1. Captain Kirk leaves one Fribble on the planet Quohog, which has plenty of food and no predators.  If each Fribble produces six offspring every eight hours (then the parent dies), how many Fribbles will there be by the end of the week?  What is their doubling time?

         N₀ = 1             Q = 6   (not 7, because the parent dies)

N_n = N₀ x Qⁿ

They reproduce every 8 hours, this means 3 times per day, at the end of the week they will have produced 3 times 7, so n = 21

            N₂₁ = 1 x 6²¹ = 2.19 x 10¹⁶ fribbles present after one week

Doubling time:

N = 6^{1/8 hours} = 2^{1/d hours}

(1/8 hours) log 6 = (1/d) log 2

d = 8 x log 2 / log 6 = 3.09 hours

2. If a town of 10,000 people doubles every five years, how big will it be in 2026?  Suppose instead toxic waste contamination kills off 20% per year; how many will be left?

        N₀ = 10,000 = 1 x 10⁴           population doubles every 5 years   2012 to 2026 = 14 years

        N_{14 years} = N₀ x 2^t/d      N_{14 years} =  (1 x 10⁴) 2^14/5

        N_{14 years} =  69,644 people (about 69,600) in the year 2026

If instead of reproduction, toxic waste kills off 20% per year, then the remaining population each year will be:
1-0.2 = 0.8 times N the previous year

After 20 years, the population N will be:
N₁₄ = N₀ x (0.8)¹⁴ = 10,000 x (0.8)¹⁴ = 440 people

3. Well's Time Traveler saw the sun appear to grow large and red. Why did this happen, in the author's view? How will our sun actually turn red some day? Why was the process of stellar evolution essential for human evolution? (Wells didn't know this, but we do.)
   
   In the nineteenth century, scientists knew that rotating objects (such as the Earth revolving around the sun) eventually lose speed as a result of frictional forces. As the Earth revolves more slowly, its orbit would decrease, and the Sun would appear larger because it it closer. Furthermore, the sun would appear red because it would "burn down," running out of fuel, and it would emit energy at lower wavelength (red instead of yellow).
   
   Today we know that the Earth's orbit will last a lot longer, because frictional forces are relatively small in outer space. The sun will not "burn down" like a flame; instead, its nuclear reactions will change from H ->> He to He reacting to form carbon and other elements. The sun will grow hotter and expand, forming a "red giant" (the energy of radiation will be lowered because of the expansion of the reaction volume). The red giant in fact will grow so large that it consumes the Earth.
   
   The process of stellar evolution in other stars was essential for life to exist because our own sun is still at the hydrogen-reacting stage. Other stars had to age and produce carbon, nitrogen and oxygen before these elements could be available to constitute our planet. In larger stars, later stages of fusion lead to explosion as a supernova. The process of the supernova includes late-stage fusion events that create the higher elements of the periodic table, including metals needed for life.
4. Why does natural selection favor individuals who overpopulate their habitat and cause precipitous population decline?  What is the real reason the lemmings "jump in the sea"? Do the lemmings have alternatives? Explain.
   
   The lemmings reproduce to large numbers. With population density too high, some will starve.  But lemmings that disperse find more food. So natural selection favors lemmings in which high population density triggers the instinct for dispersal to find new habitats.

The lemmings migrate in all directions. Some migrate to cliffs over the fjords, where they may jump in. Some that jump in may drown--but the few that make it across the fjord may find new habitat with plentiful resources, and will produce large numbers of progeny. Most will inherit the tendency to disperse--despite the fact that many (even most) die. Similarly, in human warfare a few individuals gain lots of resources, despite the fact that many die.

At the same time, there is always genetic diversity. A few lemmings will not have the gene for dispersal, and may stay behind. They will produce some offspring, especially after the others have left. So, the genes for both behaviors remain. Thus you can't say there is only one "winning" strategy; both alternatives have advantages and disadvantages.

5. Jane Grey interviews a prospective student for the Westchester School for Mutants. The student is completely resistant to all forms of influenza, including swine flu, avian flu, and tribble flu. The condition is dominant and not X-linked.
   
   If this Mutant had a son, what is the son's chance of resisting next year's sandworm flu?
   
