Measuring Biological Information

"Break or blunt any functional coded element whose loss would yield a net fitness gain." — Michael Behe, The First Rule of Adaptive Evolution, 2010¹

"But when it comes to the power of natural selection, what is most frequent versus most important can be very different things." — Richard Lenski, 2019²

"It is important to note that functional information is not a property of any one molecule, but of the ensemble of all possible sequences, ranked by activity." — Jack Szostak, Functional information: Molecular messages, 2003³

Summary

Every article in this series scores the mutations it reports.  This article says what is being measured and defines the scores.  Part 1 sets out eight measures of information and finds one that is sound and one that can be counted.  The rest starts from the scheme Michael Behe published in 2010, changes it in three places, and then tests it on twelve well-documented cases.

The main findings:

1. Functional information is the sound definition, and it cannot yet be measured on a genome. Jack Szostak and Robert Hazen define it as how rare, among all possible sequences, are those that do a stated job at least this well.⁴ It exists only for a named function at a named level of performance, and it needs the whole distribution. Its own authors write that the analysis is "not currently feasible for most complex evolving systems."⁵
2. The measures used in design and creationist writing give no usable number for a genome yet. Kirk Durston's Fits measure how alike the known members of one protein family are. A 2017 preprint showed that relatives with no function at all score like real families when they have diverged little, and Durston's reply rests on more than a billion years of separate evolution.^{6 7} The mainstream measures built the same way, Christoph Adami's physical complexity and Thomas Schneider's R_sequence, carry the same limit, and Adami stated it in 2000.⁸ Algorithmic specified complexity, from Winston Ewert, William Dembski and Robert Marks, is sound mathematics with a unit and an error rate, and it gives a number only against a stated chance model. For mutation with selection nobody has stated one, as a design researcher grants.⁹ Werner Gitt's definition tests whether information is present and has no unit, as his own book grants.¹⁰
3. The series counts something cruder that can be measured: unique sequences of nucleotides that contribute to function. At its ceiling one counted nucleotide is two bits of functional information.¹¹ The count is too high as a measure of rarity wherever many sequences do the same job, and too low as a measure of function wherever a gain comes by rearrangement.
4. Four classes, scored at the level of the molecule. An adaptive mutation is a transfer if the sequence came from another lineage, a loss if a working coded element stopped working, a gain if a coded element or a control relationship now exists that did not exist before, and a modification in every other case. The questions are asked in that order. A modification is also marked as raising, lowering or shifting the activity it changes.
5. Behe's rule is right about rates. Mutations that break a gene are far more numerous than mutations that build something, so they arrive first. Every critic read for this article grants that, and two mainstream studies with no tie to the design movement support it.^{12 13}
6. Behe's rule has not been shown to be a limit. His 2010 paper calls it "a rule of thumb" and says a gain with a large enough advantage can outcompete the losses.^{1 1} His 2019 book says degrading mutations "will dominate unguided evolution over all time and population scales."¹⁴ The second statement is an extrapolation. In Lenski's experiment presumed knockouts fall from more than half of the early adaptive mutations to about a quarter.¹³
7. The critics' strongest examples of gain are mostly inferred, not observed. Colour vision genes, smell receptors and HOX genes are known from comparing genomes. Nobody watched them arise. Behe's reply on this point is fair.¹⁵
8. The citrate mutation in Lenski's experiment is a gain of function. It meets the test Behe published in 2010, before the mechanism was known.¹ His 2019 book scores it as a modification because the promoter was "just copied."¹⁴ That reading is one of two he gave for the same kind of event in 2010.¹ This site scores it as a gain and does not walk that back.
9. Transfer needs its own class. Behe scores a gene acquired from another organism as a gain.¹ The receiving lineage originated nothing, so counting it as a gain overstates what mutation built.
10. Function and sequence are separate ledgers. The citrate mutation gave the cell a new ability and made almost no new sequence. A count of nucleotides therefore undercounts function gained. That weakens the young-earth and design side of the argument, and the series has to say so wherever it prints a count.

The rest of the section scores its cases with these definitions.  The numbers those scores feed are collected in Benchmarking Evolution.

Part 1: What information means

Eight measures of information are in use in this debate.  This part states each from its author's own words and says whether it can be measured on a genome.  It then sets the series' own working definition beside the mainstream one and shows where the two agree and where they give different numbers.

Shannon's measure counts symbols

Claude Shannon founded information theory in 1948 with a paper on sending messages down a noisy line.¹⁶  He set meaning aside in his second paragraph:

"Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities.  These semantic aspects of communication are irrelevant to the engineering problem.  The significant aspect is that the actual message is one selected from a set of possible messages."¹⁶

His measure is the uncertainty removed when one message is picked out of a set.  It is largest when every symbol is equally likely.¹⁶  DNA has four letters, so the most one nucleotide can carry is log₂ 4 = 2 bits.

That is why the measure cannot settle this argument.  A random string of a thousand nucleotides takes 2,000 bits to specify.  So does a gene of the same length.  Scrambling the gene leaves the figure where it was, and any insertion raises it.  "Mutations add Shannon information" is true and says nothing about function.

Every camp in this article agrees.  Szostak writes that classical information theory "does not consider the meaning of a message."³  Gitt writes that by Shannon's measure "a random sequence of letters possesses the maximum information content."¹⁷  Durston and his co-authors write that Shannon's formulation "does not express variations related to biological functionality."¹⁸  Robert Carter of Creation Ministries International writes that "Shannon’s ideas of information have little to do with biological information."¹⁹

Kolmogorov's measure counts the shortest description

Andrei Kolmogorov proposed a second classical measure in 1965.²⁰  The complexity of a string is the length of the shortest program that produces it:  "the minimal length … of the "program" p for obtaining y from x."²⁰  Gregory Chaitin, who reached the same idea on his own, drew the consequence for random strings:  "A series of numbers is random if the smallest algorithm capable of specifying it to a computer has about the same number of bits of information as the series itself."^{21 21}

So this measure fails for biology as Shannon's does, from a different side.  A random string scores as high as any string of its length, because nothing shorter produces it.  A copy adds almost nothing, because "repeat that stretch" is a short instruction.  Winston Ewert, Robert Marks and William Dembski, who later built a design measure on Kolmogorov's, give the example of two identical snowflakes:  "the first snowflake can be described in detail followed by the computer command DUPLICATE."²²  The measure also cannot be computed.  "There is no method to compute the Kolmogorov complexity of an object with arbitrary length."  Only upper bounds, from compression, are available.²²

They grant the main point.  Their 2015 paper opens by saying that Shannon's measure and the Kolmogorov–Chaitin–Solomonoff measure "are famous for not being able to measure meaning."^{23 23}

Functional information is the mainstream standard

Jack Szostak of Massachusetts General Hospital proposed the replacement in a one-page essay in Nature in 2003.³  The question he asks is how many of all possible sequences would do the same job:

"A new measure of information — functional information — is required to account for all possible sequences that could potentially carry out an equivalent biochemical function, independent of the structure or mechanism used."³

He defined it as the negative logarithm, to base two, of the probability that a random sequence does the job at least as well as a stated level.³  Robert Hazen, Patrick Griffin, James Carothers and Szostak put it in symbols in PNAS in 2007.⁴  Functional information is I(E_x) = −log₂[F(E_x)], "where F(E_x) is the fraction of all possible configurations of the system that possess a degree of function ≥ E_x."⁴  In plain words:  find the share of all possible arrangements that do the job at least this well, then take the negative logarithm to base two.  A job that one sequence in a thousand can do carries about ten bits.

Szostak's own example shows how this differs from counting letters.  About one random RNA strand of 70 nucleotides in 10¹¹ binds ATP.  That is about 37 bits.  Specifying one particular 70-nucleotide strand takes 140 bits.³  The gap exists because many different strands bind ATP:

"If there are multiple sequences with a given activity, then the corresponding functional information will always be less than the amount of information required to specify any particular sequence."³

The definition carries three conditions, and each one rules out a common argument.

• It is defined only for a stated function. Hazen's group writes: "Functional information is defined only in the context of a specific function x." Where no arrangement can do the job at all, the quantity "is undefined, no matter how structurally intricate or information-rich the arrangement of its agents."⁴ That removes every claim about "the information in DNA" that does not say information for what.
• It is defined only for a stated level of performance. Function is not all or nothing. In the paper's words, "functional information increases with degree of function."⁴ Szostak gives the reason: more information is needed to specify molecules that do hard tasks "than is needed to specify weak binders or slow catalysts."³
• It needs the whole distribution, not the sequences that happen to exist. Functional information "is not a property of any one molecule, but of the ensemble of all possible sequences, ranked by activity."³ To measure it "we need to know both the degree of function of that specific configuration and the distribution of function for all possible configurations in the system."⁴

The three conditions are this article's summary of the paper's constraints.  The paper does not number them.

The measured examples are small.  In the Avida digital-evolution system, a random program of about a hundred instructions performs at least one logic or arithmetic operation with a probability of about 10^-3, and no program of four instructions or fewer performs any.⁴  Among RNA strands that bind GTP, a tenfold gain in binding strength costs about ten more bits, which is a thousandfold drop in abundance among random strands.  Carothers found eleven distinct classes of such strands, different in sequence and in shape.⁴  Eleven separate solutions to one job is the reason the whole distribution is needed.

