The shape of the lesson
By the end of the lesson, learners can
- Genes, environment, or both: Start with Genes involved = 1 and Environment = 0.
- One gene or many genes: The simulator gives each tall allele a small additive effect on height.
- Is the difference significant?: Set Real difference in means to 6 mm and press Take two samples of 10.
- Discontinuous: one or a few genes, large effects, distinct classes, little environmental effect.
- Continuous: polygenes with small additive effects plus the environment.
- t-test: compares two means; degrees of freedom = n1 + n2 − 2.
- t > critical value at p = 0.05: significant; reject the null hypothesis.
One picture every idea returns to
Phenotypic variation is caused by genetic factors (different alleles, produced by mutation and shuffled by meiosis and random fertilisation), by environmental factors (diet, light, soil minerals, temperature), or by a combination of both. Discontinuous variation gives a few distinct classes with no intermediates (ABO blood group); it is controlled by one gene or a few genes with large effects and is little affected by the environment. Continuous variation gives a range with no clear classes (height, mass, leaf length); it is controlled by many genes (polygenes), each with a small additive effect, and the environment adds further variation. To decide whether the means of two samples of continuous data differ significantly, calculate t and compare it with the critical value at p = 0.05 for n1 + n2 − 2 degrees of freedom.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Why no two individuals are alike.. Some differences between individuals fall into neat categories; others form a smooth range. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Genes, environment, or both | Start with Genes involved = 1 and Environment = 0. Project tab 1 of the lab (Selection and evolution lab, the genetic basis of variation) and let a student drive it while the class predicts. | Whole class, then pairs |
| 13 to 21 min | Teach and check: One gene or many genes | The simulator gives each tall allele a small additive effect on height. | Pairs |
| 21 to 30 min | Teach and check: Is the difference significant? | Set Real difference in means to 6 mm and press Take two samples of 10. Project tab 2 of the lab (Selection and evolution lab, the t-test) and let a student drive it while the class predicts. | Connect-Extend-Challenge |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 19 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Is the difference significant?, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Connect-Extend-Challenge
After the new idea, each student writes three lines: how it connects to what they knew, how it extends their thinking, and what still challenges them. Pairs compare, then the challenges become the plenary.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Variation caused only by the environment is not passed on to offspring, because it does not change the alleles in the gametes. | Only genetic variation can be acted on by natural selection. |
| Continuous variation is not caused by alleles blending. | Each gene is still inherited as discrete alleles; it is the number of genes and the environment that make the overall range look smooth. |
| A large difference between means is not enough on its own. | If the data are very spread out (large standard deviations) or the samples are small, t can still be below the critical value. |
Variation and the t-test: worksheet
6 questions, 19 marks. Written in the style of the papers; no past paper question is reproduced.
Explain, with examples, how phenotypic variation can be caused by genetic factors, by environmental factors and by a combination of both.
Distinguish between discontinuous variation and continuous variation.
Height in a species of plant is controlled by three unlinked genes. At each gene, one allele adds 4 cm to the height and the other allele adds 2 cm. Explain why the heights of the plants show continuous variation.
Leaf lengths were measured from 10 leaves in a shady site and 10 leaves in a sunny site. Shady: mean 46.2 mm, standard deviation 3.1 mm. Sunny: mean 41.5 mm, standard deviation 2.8 mm. Use t = |x̄1 − x̄2| ÷ √(s12/n1 + s22/n2) to calculate t. The critical value of t at p = 0.05 for 18 degrees of freedom is 2.10. State your conclusion.
State the null hypothesis for the t-test in the previous question and explain why the degrees of freedom are 18.
A student finds that the mean mass of snails from two ponds differs by 3 g, but the t-test gives t = 1.2 (critical value 2.10). Suggest why the difference is not significant and how the investigation could be improved.
Answer key and marking notes
- Genetic: different alleles give different phenotypes, for example ABO blood group, which the environment does not change.
- Environmental: conditions alter the phenotype without changing the genotype, for example a scar, or a plant grown in shade having paler leaves.
- Combination: the genotype sets a potential range and the environment determines where the individual lies in it, for example height depends on alleles and diet.
- Discontinuous: distinct categories with no intermediates; continuous: a range of values between two extremes.
- Discontinuous: controlled by one gene or a few genes (with large effects); continuous: controlled by many genes (polygenes) with small additive effects.
- Discontinuous: little or no environmental effect; continuous: strongly affected by the environment.
- Each plant has six alleles for height (two of each gene), and each tall allele adds the same small amount (additive effect).
- This gives seven possible totals (0 to 6 tall alleles), so many genotypes give a range of heights from 12 cm to 24 cm in 2 cm steps.
- Intermediate numbers of tall alleles are most common, so most plants are near the middle.
- Environmental factors such as light, water and minerals add further variation, so the steps merge into a continuous range.
- s12/n1 = 9.61 ÷ 10 = 0.961; s22/n2 = 7.84 ÷ 10 = 0.784.
- √(0.961 + 0.784) = √1.745 = 1.32.
- t = (46.2 − 41.5) ÷ 1.32 = 4.7 ÷ 1.32 = 3.56.
- 3.56 is greater than 2.10, so the probability that the difference is due to chance is less than 0.05: reject the null hypothesis; the difference in mean leaf length is significant.
- Null hypothesis: there is no significant difference between the mean leaf lengths in the sunny and shady sites (any difference is due to chance).
- Degrees of freedom = n1 + n2 − 2 = 10 + 10 − 2 = 18.
- The masses within each sample are very variable (large standard deviation), so a 3 g difference could arise by chance.
