Sorry, about the outage. I accidentially cut off my machine when I left the lab yesterday.
August 2004 Archives
It has been a while since the last EvoMath. In this installment I am going to begin to discuss classical selection theory. Selection occurs when certain alleles are likely to transmit more copies of themselves to the next generation than other alleles at the same locus. The simplest way to think of this is in terms of the viabilitity of individuals. If an individual dies before it can reproduce, then it is not able to transmit its genes. If such a death was influenced by the genes it carried then selection can occur. Classical selection theory assumes that there exists viability selection and that it is constant, i.e. independent of allele or genotype frequencies. There is also theory behind frequency-dependent selection, but it beyond the scope of this article.
First up, we are going to look at selection on a haploid locus with two alleles. These are the assumptions we are going to make, so that we can develop the model.
- Infinite population size
- No mutation or migration
- Constant viability selection
- Discrete, non-overlapping generations
- Asexual reproduction
Haploids only carry one copy of each gene, thus we are concerned with two genotypes: A and a. A proportion of each of these genotypes will survive long enough to reproduce. This proportion is called the absolute, viability fitness (AVF). Let the AVFs of A and a be and respectively. To demonstrate how this selection works, we are going to temporarilly assume that each generation begins with a constant number of individuals, , where is the number of individuals of genotype , and where and are the proportions of A and a individuals respectively. Through selection, only a proportion of these genotypes survive to adulthood. Therefore, the number of adults is
where is the average fitness of the population. The proportions of individuals amongst the adults are
Because the N’s cancel out, clearly
And because the number of offspring in the next generation is infinite, the genetic makeup of the offspring will be equivalent to that of the adults. Thus if subscript represents the adult generation,
Now that we have determined the equation of evolution for our model. We can ask some questions about it. The first question usually asked is when will it stop, i.e. . The population is considered to be at equilibrium if this relationship holds true. What are the equilibria in our model? If , then at equilibrium
This implies that three are two trivial equilibria, and which correspond to the situations where only one allele remains in the population. This demonstrates an important point about evolution: no genetic diversity, no evolution. Furthermore, if , the population will always be at equilibrium regardless of the allele frequency. This demonstrates another important point, that selection produces evolution only when there are differences in fitness.
The stability of equilibria is very important. An equilibrium is considered stable if there exists a neighborhood of allele frequencies around it for which the population will end up at that equilibrium. There is a very simple way to determine if an equilibrium is stable or not. Let . If then the equilibrium, is stable. If it is unstable. And finally, if it is neutrally stable. For this model,
which implies that the equilibrium, , will be stable if and only if . Since ,
which implies that the equilibrium, will be stable if and only if .
Now the next question usually asked is what is the direction of evolution, i.e. when is positive or negative? Since, , , and are always positive, the sign of is then determined by . Thus will be positive if and only if and will be negative if and only if . From this you can see that A increase in frequency if it is favored, and will decrease in frequency if it is disfavored.
We can look at the average fitness, as the population fitness. How does evolution change the population fitness? First note that since is a linear function, its maximums and minimums will be found at the boundaries, . Therefore, will be maximized at , if , and maximized at if .
Putting this all together produces the following conclusions, if :
|Condition||Behavior of Alleles||Behavior of Population Fitness|
|A becomes fixed and a extinct.||The population fitness becomes maximized at .|
|a becomes fixed and A extinct.||The population fitness becomes maximized at .|
|Allele frequencies do not change.||The population fitness does not change.|
Since given an intital population that is genetically diverse, the population will evolve to a maximal fitness, this is sometimes refered to as a “hill-climbing” process.
In the next installment, I’ll analysize a diploid model.
It is hard to not conclude that proper peer review procedures didn’t take place with the publication of philosopher Stephen C. Meyer’s “review” in The Proceedings of the Biological Society of Washington: “The origin of biological information and the higher taxonomic categories.” It is simply attrocious, as was demonstrated on the Panda’s Thumb.
I’m having fun playing with FreeBSD. I have the box running Apache2+PHP5+SSL and MySQL. I’ve switched to Perl 5.8, installed APFL GhostScript, ImageMagick, and teTeX. I’m still not sure if I am going to move my website to the box or not.
Should I really be suprised that Agape Press is running this article: Evolution’s ‘Dictatorship’ – Student Struggles to Get Opposite Viewpoint Heard?
This is probably a foreshadowing of what science educators are going to have to put up with as the ID movement makes more and more political inroads in local communities.–Heck, we’ve probably been there for a while.–However, I can’t help but laugh when people make the following pleas as if they mean something.
As the struggle unfolded, it became obvious that those who opposed Behe coming to Emmaus didn’t seem to care about his credentials. In addition to publishing over 35 articles in refereed biochemical journals, Darwin’s Black Box was internationally reviewed in over 100 publications and named by National Review and World magazine as one of the 100 most important books of the 20th century.