It cannot be measured on a genome, and its authors say so.  The 2007 paper calls its two requirements "difficult to meet in many systems," says it is "impossible with present technology to measure all sequences in a large population" of even short RNAs, and says random sampling of this kind "is not possible with living organisms."^{4 4}  In 2023 Michael Wong and eight co-authors, Hazen among them, proposed a "law of increasing functional information."⁵  The same paper states the limit:

"Functional information analysis is thus not currently feasible for most complex evolving systems because of the combinatorial richness of configuration space."⁵

The 2023 paper proposes a law and reports no measurement.  It is cited here for two facts only:  functional information is a live mainstream research programme, and its authors cannot yet compute it for a genome.

Two things follow for any design argument.  Information is a legitimate property of biological systems.  It has a mainstream definition and has been measured in small systems.  Adopting the mainstream definition costs the argument less than vagueness does.  What does not survive is any use of the word without a stated function, a stated level and a known distribution.

Durston's Fits measure one protein family

Kirk Durston, David Chiu, David Abel and Jack Trevors published a way to estimate functional information from data that already exist.¹⁸  Take the aligned sequences of one protein family from the Pfam database.  At each position, measure how much the amino acid varies.  Subtract that from log₂ 20 = 4.32 bits, the figure for a position where any of the twenty amino acids would do.  Add up the positions.  They named the unit the Fit:

"We have extended Shannon uncertainty by incorporating the data variable with a functionality variable.  The resulting measured unit, which we call Functional bit (Fit), is calculated from the sequence data jointly with the defined functionality variable."¹⁸

They applied it to 35 families.  A set of random sequences scores about 0.  The families score up to 2,416 Fits, for an influenza protein, at 1.3 to 4.0 Fits per amino acid.¹⁸  The smallest, a 33-residue ankyrin repeat, scores 46.  Fifteen of the 18 families longer than 150 residues score 400 Fits or more, twelve of them above 500.  No family shorter than that reaches 400.²⁴  The design thresholds discussed in Evolution Creates Information are about 400 bits (Dembski) and 500 bits (Meyer).  So if Fits were functional information, most proteins of ordinary size would sit past both lines.  Whether they are is what the rest of this section tests.

The paper draws no design conclusion.  It says function "could theoretically arise stochastically through mutational changes coupled with selection pressure, or through human experimenter involvement."¹⁸  Durston has written that one of its four authors "is an atheist who does not regard intelligent design as an option."²⁵  The design argument is Durston's own, made elsewhere:

"The ability to produce statistically significant levels of functional information is a unique attribute of intelligent minds."⁷

The paper does supply the kind of number that argument uses.  It converts the Fit value of ribosomal protein S12 into "an evolutionary search target of approximately 10^-106 percent of 121-residue sequence space."¹⁸  The sentence prints the Fit value as 379.  The paper's own table gives 359, and only 359 yields the figures printed beside it.²⁶  In 2017 Durston drew the conclusion in full:  the information is "so improbable, that we can never expect nature to achieve the code for even one protein family anywhere in the universe, over the lifespan of the universe."⁷

What the measure does well.  It finds the parts of a protein that matter.  In ubiquitin, six of the seven highest-scoring positions sit on the binding domain that contains lysine 48, and the highest of all is position 47, next to the binding site.¹⁸  That is a modest, checkable result in a peer-reviewed open-access journal.

What it measures.  A Fit count is computed from the sequences in one alignment.  The authors state their assumptions:

"It was assumed that aligned sequences from the same Pfam family, could be assigned the same functionality label.  Even though the same functionality may not be applicable to individual sites, site independence and significance was assumed and the measured FSC of each site was summed."¹⁸

So the number says how closely the known members of one family resemble each other.  Szostak had named the limit of that kind of measure in 2003, four years earlier.  It "is measured by comparing alignable sequences that encode functionally equivalent structures.  But different molecular structures may be functionally equivalent."³  A second family that does the same job and cannot be aligned with the first is invisible to the method.  Durston accepts the narrower scope.  His measure, he writes, addresses "a simpler function defining a protein family … a similar 3D structure that may have one or more biological functions."²⁵

That is the information needed to land in one known family.  Hazen's formula asks for the information needed to do the job.  The 10^-106 percent figure is the share of sequence space taken up by one family as sampled.  It equals the chance that a random sequence does what S12 does only if no other family or fold can do it, and the method cannot show that.

The two papers appeared in the same year.  Hazen's group published in May 2007.  Durston's paper was received in January 2007 and published in December.  Neither cites the other, and both cite Szostak's essay.  Hazen's version was taken up as a mainstream research programme.  That is a statement about how the two were received and not a claim of priority.

The test by simulation.  In March 2017 Matthew Matlock and Joshua Swamidass of Washington University posted a preprint that tried the method on sequences with no function at all.⁶  The preprint was never peer reviewed and has no journal version, and it should be weighed with that in mind.  The authors grant the concept:  functional information "itself is a legitimate concept introduced in the literature."⁶  Their target is the estimate made from alignments, which they call MISA.  They took one ancestral sequence, let copies of it mutate under no constraint of any kind, and scored the resulting family:

"There are no functional constraints, so the FI by definition equals zero (Equation 1).  If MISA is a good estimate of FI, it should converge to zero bits too.  We find that MISA does not converge to zero, even as more extant sequences are sampled"⁶

The scores were 4.3, 2.6, 1.8, 1.2 and 0.8 bits per amino acid at 0, 0.25, 0.5, 0.75 and 1 mutation per amino acid.⁶  Real families, measured Durston's way, score "about 1 to 4 bits per amino acid."⁶  So a family with no function, a short way from its ancestor, lands in the same range as real ones.  Their conclusion is a dilemma:

"From this experiment, we must conclude either that (1) a mindless process driven entirely by randomness can reliably generate arbitrarily high FI or that (2) MISA is an extremely bad estimate of FI.  Either conclusion falsifies the FI argument entirely."⁶

The preprint states its own limit, and the limit matters.  "MISA does go to zero if the mutation rate is increased to several events per amino acid, as the memory of the ancestral sequence is wiped."  One mutation per amino acid, on the authors' figures, is "more than 30 million years of mammalian evolution."⁶  The false score belongs to families that have diverged little.

They name three further biases, all of which push the estimate up.  The genetic code makes some amino acids commoner than others, which adds 0.183 bits per amino acid that never decays.⁶  The method assumes that "only a single family of proteins can perform a specified function," which they call "not warranted."⁶  And selection on living proteins "operates at the boundary of high and low function sequences," not at the edge between working and not working.⁶

Durston's reply.  Durston answered a month later.⁷  He called the simulation "grossly inadequate to justify their conclusion that real-life data for protein families suffer from the same problem as the data generated by their simple simulation."⁷  He agreed that the estimate was wrong for the simulated family:  "The actual FI of their simulated MSA is zero, regardless of what the MISA method of estimation says."²⁵  His answer is that real alignments are different.  They span phyla and kingdoms.  For a family found across all life, the common ancestor "would go back to the earliest discovered evidence for life which, for an evolutionary scenario, is more than a billion years."⁷  He wrote a simulation with a thousand independently evolving populations and reported estimates of 0 bits and 1 bit for sequences with no function.⁷  He concluded that his method "yields an estimate that is more reliable than previously thought, at least for protein families that span numerous, independently evolving taxa."⁷

How the exchange scores.  The two simulations agree with each other.  Durston's two runs give each line of descent about five and about three mutations per site.²⁷  That is the "several events per amino acid" at which the preprint itself says the false score vanishes.  Both sides find that relatives under no constraint score high when they have diverged little and near zero when they have diverged far.  They disagree about which case real families are in.  Neither has run a corrected measure on real Pfam data.  The preprint suggests a control, using the DNA beside each gene, and leaves it "beyond the scope of this study."⁶

Three things follow.

1. Durston's reply answers the history objection only where sequences are far apart. An alignment also holds close relatives, and the preprint notes that these make the effect larger.⁶ How much of a real family's score is history has not been measured by anyone.
2. The reply needs deep time, and so does the objection. Durston's reply rests on more than a billion years of separate evolution from one ancestor. A reader who holds that life is thousands of years old cannot use it. But the objection also assumes that the whole family descends from one ancestral sequence. On a model of separately created kinds, members of a family in different kinds were never one sequence, so their likeness is not left-over ancestry. It is either constraint or a designer's reuse of one sequence where others would have worked, and an alignment cannot tell those two apart either. Within a kind, a few thousand years leave almost no time to drift, so likeness there records how the kind began. Either way a young-earth reader gets no figure for functional information out of Fits without a test of what the conserved sites do. This is this article's inference from the two sides' own positions. Neither side makes it.
3. Neither simulation touches the first problem. A perfectly corrected alignment still sees one family. Szostak's point of 2003 stands whatever the simulations show.

Fits are a real measure of conservation.  As an estimate of functional information they are unproven.  The figure is raised by shared history to a degree nobody has measured on real data, and it leaves out every other way of doing the job.

