The Hardy-Weinberg Equilibrium

It's important to understand modern evolutionary theory and that means it's important to understand the Hardy-Weinberg Equation and what it means.

The significance is explained in all the leading textbooks on genetics and evolution. I've chosen the explanation given by Carl Zimmer and Douglas Emlen because I know that Carl has spent a good deal of time getting it right in his new book Evolution: Making Sense of Life.

Imagine that you have a population with two alleles, A and a, at a single locus. The frequency of the first allele is f(A) to which we assign the value p. The frequency of the second allele is f(a)=q. In a randomly mating sexual population the probability of an A sperm being produced is p and the probability of an a sperm being produced is q. Similarly, the probability of an A egg cell is p and the probability of an a egg cell is q. These probabilities, p and q, do not have to be equal.

We can calculate the probabilities of all possible combinations or sperm and eggs in the population from a the following diagram (Punnett square). This one is from Wikipedia.


Since the total probability has to equal one, we have ....

p² + 2pq + q² = 1

This is the Hardy-Weinberg equation or the Hardy-Weinberg Equilbrium. What does it mean? Let's quote Zimmer and Emlen (page 156).

Hardy and Weinberg demonstrated that in the absence of outside forces (which we describe later), the allele frequencies of the population will not change from one generation to the next. As we'll see below, this theorem is a powerful tool for population geneticists looking for evidence of evolution in populations. But it's important to bear in mind that it rests upon some assumptions.

One assumption of the model is that a population is infinitely large. If a population is finite, allele frequencies can drift randomly from generation to generation simply due to chance variation, in which alleles happen to be passed on to the next generation. (We will explore genetic draft in detail later in the chapter.) While no real population is infinite, of course, very large ones behave quite similarly to the model. That's because variation due to chance is inconsequential, and the allele frequencies will not change very much from generation to generation.

The Hardy-Weinberg theorem also requires all of the genotypes of the locusts are equally likely to survive and reproduce. If individuals with certain genotypes produced twice as many offspring as individuals with other genotypes, for example, then the alleles that these certain individuals carry will comprise a greater proportion of the total in the offspring generation than would be expected given the Hardy-Weinberg theorem. In other words, selection for or against particular genotypes may cause the relative frequencies of alleles to change and results in evolution.

Yet another assumption of the Hardy-Weinberg theorem is that no alleles enter or leave a population through migration. This assumption can be violated in a population if some individuals disperse out of it or if new individuals arrive. The model also assumes that there is no mutation in the population, because it would lead to new alleles

In each of these four cases, the offspring genotype frequencies will differ from the equilibrium predictions of the Hardy-Weinberg theorem. That is, because they alter allele frequencies from one generation to the next, selection, migration, and mutation are all possible mechanisms of evolution.

The Hardy-Weinberg theorem is useful because it provides mathematical proof that evolution will not occur in the absence of selection, drift, migration, or mutation. By explicitly delineating the conditions under which allele frequencies do not change, the theorem serves as a useful null model for studying ways of allele frequencies do change. The Hardy-Weinberg theorem helps us understand explicitly how and why populations evolve. By studying how populations deviate from the Hardy-Weinberg equilibrium, we can learn about the mechanisms of evolution.

There you have it. The Hardy-Weinberg describes the situation where evolution DOES NOT HAPPEN and thus serves as the null hypothesis for testing whether evolution is happening. Every undergraduate knows this.

Let's see if the Intelligent Design Creationists know this. I'm quoting "niwrad" from a post on one of the leading ID websites, Uncommon Descent: The equations of evolution.

For the Darwinists “evolution” by natural selection is what created all the species. Since they are used to say that evolution is well scientifically established as gravity, and given that Newton’s mechanics and Einstein’s relativity theory, which deal with gravitation, are plenty of mathematical equations whose calculations pretty well match with the data, one could wonder how many equations there are in evolutionary theory, and how well they compute the biological data related to the Darwinian creation.

....

