DIGITAL GENETICS

Genetic Simulations on the TI-83

The study of genetics is included in a variety of science coarses. While it can be confusing to understand genetics by reading a text book the brilliant Austrian monk, Gregor Mendel was able to draw upon his observations of pea plants and apply mathematical principles to give us the foundation for genetics as we know it today. The following programs operate in the Texas Instruments TI-83 calculator. They simulate some of the traditional Mendelian crosses for a more realistic experience of how genetic principles work in populations. Some of the simulations will display the phenotype and genotype of each progeny or offspring as they are "produced". When the program is finished data is stored in lists for later use. Hopefully by veiwing the display and manipulating the data it will help make genetics more understandable and perhaps even fun!

There are some conversions that a user should be aware of to run these programs. If a text book has the tall and dwarf example of a monohybrid cross an uppercase "T" may denote the dominant allele for the tall trait and a lower case "t" may denote the recessive allele for the dwarf trait.. These programs use the number "1" to represent the recessive allele (dwarf) and the number "2" to represent the dominant allele (tall). The dihybrid cross uses a "3" to symbolize the recessive allele for the color yellow and the "4" to symbolize the dominant allele for the color green. The lists that contain the ratios may have zeros within the lists if the progeny numbers are small or if there are less than the total possible genotype combinations available. Please ignore the zeros since they are required to maintain the list dimension.

Another note of interest is the use of "MOM" and "DAD" to help the person decide how the parental genotypes should be arranged. Since pea plants can be self fertilized consider that the "MOM" alleles represent a traits genotype of a flower megaspore mother cell (which is 2n before meiosis) and the "DAD" alleles represent a traits genotype of a flower microspore mother cell (which is 2n before meiosis). An example of one parent or progeny genotype could be "1143" which represents the dihybrid phenotype of a dwarf(11) and green(43) pea plant.

Those more familiar with genetics may want to explore the data collected from each cross. The frequencies and ratios of both the genotypes and the phenotypes are stored into lists. This data can be used to develop models to predict how a cross with a low number of progeny may be expected to look. It should provide an excellent learning opportunity since it is easy to perform many simulations and apply Chi square analysis.

All of these programs use the "SetUpEditor" to add more lists than the six default lists. To return to the default settings press STAT then #5 then ENTER to show lists L1 to L6. See page 12-21 of the TI-83 Graphing Calculator Guidebook for more details.

The programs are basically in order of difficulty. The first program is a good introduction to how the calculator works these programs and relates to meiosis. Afterall, if you want to understand genetics you should know your M&M's. That is you Must Master Meiosis!

These genetic programs are currently in the beta stage of development. Do not resell or post any of these programs onto the internet. Please e-mail your comments or suggestions.

Use these programs at your own risk and minimize errors by practicing the programs with several of your own example problems. 

MEISOSIS: Simulates metaphase 1 of meiosis.

MONOCROS: Simulates a monohybrid cross.

SELFIT: Simulates multiple generations of selfing.

CODOM: Simulates codominance using pink, white and red pea plant flower colors..

DICROSS: Simulates a dihybrid cross.

CHISQARE: Provides simulation data and chi square analysis.

RATIOMON: Provides expected ratios for a given monohybrid cross.

RATIODI: Provides expected ratios for a given dihybrid cross.

CSPASTVA: For Chi square analysis of expected and observed values.

FREQDIST: For making a frequency distribution.

The following links are the file names of TI-83 genetic programs. Some programs have multiple files that must be included to make them work properly. Next to the link is a description of the program and what data will be required.

MEIOSIS: Simulates metaphase 1 of meiosis by randomly selecting alleles from a homologous pair of maternal and paternal chromosomes to produce digital gametes with one allele. The program display designates that the "MOM" (M prompt) contributed the #1 allele and the "DAD" (D) contributed the #2 allele as an example of a heterozygous pair of alleles. The calculator will randomly choose either 1 or 2 for the "N" number of gametes to be produced. This imitates the random alignment of maternal and paternal chromosomes in metaphase 1.