No they didn’t care about his credentials because his credentials mean jack shit. His scientific papers on biochemistry have no bearing on his statements on evolution. His book might have been reviewed much, but were they favorable? His book has been panned many times over by actual scientists of evolution. Even Behe has admitted that his initial concepts of irreducible complexity are flawed and has promised to provide new, improved ones. The world is still waiting. And come on–World and National Review?–those are not even close to being magazines of science. Why should anybody care what they say when it comes to science?
I can hardly believe that someone is actually so ignorant that they think these are credentials that matter. It’s like saying that the football coach doesn’t care about by crendentials as a short-stop. If this is the best credentials the aideeists can come up with, then there really isn’t much to do besides point and snicker.
Sorry about the lack of updates. I’ve been working hard on my research and setting up a FreeBSD server on a freebox in the lab. I don’t know yet if I will switch my website to it yet. The current machine is my dual 3ghz xeon workstation, running WinXP professional and Apache 2. The FreeBSD machine is only a 850mhz Pentium workstation. I’ll make the switch if I get too much traffic, because Windows XP professional is limited to only ten simultaneous connections at once.
I’ve also been making up some BBQ for a party the graduate students are having tonight for the new popgen students. I’ve been cooking a pork shoulder in a crock pot since 7:30 this morning. In the pot is also a can of Apple-Raspberry Juice concentrate, some additional water, honey, black pepper, red pepper, salt, and cider vinegar.
I initially made too much of the juice for the crock-pot and pork, so I turned the left-overs into a sauce. I boiled it for a while to condense the flavor, then added more vinegar, black pepper, and red pepper. Corn starch thickened it.
This is the first time I’ve tried BBQ in this fashion, and it is a recipe that I developed while doing it. So I don’t have a more detailed recipe to give you. If readers want one, I can try to work something out.
A reader, Dan Fessler, is asking me to publicize some web-based social experiments.
Dan Fessler Wrote:
All studies have been approved by the Office for the Protection of Research Subjects of the University of California, Los Angeles. Participation is completely anonymous, takes only a few minutes, and is unpaid; all studies are open to anyone over age 18. Below are the titles and links:
- An Investigation of the Subjective Determinants of Disgust Sensitivity
- Personality, Personal Taste and American Identity
- Effects of Context on First Impressions
- Are They Hot or Not?
- Salience of Personal Attributes in Social Encounters
- Emotional Reactions to Pictures
These and other surveys can also be reached via our virtual lab homepage.
I haven’t taken any of these surveys myself, so I can’t comment on them further, except to express a general reluctance to draw evolutionary implications from surveys taken over the internet. I’d feel more comfortable if these surveys were taken in multiple cultures. But this is no different than the old way to do surveys which relied on asking undergrads questions. Hopfully, Dr. Fessler will leave a comment that explains how they are going to make inferences from the surveys. As a scientist, I want to know more about the methodology.
I’m sure most of you are now aware that Koko the Gorilla, who can communicate using sign language, recently had a tooth pulled. Using a doll and a pain scale, Koko was able to signal that her mouth was in a lot of pain. Her handlers took the time to give her a full medical examination.
What you are probably not aware of is that a poster on Internet Infidels Discussion Board, Biff the Unclean, works with Koko and her companions. This recent news has encouraged him to share some Koko stories. You can find earlier threads with Koko stories by searching the board.
Apparantly Koko will tell jokes.
When asked how she had slept after her tooth was pulled she answered…”on floor with blanket” followed by a loud, Herman Munster-like, laughter.
Weeks before our male had thrown something awful at a volunteer. When he finally became friends with him a care giver asked Ndume what name should we call the volunteer? Should we call him “workman”? Koko butted in and laughing said “vomit catch man.”
And there is the ever popular “big gorilla sit want” which started life as the 500 lb gorilla joke and has lost most of its substance but none of its hilarity.
And some very interesting information about Gorilla Sign Language.
She speaks what we call GSL which is slightly different from ASL, mainly because of gorilla anatomy and custom. Holding your arms out from your body is a rude gesture to a gorilla, a threat sign. Much like “giving the finger.” Any signs that require that have been modified. Also gorillas have thumbs on their feet, so if she wants to say ‘tickle my feet’ she will sign tickle with her foot. She will also combine signs to say two things at once. Something you probably wouldn’t put up with from a deaf person, but every ASL speaker, so far, has found it fascinating.
And, wouldn’t you know it, idiots, i.e. creationists, have come out of the woodwork.
There have been phone calls this week that weren’t from well wishers. One young fellow said “You teach gorillas instead of people, you should die.”
