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?
1 Q =
6 (not 7, because the parent dies)
Nn = 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
N = 61/8 hours
= 21/d hours
(1/8 hours) log 6 = (1/d) log 2
d = 8 x log 2 / log 6 = 3.09 hours
- 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
N14 years = N0 x 2t/d
N14 years = (1 x 104) 214/5
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
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
- 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
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.
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
What fraction of the population shows flu resistance?
p = 1 in
= 1/300 =
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
q2 = (0.99667)2 = 0.99335 = aa frequency
So, the fraction that has AA or Aa is p2 + 2pq =
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.
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.
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.
- 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
- 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.
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
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
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.
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.
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.
- 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
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
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?
- 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?
= N0 x 2t/d
N0 = 500 Nt =
t = 3 hours d = ??
500000/500 = 1000 = 23/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
- 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
selection to precisely the extent of genetic
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
= desired by aliens
Aa = carriers of abduction trait
AA = normal, miss all the fun
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?
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 =
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
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:
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.
Many human societies promote “cross
What fraction of your genes do you share with your first cousin?You share 50% of genes with your
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
The proportion of genes that you share with your first cousin is:
0.50 x 0.50 x 0.50 = 0.125 = 12.5%
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?
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.
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.