Gauss, ID, and the Red Queen Hypothesis

Robert Sheldon has posted a blog entry at Uncommon Descent that is a masterpiece of misdirection, misunderstanding, and mendacity. His post is linked to a longer post at TownHall.com, which I would like to analyze in some detail, as it represents a paradigm of the kind of twisted "logic" that passes for "science" among supporters of "intelligent design". Let's start at the beginning:

First of all, Sheldon asserts that

"a "Gaussian" or "normal" distribution...is the result of a random process in which small steps are taken in any direction."

This is a gross distortion of the definition of a Gaussian distribution. To be specific, a Gaussian distribution is not "the result of a random process in which small steps are taken in any direction". On the contrary, a Gaussian distribution is "a continuous probability distribution that often gives a good description of data that cluster around [a] mean (see http://en.wikipedia.org/wiki/Gaussian_distribution). There is a huge difference between these two "definitions".

• The first – the one invented by Robert Sheldon – completely leaves out any reference to a mean value or the concept of variation from a mean value, and makes it sound like a Gaussian distribution is the result of purely random processes.

• The second – the one defined by Gauss and used by virtually all statisticians and probability theorists – assumes that there is a non-random mean value for a particular measured variable, and illustrates the deviation from this mean value.

Typically, a researcher counts or measures a particular environmental variable (e.g. height in humans), collates this data into discrete cohorts (e.g. meters), and then constructs a histogram in which the abscissa/x axis is the counted/measured variable (e.g. meters) and the ordinate/y axis is the number of individual data points per cohort (e.g. the number of people tallied at each height in meters). Depending on how broad the data cohort, the resulting histogram may be very smooth (i.e. exhibiting “continuous variation”) or “stepped” (i.e. exhibiting “discontinuous variation”).

Graphs of variables exhibiting continuous variation approximate what is often referred to as a “normal distribution” (also called a “bell-shaped curve”). This distribution is formally referred to as a Gaussian distribution, in honor of its discoverer, Carl Friedrich Gauss (this, by the way, is one of only three accurate statements conveyed by Sheldon in the post at TownHall.com). While it is the case that Gaussian distributions are the result of random deviations, they are random deviations from a mean value, which is assumed to be the result of a determinative process.

In the example above, height in humans is not random the way Sheldon defines “random”. If it were, there would be no detectible pattern in human height at all, and we would observe a purely random distribution of human heights from about 0.57 meters to about 2.5 meters. Indeed, we would see no pattern at all in human height, and every possible height would be approximately equally likely.

Instead, we see a bell-shaped (i.e. “normal” or “Gaussian”) distribution of heights centered on a mean value (around 1.6 meters for adults, disregarding gender). The “tightness” of the normal distribution around this mean value can be expressed as either the variance or (more typically) as the standard deviation, both of which are a measure of the deviation from the mean value, and therefore of the variation between the measured values.

Sheldon goes on to state in the post at TownHall.com that “[s]o universal is the "Gaussian" in all areas of life that it is taken to be prima facie evidence of a random process.” This is simply wrong; very, very wrong – in fact, profoundly wrong and deeply misleading. A Gaussian distribution is evidence of random deviation from a determined value (i.e. a value that is the result of a determinative process). Indeed, discovering that a set of measured values exhibits a Gaussian distribution indicates that there is indeed some non-random process determining the mean value, but that there is some non-determined (i.e. “random”) deviation from that determined value.

Why does Sheldon so profoundly misrepresent the definitions and implications of Gaussian distributions? He says so himself:

“Because many people predict that Darwinian evolution is driven by random processes of small steps. This implies that there must be some Gaussians there if we knew where to look.”

This is only the second accurate statement conveyed in the OP, but Sheldon goes on to grossly misrepresent it. It is the case that the “modern evolutionary synthesis” is grounded upon R. A. Fisher’s mathematical model for the population genetics of natural selection, in which the traits of living organisms are both assumed and shown to exhibit exactly the kind of “continuous variation” that is reflected in Gaussian distributions. Fisher showed mathematically that such variation is necessary for evolution by natural selection to occur. In fact, he showed mathematically that there is a necessary (i.e. determinative) relationship between the amount of variation present in a population and the rate of change due to natural selection, which he called
the fundamental theorem of natural selection.

