Quantifying Genetic Diversity

Plant Ecology II: Hardy–Weinberg equilibrium, diversity estimates, and factors shaping plant populations.

Introduction

Genetic diversity is variation in inherited genetic material within and among individuals and populations. It includes differences in alleles, genotypes, and DNA sequences.

Population size alone does not reveal genetic diversity. Thousands of shoots may belong to relatively few clones, or a large population may have developed from only a few founders.

Measuring genetic diversity helps plant ecologists study breeding systems, isolation, population history, and conservation needs.

1. Alleles, Genotypes, and Their Frequencies

A locus is a location in the genome, and an allele is a variant at that locus. At a diploid locus with two alleles, A and a, the possible genotypes are AA, Aa, and aa.

• AA and aa are homozygous genotypes.
• Aa is a heterozygous genotype.
• Genotype frequency is the proportion of individuals with a genotype.
• Allele frequency is the proportion of allele copies represented by an allele.

p = frequency of A = (2 × number of AA + number of Aa) ÷ 2N

q = frequency of a = (2 × number of aa + number of Aa) ÷ 2N

For two alleles: p + q = 1

Worked example

Among 100 plants, suppose there are 40 AA, 40 Aa, and 20 aa individuals. These plants contain 200 allele copies.

p = (80 + 40) ÷ 200 = 0.60

q = (40 + 40) ÷ 200 = 0.40

Observed genotype frequencies are 0.40 AA, 0.40 Aa, and 0.20 aa.

Counting observed alleles does not require Hardy–Weinberg equilibrium.

2. Hardy–Weinberg Equilibrium

The Hardy–Weinberg principle provides an ideal reference model. Under its conditions, allele frequencies remain constant across generations, while random mating produces predictable genotype proportions.

AA = p²; Aa = 2pq; aa = q²

p² + 2pq + q² = 1

Conditions of the standard model

• Random mating with respect to the locus.
• A sufficiently large population that drift is negligible.
• No selection affecting the locus.
• No gene flow changing allele frequencies.
• No mutation changing the alleles considered.

How the proportions arise

Under random union of gametes, an A allele has probability p and an a allele has probability q. Two A alleles occur with probability p². Aa can arise in two ways, giving 2pq.

The two heterozygous combinations add together: pq + pq = 2pq. The letters A and a do not require one allele to be dominant.

Expected counts

With p = 0.60 and q = 0.40, expected frequencies are 0.36 AA, 0.48 Aa, and 0.16 aa.

Genotype	Observed count	Expected count in 100 plants
AA	40	36
Aa	40	48
aa	20	16

Observed and expected counts need not be identical. A suitable statistical test evaluates whether the difference exceeds what sampling variation could explain.

Interpreting departures carefully

A departure does not automatically prove selection. Selfing, population subdivision, and genotyping errors can also produce unusual genotype proportions.

Non-random mating alone can change genotype proportions without immediately changing allele frequencies.

3. Estimates of Genetic Diversity

Observed heterozygosity: H_O

Observed heterozygosity is the proportion of sampled individuals that are heterozygous at a locus.

H_O = heterozygotes ÷ individuals genotyped

In the example, H_O = 40/100 = 0.40. This measure describes observed genotypes and is influenced by both allele frequencies and mating system.

Expected heterozygosity: H_E

Expected heterozygosity, or gene diversity, is the probability that two independently sampled allele copies differ. It equals expected heterozygosity under random mating in the standard diploid model.

For two alleles: H_E = 2pq

H_E = 2 × 0.60 × 0.40 = 0.48

For multiple alleles:

H_E = 1 − Σpᵢ²

Here, pᵢ is the frequency of each allele. Three alleles with frequencies 0.50, 0.30, and 0.20 give:

H_E = 1 − (0.25 + 0.09 + 0.04) = 0.62

A maximum of 0.50 applies only to a two-allele locus. Expected heterozygosity can be calculated even when observed genotypes depart from Hardy–Weinberg proportions.

Allele number and allelic richness

Allele number counts distinct alleles detected at a locus. Because larger samples usually reveal more rare alleles, raw counts can be misleading when sample sizes differ.

Allelic richness standardizes comparisons to a common sampling level, commonly using rarefaction. It is particularly useful for examining the loss of rare variants.

Percentage of polymorphic loci

This measures the proportion of examined loci containing variation under a stated criterion.

Polymorphic loci (%) = polymorphic loci ÷ total loci × 100

If 16 of 20 loci are polymorphic, the value is 80%. The marker panel and definition of polymorphism must be reported.

Nucleotide diversity: π

Nucleotide diversity is the average number of pairwise DNA differences per site. If pairs of sequences differ by an average of four bases in a 1,000-base region:

π = 4 ÷ 1,000 = 0.004

This measure incorporates sequence differences rather than simply counting distinct alleles.

Complementary indices

• F_IS describes heterozygote deficit or excess relative to the within-population expectation. A positive value does not, by itself, prove inbreeding.
• F_ST describes differentiation among populations. It complements within-population diversity measures and is not a direct, assumption-free count of migrants.