The Hardy-Weinberg law mathematically describes how a population is in equilibrium both for the frequency of alleles and for the frequency of genotypes. Indeed because this law is a fundamental principle of genetic equilibrium, it doesn’t support Darwinism, which means exactly the contrary, the breaking of equilibrium toward the increase of organization and creation of entirely new organisms. To claim that the Hardy-Weinberg law explains evolution is as to say that in mechanics a principle of statics (immobility) explains dynamics (movement and the forces causing it).

....

So the initial question, how well math support Darwinian evolution, has the short answer: it doesn’t support evolution at all. Despite of the pretension of evolution to be a scientific theory with the mathematical certitude of the hard sciences, properly the equations of evolution do not exist.

As you can see, the Intelligent Design Creationists interpret the "Hardy-Weinberg law" very differently, I wonder who is right?

Let's check with Joe Felsenstein. He's an expert on population genetics so he should know. Read his decision at: Evolution disproven — by Hardy and Weinberg?.

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He Likes Me ... He Really Likes Me!

David Klinghoffer likes me and he's not afraid to say so [Laurence A. Moran, University of Toronto Biochemist and Darwin Skeptic]. He says,

Welcome aboard, Dr. Moran! The U. of Toronto biochemist surprised us by indicating in a post at his Sandwalk blog that he could sign on to the statement in the Scientific Dissent from Darwinism ....

Let me remind readers what the statement says ...

We are skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged.

Just about every evolutionary biologist would have to agree with this statement if they were being honest. So why is this such a big deal for the Intelligent Design Creationists? Why do they promote their list of signatories in their publications and why do they continue to solicit signatures on their website? [A Scientific Dissent from Darwinism]

David Klinghoffer has the answer. Do you believe him?

... no one says that the signers of the Dissent list are creationists, other than Darwin advocates who dishonestly try to cement the absurd, fallacious equation of Darwin skepticism with Young Earth Creationism. The list has nothing to do with creationism. Nor does it say anything about intelligent design, which also has nothing to do with creationism.

Okay, so the list has nothing to say about intelligent design. So what is its real purpose?

Any scientist who agrees with the statement that heads the Scientific Dissent from Darwinism is a Darwin doubter, that's all -- and congratulations to him or her! Simply to relay the fact of his skepticism on orthodox evolutionary theory is hardly a misuse of anyone's name. It just reports some interesting and good news. What's wrong with that? For Darwin defenders, the thing that's wrong is that it undercuts their main defense: the assertion that nobody doubts Darwin's theory, or only religious nuts do so, and so there is no legitimate controversy on evolution.

We've always said that private doubts about Darwinian theory are far more widespread in scientific life than the media let on. Now on that point we have Dr. Moran's helpful confirmation.

Hmmm ... that's what this is all about? The IDiots know full well that most evolutionary biologists aren't strict Darwinists but they just want this to become more widely known? If that's true then they could certainly help out by explaining the correct version of modern evolutionary theory—including random genetic drift— to their supporters and advising them not to use the term "Darwinism" as a synonym for "evolution." That would make sense, right?

From now on, I expect David Klinghoffer and all his friends to use "modern evolutionary theory" to describe the position of their opponents. I expect them to avoid the word "Darwinism" since, by their own admission, they know that it's wrong.

Not holding my breath .....

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The title of this post is a reference to a statement by Sally Field

at her Oscar acceptance speech in 1985. I know that I'm paraphrasing a misquote.

Doug Axe Challenges Darwinian Evolution

Here's a video where Douglas Axe tries to explain why Darwinism is wrong. I'm going to let Sandwalk readers discuss the many flaws in his argument but first I want to mention two things.

1. Jeffrey Shallit shows that his statements about information theory are about as accurate as his statements about evolution. [Doug Axe Doesn't Understand Information Theory]
2. Like most IDiots, Doug Axe continues to equate Darwinism and natural selection with evolution. He does this in spite of the fact that his colleague, Ann Gauger, claims to understand the difference. According to her, scientists who doubt Darwinism can still be firm supporters of evolution. If the IDiots actually believe this then why do they keep using the term "Darwinism" to describe their opponents?