The same sum in mainstream hands

Durston's method is not a design invention.  The same quantity, a sum over sites of how strongly each site is conserved, was already the working measure of two mainstream research programmes by 2000, and both used it to show information rising under selection.  Durston's paper cites neither.

Adami's physical complexity.  Christoph Adami and Charles Ofria of Caltech and Travis Collier of UCLA defined the complexity of a genome as its length less the summed entropy of its sites, measured across a population.⁸  "A site stores maximal information if, in DNA, it is perfectly conserved across an equilibrated ensemble."⁸  They describe the result in words close to this series' own unit:  "Physical complexity, roughly speaking, reflects the number of base pairs in a sequence that are functional."⁸  In the Avida digital-evolution system they watched it climb:  "the physical complexity, measuring the amount of information coded in the sequence about its environment, indeed steadily increases."⁸

Adami named the bias that the Matlock and Swamidass preprint reported seventeen years later.  Just after a new type spreads, "previously 100% variable sites will appear fixed by “hitchhiking” on the successful genotype".  The same "overestimate of complexity" appears "at the beginning of evolution, where the population is seeded with a single genome with no variation present."⁸  That is the shared-history problem, stated by the author of the mainstream measure.  His remedy was to wait for the population to settle, and in Avida to estimate each site by "creating all single-mutation genomes and examining them independently in isolation."⁸  A scan of that kind asks what works rather than what happens to exist, which is Hazen's question.

Schneider's ev.  Thomas Schneider of the US National Cancer Institute measures the information in DNA binding sites with the same per-site sum, which he calls R_sequence.²⁸  His ev program evolves a recognizer and 16 binding sites in a 256-base genome.  The simulation "begins with zero information".²⁸  One run produced an organism making no mistakes in 704 generations, and the sites settled at 3.983 ± 0.399 bits each, against the 4 bits his theory predicts and a possible 12.²⁸  Sixteen sites at about 4 bits each is about 64 bits in all.²⁹

The design reply came in 2010 from George Montañez, Winston Ewert, Dembski and Marks:  "The sources of knowledge in ev include a Hamming oracle and a perceptron structure that predisposes the search towards its target."^{30 30}  Their own upper bound on how hard ev's target is to hit by drawing genomes at random is 90 bits.³⁰  Schneider answered that the information comes from the setting, as it does in nature:  "Chris Adami has pointed out that the genetic information in biological systems comes from the environment.  In the case of Ev, the information comes from the size of the genome (G) and the number of sites (γ)".^{31 31}  So both sides agree that the 4 bits per site were fixed by the set-up.  They disagree whether a fitness rule written by a programmer stands for an environment or hands the program its answer.  Evolutionary Computation weighs that dispute.

Three things follow.

1. The objections to Fits apply to these measures too. Each counts conservation in a set of sequences. Each is raised by shared history until the set has settled, and Adami says so. Each sees one family of solutions. A critic who sets Durston's numbers aside for these reasons must hold population counts of physical complexity and R_sequence to the same standard. The design side's measure was not held to a special test here. It was held to the test its mainstream twin already stated.
2. The gains these programmes record are small. ev's sites hold about 64 bits, and the design side's own bound puts the difficulty of its target, for a random genome, under 90 bits. That is far below the 400 and 500 bits of the design thresholds. These results show that a conservation measure rises under mutation and selection by tens of bits, which the design writers grant for small amounts. They do not test the threshold either way.
3. The series' unit has a mainstream counterpart. Adami glosses physical complexity as "the number of base pairs in a sequence that are functional."⁸ That is close to the count this series makes, which differs mainly in refusing to count copies. Counting functional nucleotides is not a creationist invention.

Algorithmic specified complexity needs a chance model

The design movement's formal measure was built on Kolmogorov's.  Winston Ewert, William Dembski and Robert Marks set it out in a 2013 conference paper.²²  In symbols, ASC(X, C, P) = −log₂ P(X) − K(X|C).  The first term is how improbable the object X is under a stated chance model P.  The second is the length of the shortest description of X given a context C, such as a knowledge of English.²²  An object scores high only when it is both improbable and briefly described.  The paper proves that, under the stated model, the chance of an object scoring α bits or more is at most 2^−α.  In 2015 the same authors wrote that "Durston et al.’s functional information model [13] is a special case."²³

What it does well.  It repairs both classical measures.  A random string is improbable but has no short description, so it scores near zero.  A short repeat has a short description, so it scores high only if the model makes it improbable.  The authors argue that working machines have short descriptions too, because they "can be described by their functionality rather then the system that produces that functionality."²²  And because K can only be bounded from above, a computed score is a floor and not an inflated figure.³²  The output is a bound with a stated error rate, which is the right form for a scientific claim.

What it cannot do for biology yet.  The bound holds only for the model it is given.  The 2013 paper says what a high score shows:  "Given a high ASC object, we have evidence that the assumed probability distribution was incorrect."²²  That is evidence against one chance model, not evidence for design.  For a protein the model that matters is mutation with selection, and George Montañez, who extended the framework in 2018, states the difficulty from the design side:

"Although the true distribution of nature is unknown (and possibly unknowable), one might estimate p̂(x) using frequentist methods or upper bound it by considering only the appearance of some necessary subsystem, such as a single gene sequence, for which the probabilistic resources and selection landscape are much better understood."^{9 9}

His answer to the missing model is a burden of proof.  The score under the equal-chance model says how much any proposed mechanism must raise the probability of what is seen:  "Simply put, s is the entry fee for a probabilistic mechanism to even enter the tournament of competing explanations.  Without demonstrating that this burden has been met (or at very least demonstrating that p(x) boosts the probability on the scale of s), p(x) cannot yet be considered a plausible explanation of observation x."⁹  That is a fair demand.  An evolutionary account of a protein owes a number, and Benchmarking Evolution tries to supply one from observed rates.  The skeptic's reply is also fair:  a mechanism that has not been priced is unpriced, not refuted, and a design explanation states no probability of its own to set beside it.

The critic Sean Devine presses from the other side.  His "deficiency in randomness," the length of a string less its shortest description, is what ASC becomes when every sequence is equally likely and no context is given.  He grants that it "provides an information measure with exactly the properties required by Dembski."^{33 33}  His objection is that law-like processes produce short descriptions all the time:  "Most structures in the living biosystem are highly ordered and far from even a local equilibrium.  Each of them can be described by an algorithm that has fewer bits relative to the description of an equilibrium configuration."³³  A high score against the equal-chance model flags order, and order has many causes.

So algorithmic specified complexity is the soundest measure the design side has.  It has a unit, a theorem and an error rate, and it fixes what is wrong with Shannon's and Kolmogorov's measures.  It gives a number for a genome only after someone writes down the chance model with selection included, and the measure cannot supply that model.  This review found no paper that computes it for a protein or a genome under such a model.  The Design Inference reaches the same verdict on Dembski's earlier forms of the measure.

Gitt's definition tests for presence and has no unit

Werner Gitt, an engineer who was a director and professor at Germany's Federal Institute of Physics and Technology, gives the definition that Robert Carter of Creation Ministries International follows.^{34 19}  He starts where everyone else does:  "there is no binding definition of information that is universally agreed upon by practitioners of engineering, information science, biology, linguistics or philosophy."³⁴  His own has five levels, and all five must be present:

"Information is always present when all the following five hierarchical levels are observed in a system: statistics, syntax, semantics, pragmatics and apobetics."³⁴

Apobetics is his word for purpose.  In one sentence, information is "an encoded, symbolically represented message conveying expected action and intended purpose."³⁴  From the definition he derives theorems.  Theorem 4:  "A code is an absolutely necessary condition for the representation of information."  Theorem 9:  "Only that which contains semantics is information."  Theorem 10:  every item of information "needs, if it is traced back to the beginning of the transmission chain, a mental source."¹⁷  His conclusion about mutation is flat:  "There can be no increase in information."¹⁰

There are two problems.

The conclusion is inside the definitions.  If information is defined as carrying meaning, and meaning is said to require a mind, then anything called information has a mind behind it by definition and not by evidence.  A sceptic has no reason to grant the definitions.

It cannot be measured, and Gitt says so.  The definition is a test with two outcomes.  It "permits a secure allocation in all cases":  a system has all five levels or it does not.³⁴  Only the lowest level, statistics, has a unit.  That unit is Shannon's bit, and Gitt's Theorem 3 calls Shannon's concept "wholly unsuitable for the evaluation of chains of symbols conveying a meaning."¹⁷  For the levels that carry his argument, his book says the work is still to be done:

"To rise above Shannon’s theory, it is necessary to define measures for semantic information which must be generally valid.  We will now discuss some aspects which may pave the way for solving this difficult problem."¹⁰

What follows in the book is a rating on scales from 0 to 1, made "from the point of view of the recipient and his subjective appraisal."¹⁰  So "there can be no increase in information" compares two amounts of a quantity that has no unit.  It cannot be checked against any observed mutation, for or against.  By Hazen's standard it names no function, no level and no distribution.