Four Fundies called seperately to tell us that we were liars. Talking gorillas cannot happen, God was against it. And a radio station in San Antonio Texas did a live interview with one of our people. The interviewer stopped her in the middle of telling about Koko’s abilities to tell her that they, the interviewer, and the audience were all Christians and did not want to hear any evolution stuff. She had no idea of how to respond this comment out of left field, and hours later was going on about what she “should have said.”
And on a final note, I once got Biff to ask Koko if humans were apes, and she responded that humans were not apes because they weren’t pretty enough. A much better argumnet than anything creationists have every come up with.
It’s that time of year again, when the golden garden spiders (Argiope aurantia) come out. We have at least three in our back yard right now. I took this picture of one today with my digital camera.
I had hoped to show some of my Yankee readers a bit of southern wildlife, but these critters range all the way up into Canada. I guess that just leaves me with pictures of the freshmen coeds as they come to campus and sunbathe on the quads. Man, we got some good scenery around here. Athens wasn’t named the top bachelor town for no good reason. I should know, I married one of them.
I’ve been using Firefox for a while as my webbrowser. It takes Internet Explorer to the wood shed. Today I started using Thunderbird as my email client. So far I’m getting everything I had with Outlook, and a little more. I do miss the nice interface of writting emails with Word.
I recommend that all my readers consider dropping Outlook and IE in favor of these new products.
Anti-evolutionists often make political inroads by relying on America’s sense of fair play in addition to our scientific illiteracy. The average American responds favorably to the loaded suggestion that all ideas are equally valid and asks, “why shouldn’t science class treat all ideas equally?” Our challenge as supporters of science education is to teach the average American that science is not a “fair” process, but one that is based on merit, and that not all ideas are equally valid. Realizing that many Americans are familiar with another merit based school program, sports, I have developed the following analogy.
Movable Type 3.0 allows blogs to have registered comments. This means that the software authenticates comments with the TypeKey servers. This should virtually eliminate spam. However, it could discourage people from commenting.
I have enable registered comments, but I’m not sure that my readers like the feature or not. Please send me an email and tell me what you think.
I’m trying to gauge the opinions of my readers on this.
The California Alternative High School in Los Angeles targets Hispanic immigrants, promising them that a 10-week course can grant them a valid diploma which can help them get a job. However, the school is not accredited and has ignored court orders to stop taking advantage of immigrants.
[California Attorney General Bill] Lockyer said the curriculum consisted of a slim workbook riddled with errors, including:
- The United States has 53 states but the “flag has not yet been updated to reflect the addition of the last three states” – Hawaii, Alaska and Puerto Rico.
- World War II began in 1938 and ended in 1942.
- There are two houses of Congress – the Senate and the House, and “one is for Democrats and the other is for the Republicans, respectively.”
The school’s chief executive officer, Daniel Gossai, claimed to have a teaching credential and two doctorates, but prosecutors said they found no evidence that he does. He was a teacher at Victor Valley Community College in the late 1970s, but was fired for immoral conduct, dishonesty and being unfit for service, Lockyer said.(CNN)
It is clear to me that Gossai is not simply teaching errors, but deliberately doing it. I bet he and his friends get a good laugh about teaching immigrants to be ignorant, while taking their money. I really hope that he gets shut down and sent to jail.
Inspired by the style I’m working on for my wife’s blog, I have decided to begin a new style on this blog. Comments are appreciated.
Our president is finally telling the truth about the politics of his administration:
Our enemies are innovative and resourceful, and so are we. They never stop thinking about new ways to harm our country and our people, and neither do we.
You probably won’t see this in a Democratic campaign ad, but if Kerry had said it, the GOP would have it in 15 second TV spots playing every hour.
A few months ago my first paper was published in Genetics: Asumssen, Cartwright, and Spencer (2004) Genetics 167 (1): 499. Since it is now publically available, I am going to now explain parts of it to my readers.
Classic models of selection usually deal with constant selection. This is where the fitness of a genotype is independent of its frequency in the population. However, we know from natural studies that this is not always the case. One classic example of frequency-dependent fitness is the advantages that rare phenotypes can have in avoiding predators or acquiring mates. (I often think of the latter as the “foreign-exchange student” advantage.) Rare phenotypes may also be disadvantaged in herding/schooling species, as another example.
In the ACS paper, we analyzed a model of frequency-dependent selection that involved dominance. The condition of dominance simplified the model and allowed us to explicitly solve it. I won’t go in to much detail about the ACS model, unless y’all ask me to. However, I will discuss our results.
In the model, allele frequencies always change monotonically. They either always increase or always decrease to an equilibrium. No limit cycles or damped oscillations occur. In other words, allele frequency trajectories have simple behaviors. The structure of the mean fitness is also simple. As a function of the allele frequency, it has four simple shapes: always increasing, always decreasing, increasing to a maximum then decreasing, or decreasing to a minimum then increasing. However, when put together these two classic behaviors, produce atypical results.