The bit about junk DNA in the video reveals that Doug Axe doesn't known dick about evolution or Darwinism. The version of evolution known as Darwinism rejects the idea that most of our genome is junk. I don't think Doug Axe can handle that kind of truth.



Remember folks, this is just about the best they have to offer.

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I'm a New Friend of Ann Gauger

A few days ago I posted a message about the IDiots' list, A Scientific Dissent from Darwinism, of people who disagree with Darwinism. I specifically mentioned Joshua Youngkin who said that, " 'A Scientific Dissent from Darwin,' is a thorn in the side of those who say there's no scientific debate over whether evolution works in a completely naturalistic fashion." [Our "Scientific Dissent from Darwin" List: A Reader Inquires] Let's be clear about what he said, he said that the list reveals scientific debate over whether "evolution works in a completely naturalistic fashion." In other words, people who sign the list must be non-naturalists. That's another word for creationist.

Here's the statement ...

We are skeptical of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged.

Note that the statement says noting about whether evolution works in a completely naturalistic fashion. The IDiots know full well that most scientists would agree with the statement taken at face value but we all know that the IDiots will misuse the statement just as Joshua Youngkin did on the Evolution News & Views blog. You can find further proof of the treachery of the IDiots at the list website where the following quote from someone named Raul Leguizamon is prominently featured on the home page.

I signed the Scientific Dissent From Darwinism statement, because I am absolutely convinced of the lack of true scientific evidence in favour of Darwinian dogma. Nobody in the biological sciences, medicine included, needs Darwinism at all. Darwinism is certainly needed, however, in order to pose as a philosopher, since it is primarily a worldview. And an awful one, as George Bernard Shaw used to say.

The implication is clear.

Ann Gauger is thrilled to discover that I'm not a Darwinist [Our New Friend, Laurence A. Moran]. I guess she's under the impression that if you're not a Darwinist then you must be an IDiot like her.

Here's how her mind works ...

1. People on the Dissent from Darwinism list are supporters of the statement.
2. Larry also agrees with the dissent statement.
3. Larry says only IDiots claim that supporters of this statement are creationists.
4. Larry says that Project Steve is a excellent parody of the "creationist" list, thus in effect calling supporters of the statement creationists.

Wait. Following the logic there, that would seem to make Dr. Moran an IDiot, in his own eyes anyway. Not that, in pointing this out, I mean it unkindly.

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Who Owns Your Genome?

The sequence of your genome contains lots of information about you. It also contains lots of information about your parents, your siblings, and your children. That's why you should not make your genome sequence public without obtaining their permission.

The sequence of Henrietta Lacks' genome was just published (HeLa cells) and nobody bothered to seek permission from her survivors. Jonathan Eisen has a comment and he has also collected all the information on the internet [HeLa genome sequenced w/o obtaining permission/consent from family - some comments and background]. Be sure to read the New York Times article by Rebecca Skloot: The Immortal Life of Henrietta Lacks, the Sequel. She says,

LAST week, scientists sequenced the genome of cells taken without consent from a woman named Henrietta Lacks. She was a black tobacco farmer and mother of five, and though she died in 1951, her cells, code-named HeLa, live on. They were used to help develop our most important vaccines and cancer medications, in vitro fertilization, gene mapping, cloning. Now they may finally help create laws to protect her family’s privacy — and yours.

In my opinion, there is no excuse for publishing this genome sequence without consent.

Razib Khan disagrees. He thinks that he can publish his genome sequence without obtaining consent from anyone else and I assume he feels the same way about the sequence of the HeLa genome [Henrietta Lacks’ genome, and familial consent].

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Do Invertebrates Really Make Up 80% of All Species on Earth?

bug_girl has a new post called Planet of the Arthropods. She asks why we should care about invertebrates, "Why should we care about a bunch of squishy boneless animals? Because invertebrates make up EIGHTY PERCENT OF ALL THE SPECIES ON EARTH. They truly are the 'little things that run the world.'"

She links to this image ...


Isn't that amazing! Single-celled eukaryotes, fungi, and bacteria make up such a small percentage of total species (<1%) that they don't even register on this summary!

