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7.5 Hardy-Weinberg Equilibrium

Keywords

English Term 中文翻译 Definition & Explanation
Hardy-Weinberg Equilibrium 哈代-温伯格平衡 A principle stating that genetic variation in a population will remain constant from one generation to the next in the absence of disturbing factors.
Allele Frequency 等位基因频率 The proportion of a specific allele out of the total alleles for that gene in a population.
Genotype Frequency 基因型频率 The proportion of a specific genotype (e.g., AA, Aa, aa) among individuals in a population.
Null Hypothesis 零假设 A baseline hypothesis stating that there is no significant change or relationship; in this case, predicting that the population is not evolving.

1. The Baseline of Evolution

If evolution is defined as a change in allele frequencies over time, how do scientists actually prove a population is evolving? They need a baseline to compare it against.

The Hardy-Weinberg (H-W) principle acts as a mathematical null hypothesis. It models a theoretical, non-evolving population. If a real population's allele frequencies deviate from the H-W predictions, it provides direct evidence that the population is evolving.

The Five Conditions for Equilibrium

For a population's allele frequencies to remain constant (no evolution), five strict conditions must be met:

  1. A very large population size (to eliminate genetic drift).
  2. Absence of migration (no gene flow in or out).
  3. No net mutations (no new alleles created).
  4. Random mating (no sexual selection; everyone has an equal chance to mate).
  5. Absence of selection (no natural selection favoring one trait over another).

These conditions are seldom met in nature, but they provide a valuable baseline.

2. The Mathematics of Hardy-Weinberg

Allele frequencies in a population can be calculated from genotype frequencies using two equations. Imagine a gene with two alleles: a dominant allele (\(A\)) and a recessive allele (\(a\)).

Equation 1: Allele Frequencies

\[ p + q = 1 \]
  • \(p\) = Frequency of the dominant allele (\(A\))
  • \(q\) = Frequency of the recessive allele (\(a\))
  • (Because there are only two alleles, their total percentages must add up to 100%, or 1).

Equation 2: Genotype Frequencies

\[ p^2 + 2pq + q^2 = 1 \]
  • \(p^2\) = Frequency of the homozygous dominant genotype (\(AA\))
  • \(2pq\) = Frequency of the heterozygous genotype (\(Aa\))
  • \(q^2\) = Frequency of the homozygous recessive genotype (\(aa\))

The AP Biology Secret Weapon: Always find \(q^2\) first!

When solving H-W math problems, you can't tell just by looking at an animal if it is \(AA\) or \(Aa\) because they both have the dominant trait. However, if an animal shows the recessive trait, its genotype must be \(aa\).

Step-by-step strategy:

  1. Count how many individuals show the recessive trait. Divide by the total population to find \(q^2\).
  2. Take the square root of \(q^2\) to find \(q\).
  3. Use \(p + q = 1\) to find \(p\).
  4. Once you have \(p\) and \(q\), you can plug them into \(p^2\) and \(2pq\) to answer any question!

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