I'm not sure exactly how these "scientists" or whoever calculates these probabilities, because this situation is obviously extremely complex.
If we take the simple chain of events depicted under "real theory of abiogenesis" we can make some simpifying assumptions. If we have a situation where there are no polymers formed, then it's obvious that the formation of replicating polymers would have to happen independantly of other events, in which case we could simply take the probability that that occurs naturally and be done with it. However, I don't think you can get to "replicating polymers" without having passed the "polymers" stage, which means the events are dependant on one another. Since they are dependant, the probability changes at each step. The further down the chain you are, the more likely each new step is going to be. Lets call these events A = polymers, B = replicating polymers, C = hypercycle, D = protobiont, E = bacteria. For bacteria to occur, you need either bacteria to spontaneously appear, or if you can build your way up this chain. That is to say, if polymers are around in nature, its much more likely we'll have replicating polymers as well. So if we have polymers, then the probability of replicating polymers is affected by the existence of the polymers, and instead of just P(B) we have the situation where we are given A exists, so P(B|A). The "|" means "given" for those who don't know. Then P(B|A) = P(AB)/P(A). So now we have replicating polymers with some probability. Then if we have B, the probability of C is affected, and we have
P(C|AB) = P(ABC)/P(AB)
I have a basketball game to coach I'll come back and finish this reasoning later.
Edit: Okay I'm back.
At this point our symbolic calclations are going to get very complicated, so it might be useful to make some assumptions. In particular, That P(AB) = P(B), P(ABC) = P(C), ect. If C is contained in B is contained in A, this is true (think of them as concentric rings). What this would mean in reality is that replicating polymers can
not first happen without polymers, and if the probability of replicating polymers happening without polymers first is small enough, this assumption makes sense.
Then:
P(B|A) = P(AB)/P(A) = P(B)/P(A)
P(C|AB) = P(ABC)/P(AB) = P(C)/P(B)
P(D|ABC) = P(ABCD)/P(ABC) = P(D)/P(C)
P(E|ABCD) = P(ABCDE)/P(ABCD) = P(E)/P(D)
Then with some algebra skills, and the knowledge we want P(ABCDE)
P(ABCDE) = P(E)*P(ABCD)/P(D)
P(ABCD) = P(D)*P(ABC)/P(C)
P(ABC) = P(C)*P(AB)/P(B)
P(AB) = P(B)/P(A)
When we substitute into each expression, we end up with
P(ABCDE) = P(E)*P(D)*P(C)*P(B) / P(D)*P(C)*P(B)*P(A)
P(ABCDE) = P(E)/P(A), which is much larger than P(A)*P(B)*P(C)*P(D)*P(E)
This is the probability that the chain completes given that the first step (A) has happened and that each new step depends in the prior step. Of course, there could be assumptions that are wrong, like maybe there needs to be a critical polymer density for the next step to occur, but I'm fairly certain that the abiogenesis process does not consist of independant events in the formulation of a single bacteria.
Post has been edited 1 time(s), last time on Mar 17 2010, 2:00 am by Vrael.
None.