Biology 14
“Spring”, 2011
Problems Set 2, due March 10,
11:30 AM
(not later)
Make your written answers brief and show your quantitative reasoning, not just the answers. If you have difficulties
email, or make an appointment to see me about them. If you have any problems with the problems shoot me an
email or make an appointment.
Kin selection and reproductive value
1. This problem requires the use of kin selection reasoning. In class kin selection was introduced by an example of
altruism toward relatives: kin selection will increase the frequency of genes underlying behavior directed toward
genetic relatives if the Benefits of that behavior to the relative multiplied/ devalued by r, the coefficient of genetic
relatedness, exceeds the Costs to the actor---if Br>C, in short. Thus, kin selection will cause the evolution of
“phenotypic altruism” toward relatives (aka “nepotism”) when Br>C. An individual should be prepared to sacrifice
its life for 2+ full siblings, 2+ offspring, 4+ grandchildren, 8+ cousins, etc. However, things are usually more
complicated than that: what if the reproductive value of the relative to which nepotism is directed is very low or
very high? Maybe the reproductive value of the actor is very low or very high relative to that of the relative? (For
example, in the article assigned on siblicide at the nest, a small, weak nestling who is unlikely to survive and
reproduce (because its older and bigger nestmates have been hogging all the food) will at some point be selected to
“give up”(commit suicide), and that point would be when ½ B (the benefit to older sibs if it dies) > 1 C (the cost to
it of giving up (actually, of course, the cost to the ”giving up genes”. Note, BTW that the same kind of reasoning
applies to an implanted fetus that, because of some non-genetic accident during development or because it carries a
very detrimental mutation that will likely later kill it or reduce its reproductive value greatly, should similarly “give
up” (=abort, miscarry) because it will detract from its mother’s ability to invest in future siblings. So as in the case
of siblicide at the nest, the fetus should self abort when ½ B > 1 C, whereas the mother is selected to miscarry when
B>C (if she can detect the fetal defects and mutations). So you might think about such asymmetries in genetic
interest as contributing to mother-fetal conflict and the extraordinarily high incidence of miscarriages that occur in
human reproduction, something an Intelligent Designer should never have designed. You might also think about
why males would make up religious stories and laws against abortions. Remember, it IS males who make up and
enforce religious doctrines and laws).
Imagine a scenario like that given in class (Ego and 3 full sibs versus 3 saber toothed tigers), only a bit more
complicated: Ego and 2 sibs are confronted with a life-threatening situation, and there are 3 possible behavioral
responses on Ego’s part with 3 outcomes: (a) Ego dies and as a result the two full sibs, a brother and a sister,
survive. (b) Ego saves sister at a risk to him/herself = 0.3 of dying (hence probability of Ego living = 0.7), but the
brother dies. (c) Ego saves brother at risk to him/herself = 0.6 of dying (hence probability Ego survives is 0.4), but
sister dies. Ego’s reproductive value is 3.8, the brother’s is 5.4 and the sister’s is 4.7.
Which of Ego’s possible behaviors will be favored by kin selection? To find out how many copies of Ego’s
genes will be perpetuated in the long run for each of the 3 behaviors, multiply the probability of surviving of the
individual, times its reproductive value, times its r to Ego. Ego’s behavior, of course, affects his/her own
reproduction (r=1) as well as that of his/her siblings (r=1/2). Reproduce the table below in your answer and show
your calculations.
Copies of genes surviving in
Ego
Brother
Sister
a)
b)
c)
Total
The well known social anthropologist, Marshall Sahlins, published a book in 1977 that was supposed to be a
devastating critique of applying evolutionary social theory to human behavior and cultural evolution. Below are
some of his comments about what he thought were crucial flaws in the theory of kin selection as it applies to the
evolution of behavior in humans and animals. In the light of what you know about the theory of kin selection—and
evolutionary social theory in general---evaluate this criticism in a few sentences. (Hint: do bacteria have to know
about their biochemistry in order to evolve resistance to antibiotics? Do you need to know consciously about the
mechanisms by which molecules are broken down in order to digest your food?)