But in his post at TownHall.com Sheldon goes on to strongly imply that such Gaussian distributions are not found in nature, and that instead most or all variation in nature is “discontinuous”. Along the way, Sheldon also drops a standard creationist canard: “Darwin didn't seem to produce any new species, or even any remarkable cultivars.” Let’s consider these one at a time.

First, most of the characteristics of living organisms exhibit exactly the kind of variation recognized by Gauss and depicted in “normal” (i.e. “bell-shaped”) distributions. There are exceptions: the traits that Mendel studied in his experiments on garden peas are superficially discontinuous (this is Sheldon’s third and only other accurate statement in his post). However, almost any other characteristic (i.e. “trait”) that one chooses to quantify in biology exhibits Fisherian “continuous variation”.

I have already given the example of height in humans. To this one could add weight, skin color, density of hair follicles, strength, hematocrit, bone density, life span, number of children, intelligence (as measured by IQ tests), visual acuity, aural acuity, number of point mutations in the amino acid sequence for virtually all enzymes...the list for humans is almost endless, and is similar for everything from the smallest viruses to the largest biotic entities in the biosphere.

Furthermore, Darwin did indeed produce some important results from his domestic breeding programs. For example, he showed empirically that, contrary to the common belief among Victorian pigeon breeders, all of the domesticated breeds of pigeons are derived from the wild rock dove (Columba livia). He used this demonstration as an analogy for the "descent with modification" of species in the wild. Indeed, much of his argument in the first four chapters of the Origin of Species was precisely to this point: that artificial selection could produce the same patterns of species differences found in nature. No, Darwin didn’t produce any new “species” as the result of his breeding experiments, but he did provide empirical support for his theory that “descent with modification” (his term for “evolution”) could indeed be caused by unequal, non-random survival and reproduction; that is, natural selection.

To return to the main line of argument, by asserting that Mendel’s discovery of “discontinuous variation” undermined Darwin’s assumption that variation was “continuous”, Sheldon has revived the “mutationist” theory of evolution of the first decade of the 20th century. In doing so, he has (deliberately?) misrepresented both evolutionary biology and population genetics. He admits that the “modern evolutionary synthesis” did indeed show that there is a rigorously mathematical way to reconcile Mendelian genetics with population genetics, but he then states

”…finding Gaussians in the spatial distribution of Mendel's genes would restore the "randomness" Darwin predicted….But are Gaussians present in the genes themselves? Neo-Darwinists would say "Yes", because that is the way new information should be discovered by evolution. After all, if the information were not random, then we would have to say it was "put" there, or (shudder) "designed".

And then he makes a spectacular misrepresentation, one so spectacular that one is strongly tempted toward the conclusion that this massive and obvious error is not accidental, but rather is a deliberate misrepresentation. What is this egregious error? He equates the “spatial distribution of Mendel's genes” (i.e. the Gaussian distribution of “continuous variation” of the heritable traits of organisms) with “the distribution of ‘forks’ (i.e. random genetic changes, or “mutations”) in time (i.e. in a phylogenetic sequence).

He does so in the context of Venditti, Meade, and Pagel’s recent letter to Nature on phylogenies and Van Valen’s “red queen hypothesis”. Venditti, Meade, and Pagel’s letter outlined the results of a meta-analysis of speciation events in 101 species of metacellular eukaryotes (animals, fungi, and plants). Van Valen’s “red queen hypothesis” states (among other things) that speciation is a continuous process in evolutionary lineages as the result of “coevolutionary arms races”.

Van Valen suggested (but did not explicitly state) that the rate of speciation would therefore be continuous. Most evolutionary biologists have assumed that this also meant that the rate of formation of new species would not only be continuous, but that it would also be regular, with new species forming at regular, widely spaced intervals as the result of the accumulation of relatively small genetic differences that eventually resulted in reproductive incompatibility. This assumption was neither rigorously derived from first principles nor empirically derived, but rather was based on the assumption that “continuous variation” is the overwhelming rule in both traits and the genes that produce them.

