explain what is meant by discontinuous variation and continuous variation

Variation

Variation is the difference in observable characteristics (morphology, physiology, behaviour or biochemistry) between individuals of the same species. In the Cambridge AS & A‑Level Biology (9700) syllabus variation is divided into two contrasting types, each with its own genetic and evolutionary significance.

1. Discontinuous (qualitative) variation

• Definition: Traits that fall into distinct, non‑overlapping categories (all‑or‑nothing).
• Genetic control: Usually a single gene or a few genes with clear dominant, recessive, co‑dominant or sex‑linked relationships.
• Typical examples:
  • Human blood groups (A, B, AB, O)
  • Flower colour in peas (purple vs white)
  • Presence/absence of a tail in certain insects
  • Seed shape in beans (round vs wrinkled)
• Inheritance pattern: Follows Mendelian ratios that can be predicted with Punnett squares and tested with a χ² goodness‑of‑fit test (α = 0.05).
• Population expression: Frequencies are expressed as percentages or proportions of individuals in each class; data are displayed with bar charts.

2. Continuous (quantitative) variation

• Definition: Traits that show a range of values that blend smoothly into one another.
• Genetic control: Polygenic inheritance – many genes each contribute a small effect – and the environment also influences the phenotype.
• Typical examples:
  • Human height
  • Seed mass in wheat
  • Enzyme activity levels
  • Leaf length in Arabidopsis
• Phenotypic expression: When a large sample is plotted, values approximate a normal (bell‑shaped) distribution.
• Mathematical description: P = G + E, where P = phenotype, G = total genetic contribution, E = environmental contribution.
• Statistical measures: Mean (μ), variance (σ²) and standard deviation (σ) are used to summarise the distribution; the normal curve can be used to estimate the proportion of individuals above or below a given value.

3. Inheritance of quantitative traits – heritability

• Phenotypic variance (V_P) = V_G + V_E + V_GE
  • V_G – variance due to genetic differences (additive, dominance, epistatic).
  • V_E – variance caused by environmental differences.
  • V_GE – variance from genotype × environment interaction (often grouped with V_E in the syllabus).
• Broad‑sense heritability (H²): H² = V_G / V_P
• Narrow‑sense heritability (h²): h² = V_A / V_P, where V_A is the additive genetic variance. This value predicts the response of a trait to selection (Breeder’s equation: R = h² S).
• Relevance to the syllabus: Learners must be able to explain that the genetic contribution to a continuous trait can be quantified and that higher heritability means a stronger evolutionary response to selection.

4. Genetic basis of variation – inheritance patterns

4.1 Mendelian (monohybrid & dihybrid) crosses

• Monohybrid cross – one trait, single gene pair (e.g., Rr × Rr → 3 : 1 dominant : recessive).
• Dihybrid cross – two traits, independent assortment (e.g., RrYy × RrYy → 9 : 3 : 3 : 1 phenotypic ratio).
• Punnett squares are used to predict genotype and phenotype frequencies.
• χ² test compares observed and expected ratios (α = 0.05).

4.2 Non‑Mendelian inheritance

• Incomplete dominance: Heterozygote phenotype intermediate (snapdragon red ↔ white → pink).
• Co‑dominance: Both alleles expressed (human blood group AB).
• Polygenic inheritance: Many loci contribute additively; explains continuous traits.
• Sex‑linked traits: Genes on X or Y chromosome (colour blindness, haemophilia). Male phenotype = genotype; female phenotype follows dominant/recessive expression.
• Multiple alleles: More than two alleles in a population (ABO blood groups).

4.3 Mutation

• Spontaneous (point mutations, frameshifts) and induced (UV, chemicals).
• Typical mutation rate in eukaryotes: 10⁻⁸ – 10⁻⁹ per nucleotide per generation.
• Mutations generate new alleles – the raw material for evolution.

5. Population genetics – how variation is maintained

5.1 Hardy–Weinberg equilibrium

• Assumptions: infinitely large population, random mating, no mutation, no migration, no selection.
• Equation: p² + 2pq + q² = 1, where p = frequency of allele A and q = frequency of allele a.
• Example calculation: If 16 % of a population are aa (q² = 0.16) → q = 0.4, p = 0.6, predicted heterozygotes 2pq = 0.48 (48 %).

5.2 Gene flow (migration)

• Movement of individuals/alleles between populations; tends to reduce genetic differences.

5.3 Genetic drift

• Random changes in allele frequencies, especially in small populations.
• Bottleneck effect: A drastic reduction in population size.
• Founder effect: A new population started by a few individuals.

6. Variation and natural selection

• Variation provides the raw material on which natural selection acts.
• Fitness: Reproductive success of a genotype relative to others.
• Types of selection:
  • Directional: Favors one extreme (e.g., larger beak size in drought‑affected finches).
  • Stabilising: Favors intermediate phenotypes (e.g., human birth weight).
  • Disruptive: Favors both extremes, reducing intermediates (e.g., colour morphs in peppered moths).
• Consistent selection over many generations can change allele frequencies, leading to adaptation or speciation.
• Speciation mechanisms (brief):
  • Allopatric – geographic isolation.
  • Sympatric – reproductive isolation without physical separation (e.g., polyploidy in plants).

7. Statistical tools required by the syllabus

8. Practical investigation – example activity

1. Objective: Compare the variation in plant height under two environmental conditions (full light vs. shade).
2. Method:
   • Grow 30 genetically identical seedlings in each condition (randomised layout).
   • Measure height after 4 weeks; record to the nearest millimetre.
   • Construct histograms for each group and calculate mean, variance and SD.
   • Use the normal distribution to estimate the proportion of plants taller than a pre‑set value (e.g., 15 cm).
   • Apply a t‑test (or compare SDs) to evaluate whether the environmental difference is statistically significant.
3. Evaluation points:
   • Sample size – larger samples give more reliable estimates of μ and σ.
   • Randomisation – avoids systematic bias.
   • Control of other variables (water, soil type, temperature).
   • Potential sources of error (measurement error, edge effects, seedling mortality).

9. Comparison of discontinuous and continuous variation