Two parts of Gitt's account stand apart from that criticism.  On copies he and this series agree:  he separates new information from "simply copied information."³⁴  And the origin of the genetic code, which is the fact his theorems lean on, is unsolved on any account.  Eugene Koonin and Artem Novozhilov, in a mainstream review, call the origin of the coding principle and of the machinery that reads it "perhaps, the most formidable problem of all evolutionary biology" and describe "a dreary vicious circle" at its centre.³⁵  That problem is real without the definitions, and it is taken up in The Origin of Life.

What Creation Ministries International now says

The flat claim that mutations cannot add information has been dropped by the ministry's own scientist.  Robert Carter's article in the Journal of Creation is headed "It depends on what you mean by ‘new’ and ‘information’."¹⁹  He writes that the question of what information is "is the real crux of the argument, yet the term ‘information’ is difficult to define."¹⁹  He adopts Gitt's definition for the purpose.¹⁹  He grants that much of what he means is beyond counting:  "a large, yet immeasurable, part of biological information resides in living organisms outside DNA."¹⁹  And he rejects the slogan:  "The phrase, “Mutations cannot create new information” is almost a mantra among some creationists, yet I do not agree."¹⁹

What he defends instead is narrower:  "There are no known examples of the types of information-gaining mutations necessary for large-scale evolutionary processes," and "every example I have seen involves something breaking."¹⁹  The second half does not survive the cases in Part 6.  Nothing broke in the citrate mutation or in the lambda switch.

The ministry's list of arguments creationists should not use gives the wording it recommends:

"We have yet to find a mutation that increases genetic information in ways needed for microbes-to-man evolution to be feasible.  Even in those rare instances where the mutation confers an advantage they almost always cause loss of information."³⁶

Three details should be kept when this is quoted.  The argument being retired is "There are no beneficial mutations."  The information claim is kept.  The second sentence, on advantage with loss, is part of the recommended wording.  Cutting either of those makes the page look more evasive than it is.  And the wording is "genetic information," on a page that is the ministry's own and not that of Answers in Genesis.

Even so, the recommended sentence cannot be tested as worded.  It names no unit and no amount, so no observed gain can be shown to meet "ways needed" or to fall short of it.  It owes the reader a definition that meets Hazen's three conditions and does not supply one.  The same page makes one claim that could be tested if a unit were supplied:  "We are hardpressed to find examples of even ‘micro’ increases in information, although such changes should be frequent if evolution were true."³⁶  This series supplies a unit and counts.

The working definition this series uses

The series needs a quantity that can be counted on real genomes and added up.  It uses this one:  unique sequences of nucleotides that contribute to function.

• "Contribute to function" means sequence-specific. Functional DNA defines such nucleotides as those "where a substitution mutation will alter the function or efficiency of a functional element, even if only very slightly."
• "Unique" means not a copy. A duplicated gene adds nothing until the copy changes, and then only the changes count.
• "Sequences of nucleotides" sets the unit. The count is in nucleotides and not in bits.

The purpose is narrow.  The unit measures how much work mutation and selection must do.  It is a working definition for counting.  It does not replace the others, it is not functional information, and the series does not call it that.

The working definition tested against Hazen's

Where the two agree.

1. Both require a stated function. The series scores only changes shown to help the organism, and each score names what the changed element does.
2. Neither counts a symbol that does no work. A random insertion adds Shannon bits. It adds no functional information and no unique functional sequence.
3. In the simplest case they are one quantity in two units. Suppose a function needs exactly k nucleotides to be exactly what they are, and nothing else in the sequence matters. Then one sequence in 4^k works, and Hazen's formula gives 2k bits.¹¹ The series count is k. Szostak states the same ceiling: the functional information of an RNA of length n runs from 0 bits up to 2n, "the amount needed to specify a given random RNA sequence."³ A count of nucleotides is functional information at its ceiling, two bits each.

Where the count gives a different number.

1. Many sequences do the job. This is the usual case, and here the count is too high. Szostak's ATP binder is 70 nucleotides long and carries 37 bits, the amount held by 18.5 fully specified nucleotides.¹¹ A count taken from one working sequence is therefore an upper limit on functional information and can be far above it. The cases in Part 6 show the same thing. Lactase persistence was reached by several different single substitutions.³⁷ Chloroquine transport by PfCRT was reached by "a number of distinct PfCRT haplotypes."³⁸ Each extra route makes the function commoner among possible sequences and lowers Hazen's figure. The series count for each route stays the same. This cuts against the design side. A count of nucleotides does not say how hard those nucleotides were to find.
2. A copy or a transfer. The count scores zero. Hazen's measure asks what a configuration does and not how it arose, so a genome that has just received a resistance gene has the function, with whatever information that function carries. The difference is deliberate. The series asks how much sequence mutation originated in this lineage.
3. A rearrangement. The citrate mutation in Part 5 made a working unit out of existing parts. The count is zero. Hazen's figure for "grows on citrate in oxygen" would be above zero if anyone could compute it. Here the count is too low, and the class records the gain that the count misses.
4. Level of performance. Hazen's figure rises with the degree of function. The count has no level. The direction mark on a modification stands in for it.
5. Totals. The count adds up across a genome. Functional information is defined one function at a time, and the papers read here give no rule for adding the figures for a genome's many functions.
6. Distance and rarity are different things. Matlock and Swamidass make the point against Durston: functional information "does not estimate the distance between a new function and existing functions."⁶ The series count is a distance. It is the number of changes made to a genome that already existed. It is not a probability and must not be turned into one by raising four to its power. It belongs beside the other half of each organism ledger, the number of mutations searched, which Benchmarking Evolution collects.

So the unit is cruder than Hazen's and can be measured.  It is too high as a measure of rarity wherever many sequences work.  It is too low as a measure of function wherever a gain comes by rearrangement or by copying.  This article states both errors here and again in Part 7.

How the four classes and the count rest on these definitions

The taxonomy in Part 2 and the conversion rule in Part 7 are built on the two definitions above that can be used.

• The classes apply Hazen's first condition. Every score is tied to a named function of a named element. Behe's unit, the FCT, is defined by what a sequence does, which is why his scheme is the starting point. A gain is a function that this genome could not perform at all and now performs. A loss is the reverse. A modification is the same function performed to a different degree.
• The direction marks apply Hazen's second condition. Up, down and shifted say which way the degree of function moved. Unmeasured says that nobody has measured it, so the change in information cannot even be given a sign.
• Transfer is where the series leaves Hazen. His measure cannot see where a sequence came from. The series must, because its question is origination.
• The count applies the working definition and stops where Hazen's third condition bites. A gain or a raising modification by substitution is counted as the nucleotides changed, which is at most two bits each. A new gene from DNA that was not a gene is left empty, because how many of its nucleotides matter is not known until the distribution is measured. A gain by rearrangement or copy counts zero, and the class carries the function. A loss is negative.
• A lowering modification counts zero, and Hazen's definition gives a reason. A lower degree of function is met by more sequences, so it takes less information to specify and not more. That supports not counting it as a gain. Whether it should count as a loss is still open, and it is listed under Issues.

Part 2: The taxonomy

Part 1 found that a change must be tied to a named function before any amount of information can be attached to it.  Michael Behe's scheme does that, which is why the taxonomy starts from it.

Behe's definitions of 2010

In December 2010 Michael Behe, a biochemist at Lehigh University and the best-known advocate of intelligent design, published a review of laboratory evolution in The Quarterly Review of Biology.¹  He started from a point both sides accept.  What looks like a new ability in the organism can be a broken part in the molecule:

"In order to avoid confusion concerning how adaptive evolution proceeds, these two aspects must be kept separate.  A phenotypic adaptation might have any number of underlying molecular bases, resulting from either the gain, loss, or modification of a molecular feature."¹

He then named the unit to be counted, the Functional Coded elemenT or FCT:

"An FCT is a discrete but not necessarily contiguous region of a gene that, by means of its nucleotide sequence, influences the production, processing, or biological activity of a particular nucleic acid or protein, or its specific binding to another molecule."¹

His examples include promoters, enhancers, protein coding sequences, splice sites and the codons that specify a binding site.  Base composition and the distance between elements are not FCTs.¹  He sorted adaptive mutations into three modes:

"A “loss-of-FCT” adaptive mutation is a mutation that leads to the effective loss of the function of a specific, pre-existing, coded element, while adapting an organism to its environment."¹

"A “gain-of-FCT” adaptive mutation is a mutation that produces a specific, new, functional coded element while adapting an organism to its environment.  The construction by mutation of a new promoter, intron/exon splice site, or protein processing site are gain-of-FCT mutations.  Also included in this category is the divergence by mutation of the activity of a previously duplicated coded element."¹

"A “modification-of-function” adaptive mutation is a mutation whose defining property is negative—while adapting an organism to an environment, it does not lead to the loss or gain of a specific FCT.  This definition is intended to be broad enough to act as a “catch-all” for anything that falls outside the first two modes."¹

Two details of the third mode matter later.  It includes "the simple duplication of features, without divergence of activity," and mutations that act by "rearranging gene order" fall in it too.¹  Only adaptive mutations are scored.  A neutral or harmful change is left out.¹

The scheme is not rigged to exclude gains.  Behe scored sickle haemoglobin, a single substitution, as a gain, "because a codon helping to specify a new, albeit weak" protein binding site had appeared.¹  He scored a duplication in the virus MS2 as a gain:  "The 14-nucleotide duplication led to the formation of new functional coded elements (it did not simply repeat pre-existing elements), so it is not just a modification-of-function mutation."¹  Haemoglobin C, a different substitution at the same codon, he scored as a modification, because no new feature appeared.¹

Behe's definitions of 2019

Darwin Devolves restates the scheme for general readers, and the wording is looser:¹⁴

"A FCT is a stretch of information-bearing sequence that encodes a defined feature in either DNA or protein.  Examples of FCTs are genes, control regions, protein-binding sites, protein-modification sites, and other such features."¹⁴

Modification is now a mutation that will "either tweak an old FCT in a way that leaves it still working or affect some noncoded feature of a cell" and no more is said.¹⁴  The 2010 text says what an element does.  The 2019 text says what it is.  The difference decides the citrate case in Part 5, so this series scores with the 2010 definitions and says so.