Here's a phylogeny of eukaryotes (no bacteria) from Keeling et al. (2005). If you look closely, you can find "animals" down in the lower right-hand corner. Isn't it amazing that one little insignificant branch represents 83% of all species on the planet? Seriously, something is wrong with taxonomy if this is even close to being true.


Estimates of the total number of bacterial species range from about one million to about one billion [Jonathan Eisen]. Read Carl Zimmer's New York Times article: How Many Species? A Study Says 8.7 Million, but It’s Tricky for an interesting perspective.

The general public has a very poor understanding of our relationship to all other species on this planet. We should be working hard to dispel the major misconceptions about biology and evolution.

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Keeling, P.J., Burger, G., Durnford, D.G., Lang, B.F., Lee, R.W., Pearlman, R.E., Roger, A.J., Gray, M.W. (2005) The tree of eukaryotes. Trends Ecol. Evol. 20:670-676. [doi:10.1016/j.tree.2005.09.005]

Estimating the Human Mutation Rate: Direct Method

This is the fourth in a series of posts on human mutation rates and their implication(s). The first three were ...

What Is a Mutation?
Estimating the Human Mutation Rate: Biochemical Method
Estimating the Human Mutation Rate: Phylogenetic Method

There are basically three ways to estimate the mutation rate in the human lineage. I refer to them as the Biochemical Method, the Phylogenetic Method, and the Direct Method.

The Biochemical Method is based on our knowledge of biochemistry and DNA replication as well as estimates of the number of cell divisions between zygote and egg. It gives a value of 130 mutations per generation. The Phylogenetic Method depends on the fact that most mutations are neutral and that the rate of fixation of alleles is equal to the mutation rate. It also relies on a correct phylogeny. The Phylogenetic Method gives values between 112-160 mutations per generation. These two methods are pretty much in agreement.

The Direct Method involves sequencing the entire genomes of related individuals (e.g. mother, father, child) and simply counting the new mutations in the offspring. You might think that the Direct Method gives a definitive result that doesn't rely on any assumptions, therefore it should yield the most accurate result. The other two methods should be irrelevant.

This would be true if the Direct Method were as easy as it sounds but things are more complicated.

Michele Bachmann Lies About Socialized Medicine

Michele Bachmann is an IDiot but I try to avoid commenting on the fact that she's a duly-elected congresswoman from Minnesota. If Americans want to elect someone like her to run their country then that's up to them.

People in the civilized world outside of the USA are puzzled by some of the things she says—they wonder how she can get away with such statements and still be elected. Her recent speech on "Obamacare" in Congress is a case in point. You can see it in the video below. This is the speech where she says, ""Repeal this failure [Obamacare] before it literally kills women, kills children, kills senior citizens."


Later on her spokesman, Dan Kotman, issued the following statement.

Obamacare is forcing doctors into the employ of cost-cutting hospitals, gives government the authority to determine services that will and will not be covered, has a board independent of Congress that can cut payments for care, and allows the Secretary of Health and Human Services to force all health plans to eliminate any doctor that doesn't practice medicine the government's way. The history of government-run health care systems around the world is a history of denial, delay and sadly even death.

It's one thing to attack "Obamacare" but when she attacks healthcare in Canada and all other civilized countries, that's a different issue.

Let me remind you that there's tons of data showing that people live longer in other countries and they survive cancer better. Infant mortality is lower in other countries. And this success is achieved at lower cost than health care in the USA. In other words, Michele Bachmann is dead wrong when she says that socialized medicine is a "history of death."

As I was preparing this post I stumbled across a video of Senator Jeff Sessions of Alabama defending American health care in the Senate of the United States Congress. Are Americans embarrassed by speeches like this or is this typical of Americans who have been elected to the Senate? Is it the best that Alabama has to offer?

Sen. Jeff Sessions: 'So We've Got People Who Die Sooner'

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Mocking Friedman's MOOCs

Thomas L. Friedman is the Op-ed columnist for foreign affairs at the New York Times. He has won three Pulitzer Prizes (1983, 1988, 2002).

