Anthropology 7 Problem Set #2

Anthropology 7 Problem Set Inclusive fitness, kin selection, and altruism

This series of problems will help you prepare for the examinations, by making certain principles that are important for the course clear. Problem sets are to be turned in to your teaching fellow, and are graded on a satisfactory / unsatisfactory basis. The questions are designed to be easily answerable. If you are having difficulty, see your TA for help.

Background: Recall that you, being human, are diploid. This means that you carry two complete sets of genes, one supplied from your mother in the egg, one from your father in the sperm. The sperm and egg fused to form the zygote that developed into you. These sets of genes exist in the form of two haploid sets of 23 chromosomes (N=23), for a total diploid set of 46 chromosomes (2N = 46) present in the zygote and in every normal cell of your body (all of which were formed by cell division from the original zygote). Thus, each chromosome in you from one parent has a counterpart from the other parent, and such pairs of corresponding chromosomes are called homologous. When you as a female produce eggs, or as a male produce sperm, one of each pair of your chromosomes is randomly selected for placement into the haploid gamete (sperm or egg). Each sperm or egg therefore has 23 chromosomes. Equally, at every gene locus (i.e., particular location in the 23-chromosome genome or haploid gene set) you have two homologous alleles — one from your mother and one from your father. Allele is a term that refers to any of the specific forms of a gene that exist at a locus in a species or population. Thus, A, B and O blood groups reflect different alleles. Meiosis is a specific form of cell division that happens during gamete formation. During meiosis, beginning with the individual’s full diploid gene set (46 chromosomes), gametes with 23 chromosomes are formed. Then, at conception, a sperm with 23 chromosomes unites with an egg with 23 chromosomes to produce a new individual with the normal 46 chromosomes (23 homologous pairs of chromosomes). During meiosis, each pair of homologous chromosomes pair up, and in the process of “crossing over” exchange homologous chunks of their chromosomes. This produces new chromosomes that are combinations of the chromosomes in the gamete producer. When forming a gamete, your body randomly places one of each of these two new homologous chromosomes into the sperm or egg. Thus, a mother places exactly half of her genes into each offspring, and each allele in the mother has a 50% chance of making it into any of her offspring, and the same holds true for the father. More specifically, each parent carries 2 alleles, inherited in the same way from his or her parents. You are equally likely to inherit either one of the two alleles that a parent carries at a given locus (but not both). Thus, in transmitting genes from one parent to her or his child, each parent throws away half of her/his genes during meiosis, and passes on only half.

1. What fraction of alleles in you are direct copies of the genes in your mother? Your father?

2. What is the probability that any given allele in your mother (or father) is in you?

3. What is the probability that any given allele in you is in your mother (or father)?

4. Because of this system of sexual reproduction, how many offspring must a parent have, on average, for a gene to maintain itself at the same frequency in the population in the next generation?

5. What is the probability that any given allele in you is also in your grandmother?  The probability that two alleles, sampled at random from the same locus in two individuals, are identical by virtue of having been serially copied from parent to child from the same common ancestor or ancestors, is called the degree of relatedness, symbolized by r. Every parent-offspring link reduces the probability a given allele has been passed on by ½. Thus, if two individuals have only one common ancestor (e.g., a mother, or a father, a grandmother, a grandfather, a greatgrandmother, etc.), the degree of relatedness can be calculated by counting the number of parent-offspring links and multiplying by ½ for each link. Thus, the degree of relatedness of a parent for a child is ½. Any gene found in the parent has a 50% chance of being in the offspring because it was copied during reproduction. The probability a gene in a grandmother is present in a specific grandoffspring is (½ x ½) = 1/4 . If two individuals share a mother in common, but not a father, they are half-siblings. An allele in one sib has a ½ chance of having come from the mother, and another ½ chance of having been passed from the mother to the other sibling. So, the r between two half sibs is ¼ (that is, the chance that an allele sampled from one half sibling is also in the other half sibling because of a recent common ancestor is ¼. Full cousins are 1/8. r for an aunt, uncle, niece or nephew is ¼.  If two individuals have two ancestors in common, then the probability that they share a particular allele must be calculated for each set of parent-offspring links, and summed. For example, full siblings share two ancestors in common, a mother and a father. There are two generational steps through the mother (½ from offspring to mother x ½ from mother to other offspring = ¼) and two steps through the father (½ x ½ = ¼). Because we sum the contribution made by each pathway from each common ancestor, ¼+¼= ½, the r between full sibs is ½. In contrast, half-siblings share only a mother as a common ancestor, or a father, and so the r between half-sibs is a single path: ½ x ½ = ¼.