Three changes

Transfer becomes a fourth class.  Behe counts a gene acquired from another organism as a gain.  His opening example in 2010 is a bacterium that "might acquire a gene or gene cluster by horizontal transfer," which "would be a gain of a functional molecular feature."¹  He scores the plasmids that made the plague bacterium as gains in both the paper and the book.^{1 14}  For the organism that is correct.  For the question this series asks it is misleading.  The series measures how much working sequence mutation and selection originate.  A transferred gene was originated somewhere else, at some other time, by a process the transfer says nothing about.  Scoring it as a gain credits the receiving lineage with work it did not do.  Scoring it as nothing hides a real change in what the organism can do.  A separate class avoids both errors.  Transfer covers plasmids, viruses and mobile elements carrying genes between bacteria, and introgression, which is the entry of DNA from one species into another by hybridisation.

Modification carries a direction.  Behe's third mode is a catch-all by his own description, and it holds most of his cases.  He argues that most of them lower activity, but his tables do not record it.  Here every modification is marked up, down or shifted.  Where the activity has not been measured the mark is unmeasured.

A new control relationship is a gain.  When a rearrangement puts a gene under a control element that never controlled it, and the gene is now made under conditions where it was silent, this article scores a gain.  Part 5 gives the reason and Behe's two readings of the same event.

The scoring procedure

Ask four questions in order and stop at the first yes.

Four rules go with the table.  A mutation that both destroys one element and creates another is scored gain with loss, and both halves are reported.  The class describes the molecule, so the effect on the organism is reported beside it and never replaces it.  Each case is also marked observed or inferred.  Observed means the change was watched as it happened in a laboratory, a clinic or a monitored population.  Inferred means it was reconstructed by comparing genomes.  Finally, a change that has not been shown to help the organism is not scored at all.

Two senses of gain

The word "gain" is used in two ways in this series, and one case can carry both.

In the plain sense, a gain is a change after which the organism can do something it could not do before and has lost nothing to get it.  In the taxonomy a gain is narrower:  a coded element, a binding site, an activity or a control relationship that did not exist in the genome.

TEM-1 β-lactamase shows the difference.  Five point mutations raise resistance to the drug cefotaxime by a factor the paper's abstract gives as about 100,000.³⁹  Antibiotic Resistance works the factor out from the paper's table as about 46,000.  In the plain sense that is a gain.  It is the case behind this series' standing concession that some antibiotic resistance is a real gain, and that article says so in its Summary.  In the taxonomy it is a modification, shifted, because the enzyme already broke down drugs of this class and the mutations shifted its range to take in a new one.  No new coded element appeared.

The two labels describe one event and do not conflict.  Neither is a loss.  In Hazen's terms the degree of function for breaking down cefotaxime rose, and a higher degree of function takes more information to specify.  The count is five nucleotides under either label.  Where an article in this series says "gain" without the class beside it, it means the plain sense, and it should say so.

Part 3: Behe at full strength

What the 2010 tables show

Behe scored the published results of about four decades of laboratory evolution in bacteria and viruses.  His Tables 2 to 4 hold 66 scored entries:  6 gains, 21 losses and 39 modifications.⁴⁰  Four of the six gains are repairs.  The experimenters had cut a piece out of the virus MS2 and the virus rebuilt it.  Setting those aside, Behe found two:

"only two gain-of-FCT events have been reported:  the development of the ability of a fucose regulatory protein to respond to d-arabinose (Lin and Wu 1984), and the antibiotic gene capture by f1 (Sachs and Bull 2005)."¹

The second of those is a transfer under this article's rules, which leaves one.

His table for Lenski's Long-Term Evolution Experiment has six losses, seven modifications and no gains.⁴⁰  The clearest loss is the ribose operon.  All twelve populations deleted part or all of it within 2,000 generations, and the mutants were "about 1 to 2% more fit than the progenitor."⁴¹  The details are in Long-Term Evolution Experiment.

The rule and the reason for it

Behe's explanation is about targets.  A gene of a thousand nucleotides can be broken by an insertion or deletion almost anywhere in it.  A new binding site needs a particular change at a particular place.  So:

"the rate of appearance of an adaptive mutation that would arise from the diminishment or elimination of the activity of a protein is expected to be 100–1000 times the rate of appearance of an adaptive mutation that requires specific changes to a gene."¹

From that he states the rule quoted at the head of this article, and he limits it at once:

"It is called a “rule” in the sense of being a rule of thumb.  It is a heuristic, useful generalization, rather than a strict law;  other circumstances being equal, this is what is usually to be expected in adaptive evolution."¹

It is the "first" rule because losses are expected "to appear first, by far, in a population under selective pressure."¹

The saturation argument

The strongest argument in the paper answers the objection that the experiments were too small.  Behe's Table 5 estimates that the E. coli experiment had made each possible point mutation 7 × 10³ to 7 × 10⁴ times over.¹  So single-step gains had every chance to appear:

"Thus, one would expect to have observed simple gain-of-FCT adaptive mutations that had sufficient selective value to outcompete more numerous loss-of-FCT or modification-of-function mutations in most experimental evolutionary studies, if they had indeed been available."¹

The rule in nature

Behe does not rest the rule on flasks alone.  His first table scores eight human mutations selected by malaria:  one gain, two modifications and five losses.⁴⁰  The gain is sickle haemoglobin.  The losses include thalassaemia, G6PD deficiency and the loss of the Duffy antigen from red cells.¹  The plague bacterium acquired plasmids carrying genes it needed to live in fleas, and then lost about 150 genes of its own.¹

What the 2019 book adds

Darwin Devolves makes three additions.  The first is more examples from nature:  polar bears, mammoths and dog breeds, where "the great majority of dog mutations unwittingly selected by us humans are very likely to be damaging, degrading, or outright loss-of-FCT ones."¹⁴

The second is the competition argument, which is the core of the book:

"it’s not so much the rarity of constructive mutations that undermines Darwinian evolution—it’s the frequency of damaging but helpful ones."¹⁴

"Damaging yet beneficial mutations will rapidly be selected when nothing else is available and compete fiercely with any gain-of-FCT mutations that might eventually arrive on the scene."¹⁴

The third is permanence.  A helpful loss is spread by selection, and once fixed it is gone.  Behe calls such mutations "the poison pills of Darwinian evolution."¹⁴  His conclusion is that the mechanism "is powerfully devolutionary" and that "unguided evolution is self-limiting."¹⁴

Support from outside the design movement

Two mainstream studies support the rate half of the rule.  Alison Hottes and colleagues pooled fitness data on gene knockouts in E. coli across 144 growth conditions:

"Overall, at least one beneficial null mutation was identified in all but five of the 144 conditions considered."¹²

Alejandro Couce and colleagues, with Lenski among the authors, sorted the adaptive mutations of the Long-Term Evolution Experiment by type:

"We find that these presumptive inactivating mutations contribute most (>50%) of the early adaptive mutations in the LTEE, and they continue to be a sizable fraction over the long run (~25%, Fig. S18B)."¹³

More than half is what Behe's rule predicts for the first response.  About a quarter is a floor on loss, because the count leaves out substitutions that merely weaken a protein.  It still shows the share falling with time, which a claim of dominance "over all time and population scales" does not predict.¹⁴

Part 4: The critics, and Behe's replies

Jerry Coyne, 2010

Jerry Coyne, an evolutionary geneticist at the University of Chicago, answered the paper on his blog the same month.  He granted the survey:

"I think that while Behe’s summary of the results of these short-term lab experiments is generally accurate, one would be completely off the mark to extend his conclusions to evolution in general—that is, evolution as it has occurred in nature, be it in microbes or eukaryotes."⁴²

He gave three reasons against extending it.  First, the experiments shut out the way many bacteria adapt in nature, which is "by the uptake of DNA from other microbes."⁴²  Second, the experiments were short, and complex elements "take time to build or acquire from a rare horizontal transmission event."⁴²  Third, animals and plants get new genes by duplication followed by divergence, which Behe's own scheme scores as a gain.⁴²

Coyne's first reason is about transfer.  It shows that bacteria in nature gain abilities faster than bacteria in a flask.  It does not show that mutation builds new elements faster.  His third reason rests on comparing genomes, so it is inferred.  To make it observed, someone would have to watch a duplicate diverge into a new function.