According to Wikipedia, Friedman has an undergraduate degree from Brandeis University (Boston, USA) and a Master's degree from Oxford (UK). He taught a class at Brandeis in 2006 but as far as I can tell that's his only experience with university outside of being a student. He does not appear to be an educator and he doesn't appear to have any expertise in pedagogy.

That hasn't prevented him from writing three opinion pieces on the imminent demise of universities and the glorious future of online courses—especially MOOCs (Massive Open Online Courses).

Come the Revolution May 15, 20012
Revolution Hits the Universities January 26, 2003
The Professors’ Big Stage: March 5, 2013

Goodbye John Witton

I'm rather proud of the fact that few people have been banned from this blog. That's why it's worth a special post when someone gets banned.

John Witton can no longer post comments on Sandwalk. He has proven that he is a liar when he backed out of his offer to pay $1000 to anyone who would answer his questions [John Witton Will Pay You $1000 to Answer One of His Questions].

More importantly, he continues to spam the comments sections of several posts. Nothing that he says is relevant to the topic and many of his recent comments are delusional.

Goodbye John Witton.

He joins a special group of people who have been banned from Sandwalk: Joe (Joseph) Bozorgmehr (Atheistoclast), David Roemer, and Douglas Dobney. The fastest and easiest way to get banned is to try and intimidate me (or any other blogger) by writing nasty letters to our employers and/or bosses. That's how David Roemer, and Douglas Dobney got banned. Equally efficient is to post lots of comments attacking my integrity and accusing me of all sorts of vile (untrue) things (Atheistoclast). Witton took the slow route to being banned.

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Estimating the Human Mutation Rate: Phylogenetic Method

This is the third in a series of posts on human mutation rates and their implication(s). The first two were ...

What Is a Mutation?
Estimating the Human Mutation Rate: Biochemical Method

There are basically three ways to estimate the mutation rate in the human lineage. I refer to them as the Biochemical Method, the Phylogenetic Method, and the Direct Method¹.

The phylogenetic method relies on a known phylogenetic tree to pick out close relatives and the approximate time to the last common ancestor. In the case of humans, we know that chimpanzees and bonobos are our closest cousins and we think that the homind line diverged from the chimp line about 5 million years ago.

On the Effectiveness of Ridicule and Mockery

From time to time we hear from religious people who are upset about the way we treat their faith. They claim that by making fun of their logic and their defense of god we are only making religious people more convinced that they are right. According to them, we'll never convince any religious person to abandon god(s) by using ridicule and mockery.

Perhaps that's right but I very much doubt it. Here's Sam Harris illustrating the power of ridicule to make a point.

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[Hat Tip: lutesuite]

ENCODE & Junk and Why We Call Them IDiots

The Intelligent Design Creationists have been following the debate over the ENCODE results. For them this is a serious issue since they are committed to the idea that well-designed genomes should not be full of junk. You'd think that the IDiots would make an attempt to learn the real scientific issues at stake.

Let's see how andyjones does on Uncommon Descent: Function, the evolution-free gospel of ENCODE. He says,

Apparently, ENCODE are to be criticised for using an ‘evolution-free’ definition of function. Yep, you heard that right. You thought that function was function was function, but oh no, you must use a evolution-y definition or you will not get the ‘correct’ evolution-y answer. It seems awfully like you need to presuppose Darwinism or you will not find Darwinism. Can that be right?

The excuse for this is some interesting Darwinian philosophy (or do I mean sophistry? – make up your mind below): the authors believe that function means nothing (is purely subjective) unless it is selected for. For example, the heart causes the pericardium (the membrane around the heart) to not collapse by filling space, so we could call that a function, but it is selected for pumping blood.

....

Amongst other things the ENCODE authors are lambasted for not distinguishing between ‘Junk DNA’ and ‘Garbage DNA’. No seriously, ‘junk’ now means stuff that is functional, but not used very often, but could be used, like stuff in your attic is ‘junk’. It is different from ‘garbage’, which is the stuff that you would put straight in the bin. ‘junk’ is now a rather misleading word for ‘functional’. So our genome is full of ‘junk’ that is useful and functional, but to a Darwinian it does not count until it starts getting used so that natural selection can get the credit. How convenient! The possibility of design is sidestepped by careful choice of language. Welcome to 1984! A better word might be ‘archived’ rather than ‘junk’.

