Anth 5_ Problem Set 3

Anthropology 005 Problem Set # 3: Fall 2023 Scientists have various methods for studying the world we live in; one of those is building mathematical models of it. A mathematical model makes certain assumptions and attempts to answer what would happen if those assumptions were true. A field called population genetics focuses on mathematical models of evolution. Question 1 on this problem set will introduce you to some basic population genetics. While the field can be quite complex, this problem set isn’t, and won’t go past simple Algebra I. To answer the various parts of question 1, you’ll need the equations and techniques developed on pages 64-66 of your textbook. They rely on the binomial expansion; remember that? It’s the key to the “proportional Punnett Square”. (In case you need additional support on this question, I put a video called “Supplemental video explaining the mathematics of population genetics” on the website, in the Week 4 module.) 1. Sickle-cell anemia is a disease that occurs when a person is homozygous for a particular allele, s , and this condition is very often fatal. It might seem odd that there would be an allele that causes a fatal disease. You probably wonder why selection hasn’t gotten rid of this allele, and we’re going to help you figure that out. Follow the stepping stones… A. The Hardy-Weinberg Equilibrium is written as: 1 = (p 2 + 2pq + q 2 ) Please define each of the four terms in the equation (1, p 2 ,2pq, q 2 ); what does each represent? In the Hardy-Weinberg Equilibrium no natural selection, mutation, or genetic drift is happening, and mating is randomly occurring. This being said, the number value of 1 is equal to the total frequency of alleles. Because there are only two variables (p and q) the sum of the equation must be 100% or in other words must equal 1, you can’t have a population value less than or greater than one during equilibrium . The p 2 value is equal to the frequency of dominant homozygous alleles in the population. The q 2 value is equal to the frequency of recessive homozygous alleles in the population. The 2pq value represents the frequency of heterozygous alleles in the population. The reason there is a 2 in front of the pq is because there are two different instances in which heterozygous offspring can occur (and they occur at the same proportional value). The first is in which the mother gives the dominant allele and the father gives the recessive allele, and the second is when the mother gives the recessive allele and the father gives the dominant allele. So within the proportionate punnett square there are two “boxes” that contain the same value and that’s why a 2 is placed in front of the pq value. B. Now let’s see if population genetics can help us understand the fate of the sickle-cell allele. Let’s assume that some homozygote ss individuals do survive and reproduce, but on average they produce only 12% as many offspring as homozygote SS and heterozygote Ss individuals; they are experiencing strong negative selection. For now, let’s explicitly assume that the SS and Ss types don’t differ from each other in their reproductive success. Finally, let’s specify that the starting

frequencies of the S and s alleles (p and q) are 0.75 and 0.25, respectively. Given these values, please solve for p’ and q’ (the frequencies of S and s after one generation of selection ). After one generation, has anything changed? Does that answer make sense? Please show your work! DAD MOM S = 0.75 s = 0.25 S = 0.75 SS 0.5625 Ss 0.1875 s = 0.25 Ss 0.1875 ss 0.0625 p 2 + ½ (2pq) + 0.12(q 2 ) → equation fitted for a strong negative selection against homozygous ss individuals (0.5625) + (2*0.1875) + (0.12*0.0625) (0.5625) + (0.375) + (0.0075) = 0.945 p’ = [p 2 + ½(2pq)] / 0.945 q’ = [(0.12*q 2 ) + ½(2pq)] / 0.945 p’ = [0.75] / 0.945 q’ = [0.195] / 0.945 p’ = 0.79365079 q’ = 0.20634921 After one generation of selection p’ has increased in comparison to p and q’ has decreased in comparison to q. The frequency of the dominant allele increased, this makes sense because the selection within this generation was against the homozygous recessive allele, meaning that allele would occur less frequently in the population. C. If selection were to operate in this same way for many generations, what would be the eventual frequency of the (recessive) s allele? Why? If selection were to keep operating with the strong negative selection against the s allele that would mean with each generation recessive homozygous offspring would become more and more obsolete. With the selection against the s allele there would be a smaller frequency of s allele in each generation, meaning smaller and smaller frequencies of recessive homozygous offspring would be produced. I’m not sure if it’s accurate to say the recessive homozygous offspring would completely disappear but they would become a smaller and smaller part of the population with each new generation. D. Now let’s add an important real-world observation: Heterozygote individuals (who have one copy of the s allele) have some resistance to malaria, an insect-transmitted disease which can also be fatal (hundreds of thousands of people die of malaria every year). In a particular area where malaria is common these heterozygotes ( Ss ) have the highest reproductive success; ss