   Since the flu resistance is dominant, and seems to apply to all forms of flu: The son has 50% chance of inheriting the flu resistance gene.  This answer assumes that the student has only one mutant flu-resistance allele; the other allele is normal.
   
   Suppose on another planet the Mutant allele frequency (p) is one in three hundred.
   What fraction of the population shows flu resistance?

If p = 1 in 300             p = 1/300 = 0.00333              p + q = 1         q = 1 – p         q = 0.99667

p² =  (0.00333)² =  1.111 x 10^-5 = AA frequency

2pq = 2(0.00333)(0.99667) = 6.64 x 10^-3 = Aa frequency

q² = (0.99667)² = 0.99335 = aa frequency

So, the fraction that has AA or Aa is p² + 2pq = 0.00665

Check: p² + 2pq + q² = 1
1.111 x 10^-5 + 6.64 x 10^-3 + 0.99335 = 1.0000

Suppose we find that the rare individuals who inherit two copies of the flu Mutant allele have defective immune systems and die by age 20. How does this modify our definition of "dominant" inheritance for this

This Mutant allele has multiple effects, and one of its effects (immune system defect) is actually recessive. This situation is analogous to the case of sickle cell trait, in which one copy confers malaria resistance, but two copies confer the recessive disease of sickle cell anemia.

6. What is the role of population size, gene frequencies, and genetic drift in evolution of new species? Explain.
   
   The smaller the population, the more rapid the change in gene frequencies; thus, the more rapidly the population can change its genetic character. For a new species to evolve, it must go through a period in which a small population is isolated, allowing genetic drift as well as propagation of new genes favored by natural selection. The new genes can then propagate throughout the population. As the population grows, the new genes become "fixed" as drift becomes less likely. When the population becomes so different as to prevent natural interbreeding with other descendents of the original population, there is a new species.
7. If natural selection means "survival of the fittest," than how can one "fittest" species evolve into more than one? How can more than one be "the fittest"? Explain.
   
   Natural selection is always relative; a particular group produces more offspring than another group. But natural selection depends on the particular environmental conditions. If two groups split off and experience different environments (such as underground vs. living in a tree), then natural selection will drive the populations in different directions. Also, selection involves random genetic drift. If animals end up on different islands, their small populations will experience drift in different directions. For the test, you should be able to apply this question to Galapagos, for example, the evolution of diverse finches or tortoises.
   
   Note: "Environment" also acts on INDIVIDUALS without changing their genes. On the "genes vs. environment" question, what I am getting at is how an INDIVIDUAL can experience environment; for example, a person's height can be shorter than one's genetic potential, if one receives poor nutrition.

8. In the X-Files, the giant fluke evolved to look like a primate. What do we call this kind of evolution? Can you imagine (in a followup episode) a possible explanation (however unlikely) for how this might occur? Would the fluke ever be able to interbreed with real primates? Why or why not?

Perhaps if the fluke looks like a primate, it can “hide” among humans, for example homeless people living in the sewer system. The more like a human it looks, the better the chance of survival, and the more offspring it will produce.

However, the fluke will never have DNA similar enough to interbreed. DNA of the human genome has 3 billion base pairs, and the chance of the fluke evolving a similar DNA sequence is vanishingly small.

9. In Galapagos, explain how Mary ensures the future of the human species, and how her actions differ from "Eve." Why does natural selection sometimes favor individuals who help neighbors raise offspring, instead of raising their own? What conditions favor this kind of selection?

Mary can no longer reproduce herself with her own genes.  But humans actually share 99.99% of their DNA sequence.  So, relatively speaking, Mary is related to the Kanka-bonos.  She assists their reproduction using sperm from the Captain.  In this way, the genes available that are most related to hers are propagated.

In real natural selection, an individual may be favored to assist the reproduction of relatives, under conditions in which the individual can propagate more copies of its (shared) genes than by having its own young.  For example, in a resource-poor environment, a male bird may produce more chicks with its shared genes by helping its mother reproduce than by trying to father its own chicks.

10. Explain how each of the following traits is determined by genes and/or environment: Huntington’s disease; Diabetes; Cancer; Spoken language.

