbitrary aspects of its complexity, to have been invented twice.Dawkins, Richard. The Ancestor’s Tale: A Pilgrimage to the Dawn of Evolution
An argument from incredulity.
Probabilities are Important
The importance of probablity in evolutionary thinking might best be seen in the following text:
If there are versions of the evolution theory that deny slow gradualism, and deny the central role of natural selection, they may be true in particular cases. But they cannot be the whole truth, for they deny the very heart of the evolution theory, which gives it the power to dissolve astronomical improbabilities and explain prodigies of apparent miracle.Dawkins, Richard. The Blind Watchmaker: Why the Evidence of Evolution Reveals a Universe without Design
Independence of Events
While having said all this, I’d like to focus on the idea that evolutionary events are not independent and that this somehow rescues evolutionary theory from being guilty of appealing to vastly improbable outcomes, aka miracles.
Consider a toss of the dice in a game of craps. The odds of double six is 1/36. Sure, we can roll a single die twice, and the odds of a six on each roll is now only 1/6 vastly more likely to occur by chance (not really). 1/6 x 1/6 is still 1/36. The probabilities are multiplicative because the events are independent events. The fact that if you have two dice and you roll the first die until you get a six and then you keep that (by cumulative selection) and then roll the second die until you get the second six and now you have two sixes doesn’t change the probabilities one whit. Doesn’t that demonstrate that cumulative selection is helpless in reducing probabilities?
Well, you might say, you need to roll BOTH dice until only one of them shows a six and then keep that one and then roll the second die. But what in evolution is analogous to that?
Sure, if you roll two dice trying to roll a six you have a better chance of a six showing on one of the two dice than if you roll just one. It’s like rolling one die twice in an attempt to get a six rather than just once. Of course the probability of the second six would still be 1/6. But why aren’t justified in adding a third die after our first six is rolled so that once again we are trying to get a six from two dice and not just one? And doesn’t this again demonstrate that it is not cumulative selection at all that is responsible for the reduction in probability but rather the number of trials we allot each attempt to roll a six?
The fundamental question is why aren’t evolutionary events independent and thus multiplicative?
The secondary question is what is the true role of cumulative selection in reduction from the miraculous to the mere appearance of the miraculous?