Lents, Swamidass and Lenski in Science, 2019

Nathan Lents, Joshua Swamidass and Richard Lenski reviewed Darwin Devolves in one page.  They granted the losses and charged Behe with selecting his examples:  "There are indeed many examples of loss-of-function mutations that are advantageous, but Behe is selective in his examples."⁴³  In their account he stresses the mutations that degraded function in Lenski's experiment and dismisses the ones that improved it.  Their positive case for gains is gene duplication, for which they cite colour vision in primates, smell receptors in mammals and the HOX genes of animals, and one laboratory study.⁴³

Lenski's blog, 2019

Lenski made the argument at length on his blog.  He accepted the rate claim in a weaker form:  "The tendency of random mutation is to degrade genes, and that is sometimes helpful."²  He rejected the conclusion:

"Summing up, Behe is right that mutations that break or blunt a gene can be adaptive.  And he’s right that, when such mutations are adaptive, they are easy to come by.  But Behe is wrong when he implies these facts present a problem for evolutionary biology, because his thesis confuses frequencies over the short run with lasting impacts over the long haul of evolution."²

His reason is that rare events can outweigh common ones.  In reply to a reader he answered the competition argument directly:

"For example, several common mutations that break unused genes might confer a 1% benefit, whereas a beneficial mutation that improves a gene’s encoded function in that same environment might confer a 5% benefit.  For a while, all of them will increase in frequency (assuming they survive drift loss when they are rare) relative to the average member of the population (i.e., their common progenitor), but eventually the one with the larger advantage will prevail over those with blunted or broken genes."²

On his own experiment he made two points.  A flask of glucose needs almost nothing the ancestor could do, so it is "just about the best case possible to showcase his rule."⁴⁴  And Behe's reading of substitutions as damage assumes the ancestral protein was already at its best, which a new environment makes false.⁴⁴  Lenski adds that the effects of most of these mutations on protein function "have not been measured under relevant conditions."⁴⁴  That cuts both ways.  It bars Behe from calling them damage and bars his critics from calling them improvements.

Lang and Rice in Evolution, 2019

The one review in a research journal came from Gregory Lang and Amber Rice, two of Behe's colleagues in his own department.⁴⁵  They also grant the starting point:  "Behe rightly points out that loss-of-function mutations are common in evolution, and that breaking or blunting a functional gene can sometimes be beneficial."⁴⁵  Their reasons against extending it are the most specific of any critic.  Losses are over-represented in experiments, "where selective pressures are high and conditions are constant, or nearly so."⁴⁵  And a loss that pays in one setting fails in another:

"No deletion is beneficial in all environments and beneficial loss-of-function mutations that arise in experimental evolution are unlikely to succeed if, say, cells are required to mate (Lang et al. 2009), the static environment is disturbed (Frenkel et al. 2015), or glucose is temporarily depleted (Li et al. 2018)."⁴⁵

They add that gene gain by "gene duplication, horizontal gene transfer, and introgression" balances gene loss over long periods.⁴⁵

Behe's replies

Behe answered each review.  His main reply is that none of them compares rates:

"Yet nowhere do the authors even try to show why the First Rule isn’t a correct statement.  They point to mutations that are not degradative, but fail to show quantitatively that those other types will arise faster than degradative ones."⁴⁶

On the duplication examples he answered that the cited papers "simply describe the occurrence of the genes" and do not test how they arose.¹⁵  He accepted that the members of each family arose by duplication.¹⁵  On the charge that the laboratory is artificial he pointed to polar bears, mammoths, malaria and dogs, none of which evolved in a flask:  "Every species that has been examined in sufficient detail so far shows the same pattern as seen in lab results."⁴⁶

He also made two concessions that his critics have not used.  The first is about the citrate mutation:

"The initial citrate mutation was not degradative;  rather, it involved a rearrangement of the bacterium’s DNA."⁴⁶

The second is that the rule has an exception where nothing useful can be broken.  His example is chloroquine resistance in the malaria parasite, "which occurred mainly by multiple point mutations in the PfCRT protein."⁴⁶

Where each side misstates the other

Lenski writes that Behe "won’t count any newly evolved function as a gain of function unless some entirely new gene or control region “poofs” into existence."⁴⁴  Lang and Rice write that the book "accepts as evidence only de novo protein evolution" when it argues for the rule.⁴⁵  Neither is what Behe's definition says.  It scores one substitution in haemoglobin as a gain.

Behe, for his part, wrote in 2019 that it is "very likely that all of the identified beneficial mutations" in Lenski's experiment worked by degrading or breaking genes.¹⁴  The measured share of presumed knockouts is about a quarter in the long run, and the rest have not been assayed.  "All" is not supported.

How the exchange scores

Three things are settled.  Breaking mutations are more numerous than building ones.  They often help.  They arrive first.  No critic disputes any of these.

Two things are not settled.  The first is whether helpful losses block later gains.  The one measured case is the citrate mutation itself.  Competition from other beneficial mutations delayed it and did not stop it, as the Long-Term Evolution Experiment article reports.  The second is whether gains of the size life needs have ever been watched.  Here the critics lean on inferred cases and Behe leans on the absence of observed ones.  Neither is a measurement.  The series exists to collect the measurements.

Part 5: The citrate concession

What happened

Lenski's twelve populations of E. coli grow in a medium that contains citrate.  The bacteria cannot use it when oxygen is present, because the gene for the citrate transporter, citT, is switched off in oxygen.  After more than 30,000 generations one population began to use it.  Zachary Blount and colleagues found the cause in 2012:

"The Cit+ trait originated in one clade by a tandem duplication that captured an aerobically-expressed promoter for the expression of a previously silent citrate transporter."⁴⁷

A stretch of 2,933 base pairs was copied and the copy was set down beside the original.  At the join, the control region of a neighbouring gene called rnk came to sit in front of the copy of citT.  The rnk control region is active in oxygen.  Blount's group tested the parts separately.  The native control region of citT "showed no expression (above background) in any strain," and the new rnk-citT unit did drive expression in oxygen.⁴⁷  Nothing was deleted.  The original rnk and the original citT were still in place.

Behe's test, written before the answer was known

In 2010 the mechanism had not been published.  Behe said in advance how he would score it:

"If the phenotype of the Lenski Cit+ strain is caused by the loss of the activity of a normal genetic regulatory element, such as a repressor binding site or other FCT, it will, of course, be a loss-of-FCT mutation, despite its highly adaptive effects in the presence of citrate.  If the phenotype is due to one or more mutations that result in, for example, the addition of a novel genetic regulatory element, gene-duplication with sequence divergence, or the gain of a new binding site, then it will be a noteworthy gain-of-FCT mutation."¹

No regulatory element lost its activity.  A regulatory unit that had never existed, the rnk control region driving citT, was added.  By the test as written, the mutation is a gain.

Behe's answer in 2019

Behe described the mechanism accurately and scored it the other way:

"In my QRB classification scheme the mutation would be counted as modification-of-function—because no new functional coded element was gained or lost, just copied."¹⁴

The answer has a basis.  The 2010 definition of modification does include "the simple duplication of features, without divergence of activity" and it names "rearranging gene order" as an example.¹  A reader who takes an FCT to be a stretch of sequence will agree with him.  The promoter sequence is old.  The gene sequence is old.  Only their position is new.

The ambiguous case

The 2010 paper had already met this problem.  Behe discussed a mutant studied by Zinser and colleagues in which an inversion moved a gene, ybeJ, under a control element that had regulated a different gene.  He called it "an ambiguous case" and gave two readings.  This article has not read Zinser's paper and relies on Behe's account of it:

"One can view the adaptation investigated by Zinser et al. (2003) in several ways:  1) as a modification-of-function event (i.e., the insertion of a duplicate IS element) followed, as a result of the inversion, by the loss of a functional coded element controlling the cstA gene (the CRP box) and the gain of a functional coded element controlling the ybeJ gene (the same CRP box);  or 2) since no FCT was gained or lost in the inversion but rather was simply rearranged, the inversion sums to a second modification-of-function mutation"¹

Reading 1 treats a control element as defined by what it controls.  Moved in front of a new gene, the same sequence is "a functional coded element controlling the ybeJ gene" and so counts as a gain.  Reading 2 treats the element as defined by its sequence, and nothing is gained.

In 2019 Behe applied reading 2 to the citrate mutation.  He did not mention reading 1.  He did call it "the ambiguous citrate mutation" one page later, and in his reply to Lang and Rice he wrote that it "was not degradative" and was a rearrangement.^{14 46}

Why this site scores it as a gain

Three reasons, all from Behe's own text.

