Large Populations - Biology

1. Fundamental Concepts

Definition: The Hardy-Weinberg equilibrium is a principle that states the allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.
Assumption: One of the key assumptions for the Hardy-Weinberg equilibrium to hold is that the population must be large.
Implication: In a large population, random mating and genetic drift have minimal effects on allele frequencies.

Population Size: $p^2 + 2pq + q^2 = 1$

Gene Frequency: $p + q = 1$

Application: Used to predict the frequency of alleles and genotypes in a population

Problem: Suppose in a large population, the frequency of the dominant allele $A$ is $0.7$. What is the frequency of the recessive allele $a$?

Given $p = 0.7$, where $p$ is the frequency of the dominant allele $A$.
Using the equation $p + q = 1$, solve for $q$: $0.7 + q = 1 \Rightarrow q = 0.3$.

Validation: Substitute $p = 0.7$ and $q = 0.3$ into $p + q = 1$: $0.7 + 0.3 = 1$ ✓

Problem: If the frequency of homozygous recessive individuals ($aa$) in a population is $0.09$, what are the frequencies of the alleles $A$ and $a$?

Validation: Substitute $q = 0.3$ into $q^2 = 0.09$: $0.3^2 = 0.09$ ✓

Visual Strategy: Use pie charts to represent allele frequencies visually.
Error-Proofing: Always check if the sum of allele frequencies equals 1.
Concept Reinforcement: Practice with different scenarios to understand the impact of population size on genetic variation.