Marshal Sahlins, 1977, The Use and Abuse of Biology, a critique of sociobiology
“(In passing it needs to be remarked that the epistemological problems presented by a lack of linguistic support
for calculating r, coefficients of relationship, amounts to a serious defect in the theory of kin selection. Fractions
are of very rare occurrence in the world’s languages, appearing in Indo-European and in the archaic civilizations
of the near and Far East, but they are generally lacking among the so-called primitive peoples. Hunters and
gatherers generally do not have counting systems beyond one, two and three. I refrain from comment on the even
greater problem of how animals are supposed to figure out how that r between ego and first cousins equals 1/8.
The failure of sociobiologists to address this problem introduces a considerable mysticism in their theory.)”
Kin selection
2. In a species such as our own, what is the degree of relatedness between one sperm cell and another from the
same male? (Hint: How many copies of our genes do our non-gamete (somatic) cells have? How many copies are
present in a gamete cell (egg or sperm)?) What would it be between the sperm of male ants, which are haploid?
Under what conditions (B>C) would natural selection favor an act of "altruism" by one sperm to another in these
two species (sperm from same male in each case)? So would you expect to find helper sperm more frequently in
haploid males (bees, ants and wasps) or diploid males (such as in mammals)? (If you don’t believe helper sperm
exist, google it. Yes, they duke it out in the reproductive tracts of females in some animals.) State or show your
reasoning.
3. In the Tasmanian Native Hen about half of the adults are monogamous and the other half participate in
polyandrous matings (one female, two males, thus a "trio"). Almost invariably the polyandry is adelphic: two
brothers are mated to an unrelated female. The reproductive success of trios is greater than that of monogamous
pairs, especially when members of the trio are more than one year old (they are more experienced). The data on
reproductive success (average numbers of surviving offspring per group) are as follows:
pairs
trios
one year olds
1.7
4.9
older birds
3.7
6.1
a)Should a female prefer monogamy or polyandry? (Hint: the numbers of copies of genes underlying preference for
monogamy versus the number underlying preference for polyandry is found by multiplying r of mother to her
offspring times the number of offspring she can have under the two mating arrangements. Natural selection will, of
course, favor the behavior (preference for monogamy or for polyandry) that leads to the greatest number of
descendants).
b) In his first year of life should a male who is already mated to a female permit a second male to join the pair?
(Hint: If he does and the two males (he and the one he let join) mate equally with the female, he will be the father
of the offspring half the time.)
Again, calculate the numbers of copies of genes that will be produced in the different arrangements). Does it make
any difference whether the second male is a brother? Explain and show your quantitative reasoning. (Hint: how to
go about this will be discussed with regard to kin selection in lions. Multiply number of offspring by degree of
genetic relatedness and you get the number of copies of genes reproduced, namely the genes underlying the neural
mechanisms for recognizing kin and assessing the prospects for improving reproductive success. Note, then, that
the average r between males and offspring in a trios in which the males are unrelated is ½ x ½ (his) + ½ x 0 (other
male’s) = ¼ . If they are related, say full brothers, then r is something else, calculated in a similar way.
(c) Should an older male permit an equally old brother to join his marriage, assuming that his brother will be
incapable of finding a mate on his own? Should he allow an older unrelated male to join? To make things simpler,
assume that the brothers themselves are the products of a monogamous mating. Show your quantitative reasoning.
Kin selection and parent-offspring conflict
4. In monkey troops older daughters often have the opportunity to help their mothers rear younger siblings. Assume
that by taking care of her younger sibling the older daughter gains a benefit, B, (increased mothering ability through
practice, measured as an increase in her later reproductive success), while the younger sibling suffers a cost in its
own survival, C, due to the ineptitude of the older sibling. But the younger sibling also gains an indirect benefit
from its older sister’s better ability to mother its (the younger sibling’s) future nieces and nephews. Assume that the
mother gains nothing herself in terms of her ability to produce additional future young—that is, her only benefit
from practice mothering by her daughter is the improved ability of her daughter to produce offspring that will
survive. Also, neglect the difference in age between the younger and older siblings. As in all questions about
evolutionary social theory, set up the inequality, B>C, and devalue B and C by the coefficient of genetic relatedness
between the individual whose “viewpoint” you are considering and the individuals upon which/whom the benefits
or costs are impacting. What you are calculating here, of course, is how you would expect natural (kin) selection to
automatically change the frequency of genes underlying the development of (a) “offspring control behavior” in the
mother (she allows or stops practice mothering) , (b)“eagerness to practice mother” in the older daughter, and (c)
“amount of pain or risk of injury experienced by younger sibling before yelling for mother” by the younger sibling.