1. His definition of an FCT is about what the sequence does. An FCT is a region that "influences the production, processing, or biological activity of a particular nucleic acid or protein, or its specific binding to another molecule."¹ After the duplication there is a region that causes the citrate transporter to be made in oxygen. Before it there was none.
2. The citrate case is cleaner than his ambiguous case. In Zinser's mutant the control element left one gene to serve another, so reading 1 has a loss beside the gain. In the citrate mutation the element was copied. The old relationship survived and a new one was added.
3. His own precedent for a duplication points the same way. He scored the MS2 duplication as a gain because it "did not simply repeat pre-existing elements" and formed new ones.¹ The citrate duplication also did more than repeat. It made a working unit that neither copy contained.

Lenski calls the event "a physical rearrangement that brought together regulatory and protein-coding sequences in a new way" and a gain of function.⁴⁴  He and Behe agree on the mechanism.  The dispute is over the label.

What the concession does not include

The gain is real and it is small.  It happened in one population of twelve.  In 2019 Lenski wrote that "none of the other LTEE populations has managed to evolve this new ability, despite its great benefit to the bacteria."⁴⁴  The sequence it made is close to nothing:  the 2,933 base pairs are a copy, and the only new thing is the join.  The mutations that followed it, which tuned the cell to live on citrate, include several that lowered or removed the activity of other genes, as Behe says.⁴⁶  So the citrate result refutes "evolution only breaks things."  It does not show that evolution writes new sequence quickly.  Those are different claims, and Part 7 separates them.

Part 6: Twelve cases scored

The cases below were chosen to test the definitions.  They are not a sample, so the number of rows in each class says nothing about how often each kind of change occurs.  "New sequence" counts nucleotides that were changed by the mutation and are not a copy of sequence that already existed.  Part 7 explains the count.

Behe's scores are from his 2010 paper for the ribose operon and the two haemoglobins, from his 2019 book for citrate, from his 2012 article for lambda, and from his 2019 reply for PfCRT.^{53 46}  The score for CTX-M follows from his rule that an acquired gene is a gain.¹⁴

The hard cases

Two haemoglobins, one codon.  Sickle haemoglobin and haemoglobin C change the same codon.  The first makes a contact between molecules that did not exist, so it is a gain.  The second "confers resistance to malaria for reasons that are unclear."¹  No new feature is known, so it is a modification.  The class depends on the mechanism, and where the mechanism is unknown the class is provisional.  Sickle haemoglobin is also a gain that harms.  Two copies cause sickle-cell disease.  Behe says so:  "Just as loss-of-FCT mutations can be helpful, gain-of-FCT mutations can be harmful."¹⁴

Phage lambda.  The virus normally enters E. coli through a surface protein called LamB.  In Justin Meyer's experiment it evolved to enter through a second protein, OmpF, in 24 of 96 populations, and it needed four substitutions to do so.^{48 48}  Lenski scores a gain:  "Remember, too, that nothing is broken."⁵⁴  Behe scores a modification, because, he argues, the same part of the J protein binds both receptors and the receptors are alike in shape.⁵³  His 2010 definition does place binding "a structurally-related ligand at the same site" under modification.¹  Meyer's paper supports him on the likeness.  It reports that OmpF "has the most similar crystal structure to LamB of any E. coli protein determined to date" while differing more in sequence.⁴⁸  This article scores a gain because the virus gained a second way in and kept the first.  A reader who follows Behe's ligand rule will score it a modification, shifted.  Both scores follow from published rules, which is why the case is marked hard.  Darwin Devolves does not mention the experiment.

PfCRT.  The normal transporter does not move chloroquine.  The resistant forms do.  That is a new activity and a gain.  The core changes remove one charge from the protein and add another:  "the loss of the positive charge (K76T) and the gain of the negative charge (N75E or N326D) are sufficient to confer a low level of CQ transport activity."  Resistant parasites are outcompeted by normal ones when the drug is withdrawn.^{38 38}  The protein's normal work is "essential but as yet unknown" in the authors' words, so the cost to it cannot be scored as a loss.³⁸  The full ledger is in Plasmodium falciparum.

Lactase persistence.  The variants raise transcription of the lactase gene.³⁷  If a substitution built a new binding site for an activating protein, the class is gain.  If it spoiled the site that shuts the gene down after weaning, the class is loss.  Lactase Persistence reads the functional studies and settles it for the two best-studied variants.  Each strengthens the binding of an activating protein at an enhancer that already worked.  Behe's 2010 paper scores the same kind of change, "an existing promoter" altered so that it binds "a transcription factor more strongly", as a modification.¹  So the score is modification, up.  That article counts at least five separate origins, one more than Tishkoff's abstract.  It leaves one variant unsettled and scores another, -14009G, as a candidate gain, because it appears to create a binding site that was not there before.

The dog retrogene.  The inserted copy has "a coding sequence that is identical to that of the source gene" and none of its introns.⁵¹  Parker's team found no upstream promoter in the insert and expected the copy to need a new one.⁵¹  Eight years later Brown's team sequenced the inserts in full.  Each carries most of the parent gene's own leading region, including the point where copying into RNA starts, and they judged it "more likely that the CpG island included in the retrogene is driving expression."^{55 55}  The parent gene is already active in the same tissues, and dogs with the insert make more of it.⁵⁵  So this is not the citrate pattern.  The copy brought its own switch and raised the output of a gene where that gene already worked.  The score is modification, up, by copy, and Dog Breeds gives the detail.  Behe's list of dog mutations names short legs and leaves this mutation out.¹⁴  Two cautions apply.  The result is a form of dwarfism that breeders chose and nature did not.  And the insertion was not watched.  It is inferred from a shared stretch of DNA in 19 breeds.

A case that cannot be scored.  In Lenski's populations nine stretches of DNA that were not genes began to be transcribed, some through "point mutations and a small deletion that created new promoters."⁵⁶  A new promoter made by mutation is the first item in Behe's definition of gain.  No benefit to the cell has been shown, so these stay off the ledger.

What the table shows

Four rows are gains.  The largest made ten new nucleotides.  One made none.  Two of the four were watched as they happened.  Both transfers added a working gene to the receiver without any origination in it.  Behe's scheme and this one disagree on three rows:  citrate, lambda and CTX-M.  On the retrogene, his rule for duplication without divergence gives modification, and this article agrees.

Part 7: From a scored gain to a nucleotide count

The unit

The series does not stop at classes.  Its organism articles end on a number:  how much unique functional sequence was created per organism and generation.  Unique functional sequence means nucleotides whose identity matters to some function and which had to be originated instead of copied.  A duplicated gene adds nothing to it until the copy changes.  The purpose of the unit is to measure how much work mutation and selection must do.  Part 1 tests this unit against Hazen's functional information.  At its ceiling one counted nucleotide is two bits.  Everywhere else the count is the larger figure, because Hazen's measure takes in every sequence that does the job and the count looks at the one that was found.

The conversion rule

For each scored mutation, count the nucleotides that the mutation changed or brought into use, that matter to the function, and that are not a copy of sequence already present in the genome or in a donor.⁵⁷  Then apply the class:

Where the conversion works

Substitutions convert cleanly.  Sickle haemoglobin is one nucleotide.  The lambda switch is four.  Chloroquine transport by PfCRT is four to ten, with two as the least that gives any activity.³⁸

Where it fails

Rearrangements.  The citrate mutation produced a working unit from existing parts.  The count is zero and the function is real.  The unit of account cannot see this kind of gain.  The dog retrogene is a second change with a real effect and a count of zero:  a copy that raised the output of a gene where it already worked.

New genes.  When DNA that was not a gene becomes one, a single enabling mutation can bring hundreds of nucleotides into use at once.  How many of them matter is not known without measuring, so the cell stays empty.  It must not be filled with protein-rarity arithmetic.  The figures of 1 in 10¹¹ and 1 in 10⁷⁷ were measured on folded proteins of 80 and 153 amino acids with stated functions, and length alone accounts for about thirty-one of the sixty-six orders of magnitude between them, as How Rare Is a Working Protein? shows.  Figures that sensitive to length and to the function tested do not transfer to the short, loosely structured products reported for new genes.

Regulatory gains.  A new binding site for a regulator may need one nucleotide or several, depending on how close the old sequence already was.  Behe makes the same point:  a mutation may "construct a new genetic control element from a sequence that was already a near-match" to it.¹  The count is the changes made, which can understate the length of the site that now works.

Transfers.  Zero in the receiver does not mean zero.  The sequence was originated in the donor lineage, and the debt moves there.  For a resistance gene on a plasmid the donor may be a soil bacterium.  For EPAS1 it is an extinct human population.

What this means for the ledger

One of the four gains in Part 6 scores zero nucleotides, and so does the dog retrogene, a modification with a real effect.  Every ledger in this series is therefore a lower bound on what evolution produced, and the series says so in each organism article.  That is a weakness in the argument the series is making, and it cuts against the young-earth side.

The count is also not a measure of how rare the result was.  Where several routes reach one function, as with lactase persistence and PfCRT, each route's count is unchanged and the function is commoner among possible sequences than the count suggests.  Part 1 gives the reason.  A count is a distance travelled from a genome that already existed.  It is not a probability.

