Dihybrid Corn Lab, Chi-Square Test, Probability Lab

Dihybrid Corn Lab, Chi-Square Test, Probability Lab

Laboratory 6, AP Biology 2012

Kavinmozhi Caldwell, Spurthi Tarugu

Abstract
Genetics is the study of gene inheritance. These genes are located in the DNA, which is of course in the nucleus. Each DNA molecule is a chromosome, and each chromosome contains thousands of genes. The genotypes are the genetic makeups of traits, while phenotypes are the physical manifestations of that trait. At the most basic level, an offspring gets one allele from the father, and one allele from the mother. Which allele the offspring inherits from each will determine the manifestation of the trait. Probability plays a major role in genetics. Suppose a mother is homozygous recessive for blue eyes, while the father is homozygous dominant for brown eyes. The offspring will most definitely inherit a dominant brown eye allele from the father and a recessive blue eye allele from the mother; the child will have brown eyes 100%. The situations can of course get much more complicated, and sometimes, probabilities of inheritance are not as simple. There are expected outcomes, but many of the times, what is observed is different. The degree of variance between the expected outcome and the observed outcome can be calculated by the Chi-Squared Test.

Introduction
The Dihybrid Corn lab was used to study the inheritance of genes in the F2 generation using phenotypes. The ears of the corn had four phenotypes which we observed and recorded: purple starchy, purple sweet, yellow starchy, and yellow sweet. As we analyzed the phenotypes, we were able to see how the observed results did not match the expected results and how the genotypes manifested themselves in different ways.
As I stated before,  the  Chi-Squared Test is used to determine the variance between two sets of data, and in this case, the variance between the expected outcome and the observed outcome. By using these two values, we are able to calculate chi-squared value, degrees of freedom, and the P-Value, which tells us how big the variance actually is.
The Probability Lab was used to establish how the expected outcome isn’t necessarily the observed outcome. First, we tossed a coin 100 times, recording the number of heads and tails. Then we tossed two coins 60 times, recording the number of heads and tails on each one.

Methods
Corn Dihybrid Genetics

In this lab we used one ear of corn. The grains in the years were of two different colors: purple and yellow. They were also of two types of textures wrinkly and smooth. The purple colored grains represent pigmented layers while yellow is not pigmented. The wrinkled grains represent sweet corn while the smooth grains represent starchy ones. We counted the different phenotypes represented in one ear of corn. We recorded the data two tables. After one group of us found our data, we received information from another group who followed the same procedures. Using the two tables we were able to see dihybrid inheritance.


Probability

In this lab we used two coins of different kinds, a tabletop, and a cup. For the first part of this lab, we assigned one person in each pair to place one coin in the cup, shake it, roll it onto the tabletop, and inform the other person (the recorder) whether it was heads or tails. The tosses were repeated 10 times for each trial with a total of 10 trials in all totaling 100 tosses in all. During the second part of this lab, we switched roles. However this time instead of tossing one coin, we tossed two coins of different values. The rest of the steps remained the same. We tossed these two coins 10 times each trial for a total of 6 trials equaling 60 tosses in all. All of this data was recorded in tables.


The Chi-Squared Test
Using background information given, we were able to prove the dihybrid genetics crosses and the probability results. We created a null hypothesis: If we observe two heterozygous individuals crossed, then the expected ratios for their offspring 9:3:3:1 will not occur. We also formed an alternate hypothesis: if we observe two heterozygous individuals crossed, then the expected rations for their off springs will be 9:3:3:1. We tested these two hypothesis using dihybrid crosses.

Observation/Results
Corn Dihybrid Genetics
Table 1

Purple Starchy Purple Sweet Yellow Starchy Yellow Sweet
Total Ear 1 143 73 97 26
Total Ear 2 201 51 111 43
Total Ears 1 & 2 344 124 208 69

Table 2

1 2 3 4 4 Classes
Phenotype Class Purple & Starchy Purple & Sweet Yellow & Starchy Yellow & Sweet Total (1-4)
Number of Individuals (Actual count) a1 = 344 a2 = 124 a3 = 208 a4 = 69 745
Expected number e1 =420 e2 =140 e3 =140 e4 =47 747

Probability Lab
Table 1: Tossing a single coin

Trial No. Heads No. Tails
1 5 5
2 3 7
3 4 6
4 2 8
5 5 5
6 6 4
7 3 7
8 7 3
9 7 3
10 5 5
Totals 47 53

Table 2: Tossing two coins together

Trail H1H2 (Quarter;Penny) H1T2 H2T1 T1T2
1 3 3 4
2 1 2 2 5
3 2 6 1 1
4 4 1 5
5 3 2 1 4
6 1 3 3 3
Total 14 14 10 22

Discussion

In a series of 10 tosses of the single coin we expected 5 heads and we even obtained the expected results in three of our series of 10 tosses. Instead of a 50/50 probability, our results for 100 tosses of a single coin ended up as a 47/53.The difference between heads and tails was 6 off. Increasing the number of tosses verified the expected value with recurring probabilities.  14/60 times heads appeared for both coins in the total number of tosses in part 2 of the lab. 22/60 were tails while 24/60 were heads for one coin and tails for the other. The fraction for two heads is closer to the product of the two fractions for the expected number of heads from each coin because when two coins join together, the probability decreases. Our answer is the same for two tails because the same situation occurs with attaining two tails just like with two heads. The expected relationship between the two chance events is the probability of the first event occurring times the probability of the second chance event occurring.

With our Chi-Squared practice we are able to see that expected values can be calculated using observed results. Chi-Squared can only be used when comparing expected theoretical outcomes and experimental results. From our observation of the probability lab and the corn dihybrid lab we were able to calculate how much the observed results differed from the expected results:

Chi_squared for Single Toss: Observed results differed from expected results by 80% to 50%.

Chi-Squared for double toss: Observed results differed from expected results by 20% to 10%.

Corn Lab: Observed results differed from expected results by less than .1%.


Conclusion

By studying the concepts of chi-squared, punnett squares, and probabilities of outcomes in mono-hybrid and dihybrid crosses, we are able to clearly see how these topics interrelate. The observation and experimental data results we gathered from the dihybrid corn lab and the probability lab varied from the expected outcomes that were set. The Chi-squared test allowed us to calculate the difference between the expected and observed results and has taught us that probabilities of inheritance undergo many mutations and do not always result in what is expected.