Name: _________________________________________ Date: ___________________________ Block: ________
Hardy-Weinberg & Chi-Square (𝒳2) Analysis
Recall:
p2 + 2pq + q2 = 1
p + q =1
Example #1 – Poisonous Newt Population
1.
In a certain population of newts, being poisonous (P) is dominant over not being poisonous (p). You count
200 newts, and 8 are not poisonous. What are the allele frequencies of the parent population?
2.
Fifty newts are washed downstream after a big storm and colonize a new pond. What do you expect the
frequency and number of each genotype to be?
3.
You count the new population of newts and find 21 homozygous poisonous newts, 23 heterozygous
poisonous newts, and 6 homozygous non-poisonous newts. Is this what you expect? (Test using Chi
square). If it is not, what are the new allele frequencies?
a. For this, you set up the same Chi square table as for the Punnett square crosses, with one
difference: instead of an expected ratio, you will have an expected frequency.
b. You already calculated the expected frequency and the expected number of newts for each
genotype, so write those numbers in the table.
c. Complete the rest of the table (or you may simply use the Chi square formula directly).
Obs.
Poisonous (PP) p2
Poisonous (Pp) 2pq
Non-poisonous (pp) q2
Total
Biology 11 Enriched
Efreq.
E
0–E
(0 – E)2
(0 – E)2/ E
21
23
6
50
Mr. Lau
Name: _________________________________________ Date: ___________________________ Block: ________
4.
d.
Recall that a chi-square analysis is to determine whether the differences between observed
frequencies and expected frequencies are the results of random occurrences ( or chance).
What would your null hypothesis (Ho) be?
e.
You have 2 alleles (two categories), so your degrees of freedom (d.f.) is
one less than that: 2-1=1. The table value for 1 d.f. is 3.841.
Do you reject or accept the null hypothesis (H o)?
Calculate new allele frequencies (of the new population) using the Hardy-Weinberg formula.
Note: In some problems you may know only the phenotypes instead of the genotypes. In that case, combine the p2
and 2pq rows of your table for the appropriate phenotype. For example, in the previous problem, if you knew only
that there were 44 poisonous newts and 6 newts that were not poisonous, your table would look like this:
Obs.
Poisonous (PP + Pp)
(p2 + 2pq)
Non-poisonous (pp) q2
Total
Biology 11 Enriched
Efreq.
E
0–E
(0 – E)2
(0 – E)2/ E
44
6
50
Mr. Lau
Name: _________________________________________ Date: ___________________________ Block: ________
Practice Problems:
1.
A) Walking through the forest, you find a large population of toadstools. From your extensive knowledge of
the Kingdom Fungi, you know that the allele for being spotted (S) is dominant over the allele for being
plain (s). In this population of 1007, you find 14 toadstools that are not spotted. What are the allele
frequencies?
B) In a different forest, you find a somewhat smaller population of 549. Through genetic testing, you
determine that there are 308 homozygous spotted, 206 heterozygous, and 34 homozygous plain
toadstools. Is this what you expected? If not, what are the allele frequencies of this population?
2.
You that know the allele for fuzzy peaches is recessive and that its frequency is 0.7. In an orchard of 500 trees,
you pick one peach from each tree. How many fuzzy peaches do you expect to find? (Hint: fuzzy peaches’
genotype is ff). You count 250 fuzzy peaches and 250 bald peaches. Is this the same as you expected? Test
using Chi square analysis.
3.
A)
4.
A) NASA finally sends a manned flight to Mars. The astronauts discover that Martian rocks are alive and can
reproduce. In a sample of 290 rocks, they count 130 red rocks and 160 brown rocks (red is dominant over
brown). What are the allele frequencies for red and brown?
B) The astronauts bring a group of 20 rocks back with them for further study. Of these rocks, 10 are red and
10 are brown. Given the parental population’s allele frequencies, is this what you would expect (test with
Chi square)? If not, what are the new allele frequencies?
5.
A) On your Spring Break in Mexico, you take a break to count the starfish in a tidal pool. You notice that
there is a rare recessive trait that causes the starfish to have 6 legs instead of 5. Of the 27 starfish you can
find, only 1 has 6 legs. What are the allele frequencies for this population?
B) Two years later, you return to the same beach and count the starfish again. This time you find 4 starfish
out of 31 that have 6 legs. Are the genotype frequencies the same as two years earlier? Test using Chi
square. If it is not, calculate the new allele frequencies.
C) Seven years later, you come back to the beach. This time you can find no starfish with 6 legs. Given the
most recent allele frequencies you know, is this what you would expect?
In a population of Venus fly traps in North Carolina, you observe 150 that can eat large flies, and 400 that
can eat only small flies. If the ability to eat large flies (s) is recessive, what is the allele frequency?
B) Back in BC, you visit a specialty store that sells Venus fly traps. Of the 56 plants in the store, how many do
you expect to eat large flies?
C) You count and see that 25 can eat large flies. Is this what you expected? (Test with the Chi square.) If not,
what are the new allele frequencies?
Biology 11 Enriched
Mr. Lau