Some differences between individuals fall into neat categories; others form a smooth range. The difference comes down to how many genes are involved and how much the environment adds. The t-test then tells you whether two samples really differ.
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.
Fig. 1: discontinuous variation (a few distinct classes) compared with continuous variation (a smooth, roughly normal distribution)
Section 01
Genes, environment, or both.
Start with Genes involved = 1 and Environment = 0. The 60 plants fall into three distinct height classes. Now raise the number of genes to 6, then raise Environment, and watch the bar chart turn into a smooth bell shape.
Genetic causes: individuals carry different alleles. New alleles arise by mutation; meiosis (crossing over and independent assortment), random mating and random fertilisation produce new combinations.
Environmental causes: the conditions an organism experiences change how its genes are expressed. A plant with alleles for tall growth stays short in poor soil or low light; a person's mass depends on diet as well as genes.
Both together: most continuous features are set by genotype and environment acting together. The genotype sets a range of possible phenotypes; the environment decides where in that range the individual ends up.
Purely environmental: some differences have no genetic basis at all, such as a scar or a language spoken. These are not inherited.
Examiner trap
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.
Section 02
One gene or many genes.
The simulator gives each tall allele a small additive effect on height. With one gene there are only three genotypes; with six genes there are many.
Feature
Discontinuous variation
Continuous variation
phenotypes
a few distinct classes, no intermediates
a continuous range between two extremes
genes involved
one gene, or a few genes
many genes (polygenes)
effect of each allele
large; different alleles give clearly different phenotypes
small and additive; each allele adds a little
effect of the environment
little or none
large
shown by
bar chart
histogram, often a normal distribution
examples
ABO blood group, albinism
height, body mass, leaf length
Discontinuous: the ABO gene has three alleles, IA, IB and Io, giving four blood groups. You are either group A or group B; there is no in-between, and diet cannot change it.
Continuous: if several genes each have an allele that adds a little to height, there are many possible genotypes, each giving a slightly different height. Environmental effects then smooth the steps into a continuous range.
Examiner trap
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.
Stage 1 · Learn
Check what the sim just showed you
Four quick checks. Each correct answer earns XP and records this skill on your profile.
Quick check+10 XP
With Genes involved = 1 and Environment = 0, the simulator shows three distinct height classes. Why three?
Quick check+10 XP
You raise Genes involved to 6 and Environment to 1. What happens to the bar chart, and why?
Quick check+10 XP
The simulator samples 10 sunny and 10 shady leaves and reports t (df = 18). Why is the number of degrees of freedom 18?
Quick check+10 XP
With Real difference in means set to 0, a sample gives t = 0.85. What should you conclude?
Section 03
Is the difference significant?
Set Real difference in means to 6 mm and press Take two samples of 10. Then set it to 0 and sample again. Compare the value of t with the critical value of 2.10 for 18 degrees of freedom.
When to use it: to compare the means of two samples of continuous data, which should be roughly normally distributed, for example leaf lengths from two places.
Null hypothesis: there is no significant difference between the two means; any difference is due to chance.
Formula (given in the exam): t = |x̄1 − x̄2| ÷ √(s12/n1 + s22/n2), where x̄ is the mean, s the standard deviation and n the number of readings.
Degrees of freedom: n1 + n2 − 2. Two samples of 10 give 18.
Decision: look up the critical value at p = 0.05 (2.10 for 18 degrees of freedom). If t is greater, the probability that the difference is due to chance is less than 5%, so reject the null hypothesis: the difference is significant. If t is smaller, accept the null hypothesis.
Examiner trap
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.
Stage 2 · Exam
Exam-style questions
Unlocks once the four checks above are done. Worth more XP, written to A Level Paper 4 standard.
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Which feature is most likely to show continuous variation?
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Identical twins raised apart differ in body mass by 9 kg but have the same blood group. What does this show?
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Two samples of 10 have means of 12.0 and 10.0 and s2/n = 0.5 for each sample. The critical value of t at p = 0.05 is 2.10. Which conclusion is correct?
Exam style+20 XP
Which explains the genetic basis of continuous variation?
Skill unlocked
Variation and the t-test, mastered.
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