- The samples may be too small: fewer readings make s2/n larger and t smaller.
- Improvement: take larger random samples from each pond (and control the time of collection) so that a real difference is more likely to be detected.
8 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
Which example of variation is caused by environmental factors only?
- Aa scar left on the skin after an injury
- Bthe ABO blood group of a person
- Cthe height of a sunflower plant
- Dthe colour of a person's eyes
Which description fits discontinuous variation?
- Aa few distinct phenotypes, controlled by one or a few genes, little affected by the environment
- Ba range of phenotypes, controlled by many genes, strongly affected by the environment
- Ca few distinct phenotypes, controlled by many genes with additive effects
- Da range of phenotypes, controlled by one gene with two codominant alleles
Seed mass in a bean variety is measured in a large sample. The histogram is smooth and bell-shaped. Which explanation is most likely?
- Aseed mass is polygenic, each allele adding a small amount, and is also affected by the environment
- Bseed mass is controlled by one gene with a dominant and a recessive allele
- Cseed mass is affected only by the environment, so the genes have no effect
- Dthe alleles of a single seed-mass gene blend together in the offspring
When is the t-test the appropriate statistical test to use?
- Ato compare the means of two samples of continuous data that are roughly normally distributed
- Bto test whether observed numbers of offspring fit a predicted genetic ratio
- Cto find whether there is a correlation between two variables measured on the same individuals
- Dto compare the numbers of individuals in different categories of discontinuous data
Two samples of 10 limpets have mean shell heights of 18.4 mm and 15.9 mm. For each sample s2/n = 0.40. What is the value of t?
- A2.80
- B3.95
- C6.25
- D1.25
A t-test compares sample A (8 leaves) with sample B (10 leaves) and gives t = 2.11. Use the table to decide the conclusion.
- Adf = 16, critical value 2.12; t is smaller, so the difference is not significant
- Bdf = 18, critical value 2.10; t is larger, so the difference is significant
- Cdf = 16, critical value 2.12; t is smaller, so the difference is significant
- Ddf = 14, critical value 2.15; t is smaller, so the null hypothesis is rejected
In a plant, three unlinked genes each have an allele that adds 2 cm to stem height and an allele that adds 1 cm. Ignoring the environment, how many different stem heights are possible?
- A7
- B3
- C6
- D27
Genetically identical cuttings of one plant are grown at three light intensities. Mean leaf area differs significantly between the groups. What can be concluded?
- Athe differences are environmental, because the plants share the same genotype
- Bthe differences are genetic, because leaf area is a polygenic trait
- Cthe differences show discontinuous variation, because there are three groups
- Dthe differences are due to mutations caused by the different light intensities
Quiz key
A scar results only from an event in the environment; it does not change any alleles and is not inherited. ABO blood group is determined by the alleles of one gene and is not affected by the environment. Sunflower height depends on both alleles and conditions such as light and minerals. Eye colour is mainly genetic (several genes), so it is not caused by the environment alone.
Discontinuous variation has distinct classes with no intermediates; it is controlled by one or a few genes with large effects and is little influenced by the environment. A range of phenotypes from many genes plus environment is continuous variation. Many genes with additive effects give many genotypes and therefore a range, not a few classes. One gene with two codominant alleles gives just three phenotypes, which is still discontinuous, not a range.
A smooth bell-shaped distribution shows continuous variation, which comes from many genes with small additive effects plus environmental variation. One gene with dominance gives two distinct classes. Saying genes have no effect ignores the fact that seed mass is heritable; environment adds to, but does not replace, genetic variation. Alleles do not blend: each is inherited as a discrete unit, and the smooth range is due to many genes and the environment.
The t-test compares the means of two samples of continuous, roughly normal data, such as leaf lengths from two sites. Comparing observed and expected offspring ratios uses the chi-squared test. A correlation between two variables uses a correlation coefficient (such as Pearson's or Spearman's). Counts in categories are discontinuous data and suit the chi-squared test, not a comparison of means.
Difference in means = 18.4 − 15.9 = 2.5 mm. √(0.40 + 0.40) = √0.80 = 0.894. t = 2.5 ÷ 0.894 = 2.80. 3.95 comes from dividing by √0.40 (one sample only). 6.25 comes from dividing 2.5 by 0.40 without adding or square-rooting. 1.25 comes from dividing 2.5 by 2, treating the denominator as a simple count of samples.
Degrees of freedom = 8 + 10 − 2 = 16, so the critical value is 2.12. t = 2.11 is below it, so the probability that the difference is due to chance is more than 0.05: accept the null hypothesis, the difference is not significant. Using df = 18 forgets to subtract 2 (or uses n1 + n2). Saying a smaller t is significant reverses the decision rule. df = 14 subtracts too much, and a t below the critical value never leads to rejecting the null hypothesis.
Each plant has two alleles at each of three genes, so six alleles. The number of 2 cm alleles can be 0, 1, 2, 3, 4, 5 or 6, giving seven different heights (6 cm to 12 cm in 1 cm steps). 3 is the number of phenotypes for one gene with additive alleles. 6 is the number of alleles, not the number of totals. 27 is the number of genotypes (3 × 3 × 3); many different genotypes give the same total height.
Cuttings from one plant are clones with identical genotypes, so any significant difference between groups must be caused by the environment (light intensity). Leaf area is polygenic, but genetic differences cannot explain variation between identical genotypes. Three treatment groups do not make the trait discontinuous; leaf area within each group still varies continuously. Light intensity does not cause the mutations needed to explain a consistent difference; the effect is on growth, not on alleles.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.