...

I, and many of us, hold to an ID worldview firstly and most securely because of what we know about prebiotic chemistry and thus the origin of the first life form. Based on that, because I know there has been a designer involved, I think probably a lot of ‘junk’ will turn out to be ‘brought down from the attic’ at various stages of an organisms life, especially in the developing stages. Time will tell.

Scientific means finding out what is actually there. ENCODE are to be praised for doing that. Darwinism has always been about telling creation myths from the point of view of naturalism (roughly, physics only), and shoehorning every fact into the story. ENCODE are now receiving scorn because they did not wait for the Darwinian imprimatur. Intelligent Design people and creationists (in fact everyone who is not a Darwinist) should take courage from this, jump in and start driving forward ordinary mainstream science, but just make sure they sidestep the attempts to sign them up to that cult.

Does anyone still wonder why I refer to Intelligent Design Creationists as IDiots?

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Estimating the Human Mutation Rate: Biochemical Method

This is the second in a series of posts on human mutation rates and their implication(s). The first one was ...
What Is a Mutation?

There are basically three ways to estimate the mutation rate in the human lineage. I refer to them as the Biochemical Method, the Phylogenetic Method, and the Direct Method.

The biochemical method relies on the well-known fact that the vast majority of mutations are due to errors in DNA replication. Since we know a great deal about the replication complex and the biochemistry of the reactions, we can calculate a mutation rate per DNA replication based on this knowledge. The details are explained in a previous post [Mutation Rates]. I'll give a brief summary here.

The overall error rate of DNA polymerase in the replisome is 10^-8 errors per base pair. Repair enzymes fix 99% of these lesions for an overall error rate of 10^-10 per bp. That means one mutation in every 10 billion base pairs that are replicated.

Theme

Mutation

-definition
-mutation types
-mutation rates
-phylogeny
-controversies
The human haploid genome is 3.2 × 10⁹ bp. [How Big Is the Human Genome?] [How Much of Our Genome Is Sequenced? ]. That means that on average there are 0.32 mutations introduced every time the genome is replicated. In the male, there are approximately 400 cell divisions between zygote and the production of a sperm cell.¹ This gives a total of about 128 new mutations in every sperm cell. In the female, there are about 30 cell divisions between zygote and the production of egg cells. That's about 10 new mutations in every egg cell.

Adding these together gives us about 138 new mutations in every zygote. Let's round this down to 130. Thus the estimate from the Biochemical Method is ..

130 mutations per generation

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[Image Credit: Wikipedia: Creative Commons Attribution 2.0 Generic license]

1. This depends on the age of the man when he has children. The value used here is approximately the average for a 30 year old man.

Monday's Molecule #200

This is the 200th Monday's Molecule. I started this series back on November 13, 2006. Today's molecule is a repeat of that first one. Let's see if readers in 2013 can do better than those in 2006! The last "Monday's Molecule" was puromycin [Monday's Molecule #199]. The winners were Bell Gunn and River Jiang. River needs to contact me by email to set up a lunch date. I'm going to try and treat all the previous winners this week so if I owe you a lunch you should get in touch right away to collect.

The mystery molecule is an aldohexose. There are 16 different aldohexoses. The structures and names of 8 of them are show below in order to help you out.

This is a tough one. You have to know several carbohydrate naming conventions and you have to understand Fischer projections. Good luck.



Post your answer as a comment. I'll hold off releasing any comments for 24 hours. The first one with the correct answer wins. I will only post mostly correct answers to avoid embarrassment. The winner will be treated to a free lunch.

There could be two winners. If the first correct answer isn't from an undergraduate student then I'll select a second winner from those undergraduates who post the correct answer. You will need to identify yourself as an undergraduate in order to win. (Put "undergraduate" at the bottom of your comment.)