If 1 is selected for the "M" prompt and 2 is selected for the "D" prompt then the selected gamete allele will be displayed. The right side of the screen will show the current number of gametes produced. When the program is done the display will show the number of gametes with the "MOM" and "DAD" alleles. Press STAT then ENTER to veiw the stored data. List L1 labels alleles 1 and 2 which corresponds to their frequencies in list L2. Under ideal conditions both numbers in L2 should be close or the same.

MONOCROS: MONOGENO: MONOPHNO: Simulates a monohybrid cross representing tall and dwarf alleles from Mendel's pea plant crosses. "Monocros" is the main program to activate but all three programs must be in the TI-83. The "N" prompt is the number of desired progeny. The "A" and "B" prompts represent maternal alleles which can be any combination of 1 or 2. Likewise, the "C" and "D" prompts represent paternal alleles which can also be any combination of 1 or 2. When the program is executed each of the progeny phenotypes (tall or dwarf) with their respective genotypes are displayed and scrolled onto the screen. When the program is finished press STAT then ENTER to veiw the lists. List L2 labels the three relevant genotype combinations which correspond to their frequencies in list L3 and genotype ratios in list L4. List L5 labels the two phenotype combinations which also match to their frequencies in L6 and phenotype ratios in List "PR".

It is important to note that their are 4 possible genotype combinations (11,12,21,22) in a double heterozygous monohybrid cross but only 3 relevant genotypes (11,21,22). For example, 12 is the same as 21. When the phenotypes and genotypes are scrolled onto the display they appear exactly as they occur and it is possible to veiw a "TALL,12" and later a "TALL,21". List L2 shows only the label "21" but all the genotype frequencies of "12" are included in L3 and L4 under the "21" label.

SELFIT: Simulates the effects of multiple generations of inbreeding. A single offspring is crossed by itself by the "G" number of generations. When the program is executed all of the generation phenotypes (tall or dwarf) and respective genotypes are displayed. When the program is done press STAT then ENTER to veiw list L1 which shows the order of the genotypes. The "G" prompt is the number of generations desired. Input any combination of 1 or 2 at the "A" or "B" prompt for a parents alleles. Input any combination of 1 or 2 at the "C" and "D" prompt for the other parents alleles.

CODOM: COGENO: Simulates codominance using Mendel's pink, red, and white pea flower phenotypes. "Codom" is the main program to activate but "cogeno" must also be in the TI-83. The "N" promt is the number of progeny desired which is limited to 999. The A and B prompts represent maternal alleles which can be any combination of 1 or 2. Likewise the C and D prompts represent paternal alleles which can be any combination of 1 or 2. When the program is executed each of the progeny phenotypes (pink,red or white) are combined with their genotypes and displayed onto the screen. When the program is finished press STAT then ENTER to veiw the lists.

List L1 and L2 will show the random alleles selected and L3 shows the corresponding arrangement of alleles which represent the genotype for each plant. List L4 labels the three relevant genotype combinations which match to their frequencies in L5 and ratios in L6. The genotype ratios are the same as the phenotype ratios in codominance modes of inheritance.

DICROSS: DGRATIO: DPRATIO: Simulates a dihybrid cross representing tall,dwarf alleles (1 or 2) and green, yellow alleles (3 or 4) from Mendel's pea plant crosses. "Dicross" is the main program to activate but all three must be in the TI-83. The "N" prompt is the number of desired progeny. The A and B prompts represent maternal alleles which can be in any combination of 1 or 2 then the C and D prompts can be any combination of 3 or 4. Likewise the E and F prompts represent paternal alleles which can be in any combination of 1 or 2 then the G and H prompts can be any combination of 3 or 4. When the program is executed each of the progeny phenotypes (tall or dwarf and green or yellow) with their proper genotypes are displayed onto the screen. When the 1133 genotype is encountered the display will indicate that it is rare and show 1/16. This fraction represents that 1133 is a one in 16 phenotype probability when both parents are double heterozygous. When the program is finished press STAT then ENTER to veiw the lists.

List L2 labels the 9 relevant genotype combinations which correspond to their frequencies in list "GFREQ" and genotype ratios in L3. List L4 labels the 4 possible phenotype combinations which also match to their frequencies in L5 and ratios in L6.

