Lesson 15

This lesson we're going to explore mutation. Our goal is to basically follow mutants and see how different factors influence how the frequency of new mutations changes, though that is largely going to be driven by selection. But also to understand how recombination and new alleles interact with one another. And to gain an understanding of something called coalescence, and the time to the most recent common ancestor. This refers to the fact that, while you think of yourself as having parents, plural, each individual locus in you has one parent, singular. You have 2 copies of each locus, but those 2 copies each came separately from a different parent, and each came separately from a different grandparent. So while you have 4 grandparents, you only have 2 copies of each locus, which means each of your loci can be traced back to one grandparent, and one copy in that grandparent. Another way to think about this, kind of counterintuitively, is that because of recombination, you get something very close to asexual reproduction from the standpoint of a single locus. As a result, we can trace the ancestry of individual loci back separately from the ancestry of a whole organism.

We are going to play a little game for this part A. You can play the game yourself by hitting Play the season, or you can let the computer play it and just watch. But if you play it or just watch, you're going to control a snake. A garter snake. Garter snakes, at least on the west coast, like to eat newts, the genus Taricha, and they are going to be eaten in turn by hawks. You are going to be in a little population, filled with many other garter snakes, competing for a limited number of newts. The more newts you eat, the more energy you have; the more energy you have, the more offspring you can make. So you're going to have a period of time in which you are eating newts and being eaten by hawks, and at the end a random mate will be chosen. The genotype of you and the genotype of your mate will be shown to you. Recombination and meiosis will occur behind the screen to produce some number of offspring; the number is going to be a function of how many newts you managed to eat. And you'll answer some basic questions about whether or not any of your alleles failed to get passed on, about whether your offspring have any recombinant chromosomes (now, recombination is always happening, but a recombinant chromosome will be one where there is a different sequence of alleles along one chromosome than you had to pass on), and whether or not your offspring have any new mutations. You will then, for the next generation, play one of your own offspring, and continue the game.

Eventually you have a long pedigree of 15 generations of snakes. If you play each round, you will create it physically; if you just let the season play, or run for a set number of generations, it will do the exact same thing, just quickly, behind the scenes. Once you have that, you can examine the pedigree by clicking on individual snakes and see their ancestors, shown with red lines, and their descendants, shown with blue lines. You will then have to select the correct things on the pedigree to answer the questions shown at the bottom of the pedigree panel. When you're looking at the pedigree, you can take an organism view, a chromosome view, and an individual locus view. I would recommend exploring all of these. You can see how individual new alleles change in frequency over time, but your goal will be to identify the ancestors of individual loci.

Below the pedigree, I have also given you a manipulable plot, so you can plot different kinds of data over time: the number of snakes, the frequency of alleles at a given locus, the heterozygosity at a given locus, the time at which alleles emerged (arrived by mutation) or were lost (went extinct), and the time to the most recent common ancestor across loci. The time to the most recent common ancestor, the MRCA, is an interesting plot, because if you look at it, you will notice that it doesn't always go up. That's worth pondering over.

This is the same as part A, but with one very small difference. Now, each new mutation is going to have some effect on your fitness. In the first run, you needed 2 newts to make one new snake. So if the 2 snakes came together and they had eaten a total of 6 newts, you could have 3 babies. That's how the number of offspring was determined by how much you had eaten, and that was the same for every snake. Now the number of newts a snake needs to have one offspring's worth of energy is different as a function of their genetics. Individual alleles will have some effect on fitness, s, that controls how many newts you need for a baby, and some heritability, h, which controls the heterozygote condition. Each new mutation will have a randomly drawn s and h. You can see the distributions that they are drawn from at random as blue lines.

Over time, alleles are going to rise and fall in frequency. You will be able to see the distribution of fitness effects that persist in the population at any given time by looking at the gray. The thing to remember is that the alleles present at one time are going to be a function of how many alleles are newly arisen, pulled from the distribution, and how many alleles have been inherited, pulled from the distribution some past generation and not gone extinct yet. As a result, the mismatch between the distribution that is generating and the distribution you see can be quite informative.

The Price equation describes the observed change in frequency of a transmissible trait over time as a function of who transmits, and what gets transmitted. The covariance of fitness (number of offspring) and trait is selection: who gets to transmit. The expectation, the expected value of wΔz, is what gets transmitted: the transmission bias. In the case of genetics, organisms transmit. We reproduce via gametes, which are cells, and the cells contain DNA. The trick is that cells transmit; they transmit by way of mitosis and meiosis. And loci transmit; they transmit by way of copying. What that means is that the transmission bias term for an organism itself contains the change in frequency at the cellular level, and the transmission at the cellular level contains the changes associated with the genetic level. It's a series of nested hierarchies.

The rules in biology do not exist because of some independent auditor. Instead, they are what has evolved. You never hear the jokes that don't get retold. You never watch the films that don't get made. You never see the adults that died in infancy. That's a fundamental truism.

What we're going to see here is an example where you're going to race gametes. There will be 2 alleles, a gray allele and a gold allele. Gray/gray homozygotes have normal fitness. Gray/gold heterozygotes have low fitness at the organism level, and gold/gold homozygotes are sterile. The trick is that in this case, the gold locus, even though in homozygotes it causes sterility, in the individual sperm cells increases the speed at which the sperm swims. What you're going to do is manipulate the effect the gold locus has on sperm speed, to see what happens to the frequency of this allele that causes sterility in the homozygote and poor fitness in the heterozygote. Observe how its frequency changes over time.