What Venditti, Meade, and Pagel’s analysis showed was that

“… the hypotheses that speciation follows the accumulation of many small events that act either multiplicatively or additively found support in 8% and none of the trees, respectively. A further 8% of trees hinted that the probability of speciation changes according to the amount of divergence from the ancestral species, and 6% suggested speciation rates vary among taxa. “

That is, the original hypothesis that speciation rates are regular (i.e. “clock-like”) as the result of the accumulation of small genetic changes was not supported.

Instead, Venditti, Meade, and Pagel’s analysis showed that

“…78% of the trees fit the simplest model in which new species emerge from single events, each rare but individually sufficient to cause speciation.”

In other words, the genetic events that cause reproductive isolation (and hence splitting of lineages, or “cladogenesis”) are not cumulative, but rather occur at random intervals throughout evolving lineages, thereby producing “…a constant rate of speciation”. Let me emphasize that conclusion again:

The genetic events that cause reproductive isolation…occur at random intervals throughout evolving lineages, thereby producing “…a constant rate of speciation”.

In other words (and in direct and complete contradiction to Sheldon’s assertions in his blog post), Venditti, Meade, and Pagel’s fully support the assumption that the events that cause speciation (i.e. macroevolution) are random:

“…speciation [is the result of] rare stochastic events that cause reproductive isolation.

But it’s worse than that, if (like Sheldon) one is a supporter of “intelligent design”. The underlying implications of the work of Venditti, Meade, and Pagel is not that the events that result in speciation are “designed”, nor even that they are the result of a determinative process like natural selection. Like Einstein’s anathema, a God who “plays dice” with nature, the events that result in speciation are, like the spontaneous decay of the nucleus of a radioactive isotope, completely random and unpredictable. Not only is there no “design” detectible in the events that result in speciation, there is no regular pattern either. Given enough time, such purely random events eventually happen within evolving phylogenies, causing them to branch into reproductively isolated clades, but there is no deterministic process (such as natural selection) that causes them.

Here is Venditti, Meade, and Pagel's conclusion in a nutshell:

Speciation is not the result of natural selection or any other “regular” determinative process. Rather, speciation is the result of “rare stochastic events that cause reproductive isolation.”

And stochastic events are not what Sheldon tried (and failed) to assert they are: they are not regular, determinative events resulting from either the deliberate intervention in nature by a supernatural “designer” nor are they the result of a regular, determinative process such as “natural selection”. No, they are the result of genuinely random, unpredictable, unrepeatable, and irregular “accidents”. Einstein’s God may not “play dice” with nature (although a century of discoveries in quantum mechanics all point to the opposite conclusion), but Darwin’s most emphatically does.

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As always, comments, criticisms, and suggestions are warmly welcomed!

--Allen

Random Mutation and Natural Selection Revisited

AUTHOR: Allen MacNeill

SOURCE: Original essay

COMMENTARY: That's up to you...

Promoters of "intelligent design theory" and other forms of creationism often assert that random mutation plus natural selection (RM+NS) are insufficient to explain the diversity of life on Earth. In particular, people like William Dembski assert that RM+NS cannot work fast enough (even given billions of years) to produce the complex living organisms we observe around us.

In so doing, they attack evolutionary theory using a "straw-man argument," because modern evolutionary theory is not limited to RM+NS alone to produce adaptations, nor to explain the diversity of life on Earth. In particular, while there is no empirical evidence that would lead one to believe that mutations are produced by an "intelligent designer," it is also not true that mutations alone must supply the variation necessary for evolution by natural selection.