The size of the target is taken from Functional DNA, which estimates that at least 45% of the human genome is sequence-specific.  That estimate counts duplicated sequence, which the unit excludes, and the share that is duplicated has not been subtracted.  This article therefore prints no ratio.  For scale only, and as a figure no model claims:  the largest gain in Part 6 is ten nucleotides, and 45% of a genome of about three billion letters is about 1.35 billion.⁵⁸

Objections and responses

"The information argument is about meaning, and science cannot measure meaning."  Then it is not an argument from evidence.  Gitt's theorems define information as carrying meaning, state that meaning needs a mind, and conclude that information needs a mind.¹⁷  The conclusion is inside the definitions, and his own book says that a general measure of semantic information has still to be defined.¹⁰  Hazen's measure is the alternative:  state the function, state the level, and count.  It is harder to use and it can be checked.

"Counting nucleotides is not measuring information."  Correct.  The count equals functional information only at its ceiling, where every counted nucleotide must be exactly what it is.¹¹  Elsewhere it is above Hazen's figure, and for a rearrangement it is below it.  The series uses the count because it can be read off an observed mutation and added up, and Hazen's measure cannot.  The count is a distance travelled.  It is not offered as a probability.

"Durston answered the preprint, so his numbers stand."  He answered the history objection for families whose members are several mutations per site apart, and his own simulation agrees with the preprint on where that point lies.²⁷  The answer needs more than a billion years, so it is not open to a reader who holds a young earth.⁷  On that reader's model the history objection turns into a question of whether a designer reused one sequence where others would work, and an alignment cannot answer that either.  The answer also leaves the older objection untouched.  An alignment sees one family and not every sequence that could do the job.³

"Algorithmic specified complexity measures design in bits."  It measures less than that.  A high score is, in its authors' words, "evidence that the assumed probability distribution was incorrect."²²  For a protein the distribution that matters includes selection, and nobody has written it down.⁹  Until someone does, a high score against the equal-chance model shows that a protein is not a random string, which no biologist disputes.

"Mainstream measures show information rising under selection, so the design argument is refuted."  They show a sum of per-site conservation rising.  In ev it rose from zero to about 4 bits at each of 16 sites, about 64 bits in all.^{28 29}  The design writers grant gains of that size, and the threshold they defend is several times larger.  The same measures share every limit of Fits, and Adami stated the main one himself.⁸  What remains in dispute is whether a fitness rule written by a programmer stands for a natural environment, and that is argued in Evolutionary Computation.

"Function depends on the environment, so gain and loss are not properties of a mutation."  This is correct and it limits the scheme.  The ribose operon is useless in a flask of glucose and useful in a gut.  The taxonomy handles it by scoring the molecule and reporting the environment beside it.  It cannot remove the problem.  A loss that pays in a constant flask may cost in a changing world, which is the point Lang and Rice make about mating, disturbance and starvation.⁴⁵  This weakens the design use of the rule.  A tally of losses collected where most functions are idle overstates how often losing pays in nature.

"A loss in the molecule can be a gain for the organism."  Behe agrees, and built the scheme on that point.¹  The stickleback lost an enhancer and the fish gained fitness in lakes.  Both facts are reported.  The objection does not weaken the ledger.  It does weaken the word "devolution," which describes the molecule and is read as describing the animal.

"A promoter capture only rearranges existing parts, so nothing new was made."  This is Behe's second reading, and as a statement about sequence it is true.  As a statement about function it is false, because the cell does something it could not do.  This article reports both.  The consequence runs in two directions.  It weakens the design use of the rule, because a genome full of working parts can yield new abilities by rearrangement alone, and no count of broken genes measures that.  It leaves the sequence argument standing, because a rearrangement does not explain where the parts came from.

"Modification is so wide that it can hide either result."  It holds 39 of Behe's 66 laboratory entries.⁴⁰  He writes that "there is strong reason to believe that most of the modification-of-function mutations diminished protein activity."¹  The reason is a pattern:  many different mutations in one gene all help, which is what damage looks like.¹  Lenski answers that the activities "have not been measured under relevant conditions."⁴⁴  Both are right about the state of the evidence.  Until the proteins are assayed the middle class is unmeasured, and the claim that the great majority of helpful mutations do damage rests on it.  This weakens the design use of the rule.  It weakens the opposite claim equally.

"Laboratory evolution under one strong pressure is biased toward loss."  It is.  Breaking something is the fastest route to a benefit, and an experiment that ends early sees the fastest route.  Inside Lenski's experiment the share of presumed knockouts falls by half as the easy losses are used up.¹³  Behe's reply is that the pattern also appears in nature.⁴⁶  His natural examples are scored by comparing genomes and by predicting damage from sequence, so they are inferred.¹⁴  Of the objections to the rule, this one weakens its design use most.  The rule is secure as a description of the first response to a new pressure.  It is not secure as a description of the long run.

"Conceding any gain gives away the creationist argument."  Robert Carter, a scientist at Creation Ministries International and a young-earth creationist, rejects that view:  "The phrase, “Mutations cannot create new information” is almost a mantra among some creationists, yet I do not agree."¹⁹  His position is that mutation creates new information "only in the most limited sense."¹⁹  The argument of this series is about amount.  It asks how much was searched and what it bought.  A case that scores every change as a loss is not credible and is not made here.

"Separating transfer is a way to shrink the gain column."  The transfer is reported in its own column and the receiver's new ability is stated.  What the separation prevents is crediting mutation in the receiver with a gene that was built elsewhere.  The CTX-M genes are 95 to 100% identical to a chromosomal gene of Kluyvera.⁵⁰  To count them as origination, someone must show how Kluyvera came by that gene.

Issues and unanswered questions

• Nobody has measured how much of a real protein family's Fit score is shared history. The preprint proposes a control and does not run it. Durston asks for a test on real alignments and does not run one. Durston's simulation code was not re-run for this article. Adami's remedy in Avida, a scan of every single mutant, has a real-protein counterpart in deep mutational scanning. No paper read for this article compares Durston's Fits with such data, and that comparison would show how much of the conservation is constraint.
• Algorithmic specified complexity has not been computed for a protein or a genome under a chance model that includes selection. This review found no such paper. Montañez proposes bounding the model by a single gene, where the selection landscape is better known, and does not carry it out for a real protein.
• How far each nucleotide count stands above functional information is unknown. It depends on how many other sequences reach the same function, which is known in part for lactase persistence and PfCRT and not at all for most cases.
• The aptamer figures are quoted as Hazen's group restates them. The 2004 paper by Carothers and colleagues was not read. The reply to Wong's 2023 paper that the journal printed was not read either.
• The direction of most modifications has not been measured. In Lenski's experiment enzyme activity has been assayed for citrate synthase and for little else.
• The count for a modification that lowers activity is set at zero here. That is this article's proposal. It has not been tested against the organism ledgers. Hazen's definition supports not scoring it as a gain, because a lower level of performance takes less information to specify. Whether it should be scored as a loss is undecided.
• The lactase mechanism was not settled by the sources read for this article. Lactase Persistence settles it for two variants and leaves -13915G open.
• Zinser's 2003 paper was not read. It is described from Behe's account. Weinreich's 2006 paper is quoted from its abstract. Its full text was obtained after this article was written and supplied the detail of the five mutations.
• The second part of Behe's reply to Lang and Rice was not found at its published address.
• The competition claim has not been computed. Given a population size, the two mutation rates and the two benefits, the chance that a rarer and better gain overtakes a commoner and weaker loss can be worked out. That belongs in Benchmarking Evolution.
• The warning about new genes is drawn here from what the rarity article reports about length. That article does not yet state the warning itself.

Verdict

Information in biology has one sound definition, the functional information of Szostak and Hazen, and nobody can yet compute it for a genome.  Shannon's and Kolmogorov's measures score random strings highest, and both camps agree they cannot measure function.  Durston's Fits measure conservation in one protein family and are unproven as an estimate of it.  The mainstream measures built the same way, Adami's physical complexity and Schneider's R_sequence, share that limit, and the gains they record in simulations are tens of bits.  Algorithmic specified complexity is the design side's soundest measure and gives a number only once a chance model with selection is written down, which nobody has done.  Gitt's definition has no unit, so his claim that information cannot increase cannot be tested either way.  The series therefore counts unique functional nucleotides.  That count is functional information at its ceiling of two bits each.  It runs high as a measure of rarity and low as a measure of function, and this article says where.

Behe's scheme is the right place to start for scoring.  It scores the molecule, it admits gains, and it was published with a test that could fail.  His First Rule is correct as he stated it in 2010:  a rule of thumb about what arrives first.  The critics concede that much, and Couce's count of more than half confirms it for the early generations of Lenski's experiment.

The rule is not established in the form the 2019 book gives it.  The share of presumed knockouts falls with time in the one experiment long enough to show it.  The large middle class has not been measured.  The one gain that had to compete with helpful losses was delayed and then won.

The citrate mutation is a gain of function, by the test Behe wrote before the answer was known and by the first of his own two readings of such an event.  It is also a gain that wrote almost no new sequence.  Observed gains exist, they are few, and the largest one scored here is ten nucleotides.

That leaves the series with two ledgers.  The class says what kind of change occurred.  The count says how much sequence was originated.  The count is a lower bound, because it cannot see rearrangements or price new genes.  The remaining articles fill in both.

Sources