Unlike with constant viability selection, this model has a polymorphic equilibrium that does not coincide with the maximum or minimum population fitness. This allows evolution to actually overshoot the optimum population fitness before settling down at a lower value. Evolution can also drive the population through a fitness valley, i.e. a minimum population fitness.
In total, an atypical behavior of the mean fitness of the population resulted from 35% of the parameter space. Furthermore, the population will end up with a mean fitness lower than when it started 20% of the time and will have an average decrease of 17%. If we are discussing viability selection, this means that 17% of the adults that used to survive to reproduction no longer do. This is a situation where simple competition between individuals hurts the population as a whole.
Yesterday was our second wedding aniversery. My wife and I went out to eat in downtown Athens at The Grill, which serves the best burgers in town. We didn’t do much because I was stressed out by the fact that my department forgot to pay me for July, and we were flat broke. After dinner, I went to the lab to get some work done, which helped reduce my stress level. (My wife is understanding, adorable, and sweet.) We went to go to see The Village this afternoon to continue our date. We both liked it. It was a very interesting story, which I won’t spoil for y’all.
Here is our Wedding Announcement from two years ago:
Mr. and Mrs. Gilbert F. Andrews of Ellerslie announce the engagement of their daughter, Tiffany Brooke Andrews, to Reed Austin Cartwright, son of Mr. and Mrs. Robert Ridgway III of Athens and Mr. Marion Cartwright of Royston.
Miss Andrews is the granddaughter of Mrs. Ruth Andrews of Ellerslie and the late Mr. Charles E. Andrews, and the Rev. and Mrs. Billy Colquitt of Manchester.
Mr. Cartwright is the grandson of Mr. Homer Lee Cartwright of Tifton, Mrs. Lucile Cartwright of Athens and the late Mr. and Mrs. Kenneth Hart of Americus.
The future bride is a 1997 graduate of Harris County High School and a 2000 graduate of the University of Georgia.
The future groom is a 1997 graduate of Athens Academy and a 2000 graduate of the UGA. He is a Ph.D. student in population genetics at UGA.
The wedding is planned for 7 p.m. Aug. 3, 2002, at the Callaway Gardens Sibley Center in Pine Mountain.
I am currently working on a blog for my wife. When we’re ready, I’ll post a link to it.
I’ve updated my blog software to Movable Type 3. This is in anticipation of doing the same for PT.
I would like to follow up on Phil Jackson’s fine letter (July 28) on the origins of the term “separation of church and state” and the First Amendment.
The First Amendment is the only amendment in the Bill of Rights to state specifically “Congress shall make no law …,” or even refer to Congress. It was written this way not only to prevent Congress from establishing an “official national religion,” but so individual states could have “official state religions.”
No Constitution or Bill of Rights could have been adopted without this distinction. During the times when the Constitution and later the Bill of Rights were being debated, somewhere between four and seven states had “official state religions” (depending on how one defines official). This allowed the states to go as far as taxing their citizens to build houses of worship and pay the clergy of the official religion, and denying the right to vote and hold office in that state unless you were a member of the official religion.
It was not until 1833 (42 years after adoption of the Bill of Rights) when Massachusetts legally separated itself from the Congregational church did the practice of “official state religions” end.
On a personal note, I find it a far leap between what the Bill of Rights was written to allow and what modern courts won’t allow.
There are some major flaws in Hall’s argument. First, every state, including Georgia, incorporates the first amendment in one way or another into their consitution. So arguing on federalism doesn’t get you anywhere. Of course, state judges, who are usually elected, often refuse to apply constitutional protections to unpopular groups, particularily to minority religious groups. The failure of states to ensure the rights of their citizens one of the reasons why we have the Fourteenth Amendment.
Amendment 14, Section 1
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.
This clause is what renders the “Congress shall make no law…” obsolete in the first amdendment. Because of the fourteenth, the first amendment no long applies to just congress. It applies to every level of government. This fact of constitutional law is regularly lost on right-wingers, who are convinced that they have a slam dunk argument.
These same people often don’t realize that in arguing that the First Amendment applies only to congress that they are affecting more than just the establishment clause. In fact, if their logic holds, then States would be free to prohibit free exercise of religion (bye, bye Baptists), abridge the freedom of speech (bye, bye Rush Limbaugh), the freedom of the press (bye, bye Fox News), the right of the people to peaceably assemble (bye, bye NRA gun clubs), or to petition the Government for a redress of grievances (bye, bye ACLJ).
By arguing in favor of establishing themselves over others, they are in turn establishing their own downfall. The First Amendment, coupled with the Fourteen Amendment guarentees that a Baptist child in Utah doesn’t have to recite Mormon prayers and a Mormon child in Texas doesn’t have to recite Baptist prayers.