6. Assume that your mother has two daughters, you and your sister, by two different men. What is the probability that an allele selected at random in you is also in your half-sister?

7. Suppose you have two children and you have a sister (full-sib) who also has two children. What is the probability that an allele sampled from you also is in a child of your sister due to common ancestry?

8. Imagine that you carry a rare allele that causes you to develop brain systems that induce you to behave as follows: instead of reproducing, you devote the time, energy and resources you would have devoted to your own child to raising your sister’s child. Will the frequency of this allele in the population increase, decrease, or stay the same? (Hint: remember that an allele will only spread if it more than replaces itself in the next generation. What fraction of the number of copies of the mutant allele will your sister’s children each carry, on average, compared to the number you carry? See question 4. Remember that she has two children).

9. With this mutant allele that causes you to not reproduce, how many additional children at minimum will you have to help your sister raise in order for the helping allele to increase in the population?

10. Now suppose you carry a mutant allele that causes you not to reproduce, but instead to devote your resources to helping your parents raise more children, your younger brothers and sisters (i.e., your full sibs). How many additional full sibs do you have to enable your parents to raise in order for this mutant allele to spread? The now-famous biologist W.D. Hamilton derived a model predicting the types of neural tendencies for helping that would spread in a population by natural selection over evolutionary time based on 1) the relatedness of individuals (i.e. what the increased probability is that an allele present in one individual is also present in another because they share common ancestors), and 2) the cost of helping (to the helper) in terms of lost reproduction and the benefit to the relative that is helped in terms of increased reproduction. For example, suppose the effort necessary to help your parents raise another full sib was less than half the effort necessary to raise a child of your own; thus, you can raise two sisters for less than the “cost” of one daughter. In this example, an allele favoring this behavior, according to Hamilton’s rule, will spread. More generally, Hamilton’s Rule states that a helping allele will spread if the following equation is satisfied:

rijbj-ci > 0 (or, slightly rearranged:) rij > ci/bj where i and j are two individuals, rij = the degree of relatedness between the helper i and the recipient j, bj = benefit to the helped j, and ci = cost to helper i. So, if the probability that the two individuals share an allele by reason of common ancestry exceeds the ratio of cost to benefit as described above, then selection will favor a psychological design feature that motivates humans to help in such circumstances.

11. Would selection favor sentiments that caused a woman at the beginning of her reproductive career to sacrifice her life to save three adolescent cousins?

12. What about to save a daughter and a half-brother?

13. What is the minimum cost-benefit ratio necessary before a person will favor helping a cousin at a cost to herself?

14. What is the minimum cost-benefit ratio necessary before a mother will be in favor of her daughter helping her niece (the daughter’s cousin) – assuming kin selection were the only force shaping human psychology?

15. Do you expect the mother and daughter to disagree? Assuming kin selection is the only factor, what is a parent’s attitude about their daughter’s husband’s payment of child support to a set of children belonging not to her daughter, but to the daughter’s husband’s first wife?

16. What cost-benefit ratio is necessary to motivate assistance towards someone when the degree of relatedness is 0 (assuming kin selection is the only force)?

17. What is the degree of relatedness between two identical twins? What is r between you and a clone? What is the degree of relatedness from you to one of your gametes?

18. What is the degree of relatedness between your skin cells and your brain cells? How can a gene in your brain cell get itself passed into the next generation? 19. What is the degree of relatedness of a person to herself?

20. What about between an unrelated husband to a wife?

21. A child and a step-parent?

22. A human to a pig or chicken or lab rat?

Remember, mutations will be selected to the extent that they shape our motivational system so that (on average) they make decisions that approximate rijbj-ci > 0. 23. What would increase fitness: an act that helps your child to increase lifetime reproduction by 5%? Or an act that would help your nephew increase lifetime reproduction by 9%? Use the equation above.

Most of life does not involve saving people’s lives, but small flows of actions that may differentially help or injure others in minor ways. Also, actions do not come with with small tags on them, telling us what their effects will be. So our minds fortunately could not be expected to have an explicit equation like this inscribed in it, but instead broader dispositions and emotional responses caused by alleles that spread through their effects on our brain structure (involving motivation). 24. Does your life experience provide any support for the idea that kin selection is a force in human life?

25. Does it seem to be the only force that has shaped motivational mechanisms in humans that make people feel like being altruistic to others?