# Functional Information (again)

Thanks for the clarification, but you could have chosen a more fitting word as ‘critical’ implies something of more fundamental or decisive importance to the function, than what might amount to a minor difference.

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You are supporting your claim with a passing phrase from the paper. Not the same thing. And it’s unrelated to the math that makes up the definition of FI.

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Why do you think it is unrelated?

Why do you think it is? (Related, that is.)

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They advocate a broad definition of functional information and the math is scalable to larger functions as long as you can estimate F(Ex)… A whole genome is a linear sequence and can ultimately allow for estimations of F(Ex).

That was not a response to my question.

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What makes you think you can “estimate F(Ex) [for a] whole genome”? Have you done it yourself? Have you even seen it done?

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The paper is not word salad, but your interpretation of it would go nicely with a raspberry vinaigrette. I have been over this or similar topics with you several times, and others have tried even harder. Your ability to Copy/Pasta a definition does nothing to express your understanding of that definition. FI is a simple proportion, nothing more. Taking the negative log of a proportion just puts it on a different scale. Based on your usage. is seems you are attributing meaning to FI well beyond the definition.

This has nothing to do with the creation of MORE information. In this context more information only means a smaller proportion with a higher degree of function, and the degree of function is a choice made by the observer, NOT a property of the (biological) system being observed. If we were to instead consider some other function for the same system, the FI would also be different.

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I agree with you this is what FI is and how I am using it…

It could also mean a smaller proportion (of arrangement that meet the function) with the same degree of function.

Fi is a measure of functional complexity which can be calculated by using -log2 F(Ex) which we can estimate using empirical evidence from several papers.

I don’t see anything in the paper that claims that it is observer dependent. Please site support for this claim.

This seems unlikely.

It could also mean a smaller proportion (of arrangement that meet the function) with the same degree of function.

No. That is not the definition.

Fi is a measure of functional complexity which can be calculated by using -log2 F(Ex) …

Tell me the FI measured and I can tell you the proportion (p=2^(-FX)). Rescaling it doesn’t make it not-a-proportion, it’s just a different way of expressing it. FI measures the proportion of system configuration with (at least) a given level of function. In statistical terms, it’s a descriptive statistic - the percentile of the level of function, given a continuous scale of a particular function.

I don’t see anything in the paper that claims that it is observer dependent. Please site support for this claim.

OK, let’s think this through. Say you want to measure FI of something, what is the first thing you do? Maybe the second too, if you follow me.

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If the numerator gets smaller and denominator stays the same then FI increases. This is very basic so I must assume I don’t understand your point.

I have no idea what point your are trying to make here. No one is trying to deny it is a proportion.

You look at empirical evidence for an estimate of the amount of functional arrangements of the sequence you are observing. Then you divide that by the total calculated sequence space. Then you can convert it to bits with the formula -log2[F(Ex)]. If the function you are observing requires multiple sequences you do this for all sequences then add the bits.

Now you have it.

It could also mean a smaller proportion (of arrangement that meet the function) with the same degree of function.

^^^ This is wrong.

You are skipping steps. What must you do first?

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Hi Dan
We may not be on the same page. Can you define what you think we are doing in forming this FI estimate calculation. My sense is you think we are hypothesis testing. Is that right?

Decide on the threshold for function. You can’t measure the FI of anything without first deciding on the threshold.

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Isn’t the threshold “as functional or more functional than the system being tested”?

Well yes if you’ve decided on the minimum threshold, anything that is as “functional” or more would qualify. But you can always just decide on what the threshold should be, however high or low. If it’s an enzyme’s activity, you have to decide on what the minimum level of activity should be before you can go on to determine how many enzyme sequences meet or exceed that level of activity.
It’s totally arbitrary of course, but I think an argument could be made that a biologically meaningful threshold is the lowest level of activity that has an effect on fitness large enough to be visible to selection.

First decide what function you are measuring functional information for?

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Spoilers!

Not hypothesis testing, just estimation of FI. Read the previous three comments.

My understanding is that this is a method for determining the FI content of a particular sequence; call it a gene. The minimum threshold is therefore the activity level of the gene whose FI is being estimated. No need to decide on a threshold; it’s determined by the gene you’re estimating.

The only variable we need to estimate based on empirical evidence in order to do the math is the number of functional sequences that still work. The total sequences space is a straight forward calculation as you know.