Huntington’s disease is determined by a dominant allele of a gene that makes an abnormal protein. It is expressed late in life, causing brain degeneration, but there is little environmental effect.

Diabetes Type 2 is influenced by genes that predispose (make the disease more likely). About 10% of the disease is caused by genes, and the rest of the effect by diet and lack of exercise. So even if you have bad genes, if you eat well and exercise you will not show the symptoms. However, there is a different kind of diabetes called Type 1 in which you lack two copies of the insulin gene. In this case, you have juvenile-onset diabetes and will always have the disease.

Language is made possible by genes expressing proteins for the voicebox. Only humans can speak; chimps, our nearest relatives, cannot. However, the language that we speak is entirely environmental. The language depends on what language we hear and learn to speak.

11. Explain reductive (or degenerative) evolution.  Why does it work?  Cite examples from Wells’s The Time Machine and from Vonnegut's Galapagos.

An example of degenerative evolution is the progressive loss of eyes in cave-dwelling animals that evolve for thousands of years in a cave. It works because the loss of a trait confers an advantage in making energy available for other traits.

In The Time Machine the human descendents showed loss of intelligence and strength, because they no longer had to do things for themselves; the Morlocks provided all their needs. In Galapagos, the future humans lost their brains because they no longer needed them, and because narrower heads were selected for swimming.

12. Explain the difference between genetic and cultural evolution.  Use an example to show how these may be confused.

Genetic evolution involves natural selection based on traits specified by DNA (such as the physical ability to speak).  Cultural evolution involves selection of traits that are NOT specified by DNA, such as the particular language spoken (French vs. English).  These phenomena can be confused because children “inherit” their spoken language from their parents; but this inheritance is cultural.  A child adopted into a different country will grow up speaking the language of his or her adoptive parents.

13. Why do individuals move out of successful populations (migrate or disperse)?  Give examples of physical and biological modes of dispersion or migration.  For biological modes, give examples involving parasitism or mutualism.  Explain why each is parasitic or mutualistic.

Individuals disperse from populations in search of environments with fresh resources.  Dispersal increases the chance of survival overall, because when habitats change, organisms are more likely to find one of many available habitats still remains habitable (instead of relying on just the one original habitat).  A parasitic mode of dispersal is the parasitic worms of X-Files (based on two different kinds of worms, tapeworms and fluke worms).  The worms parasitize the internal organs of the human host, then crawl out into the drainage and disperse through the sewer system until they find a new host.  A mutualistic mode of dispersal might be the tribbles, which induce human hosts to carry them by giving “love.”

14. Vonnegut offers several hypotheses to explain how tortoises traveled to Galapagos.  Explain evidence supporting and evidence refuting each hypothesis.  Which hypotheses can neither be refuted nor proved?  Why not?
15. Suppose you ingest 500 Salmonella bacteria in contaminated turkey, and in three hours you feel sick; there are now 500,000 bacteria. What is their doubling time in your body, in minutes?

       N_t  = N₀ x 2^t/d              N₀ = 500         N_t  = 500,000             t = 3 hours      d = ??

500000 = (500)2^3/d
500000/500 = 1000 = 2^3/d
log 1000 = (3/d)(log 2)
3 = (3/d)(0.30)
d = 3(0.30)/3
d = 0.30 hours to double      how many minutes?  (0.30 hours)(60 min/hour) = 18 minutes to double

16. A male bird is equally likely to offer food to his own chicks, or to his mother's chicks. Why? Explain by calculating his percent relatedness to his own chicks, and to his mother's chicks. (Assume that both hens are 100% faithful to their mates. In real life, about 90% may be typical.)
    
    The bird shares 50% of his mother's genes with his siblings (equal chance of getting the mother's copy or the father's copy of each gene.) Similarly, the bird shares 50% of his chick's genes (the other half from the chick's mother.) Thus, from the gene's point of view, there is equal chance of the bird's genes getting passed on through a sibling as through the offspring. Natural selection favors kin selection to precisely the extent of genetic relatedness.

17. According to a study published in the Weekly World News, 1/5 of Americans have been abducted by aliens. Suppose that the trait desired by aliens is genetic, with recessive inheritance; and that every person homozygous for this trait gets abducted.

