Natural Selection (50 points)
Variability exists in all natural populations. For a wide variety of reasons, some
phenotypes (visible characters) exploit the environment more efficiently than others do.
These phenotypes leave proportionately more offspring than their counterparts. If this
phenotypic characteristic is heritable, offspring will resemble their parents, and the
population will eventually consist mostly of individuals of the successful phenotypes.
This weeding out of the less fit phenotypes is the process of natural selection, the
accompanying change in the population is evolution, and the features that ultimately
come to characterize the species are then viewed as adoptions to the environment.
Since the key to evolutionary success is the production of fertile offspring (and
grandchildren), it requires numerous generations to demonstrate change through time. A
model system then may provide a simulation of the process.
In this model system, a plastic fork and a cup represent a predator. Four seeds
represent different phenotypes within a prey species. Picking up seeds with a fork from
the tabletop and putting them in the cup can simulate a feeding frenzy. Seeds that remain
after the frenzy are the survivors and are the ones that can reproduce to reestablish the
population. [An alternative model is to use the thumb and index or middle finger on one
hand to pick up the seeds and deposit them in the cup].
Work in groups of three. For each feeding-frenzy have two predators and one
timer. You should rotate the tasks. To start, count out 100 of each seed type (corn, split
pea, pinto, and lima bean), mix them and spread them evenly on the entire table clear of
everything except the seeds. During a feeding frenzy the two predators should pick up as
many seeds as possible in a 15-second interval and place them in the cup. These are the
prey that have been removed from the population, it is the survivors that breed according
to their survivorship and reestablish the population at the equilibrium population size of
400.
Example:
Prey
Lima
Pinto
Pea
Corn
Starting
Number
Population Eaten
100
100
100
100
-
40
60
20
30
Survivors
=
=
=
=
Total
60
40
80
70
250
Proportion
Surviving
Population
.24
.16
.32
.28
1.00
x 400 =
x 400 =
x 400 =
x 400 =
Adjusted
Population
96
64
128
112
400
The adjusted population then serves as the starting population for the next 15-second
feeding frenzy. The procedure needs to be followed up to 10 generations. Merely
observing changes through time are insufficient evidence that change has occurred. We
thus need to provide statistical evidence that can be provided using a simple chi-square
test. Read the accompanying description of the chi-square procedure. Propose an
appropriate hypothesis for your model run and then determine the level of significance
following the first, fifth, and final generations. Also graph the adjusted population size of
each phenotype (on a single plot) for each generation. Start with generation zero that has
100 of each type. Incorporate these requirements into your formal write-up of this
experiment.
Required information to include in the paper: hypothesis (introduction), use of chisquared (methods and materials), table of % values for each generation (results), table of
chi-squared values following first, fifth, and final generations and the level of
significance (results), single plot that shows the population sizes over the course of the
experiment. Include all parts of a paper Intro, Methods Results Discussion, Lit cited.
Chi-square
A relatively simple yet powerful test often used in science is the Chi-square
analysis. Essentially, this is the statistical assessment of how well actual data fits an
expected pattern. For example, suppose a scientist raises 100 plants and, because of the
laws of genetics, predicts a 3:1 ratio of yellow to blue flowers (75 yellow, 25 blue). The
actual ratio was 84 yellow: 16 blue. The statistical question is:
Are the "observed" frequencies (84 to 16) significantly different from the "expected"
frequencies (75 to 25)?
Testing this question using the Chi-square method proceeds as follows:
2
X
2
=  (O  E )2
E
Where X is the Chi-square value, O is the observed frequency, E is the expected
frequency, and is the symbol for summation over k categories. In this example, there
are two categories: yellow flower color and blue flower color. In order to determine the
2
significance of the X value, you must also determine the number of degrees of freedom
for the problem. Degrees of freedom (df) refer to how many values have to be known to
know all of the values in a problem. In this case, the degrees of freedom is k-1, which
means that if you know all but one of the values for the categories, you will know the
other (i.e., if you know that out of 100 plants, 84 are yellow, then 16 must be blue if that's
the only other flower color - k = 2, so 2 - 1 = 1 df).
2
So, calculations of X may be summarized as follows:
Category (Flower Color)
__________________________________________________
Yellow
Blue
n
__________________________________________________
Observed (O)
Expected (E)
84
75
16
100
25
__________________________________________________
df = k-1 = 2-1 = 1
X2 =

(O  E )2 = (84  75) 2 + (16  25) 2
75
25
E
=
92 + 92
75
25
= 1.080 + 3.240
= 4.320
X2 = 4.32 calculated
This value is then compared to a tabled value of X2. By convention, this tabled value is
usually set at 0.05 (95% level of significance) and the df are determined by the number of
categories. Therefore, from the table (Table 4.1) at 0.05 and 1 df.:
X2 = 3.84 table
Because 4.32 is greater than 3.84, we determine that the numbers we found for flower
color are significantly different than what is expected. The observed frequencies (84 and
16) are significantly different than the expected frequencies (75 and 25) at 0.05 level and
1 df. In other words, we are 95% certain that values of 84 yellow and 16 blue flowers
came from a sample other than one which has 75 yellow and 25 green flowers.
Table 1. Chi-Square Values.
________________________________________________________________________
P Values
D.F.
0.10
0.05
0.01
0.005
____________________________________________________________________________
1
2.706
3.841
6.635
7.879
2
4.605
5.991
9.210
10.597
3
6.251
7.815
11.345
12.838
4
7.779
9.488
13.277
14.860
5
9.236
11.071
15.086
16.750
6
10.645
12.592
16.812
18.548
7
12.017
14.065
18.475
20.278
8
13.362
15.507
20.090
21.955
9
14.684
16.919
21.666
23.589
10
15.987
18.307
23.209
25.188
11
17.275
19.675
24.725
26.757
12
18.549
21.026
26.217
28.299
13
19.812
22.362
27.688
29.819
14
21.064
23.685
29.141
31.319
15
22.307
24.996
30.578
32.801
____________________________________________________________________________