Why should that be a definition of information, and why should you measure it in bits? Does transforming a probability to its negative base-2 log make it more sciencey?
Do you personally understand Hazen and Szostak’s methods for calculating functional information?
Let’s start with the paper.
https://doi.org/10.1073/pnas.0701744104
You will be familiar with their equation as it is similar to what Gil posted. What Gil quoted and Lenski did a trial of is how many generations it takes to get an adaption by natural selection given the adaption allowed a significant reproductive advantage. The number he came up with is 41 bits. Bits are used as the standard for information based on Claude Shannon’s original paper on communication theory as computers process binary information.
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Can you point me to the part in the article where they show how FI can be calculated directly from the probability of an event?
For a given system and function, *x* (e.g., a folded RNA sequence that binds to GTP), and degree of function, *Ex* (e.g., the RNA–GTP binding energy), *I* ( *Ex* ) = −log2[ *F* ( *E* x)], where *F* ( *Ex* ) is the fraction of all possible configurations of the system that possess a degree of function ≥ *Ex* .
Probability is part of basic communication theory. Functional information is derived from communication theory. The functional information is the total number of functional sequences as a fraction of all possible sequences. What Lenski was measuring was the numbers of trials required to get to a specific adaption.
With enough trials you can create a distribution curve of the probability and standard deviation of a bacteria being able to consume citrate in an aerobic environment. Lenski estimated the probability based on one trial as around 41 bits of functional information.
This is Shannon’s information theory.
A foundational concept from information is the quantification of the amount of information in things like events, random variables, and distributions.
Quantifying the amount of information requires the use of probabilities, hence the relationship of information theory to probability.
IOW, Lenski was not measuring that you just defined as “functional information,” even if that definition is correct.
OK, sure. Still not sure what that has to do with “functional information”, but OK.
Could you quote from the paper in which he stated that? How did he do that from one trial? You said one needed “enough trials.” One trial is “enough”?
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Why don’t you think he is?
You defined FI as “the total number of functional sequences as a fraction of all possible sequences.” Not as “the number of trials required to get to a specific adaption.”
Perhaps.
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You don’t see a relationship here? IF I have a bucket of red and white balls and I pull a ball out 10 different times and get 1 red ball what would your estimate the ratio of red to white balls to be. The estimate will have error due to 1 trial but let’s do it 10 times and if we get and average of I ball then we have fair confidence there are around 10 red balls in the population.
Here I have used trials to estimate the ratio of red to white balls. This is how you use sampling to estimate functional information which is a ratio of functional configurations to all possible configurations. Its not perfect as the cell is giving it mechanistic assistance but close enough for government work.
I think you’re conflating two quite different things here. That’s the information in a string. You could clearly measure the Shannon information in a DNA sequence that way, though that still has nothing to do with its functional information, as a nonsense sequence would have just as much Shannon information. The probability of a random event can’t be considered information and has nothing to do with the number of bits needed to describe the mutation. And the probability of a mutation can by no reasonable standard be considered the information content of a function. Looks all sciencey, means nothing.
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The Functional Information, as defined by Jack Szostak and Robert Hazen is:
I ( Ex ) = −log2[ F ( E x)], where F ( Ex ) is the fraction of all possible configurations of the system that possess a degree of function ≥ Ex .
In other words, there is a scale of function, you have all possible sequences of some stretch of DNA that affects that function, and you ask what fraction of all possible sequences have function as good as, or better than, that sequence. Then you take -log2 of that fraction.
Note that the “probability” is not of just that sequence, but all sequences that good or better. Note also that this is not the probabilty of function this good arising in evolution. They do not at all rule out that natural evolutionary processes could make the function higher and higher. Hazen et al.'s paper (and Szostak 2003’s paper too) are not about a Design inference.
ID advocates who argue that the Specified Complexity argument is basically the same as Functional Information are wrong – the latter uses a null distribution of equiprobable sequences, not the distribution of sequences that would result from evolutionary processes.
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Hmm. Well now I am really in a pickle. @Joe_Felsenstein and @John_Harshman are saying one thing. But @colewd and @Giltil are saying they are wrong.
How ever am I to decide who is the more reliable source? Can you tell me why I should believe you two, Bill and Gil? How about you, John and Joe?
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Cole, above, does give the probability correctly, the way Hazen and Szostak defined it. He doesn’t explain what that has to do with the probability that a function that good could evolve.
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The probability given the initial conditions ( a functioning Lenski e coli and a citrate medium) the probability is 100% that it could evolve because it did. The FI estimate could be obtained in my opinion by seeing how many average trials it takes to evolve it. Right now it is around 10^13 I think given one trial. @Giltil correct me if I am wrong. Lenski talks about these issues in the paper @Giltil cited. It appears there were at least a few more mutations involved the the Cit duplication.
I don’t see where in your discussion the FI probability is related to the probability that a function that good could evolve.
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Not sure what you mean here.
I was saying that I am not sure what you mean here. The probability calculated in order to get the value of FI is not a probability that this functional sequence can be evolved. It is not defined that way.
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