It is important to note that there are 16 total genotype combinations (2x2x2x2 = 16) in a double heterozygous dihybrid cross but there are only 9 relevant genotype classifications. For example, 2143 is the same as 2134. When the phenotypes and genotypes are scrolled onto the display they appear exactly as they occur so it is possible to observe a TALL,GREEN,2143 and later a TALL,GREEN,2134. List L2 shows only the label 2143 but the matching frequencies in list "GFREQ" and the ratio in L3 will include all the 2134 genotypes.

Since a double heterozygous dihybrid cross (1234 x 1234) would have an expected genotype ratio of 1:2:2:4:1:2:1:2:1 this matches to the genotype labels in "dicross" list L2. The combined labels and expected ratios for "dicross" L2 are as follows: 1(2244) : 2(2243) : 2(2144) : 4(2143) : 1(2233) : 2(2133) : 1(1144) : 2(1143) : 1(1133)

CHISQARE: This program will give the expected frequencies and a Chi square analysis from a previous simulation when provided the expected ratios, their matching observed frequencies, and the number of progeny that were produced. By comparing the expected and observed frequencies it is easier to understand why an observed ratio may not fit the expected ratio.

Input the expected ratios into L1 and the observed frequencies of a phenotype or genotype into L2. Input the number of progeny produced at the "N" prompt. After the program is executed the display will show the Chi square value, the P value, and the degrees of freedom. Press STAT then ENTER to veiw list L3 which is the expected frequencies based upon the expected ratios of L1 and the progeny number. List L3 is used to compare with the observed simulation frequencies in L2.

Some examples of expected genotype ratios include 1:2:1 for a double heterozygous monohybrid cross (12 x12). A double heterozygous dihybrid cross would have an expected genotype ratio of 1:2:2:4:1:2:1:2:1 which matches to the genotype labels in "dicross" list L2. The combined labels and expected ratios for "dicross" L2 are as follows: 1(2244) : 2(2243) : 2(2144) : 4(2143) : 1(2233) : 2(2133) : 1(1144) : 2(1143) : 1(1133)

RATIOMON: Finds the expected genotype and phenotype ratios when provided the parental alleles of a monohybrid cross. Expected ratios are used in the "CHISQARE" program to analyse a previous sumulation. Input the parental alleles for A,B and C,D which can be any combination of 1 or 2. After the program is executed press STAT then ENTER to veiw the lists.

List "ALLEL" is the allele combination of the parents (ABCD) to serve as a reference. List "GLABL" is the genotype label list similar to the program "monocros". List "GRATO" is for the genotype ratios. List "PLABL" is for the phenotype labels. List "PRATO" is for the phenotype ratios.

RATIODI: RDONE: RDTWO: Finds the expected genotype and phenotype ratios when provided the parental alleles from a dihybrid cross. Ratiodi is the main program to activate but all three programs must be in the TI-83. Expected ratios are used in the "CHISQARE" program to analyse a previous simulation from the program "dicross". Input the parental alleles for the prompts A,B, C,D and E,F,G,H. They can be any combination of 1 or 2 for ABEF and any combination of 3 or 4 for CDGH.

The program uses the forked-line method to obtain the expected ratios. Therefore each contrasting pair of traits are considered separately and then combined to compute the ratios. The program will first analyse the tall and dwarf traits (1 and 2) and display the output with their appropriate probabilities. Then the program calculates the green and yellow traits (3 and 4) and also displays their outcome genotypes and respective probabilities. The purpose of this display is to show that each genotype of tall and dwarf is combined with each genotype of the colored traits and then all probabilities are multiplied. Some displays may be too long to fit on the screen when the program is finished.

After the program is executed press STAT then ENTER to veiw the lists. List "ALLEL" is the allele combination of the parents to serve as a reference. Prompts ABCD are on the top line and EFGH are on the second line. List L1 are the genotype labels which correspond to their ratios in L3. List "PLABL" is for the phenotype labels. List "PRATO" is for the phenotype ratios.

CSPASTVA: For finding the computed value of a one way Chi-Square distribution based upon corresponding past or expected values used for comparison. Input the observed samples values into L1 and the past or expected values into L2. "PV" is the P value and "DF" is the degrees of freedom. See guide book page 13-31.

FREQDIST: Sorts raw data values into a frequency distribution (without classes). Input the values into L1. When the program is executed each value is stored to L3 and its corresponding frequency is in L4. An excellent program!!