Finland? Why? It’s more probable that sickle-cell anemia will be more common in Ghana. Ghana is a tropical environment and a perfect host for malaria, and as we saw from the previous two problems, with the existence of malaria, sickle-cell has a better chance of being reproduced in the offspring of generations. Finland is nontropical and not a great host for mosquitos due to the frigid temperatures. This means that without the moderate selection against the homozygous dominant individuals, sickle-cell disease is more likely to become obsolete with each reproducing generation in Finland. The tropical environment of Ghana allows malaria, which aids the reproductive success of sickle-cell. 2. In at least two ways, gradualism is central to contemporary evolutionary theory. Gradualism is not the idea that evolution is always slow. For example, you know that head and digestive anatomy changed in a Mediterranean lizard population in just 30 generations, and that coat color changed in rock pocket mice in less than 1,000 years. A. Since it’s so central, what is gradualism; what is the key idea that R. A. Fisher’s microscope analogy is intended to convey. Gradualism, at its simplest, is the idea that small mutations are more likely to be beneficial to an organism. They key idea of R. A. Fisher’s microscope perpetuates this idea because the small bump of a microscope will either move you further away–but not by much–from the optimal focus, or even in some cases a small bump can move even closer (or exactly to) the optimal focus. Whereas the large bump of a microscope would take you much farther away from the optimal focus and even if you were close to the optimal focus a large bump is likely to overshoot the optimal focus even if the bump pushed the microscope in the “right” direction. The microscope analogy is another way to say that small mutations are more likely to be beneficial. B. What is the logical defense of that key idea; what do we know about evolution that makes the idea of gradualism likely to be true? Organisms are already very well adapted to their environment, there has been a long history of natural selection that has aided in this. Because organisms are already so well adapted to their environment, it’s hard to imagine any change would be welcomed. That being said, any large mutation is going to change the organism more, and these large changes in organisms are more likely to be harmful because everything is already so well adapted. Gradualism is likely to be true because smaller mutations are more likely to be helpful (they change an organism less) thus, more likely to be preserved by the process of natural selection. When a small helpful mutation is preserved by the natural selection process, this mutation is more likely to be passed on to further generations. In which, new small positive mutations can build off of each other gradually (e.g. increase the complexity of a structure). C. How does that same key idea help us understand the evolution of complex adaptations, like the eye?

The idea that small mutations are more likely to be more beneficial is crucial to the understanding of complex adaptations like the eye because there is no support that an eye occurred in one singular large mutation. When something such as an eye evolves through many different mutations, that means each mutation that changed in the eye structure (that was positive) was kept by the process of natural selection, if the mutation were negative it would’ve been weeded out by natural selection. This means that small helpful mutations kept building off of one another in order to create a complex structure like the eye. A large mutation that affects the eye structure would’ve been likely to have been weeded out, because it would’ve been less helpful or moved the eye structure further away from an optimal eye structure for humans. D. Some mollusks (such as squid) have evolved eyes as complex as yours. What is the evidence that eye evolution in mollusks was gradual? The evidence of eye evolution in mollusks being gradual is that many mollusks today still have less complex eyes and these less complex eyes are equal to the eye components of complex human eyes. Limpets have a patch of light-sensitive cells, which is equivalent to the initial building block of our human eyes. Abalones, nautiluses and marine snails all have different levels of eye complexity, mirroring the second, third, and fourth, building blocks of human eyes. You can actually see the gradual steps of eye evolution throughout different mollusks, with squids having the human eye equivalent. E. Trust me, this is related: How do we tell species apart? We tell species apart based on their reproductive compatibility. If two populations are able to reproduce, they would be considered a species, whereas if two populations weren’t able to reproduce together they’d be considered reproductively isolated and two different species. F. Given your answer to 2E, what role does gradualism play in our model of speciation (the process that produces new species)? Explain. Thinking about the ring species model of birds that was described in lecture, gradualism can lead to the reproductive isolation of populations and thus produce different species (different species meaning reproductively incompatible). In the bird model, the intermediate species were able to reproduce with one another but the small mutations across the populations (that span a wide area of space) lead to the reproductive incompatibility of the species at the “beginning” of the ring, and the “end” of the ring. The seemingly small changes added up and exhibited the production process of a new species.