(Note, as above, that there is a benefit to the younger sibling: improved mothering skills of its sister, which benefits
its future nieces and nephews.)
(a) State the conditions (B>C) under which the 3 different social actors here (mother, daughter, younger sibling)
would be expected to favor “practice mothering”. That is, as above, devalue B and C by the r between the
individual in question (mother, daughter, younger sibling) and the individuals upon which the B and C impact. So
from the mother’s genes’ view, the benefits of practice mothering impact upon her practicing daughter and the costs
impact on the mother’s younger offspring being “practiced upon”. From the practicing daughter’s (genes’)
viewpoint the benefits impact upon her and the costs impact upon her younger sister. You should be able to figure
out from here how to devalue benefits and costs from the viewpoint of the younger sibling being “practiced upon”.
Your answer should consist simply of the inequality, “B>C” with the appropriate numbers or fractions before the
letters.
(b)What would be the conditions be (B>C) under which the mother, daughter and younger sibling favor practice
mothering if the older daughter and the younger sibling were fathered by different males( that is, older sister and
younger sibling are half siblings, r = ¼).
(c) What should be the attitude (favor or disfavor) toward practice mothering be of the different males that fathered
the young --that is, considering the benefits to their offspring and the costs toward the offspring that are not theirs?
“Attitude” here includes consideration of whether the father’s offspring is the practicing daughter or the younger
half sibling (through the mother) being practiced upon!
Intragenomic conflict and intrafamily conflict
5. Asymmetries in genetic relatedness among components of the genome (genotype) are created by sexual
reproduction and the nature of the mating system. Where there are asymmetries in genetic relatedness there are
asymmetries in genetic interest, and we expect natural selection to engender conflict.
a) In a monogamous mating system in which the offspring of a given female are all fathered by the same male what
is r between the paternal genes of siblings and what is r between the maternal genes of siblings?
b) If a mating system is polyandrous---each offspring fathered by a different male---what would r be between
paternal genes in the siblings and between the maternal genes in the siblings? How would the maternal genes in the
siblings “want” the siblings to behave toward one another (=how would natural selection affect those maternal
genes)? How would the paternal genes within the siblings “want” them to behave toward each other? In these last
two questions, state the answer in terms of “B>C” with the appropriate devaluations of B and C.
c) In a monogamous mating system the mother and father’s “view” (=how natural selection will affect the evolution
of their behavior) of how their children should interact is the same. The children’s behavioral interactions will
result in benefits and costs to their own reproduction, so we set up B>C. Next, we devalue the benefits and costs by
r between the mother and father to the children (they are the same, r=1/2), so ½ B > ½ C, which is B>C. In other
words genes in the parents underlying their control of their children’s interactions are being selected to maximize
B/C. By “control of their children’s interactions” we mean how hard they encourage their children to be nice,
sharing, cooperative with other (benefits) and how severely they punish them for being nasty and fighting (costs).
What, then, is the individual child’s “view” of how it should interact with full siblings? Hint: Consider that an
individual child is related to itself by r=1 (that is, the genes underlying its interactions with siblings are definitely in
itself!) but to its full siblings by ½. Comment briefly on how you expect parents and their children to interact with
regard to how their children should behave toward one another. Comment briefly on the corresponding differences
in “view” (of sibling interactions) if a woman has two children, remarries and has two more by the second husband.
(So yes, there is brotherly and sisterly love thanks to kin selection, but there is also sibling conflict when genetic
interests conflict (2B<C for full sibs, or 4B<C for half sibs), and conflict is predicted between parents/ stepparents
and between said parents and children and step children over investment in children and step children).