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Monday, January 16, 2017

Not your grandfather's theory of evolution, Part 1

Darwin's theory of natural selection has mutated almost beyond recognition.

W hen people think of evolution, they usually think of the Scopes monkey trial, DNA, and Gregor Mendel and his “pea” plants (as he probably told the narco squad that kept nosing around). But in mankind's unending quest to make science ever more boring ... I mean exciting ... our greatest minds are turning the theory of evolution into a mass of complicated mathematical equations.

The dryness is purposeful. It's there to disguise the unpleasantness of nature. Like Moses turning white after catching a tiny glimpse of God, we cannot face the political implications of evolution. So we cloak it in abstraction.

Small section of a DNA molecule

Before I start, let me dispel a common myth. The biggest myth about natural selection (commonly called Darwinism) is that fitness means the strongest survive. This is not true. Fitness means that individuals are selected by how well they fit the environment. If the environment favors strong, intelligent animals, they will have a selective advantage. But if the environment favors weak, stupid ones, then they will have the advantage. Natural selection is about numbers and only numbers.

When bison are being attacked by a pack of wolves, one bison will sometimes attack and cripple another, leaving its former friend behind to be eaten alive, so the rest can escape without getting injured. A female mouse will kill all its own pups if they are different in any way (a big problem in labs that breed transgenic mice). Chickens, chimpanzees, and even the normally vegetarian rabbits cannibalize each other. Baby sharks don't even wait until they're born; they cannibalize their own siblings while inside the womb.

Flour beetles possess a gene called Medea that somehow causes the heterozygous mother to kill all its own offspring that lack a copy of the allele.[4] From these and other observations, biologists invented the concept of the ‘selfish gene.’

Old-fashioned Darwinism couldn't fully explain these facts. Biology also needed some way to explain evolution in quantitative terms. It found it in, of all places, statistics.

We've come to accept that the programming in our brains has similarities to that in animals. But many resist the idea that evolution is still happening. The fact is, whenever one group increases in size and another decreases in size, whether they interbreed or not, evolution is happening before our eyes. If anything, we are evolving now more than ever.

The Great Plague and human fitness

Human history has been driven by great catastrophes: the medieval European plagues that changed our genetic makeup, both in small ways like the molecules called toll-like receptors that regulate our immune response[1], and in big ways like increased IQ. The one-two-punch of the 20th century wars changed both European culture and the European genome again—and it is impossible to disentangle them.

Evolution starts on the level of DNA molecules. But, like gravity, which starts in subatomic particles but manifests itself in the movements of colossal galaxies, evolution is most visible at the largest scales. It is mainly when populations are separated from each other, as in Samuel Huntington's clash of civilizations, that evolution takes hold.

Evolution happens when genetic traits differ in one population vs another, and when these populations change in relative size. Evolution is not just an isolated tribe changing over time. The numerical expansion and contraction of different social groups is evolution.

Some[5] dispute the idea, often attributed to Alan Grafen[6], that fitness always increases. I think the issue here has to do with how we define fitness.

We often say that evolution tries to maximize fitness. Fitness in this context has nothing to do with physical fitness, intelligence, or strength. It is a parameter that specifies how well an organism matches its ecological niche. By this definition (and it's not the only possible one) it is a tautology: whatever changes is increased fitness.

There will be math in the next section, but stick with me because it tells us something vitally important.

Fisher's Fundamental Theorem

In 1930 Ronald Fisher proposed the Fundamental Theorem of Natural Selection. As modified by George Price in 1972, it says:

The rate of increase in the mean fitness of any organism at any time ascribable to natural selection is equal to its genetic variance in fitness at that time.

Fisher thought of this as the biological analogue of the second law of thermodynamics. Because variance must always be positive, it means that populations invariably evolve toward greater fitness. One interpretation of this is that variance acts as a gradient that drives evolution, though Fisher himself disputed this.

Price, a chemist who had worked on the Manhattan project, devised a formula, now known as the Price equation, which is nowadays taken as proof of Fisher's theorem[2]. The Price equation looks like this:

wΔz = Cov(w,z) + E(w,Δz)

This formula means that the mean fitness w (where mean is indicated by the overbar)* times the mean change in some character trait z equals the covariance of w and z, which is to say by how much w and z change together, plus an expectation term E, which tells us how much the change is transmitted to the descendant—a topic for another article.

This is an amazingly beautiful equation (as equations go). This connection between natural selection and statistics is one of the foundations of modern population genetics.


Covariance is so important that it's worth getting a good intuitive feeling for what it means.

Covariance takes two sets of numbers and produces a positive number if there is a linear relationship between them, and a negative number if there is an inverse relationship. As befits a theory about population, covariance requires two sets of individuals: covariance of a person doesn't make sense, and you couldn't calculate it. But it doesn't have to be sets of people; it could just as well be alleles or anything else that evolves through natural selection.