In particular, while it is true that any given mutation is random (as far as we can tell), a series of mutations which are then preserved as the result of natural selection aren't really random at all, at least not in the way that is often depicted by critics of evolutionary theory. In classical evolutionary theory, as first mathematically formalized by R. A. Fisher, the variation that is necessary for the raw material for natural selection is the result of a large number of individual alleles, all producing variations of the same trait, such as height or skin color in humans. In this model, a normal distribution of heights or skin colors are produced by combinations of different alleles, each influencing some fraction of the overall height, producing what Fisher and others called "continuous variation." Selection then preserved one or a few of the various allele combinations by preserving the individuals that carried the controlling alleles.



In this model, evolutionary change would necessarily be slow and gradual, as changes in the overall mean value for any trait would require the gradual accumulation of mutations in each of the many alleles that controlled the trait. Since the observable mutation rate is very low (at least, the rate of mutations that significantly affect most phenotypic traits is very low), the argument was that directional change in any given trait was something like a wagon train: only as fast as its slowest constituent. That is, change in the overall distribution of the trait (such as height) depended on the rate of mutation of all of the alleles controlling it, and required that a sufficient proportion of the alleles that were preserved by selection mutate and then be selected in the same "direction" (e.g. for greater height).

However, subsequent field and laboratory investigations into the genetic and developmental control of such variable traits have shown the multiple allele/continuous variation model upon which the "modern synthesis" was based is, in fact, not the way most traits apparently evolve. For example, consider a mutation that causes an increase in size of a particular anatomical feature (e.g. a finch's beak). Most such features are regulated by a set of genes that are themselves regulated by a homeotic gene (or a few such homeotic genes; in the case of Darwin's finches, the controlling homeotic gene is called bmp4, for "bone morphology protein 4") [1]. Homeotic genes, like many but not all genes, do not produce a purely monotonic trait (i.e a trait with no variation). Instead, they produce a trait that varies somewhat between individuals, in what approximates a normal distribution. In the case of finch beaks, this means that in any population of finches, there are some individuals with small beaks, some with large beaks, and most with intermediate beaks. All of these finches could easily have the same allele for the homeotic gene controlling the trait. The variation in beak size would therefore be the result, not of the expression of different alleles, but rather of the different outcomes of the expression of the same allele of the homeotic gene, developing differently in different individuals as the result of a combination of chance and environmental conditions (this is how humans differ in heights, for example).



Now consider a situation in which an environmental change (for example, a drought), selected for individual finches with larger beaks. At the level of the controlling homeotic gene, this could mean one of two things: either the larger beaks are still within the developmental limits of the original allele, or another allele (i.e a mutant) has arisen, with an overlapping developmental pattern but a higher mean value for beak size. If the former is the case, then a return to the original environment would result in a return to the original mean beak size.

However, if the latter were the case, then there would be a built-in bias toward finches with larger beaks in the resulting population. This would also mean that the "base" allele - i.e. the new mutant allele - would start out producing a larger mean beak size along with the usual normal distribution of beak sizes. If the environmental change persisted, new alleles might arise, but they would begin with a "norm of reaction" that would produce significantly larger mean beak sizes, along with a normal distribution with significantly larger beaks at the upper tail of the distribution.

In other words, the existing alleles for such a trait would bias subsequent mutations in the "direction" of larger beaks, simply because the pool of potential new alleles would already start out biased in that direction. Therefore, the mutations and developmental changes that were available from one generation to the next would be biased in the direction of whatever phenotypic trait resulted in the highest reproductive success.

This process, called genetic accommodation [2], is part of the new science of evo-devo, which renders much of the classical "evolutionary synthesis" obsolete, and at the same time explains how such phenomena as punctuated equilibria can be integrated into a unified theory of evolutionary development. In particular, genetic accommodation and similar processes can explain how natural selection alone can produce both rapid and directional change in phenotypes over time, thereby making any resort to "intelligent design" unnecessary and irrelevant.

REFERENCES CITED:

[1] Pennisi, E. (2004) Bonemaking protein shapes beaks of Darwin's finches. Science, Vol. 305. no. 5689, p. 1383, available at : http://www.sciencemag.org/cgi/content/summary/305/5689/1383

[2] West-Eberhard, M. J. (2003) Developmental Plasticity and Evolution. Oxford, UK, Oxford University Press. See especially pages 147 to 158.

--Allen