Hardy-Weinberg Equilibrium Explained: Allele and Genotype Frequencies in a Frog Population

Overview

This Amoeba Sisters video reveals how math is used in biology by introducing Hardy-Weinberg equilibrium, detailing its five assumptions, and walking through the core equations that relate allele frequencies to genotype frequencies. A step-by-step frog population example shows how to calculate P, Q, and all genotype frequencies under equilibrium.

Key insights

• Hardy-Weinberg provides a baseline model for comparing real populations under evolutionary forces.
• The two central equations are P + Q = 1 and p^2 + 2pq + q^2 = 1, linking allele and genotype frequencies.
• Practical problem solving involves identifying which equation to use and careful interpretation of genotype data.
• Tips emphasize checking that frequencies sum to 1 and avoiding assumptions not supported by data.

Introduction: Math in Biology and the Baseline Idea

Biology is often thought of as a field driven by observation and chemistry, yet mathematics plays a crucial role in understanding how populations change over time. In this video, the Amoeba Sisters highlight Hardy Weinberg equilibrium as a baseline model for allele and genotype frequencies in a population. The idea is simple: in the absence of evolutionary forces, allele frequencies stay constant across generations, and genotype frequencies follow from those allele frequencies according to well-known equations. This baseline allows researchers to quantify how real populations diverge from equilibrium due to selection, mutation, migration, drift, or non-random mating. As a reminder, a population here is a group of organisms of the same species capable of interbreeding and producing fertile offspring, with some genetic variation among individuals.

“The Hardy Weinberg equilibrium gives you this baseline to compare how an evolving population could compare to one that remains constant without evolutionary forces acting upon it.” - Amoeba Sisters

The Five Assumptions of Hardy Weinberg Equilibrium

For a population to be in Hardy Weinberg equilibrium, five conditions must hold: no selection, no mutation, no migration, a very large population, and random mating. If any of these assumptions fails, the allele and genotype frequencies may drift or shift over time, leading to evolution. The video draws attention to how real populations often violate these assumptions, for example through predation that differentially reduces the fitness of one genotype, thereby altering allele frequencies in the next generation.

“There are five assumptions. The frogs mate without any specific choice. All five assumptions must be kept in order for Hardy Weinberg equilibrium to happen.” - Amoeba Sisters

Allele Frequencies and Genotype Frequencies: The Core Equations

The first key relationship is a simple conservation of alleles: the dominant allele frequency P and the recessive allele frequency Q must sum to 1 (P + Q = 1). The second relation translates those allele frequencies into genotype frequencies: p^2 for homozygous dominant, 2pq for heterozygotes, and q^2 for homozygous recessives, with the sum equal to 1 (p^2 + 2pq + q^2 = 1). Importantly, P and p refer to the same dominant allele frequency, and Q and q refer to the recessive allele frequency, but the equation P = p and Q = q are not interchangeable in all contexts; allele frequencies can be expressed in either lower-case or upper-case notation depending on the document, but the underlying math remains consistent.

In the video example, if 0.6 of the alleles are big G (P = 0.6) and 0.4 are little G (Q = 0.4), then the genotype frequencies under equilibrium would be 0.36 for big G big G, 0.48 for Big G little G, and 0.16 for little G little G, matching the equation 0.36 + 0.48 + 0.16 = 1.

Worked Example: A New Frog Population

The presenter then presents a new population problem: 500 frogs with 375 dark green individuals and 125 light green individuals. Because light green corresponds to the recessive genotype (little G little G), the frequency q^2 is 125/500 = 0.25, so q = 0.5. Using P + Q = 1, p = 0.5 as well. With p and q known, the genotype frequencies are p^2 = 0.25 for big G big G, 2pq = 0.5 for big G little G, and q^2 = 0.25 for little G little G. This confirms the Hardy Weinberg expectations and shows how allele frequencies drive genotype composition under equilibrium.

Key steps in solving such problems include choosing the right equation to start from, converting counts into frequencies, deriving the missing allele frequency, and then calculating all genotype frequencies. The example also illustrates why you cannot always assume the genotype composition from a single phenotype observation when multiple genotypes could produce the same phenotype.

Tips for Hardy Weinberg Problems and Practical Takeaways

The video closes with practical strategies for solving HW problems. It cautions that nice round numbers are convenient but not guaranteed in every problem, so calculators may be needed. A common check is to verify that the final frequencies satisfy both equations, summing to 1 in both allele and genotype forms. Finally, the presenter emphasizes avoiding unwarranted assumptions based on incomplete data and encourages practice problems to build intuition for how evolutionary forces shift a population away from Hardy Weinberg expectations.