Genetic Diversity and Hardy-Weinberg Equilibrium
Defining a Population
Difficulty of Definition: Similar to the concept of 'species' or 'life', a precise definition of a 'law' in law, defining 'species' in biology is notoriously difficult.
Population Definition: A group of individuals of the same species that live in roughly the same area or overlap sufficiently in time and space, making them more likely to mate with each other than with individuals of the same species in different populations.
Example: Ground Squirrels: Imagine a classroom divided by a 'Grand Canyon'. Ground squirrels on the right are more likely to mate with each other, and those on the left are more likely to mate with each other, even though they are all the same species. This geographical separation leads to greater statistical likelihood of intra-population mating.
Genetic Distinctiveness: Physical separation and isolated mating within populations allow for genetic distinctiveness, as populations adapt to slightly different local conditions (e.g., climate, vegetation, predators).
Example: Porcupine and 40-Mile caribou herds in Canada/Alaska. Although there's some overlap and crossbreeding, they generally occupy different ranges and show detectable genetic differences.
Importance for Evolution: The lowest level at which evolution can occur is the population. Individuals do not evolve; populations evolve. While evolution within populations can lead to new species, the process always starts at the population level.
Understanding Genetic Diversity
Extent of Diversity: Populations are genetically diverse, but not uniformly across the entire genome.
Fruit Fly Genome Example: Drosophila melanogaster has one of the best-understood genomes, with 13,700 genes.
Fixed Genes: Approximately 85\% to 86\% of these genes are fixed, meaning there is no allelic variation for that gene or locus (1 version only). These typically control core, fundamental biological functions (e.g., cellular metabolism, DNA packaging/storage/repair, basic substrate processing like glycolysis, ATP generation).
Heterozygous Genes: About 14\% of genes are heterozygous, meaning they have a minimum of two versions (alleles).
Evolutionary Material: Evolution primarily works with existing genetic variation (the 14\% of heterozygous genes). Core functions (the fixed genes) have been refined over billions of years, and mutations in them are likely to be deleterious or neutral, rarely beneficial.
Origin of Variation: All new genetic variation (new genes, new alleles) initially arises through mutation.
Mutation Effects: Most mutations are neutral (e.g., due to genetic code redundancy, amino acid substitutions with similar chemical properties, or occurring in introns which are not expressed). Some are deleterious (harmful), and rarely, one is positive (improving function), which tends to be retained.
Discrete vs. Quantitative Traits
Discrete Traits (Single Gene Polymorphisms):
Variations in body form controlled by a single gene, typically presenting as 'on' or 'off' states.
Examples:
Fruit Flies: Wild-type (red eyes, normal wings) vs. curly wings, orange eyes, or ebony body. Each variant is often due to a single gene mutation.
Humans: Attached vs. unattached earlobes, presence/absence of hair on the second joint of fingers, genetic disorders like beta thalassemia and sickle cell anemia (single gene mutations).
Quantitative Traits (Polygenic Traits):
Traits determined by a plurality (multiple) of genes interacting with each other.
Exhibit a continuous distribution rather than distinct categories.
Examples:
Skin Color: Determined by the collective input of about 10 to 15 genes.
Height: Influenced by multiple genes and environmental factors.
Distribution: When quantified, these traits typically show a bell curve distribution, where most individuals cluster around an average value.
Heritable vs. Environmental Influences:
Height Example: Genetically determined (tall parents tend to have tall children), but also significantly influenced by environmental factors like nutrition (malnutrition can prevent full height potential even with 'tall genes').
Evolutionary Relevance: Evolution can only shape the heritable (genetically inherited) component of variation in a population, not environmentally determined variations.
Hardy-Weinberg Principle
Mendelian Limitations: Mendelian genetics (e.g., Punnett squares in Bio 1) often implies a 1:2:1 genotype ratio (1/4 homozygous dominant, 1/2 heterozygous, 1/4 homozygous recessive) or 3:1 phenotype ratio, assuming an equal (50/50) distribution of alleles in the population. In reality, wild populations rarely show these exact ratios.
Hardy and Weinberg's Contribution: Independently developed a solution to quantify genetic variation in natural populations by accounting for actual allele frequencies.
Allele Frequencies and Population Stability:
Hypothetical Scenario: If the frequency of a red allele (C^R) is 0.8 (80\%) and a white allele (C^W) is 0.2 (20\%) in a hypothetical flower population.
Common Misconception: Many expect the dominant allele's frequency to increase over time because it's 'dominant'.
Truth: In the absence of other evolutionary forces, the allele frequencies will remain constant over generations. Dominance does not inherently cause an increase in allele frequency.
Explanation: When rebuilding the next generation, if a population has 64\% C^R C^R, 32\% C^R C^W, and 4\% C^W C^W genotypes, the overall proportion of C^R alleles (from 2 imes 64 + 32 = 128 + 32 = 160 in a hypothetical 200 alleles) remains 160/200 = 0.8. The C^W allele count is (32 + 2 imes 4 = 32 + 8 = 40 in 200 alleles), which remains 40/200 = 0.2. The allele frequencies simply transfer to the next generation without change.
Hardy-Weinberg Equations: Provide a quantitative framework to relate allele and genotype frequencies.
Allele Frequencies: Let p be the frequency of the dominant allele and q be the frequency of the recessive allele. Since these are the only two alleles, their frequencies must sum to 1:
p + q = 1Genotype Frequencies: If mating is random, the probability of different genotypes can be derived:
Frequency of homozygous dominant (e.g., C^R C^R): p^2
Frequency of heterozygous (e.g., C^R C^W): 2pq
Frequency of homozygous recessive (e.g., C^W C^W): q^2
The sum of these genotype frequencies must also be 1:
p^2 + 2pq + q^2 = 1
Conditions for Hardy-Weinberg Equilibrium (No Evolution): For allele and genotype frequencies to remain constant across generations, the following conditions must be met:
No Mutation: No new alleles created or altered.
Random Mating: Individuals mate without preference for genotype.
No Natural Selection: All genotypes have equal survival and reproductive rates.
Extremely Large Population Size: Prevents random fluctuations in allele frequencies (genetic drift).
No Gene Flow: No migration of individuals into or out of the population.
If any of these conditions are violated, the population is evolving.
Practical Application: Genetic Counseling (PKU Example)
Phenylketonuria (PKU): A rare recessive disorder affecting approximately 1 in 10,000 people in the United States.
Public Health Question: What percentage of Americans are carriers (heterozygotes) for PKU?
Using Hardy-Weinberg:
Identify Known Value: The affected individuals (recessive disorder) are homozygous recessive. Therefore, the frequency of homozygous recessive individuals is q^2 = 1/10,000 = 0.0001.
Calculate Recessive Allele Frequency (q): Take the square root of q^2:
q = \sqrt{0.0001} = 0.01Calculate Dominant Allele Frequency (p): Using p + q = 1:
p = 1 - q = 1 - 0.01 = 0.99Calculate Carrier Frequency (2pq): Carriers are heterozygotes:
2pq = 2 \times 0.99 \times 0.01 = 2 \times 0.0099 = 0.0198Convert to Percentage: 0.0198 imes 100\% = 1.98\% or approximately 2\%.
Conclusion: Approximately 2\% of individuals in the U.S. are silent carriers for PKU, meaning they carry the disease allele but do not express the phenotype.