Download Natural selection of paper bugs

HARDY-WEINBERG AND EVOLUTION
The Hardy-Weinberg principle is straightforward: if p + q = 1, then p2 + 2pq +q2 = 1.
Arithmetically, this is trivial. Biologically it is astonishingly profound. This is a lab exercise in
which your lab class will become a population of fishes. In becoming this population, you will
learn that by simple, straightforward exchange of gametes, several remarkable evolutionary
processes can occur: genetic drift, mutation, natural selection, gene-flow, and nonrandom
mating. You will even gain insights into the processes that can lead to speciation.
Summary:
The biological principle illustrated by the Hardy-Weinberg equation is this: If a population has
only two alleles at a given locus, and their frequencies are known, we can call those frequencies
p and q. Since there are only two alleles, it must be true that p + q=1. For example, let’s say we
have a population of 100 diploid individuals. Among them they have 200 alleles at the locus of
interest; 120 are of one form and 80 are of the other form. The frequency of the first allele form
is 120/200 (p = 0.6), and the frequency of the second is 80/200 (q = 0.4). Note that it doesn’t
really matter which allele gets described by p and which by q. However, a common convention
is to give the p label to the frequency of the more common allele.
In a diploid population, every individual has two copies of each gene (two alleles). Since the
probability that an individual has one copy of the first allele is p, then the probability that it is
homozygous for that allele is p2. This is just an illustration of the law of independent
probabilities. The same argument can be used to describe the probability that an individual is
homozygous for the second allele, q2, or in fact that the individual is heterozygous, 2pq. The
point is this: if you know p and q, you can predict what the frequency of each genotype will be in
the population using the law of independent probabilities. Predicting the future of populations is
the brass ring of ecology and conservation biology, and in population genetics, we have captured
that ring. Since there are only three possible genotypes, then the sum of those three frequencies
must equal one. Thus we come by a biological argument to the same equation, p2 + 2pq +q2 = 1.
Here a numerical example is very helpful.
Say we have a population of 100 diploid individuals. Among them, there are 200 alleles of the
gene we are interested in (because each individual has two copies). If we know that the first
allele, let’s call it A, occurs with a frequency p = 0.6, and the second, a, with a frequency q = 0.4,
then we can predict that in that population, 0.36 will have the genotype AA (0.62), 0.16 will be
aa (0.42), 0.48 will be Aa (2 x 0.6 x 0.4). At this point, students usually yawn, bored stiff,
knowing that this is ridiculously obvious. Unfortunately, it isn’t. If you go to that population of
100 individuals, and count the number of homozygotes of each kind and the number of
heterozygotes, the proportions of each may not be the proportions predicted above. For example,
a population with 60 AA and 40 aa individuals does not meet the predictions of HardyWeinberg. Populations do not have to be in Hardy-Weinberg proportions, and in fact they
usually aren’t. In this demonstration, p = 0.6 and q = 0.4, but the frequency of AA is not the
predicted 0.16, instead it is a whopping 0.6. This is why Hardy-Weinberg equilibrium is
interesting: A population can have other-than-predicted frequencies of genotypes. In fact, when
a population deviates from the expected proportions of genotypes, when it is out of HardyWeinberg equilibrium, we have proof of evolution acting on the population. Proof of evolution
is a wonderful thing because many don’t think that this kind of proof is easy to come by. In fact,
many people are under the impression that evolution is not demonstrable. But here we have it: if
a population is out of Hardy-Weinberg equilibrium, it is because something (evolution) has
interfered with the law of probabilities which govern that equilibrium. There is another
interesting consequence of the Hardy-Weinberg law: if a population is out of Hardy-Weinberg
equilibrium in one generation, it will be back in equilibrium in the next generation (if generations
are non-overlapping, which is to say that everyone mates and then dies before its offspring are
mature). That means that in every generation we can look for evidence of evolution, because
every time we expect the population’s genotypes to be in Hardy-Weinberg proportions. So how
can populations find themselves out of Hardy-Weinberg equilibrium? There are five
qualitatively different ways, and each is considered an evolutionary process. These ways are:
1.
2.
3.
4.
5.
Genetic drift (sampling error in alleles getting from one generation to the next)
Gene flow (migration of alleles into or out of the population)
Mutation (spontaneous change of alleles within the population)
Natural selection (differential success of one allele over another)
Nonrandom mating (preferential mating of some allele combinations over others)
NATURAL SELECTION OF PAPER BUGS
The scenario:
Paper Bugs are little creatures that live in a curious habitat: they live atop fabric of varying
patterns in biology laboratories. Just prior to their breeding season, they are terrorized by their
major predator: Tweezer Birds. Tweezer Birds descend on the Paper Bugs, typically eating
about half of the population of bugs before flying off to parts unknown for the rest of the year.
The surviving Paper Bugs reproduce immediately after the departure of the birds (therefore the
Paper Bugs that were eaten do not reproduce) and the population returns to approximately the
same size it was before the arrival of the birds. Old Paper Bugs die after reproducing, so when
the Tweezer Birds return the following year, they are returning to a completely new generation
of bugs.