Covariance is similar to correlation except instead of going from −1 to +1 it goes to infinity. Here are some examples to give you an intuitive feel for how covariance and correlation differ.

     w        z     cov(w,z)   cor(w,z)   w   Δz
1 1, 2, 3, 4 1, 2, 3, 4 +1.667 +1.000 2.500 +0.667
2 4, 3, 2, 1 1, 2, 3, 4 −1.667−1.0002.500 −0.667
3 −1, −2, −3 ,−4 1, 2, 3, 4 −1.667−1.000−2.500+0.667
4 −4, −3, −2, −1 1, 2, 3, 4 +1.667+1.000 −2.500−0.667
5 −1, −2, −3 ,−4 −4, −3, −2, −1 −1.667−1.000−2.500+0.667
6 −1, −2, −3, −4 −1, −2, −3, −4 +1.667+1.000 −2.500−0.667
7 1, 1, 1, 1 1, 2, 3, 4 0.000 0.000 1.000 0.000
w=fitness, z=traits, w=mean fitness (see note below)

In the above table, we also calculated Δz, which is what we want to know, since we can measure the fitness by counting the number of descendants. If Δz is plus, it means the trait is being selected for and it will increase. If it is minus, the trait will decrease. From the table you can see that both beneficial traits and harmful traits (that is, traits that tend to kill the individual off, or in other words, traits that reduce individual fitness) can be selected for. Old-fashioned Darwinism could not predict this.

Negative traits

One example people usually give of a negative trait that increases fitness is altruism. Another is spite, where an individual gets harmed in order to harm a competitor more. It may be surprising, but nature does not select for traits in isolation, only for individuals, who have hundreds of thousands of alleles and perhaps millions of traits.

Culture increases that number, and cultural memes can affect survival as surely as genes. We don't have to be slaves to our genes, and cultural memes evolve just as surely as genes do.

The cartoon version of Darwinism that the Social Darwinists believed—that increased genetic fitness meant improved physical and mental strength—and the 20th century ideologies (Progressivism and Nazism) that tried to implement that cartoon have hampered discussion of important issues.

Evolution is occurring now, as we speak, and whether we acknowledge it or not, evolution will affect the way we respond to disease and interact with each other.

The theory of evolution, now properly called population genetics, has cross-fertilized with information theory in interesting ways. In part 2 we'll discuss what's known as the energy landscape of evolution and some of the current controversies surrounding it.

George Price

Steven Frank's mini-biography of George Price[2] shows that Price was a restless character. Dissatisfied with his work on population genetics, he left his position at University College London hoping to switch to economics. After making brief but fundamental contributions to game theory, he worked for a time as a night office cleaner and became highly religious, giving all his clothes, money, and possessions to homeless alcoholics. In his last year he became engaged in biblical scholarship and tried to untangle apparent contradictions in the New Testament. He died at age 52 in abject poverty as a squatter in London.

1. Laayouni H, Oosting M, Luisi P, Ioana M, Alonso S, Ricaño-Ponce I, Trynka G, Zhernakova A, Plantinga TS, Cheng SC, van der Meer JW, Popp R, Sood A, Thelma BK, Wijmenga C, Joosten LA, Bertranpetit J, Netea MG. (2014). Convergent evolution in European and Rroma populations reveals pressure exerted by plague on Toll-like receptors. Proc Natl Acad Sci U S A. 2014 Feb 18;111(7):2668–73. doi: 10.1073/pnas.1317723111.

2. Frank SA (1995). George Price's contributions to evolutionary genetics. J Theor Biol 175, 373–388.

3. Birch J (2016). Natural selection and the maximization of fitness. Biol. Rev. 91, 712–727.

4. Wade MJ, Beeman RW (1994). The population dynamics of maternal-effect selfish genes. Genetics 138, 1309–1314.

5. Ewens WJ (2014). Grafen, the Price equations, fitness maximization, optimisation and the fundamental theorem of natural selection. Biol. Philos. 29, 197–205.

6. Grafen A (2014). The formal darwinism project in outline. Biol. Philos. 29, 155–174.

7. Ewens WJ (2010). Mathematical Population Genetics I. Theoretical Introduction, 2e, p. 17.

8. Gillespie JH (2004). Population Genetics: A Concise Guide 2e.

* Many terms in population genetics are used in different ways depending on context in a way that can cause confusion. In this case w is individual fitness: w = ∑iwi / N.[5] Elsewhere w is the classical mean fitness of an allele weighted for frequency: w = w11x2 + 2w12x(1−x) + w22(1−x)2 (where x is frequency), or w = ∑gwgqg, where q is the parental generation frequency of the genotype g[5,7] . There are still more definitions in Gillespie[8].

Last edited Jan 22, 2016, 4:55 am

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