Lab Report: Testing the Hardy-Weinberg Principle

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Abstract

In this experiment, we aimed to test the Hardy-Weinberg equilibrium using a population simulation with 100 colored beads. The beads were divided equally into two colors, blue and yellow, representing different genotypes. We applied the Hardy-Weinberg formula to calculate the expected genotype and allelic frequencies. Through random sampling with replacement, we generated observed genotype frequencies for 50 individuals. Our results were compared to the expected frequencies to determine if the population was in genetic equilibrium.

Introduction

The Hardy-Weinberg principle, developed by Godfrey Harold Hardy and Wilhelm Weinberg in 1908, is a mathematical model that describes the genetic equilibrium in sexually reproducing populations.

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Genetic equilibrium occurs when neither allele nor genotype frequencies change across generations. This equilibrium relies on specific conditions: the absence of mutations, a closed population, infinite size, equal survival and reproduction of all genotypes, and random mating.

The Hardy-Weinberg formula is expressed as:

P² + 2pq + q² = 1

Where P², 2pq, and q² are the frequencies of the genotypes AA, Aa, and aa, respectively.

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Deviations from these conditions, such as mutations, gene flow, genetic drift, natural selection, and non-random mating, can lead to microevolutionary changes.

Natural populations rarely meet all the Hardy-Weinberg conditions due to various factors leading to microevolution. Mutations may accumulate over time and influence gene pools in subsequent generations. Other factors also impact allele frequencies in populations.

Materials

A plastic bag containing 100 beads of two colors (blue and yellow).

Procedures

In a plastic bag, there were 100 beads, equally divided into blue and yellow.
Blue beads represented homozygous dominant individuals, yellow beads represented homozygous recessive individuals, and a mix of blue and yellow beads represented heterozygous individuals.
We randomly removed two beads from the bag and recorded their colors to denote the genotype of one individual.
The beads were returned to the bag and shaken to redistribute the gene pool (sampling with replacement).
We repeated these steps for 50 individuals, representing the population of the next generation.

Results

1. Expected Genotype and Allelic Frequencies

Using the Hardy-Weinberg equation:

P² + 2pq + q² = 1

Where P = 0.50 and q = 0.50, we calculated the following:

Allelic Frequency	Genotypic Number (and Frequency)	Allelic Frequency
A	a	AA	Aa	aa	A	a
0.50	0.50	0.25 * 50 = 12.5	0.50 * 50 = 25	0.25 * 50 = 12.5	0.50	0.50

2. Observed Genotype and Allelic Frequencies

Genotype frequency:

Genotype	Total Number of Individuals	Genotype Frequency	Number of A Alleles	Number of a Alleles
AA	12	12/50 = 0.24	2 * 12 = 24	0 * 12 = 0
Aa	22	22/50 = 0.44	1 * 22 = 22	1 * 22 = 22
aa	16	16/50 = 0.32	0 * 16 = 0	2 * 16 = 32
Totals	50	1.0	46	54

Allele frequency:

Total Number of A Alleles + Total Number of a Alleles
46 + 54 = 100

p = Frequency of A = 46/100 = 0.46

q = Frequency of a = 54/100 = 0.54

3. Chi-Square of Results

Genotype	Observed Value (o)	Expected Value (e)	Deviation (o - e)	d²	d²/e
AA	12	12.5	-0.5	0.25	0.02
Aa	22	25	-3.0	9.0	0.36
aa	16	12.5	3.5	12.25	0.98

Chi-Square (X²) = ∑d²/e = 1.36

Discussion

Our results showed that there were 12 individuals with homozygous dominant genotypes (AA), 16 individuals with homozygous recessive genotypes (aa), and 22 individuals with heterozygous genotypes (Aa).
The observed results deviated slightly from the expected results, indicating that the population size was not infinite.
There was variability among different teams' results, highlighting the lack of consistency in our findings.
However, our results matched the prediction that allele frequencies would remain constant for the next 25 generations, but genotype frequencies would stop changing after the first generation.

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This suggests that the population reached genetic equilibrium.
It's important to note that our population model did not meet all the conditions of the Hardy-Weinberg principle due to limitations in our experiment.

Conclusion

The Hardy-Weinberg principle is a valuable tool for determining whether a population is evolving. Our experiment demonstrated that when certain conditions are met, allele frequencies remain constant, and genetic equilibrium is achieved. However, real-world populations rarely fulfill all the conditions, leading to microevolutionary changes over time.

Works Cited

Ayala, F. J. (2019, January 11). Evolution. Retrieved from Encyclopaedia Britannica: https://www.britannica.com/science/evolution-scientific-theory/The-science-of-evolution

Britannica, The Editors of Encyclopaedic. (2006, May 18). Hardy-Weinberg law. Retrieved from Encyclopaedia Britannica: https://www.britannica.com/science/Hardy-Weinberg-law

Jack E. Staub, K. B. (1994). Crossover: Concepts and Applications in Genetics, Evolution, and Breeding: An Interactive Computer-Based Laboratory Manual. London, England: The University of Wisconsin Press.

Peter J. Russell, P. E. (2017, 2014). Biology: The Dynamic Science. Boston, USA: Cengage Learning.

Theodosius Dobzhansky, Arthur Robinson, Anthony J.F Griffiths. (2019, January 10). Heredity. Retrieved from Encyclopaedia Britannica: https://www.britannica.com/science/heredity-genetics/Extranuclear-DNA

Lab Report: Testing the Hardy-Weinberg Principle. (2024, Jan 04). Retrieved from https://studymoose.com/document/lab-report-testing-the-hardy-weinberg-principle