Some more details:
 There are three color morphs of Paper Bugs: red, white and blue.
 Populations of Paper Bugs live on different fabric habitats.
 The color of Paper Bugs is determined by a single genetic locus and there are two possible
alleles for that locus. The B allele codes for red color and the b allele codes for white color.
 The Paper Bug color trait shows incomplete dominance (also know as co-dominance). Bugs
that are homozygous for the B allele (genotype BB) are red, bugs homozygous for the b
allele (genotype bb) are white, and heterozygotes (genotype Bb) are blue.
 Paper bugs breed randomly with respect to color and the Hardy-Weinberg equation
accurately predicts the genotypic and phenotypic composition of the new generation after
each breeding season.
The activity:
Paper bugs are, in reality, small paper disks cut out of construction paper.
The professor has given each group a population of Paper Bugs in which the frequency of each
allele is 0.5. Students should check that each group indeed has a total population of 99 Paper
Bugs, 33 of which are red, 33 of which are white and 33 of which are blue. Fold each disk in
half to facilitate its being grasped with tweezers.
Students will play the role of the Tweezer Birds. Two students in each group will use the
tweezers to represent the bird’s beak and a plastic dish to represent the bird’s stomach. Place the
starting population of bugs in a bag, shake it and sprinkle the bugs onto the habitat. Feeding by
Tweezer Birds is a competitive affair. After placing the bugs in the habitat, each student will
turn their back to the habitat. On the word “go,” each student will turn around and try to be the
first to put 20 bugs into his or her plastic dish.
After each round of competition the Tweezer Birds will have removed 40 Paper Bugs from the
habitat. The allele frequencies for the two alleles can then be calculated. Every red bug
contributes two B alleles to the total allele count and every blue bug contributes one B allele. The
allele frequency for B is obtained by counting up the total number of B alleles in the surviving
population and dividing by the total number of alleles in the survivors (round off the answers to
two digits). Students should calculate the frequency of the b allele in the same manner. They
can check their arithmetic by checking to see that the two allele frequencies sum to 1. Students
should record the allele frequencies after each round of selection so that they can be graphed out
later.
We assume that no evolutionary forces act on the Paper Bugs after the predation event.
Therefore, the next generation should adhere to the Hardy Weinberg Equilibrium. Therefore, the
next step is to use the Hardy-Weinberg equation (p2 + 2pq + q2 = 1) to generate the phenotypic
composition of the next generation. Each student should make the calculations independently
(using the attached table) to assure understanding of the mathematics involved. Take the
frequency of B as p and the frequency of b as q. The frequency of red bugs in the next
generation is p2, the frequency of blue bugs is 2pq, and the frequency of white bugs is q2.
Calculate the actual number of bugs of each color by multiplying the frequencies of the three
phenotypes by the total number of bugs in the next generation (round up to whole numbers).
Bring the population back to the same size, 100 total Paper Bugs, before the predation event.
Repeat the process for 10 generations, or until the professor indicates that it is time to stop.
A graph of p vs. round of selection will reveal if evolution by natural selection has occurred.
Each group will transfer their graph to a transparency for class discussion.
After discussion of the first round of results, students will develop their own hypotheses and test
them. There are additional colors of construction paper available, if needed.
Acknowledgements:
This exercise was modified from one developed by Douglas B. Woodmansee (Wilmington
College), who was inspired by Stebbins, R. C., and B. Allen. 1994. Simulating evolution. In
Investigating Evolutionary Biology in the Laboratory, National Association of Biology Teachers,
Reston, VA. Additional advice was provided by Douglas J. Burks to DBW.
FIRST SIMULATION:
Description of Habitat: __________________________________________________________________________________
Proportion of each
genotype predicted from
Hardy-Weinberg
Generation Red
Blue
White
(p2)
(2pq)
(q2)
1
2
3
4
5
6
7
8
9
10
Paper Bugs Before Predation
Red
(BB)
33
Blue
(Bb)
33
White
(bb)
33
Paper Bugs After Predation
p
q
0.5
0.5
Red
(BB)
Blue
(Bb)
White
(bb)
p
q
Sketch graph of results below:
p (allele frequency of B)
1.0
0.75
0.5
0.25
0.0
1
2
3
4
5
6
7
Number of Generations
8
9
10
SECOND SIMULATION:
Description of hypothesis tested/experimental design:
Proportion of each
genotype predicted from
Hardy-Weinberg
Generation Red
Blue
White
(p2)
(2pq)
(q2)
1
2
3
4
5
6
7
8
9
10
Paper Bugs Before Predation
Red
Blue
White
p
Paper Bugs After Predation
q
Red
Blue
White
p
q
Sketch graph of results below:
p (allele frequency of B)
1.0
0.75
0.5
0.25
0.0
1
2
3
4
5
6
7
Number of Generations
8
9
10