No single estimate captures all genetic diversity. Two populations can have similar heterozygosity but different numbers of rare alleles. Neutral-marker diversity also does not measure every aspect of adaptive potential.

4. Genetic Drift

Genetic drift is chance-driven change in allele frequencies. The alleles contributing to each generation are a finite sample of the gene pool, so frequencies can change without any allele having a selective advantage.

Drift can cause fixation, when an allele reaches frequency 1, or loss, when its frequency reaches 0. Across replicate isolated populations, drift tends to reduce diversity within populations.

Effective population size

Drift is stronger in small effective populations. Effective population size, N_e, represents an idealized population with equivalent drift or inbreeding, depending on the measure used.

It may differ from census size because reproductive success is unequal, population size fluctuates, or many shoots belong to the same clone.

A stand may contain hundreds of plants, but if only a few contribute most successful offspring, its effective size can be much smaller than its visible abundance suggests.

5. Bottlenecks and Founder Effects

Population bottlenecks

A bottleneck is a sharp reduction in an existing population. The survivors may carry only a subset of the original alleles, with rare alleles especially vulnerable to loss.

Population numbers may recover while genetic diversity remains reduced. Producing many descendants does not automatically restore alleles that disappeared.

Founder effects

A founder effect occurs when a small group establishes a new population. Its allele frequencies may differ from those of the source simply because the founders represent a limited sample.

For example, a few seeds reaching an isolated site may establish a population containing only some source alleles.

A simplified allele-sampling illustration, not a count of diploid individuals. Both events can reduce diversity, but a bottleneck affects an existing population whereas a founder event establishes a new one.

Real disturbances can also impose selection. Not every difference between survivors and the original population is necessarily caused by chance alone.

6. Gene Flow

Gene flow transfers alleles among populations. In plants, pollen and seeds are major routes, but movement alone is insufficient: migrants must contribute genetically.

Pollen may arrive but fail to fertilize. Seeds may disperse but fail to establish. Effective gene flow depends on successful reproduction and recruitment.

Gene flow can introduce variation into a population, counter some effects of drift and inbreeding, and reduce differentiation among populations. However, incoming alleles may sometimes be poorly suited to local conditions.

A pollinator corridor can reconnect isolated plant populations, but its genetic benefit depends on compatible mating and successful offspring—not simply pollinator movement.

7. Mutation

Mutation changes DNA and is the ultimate source of new alleles. Its effects can be harmful, neutral, or beneficial, depending on the variant and environment.

Mutations do not arise because a plant needs a particular solution. Their later frequencies depend on transmission, drift, and selection.

At an individual locus, mutation often introduces variation slowly compared with the speed at which strong drift can remove it from a small population.

Mutation versus recombination

Recombination rearranges existing alleles into new combinations. It generates genotypic diversity but does not ordinarily create new alleles at a locus.

8. Natural Selection

Natural selection occurs when heritable differences affect survival or reproduction, causing variants to contribute unequally to later generations.

Unlike drift, selection is associated with fitness differences. Its effects on diversity depend on the form of selection:

• Directional selection can increase a favorable allele toward fixation and reduce variation at the locus.
• Purifying selection removes harmful variants.
• A selective sweep can reduce diversity at nearby linked sites.
• Balancing selection can maintain multiple alleles, for example through heterozygote advantage.
• Different environments can favor different variants, contributing to local adaptation and differentiation.

Fixation does not prove adaptation because drift can also fix alleles. Likewise, high neutral diversity does not prove that a population is well adapted to its present environment.

9. Comparing the Processes

Process	Main action	Common consequence
Drift	Chance sampling of alleles.	Loss or fixation, especially in small effective populations.
Bottleneck	Sharp reduction of an existing population.	Loss of rare alleles and stronger drift.
Founder effect	Establishment by few colonists.	An unrepresentative sample of source variation.
Gene flow	Transfer of alleles among populations.	Can increase local variation and reduce differentiation.
Mutation	Creation of new alleles.	Provides genetic novelty.
Selection	Unequal reproduction of heritable variants.	Can reduce or maintain variation.

10. Important Considerations in Plants

• Selfing increases homozygosity, so low observed heterozygosity does not necessarily mean few alleles.
• Clonal growth can produce many shoots from one genetic individual; repeated sampling of a clone can distort estimates.
• Polyploid plants require methods accounting for allele dosage and inheritance rather than automatic application of diploid equations.
• Pooling populations with different allele frequencies can produce a heterozygote deficit—the Wahlund effect.
• Seed banks preserve genetic material from earlier seasons, so adult-only samples may miss part of the variation.

Reliable studies combine suitable markers, comparable sampling, and knowledge of mating system, dispersal, population history, and habitat conditions.

Key Takeaways

• Hardy–Weinberg equilibrium provides a genotype-frequency baseline.
• Different diversity measures answer different questions.
• Drift, gene flow, mutation, and selection act together.
• Bottlenecks and founder events can leave lasting genetic effects.
• No single estimate identifies the full history of a population.

Interactive Quiz: 20 Questions

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Further Reading

• OpenStax: Population Evolution and Hardy–Weinberg Equilibrium
• OpenStax: Population Genetics
• University of Wyoming: Heterozygosity