What is the allele frequency (p) of the alien abduction trait?

       1/5 Americans abducted by aliens = f(aa) = 0.2

aa = desired by aliens
Aa = carriers of abduction trait
AA = normal, miss all the fun

Allele frequency of alien abduction trait: if f(aa) = 0.2 = p²           then p = sqrt(0.2) = 0.447

What percentage of Americans are carriers of the alien abduction trait; that is, they don't get abducted, but could pass it on to a child?

Carriers have the genotype Aa       f(Aa) = 2pq     if p = 0.447     then q = 1 - 0.447 = 0.553

            F(Aa) = 2(0.447)(0.553) = 0.494

            Double check: q² = (0.553)² = 0.305         
 p² + 2pq + q²= 0.2 + 0.494 + 0.305 = 1.000,  value should be 1, checks OK


If some of those abducted never come back, what will happen to the Hardy-Weinberg equilibrium? What do we call this effect?

If some of the abducted people never return to produce children, then natural selection acts against the abduction trait. Natural selection (negative, in this case) perturbs the Hardy-Weinburg equilibrium and leads to evolution of the population, so that the remaining individuals tend NOT to get abducted. (Remember, this assumes the abduction tendency is genetically inherited by the humans; it would be different if it depends upon the traits of the alien abductors.)

In one very small, isolated town, the entire population claims to have experienced abduction. What do we call this effect?

In a small population, random fluctuations in number of offspring lead to random changes in the allele frequencies. The frequencies of alleles are no longer in equilibrium, and they change by genetic drift.       

18. Explain the inheritance of the trait in this pedigree. If there are carriers, name as many as you can.

The family shown is the famous royal family of Queen Victoria, who had a mutation in one of her X chromosomes in the gene for blood clotting. She transmitted this allele to many children and grandchildren. Several of the males showed hemophilia, because they inherited only one X, which had the defect. This image shows a version of the tree in which carrier females are marked by a half-symbol:
http://3.bp.blogspot.com/-5G8wDgFU9Ec/TvvGIUNEuHI/AAAAAAAAEhc/inykTqHQ9_k/s1600/ftree.gif
Note that Leopold was a rare male hemophiliac who survived to have children. The daughter had to be a carrier, but the son had to be normal, because he got his father’s Y chromosome and his (normal) mother’s X chromosome.

19. Many human societies promote “cross cousin marriage.”

a. What fraction of your genes do you share with your first cousin?

You share 50% of genes with your parent.
Your parent shares 50% of genes with their sibling (your aunt or uncle).
Your aunt or uncle shares 50% of their genes with their son or daughter (your cousin).
The proportion of genes that you share with your first cousin is:
0.50 x 0.50 x 0.50 = 0.125 = 12.5%

b. Under what conditions would marrying your cousin be favored biologically? Under what conditions would it be detrimental?

Marriage to a cousin is favorable genetically if the frequency of recessive lethals is low, and the frequency of shared complementary traits (traits that fit well together, such as large mouth and large teeth) is high. Marriage to a cousin is detrimental if the family has recessive lethal alleles that could come together in one offspring.

20.  A Klingon anthropologist tries to explain the pointed ears of Vulcans by the hypothesis that Vulcan women prefer men with more pointed ears, so many generations lead to Vulcans with extremely pointed ears.

What form of natural selection does this illustrate? What problems do you see with the Klingon hypothesis? How might the hypothesis be modified?

The evolution of pointed ears is an example of runaway selection: After many years of natural selection favoring pointed ears, the Vulcans have extremely sharp pointed ears.  The problem here is how to explain the source of selection pressure.  The Klingon argues that Vulcan women irrationally prefer pointed ears.  But if that were the case, then any woman with a mutant allele (not preferring pointed ears) would drive selection in the opposite direction; especially if developing pointed ears is energetically expensive.  Furthermore, it could just as easily be that the men prefer women with pointed ears.

A possible modified hypothesis would be that pointed ears are linked to the trait of men providing resources for children.  In this case, women that select men with pointed ears would be likely to raise more children, and thus natural selection would occur.  This hypothesis would be hard to test, however, since Vulcans don’t let Klingons tell them who to marry.