Inheritance and DNA · Investigation
Variation: continuous and discontinuous
Line a class up by height and you get a smooth ramp with no gaps. Line the same class up by blood group and you get four piles and nothing in between. The difference is not what you measured with.
Start here
Nobody is halfway between blood group A and blood group B.
Somebody in your class is halfway between the two tallest people, and somebody is halfway between them. Keep going and you never run out of in-between values. Do the same with blood group and you stop immediately: there are four, and nothing sits between them.
What decides which kind of variation a characteristic shows?
Whether intermediate values exist. If any value between two others is possible, the variation is continuous; if the characteristic falls into separate groups with nothing between them, it is discontinuous. That is the whole definition, and it says nothing yet about what causes the variation.
At the bench · sixty students, six characteristics
Predict the graph, then plot it
0 of 6 plotted
Data from one year group. The cause line underneath is a separate question from the shape.
Characteristic
Height, in centimetres
Before you plot it — which shape do you expect?
height in cm · 60 students · bars touch because the categories are ranges
Your prediction was right
Not what you predicted
Continuous — a histogram, bars touching
A smooth hump with no gaps. Every value in the range is possible, and most people are near the middle — which is what the shape of nearly all continuous data looks like.
What causes it: Both. Hundreds of genes each contribute a little, and childhood nutrition and health move the whole thing up or down. The clearest example there is of a characteristic with two causes at once.
Hand span, in centimetres
Before you plot it — which shape do you expect?
hand span in cm · 60 students · bars touch because the categories are ranges
Your prediction was right
Not what you predicted
Continuous — a histogram, bars touching
The same hump. Any span between the smallest and largest is possible, so the data has no gaps and the bars have none either.
What causes it: Both, and mostly genetic — hand span is closely related to height, which is the same argument one step removed.
Body mass, in kilograms
Before you plot it — which shape do you expect?
mass in kg · 60 students · bars touch because the categories are ranges
Your prediction was right
Not what you predicted
Continuous — a histogram, bars touching
Continuous, and wider than the height curve. Mass has more room to vary because it responds much more strongly to how someone lives.
What causes it: Both, and the environmental share is larger than for height — diet and activity can move an individual a long way, which is why this curve is the broadest of the three.
Blood group
Before you plot it — which shape do you expect?
blood group · 60 students · bars are separated because the categories are
Your prediction was right
Not what you predicted
Discontinuous — a bar chart, bars separated
Four separate columns and nothing between them. There is no such thing as being partway between group A and group B, so the bars are drawn apart.
What causes it: Genes only. One gene, three versions of it, and nothing you eat, do or experience can change your blood group.
Able to roll the tongue
Before you plot it — which shape do you expect?
can or cannot · 60 students · two separate categories
Your prediction was right
Not what you predicted
Discontinuous — a bar chart, bars separated
Two columns. You either can or you cannot, with no halfway, which makes this the simplest discontinuous characteristic to survey in a classroom.
What causes it: Largely genetic, and the textbook version that calls it a single gene is now known to be too simple — identical twins sometimes differ, and some people learn it. A good reminder that a tidy example is usually a simplified one.
Eye colour
Before you plot it — which shape do you expect?
recorded colour · 60 students · categories, so the bars are separated
Your prediction was right
Not what you predicted
Discontinuous — a bar chart, bars separated
Recorded as categories, so it is plotted as separate bars — though real eyes grade into one another more than three columns suggest, which is why the categories have to be agreed before the survey starts.
What causes it: Genes only, but several genes rather than one. Nothing in the environment changes it, and the old rule that two blue-eyed parents cannot have a brown-eyed child is not reliable.
Two questions, asked separately
What shape is it, and what caused it.
Question one · shape
Continuous
Any value between the extremes is possible. Plotted as a histogram with the bars touching, because the categories are ranges that join up.
Height, mass, hand span, leaf length
Question one · shape
Discontinuous
Separate categories with no values in between. Plotted as a bar chart with gaps, because the categories really are separate.
Blood group, eye colour, tongue rolling, number of siblings
Question two · cause
Genes
Inherited from your parents and fixed at conception. Nothing you do changes it, and you can pass it on.
Blood group, eye colour, natural hair colour
Question two · cause
Environment, or both
Shaped by food, exercise, illness, sunlight or accident. Most characteristics are both: genes set a range and the environment decides where in it you land.
Height, mass, scars, language spoken
Key fact
Continuous variation has intermediate values and is plotted as a histogram; discontinuous variation falls into separate groups and is plotted as a bar chart. Whether variation is continuous is a question about the data. What caused it — genes, environment or both — is a separate question with a separate answer.
Think again
“Continuous variation is caused by the environment; discontinuous variation is genetic.”
Height is the counter-example that settles it: it is continuous, and it is one of the most strongly inherited characteristics there is — tall parents have tall children with great reliability — while also being affected by childhood nutrition. Both causes, one smooth curve. What actually makes a characteristic continuous is the number of genes involved. Blood group is decided by a single gene with a few versions, so you get a few discrete groups. Height is influenced by hundreds of genes, each contributing a small amount, and hundreds of small contributions added together produce a smooth range with no gaps in it — then the environment moves everyone a little further along. So the honest summary is: one gene tends to give discontinuous variation; many genes tend to give continuous variation; and the environment can adjust anything that is not fixed at conception.
“If you can measure it with a ruler it is continuous.”
Close enough to be dangerous. Number of brothers and sisters is a number, you can count it precisely, and it is discontinuous — nobody has 2.4 siblings, and the average being 2.4 does not make it a possible value for a person. Number of leaves on a plant, number of petals, shoe size in the UK system: all counted, all discontinuous, because the values step rather than flow. The test is not can I put a number on it but can a value exist between two neighbouring values. Between 172 cm and 173 cm there is 172.4 cm and a student who is exactly that; between two and three siblings there is nothing at all. Get that test right and the graph follows automatically: bars that touch for continuous data because the categories are ranges that join up, bars with gaps for discontinuous data because the categories genuinely are separate.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Sort them
Which of these shows discontinuous variation?
Rung 2 · The one that catches people
Height is continuous. What does that tell you about its cause?
Rung 3 · Explain the smooth curve
Blood group falls into four sharp categories and height forms a smooth curve, although both are strongly influenced by genes. Explain the difference, and say what part the environment plays in each.
Rung 4 · Take it somewhere new
Plan an investigation into variation in leaf length on a single tree. Say how you would collect the data, how you would present it, and how you would avoid the sampling problem you met in Sampling an ecosystem.
Key note
Continuous variation has values that grade into one another with no gaps, and is shown on a histogram with touching bars. Discontinuous variation falls into separate categories with no intermediates, and is shown on a bar chart with gaps. Characteristics controlled by one gene tend to be discontinuous; those influenced by many genes tend to be continuous, and the environment can shift anything that is not fixed at conception.
Going further
Dutch men are now the tallest in the world, averaging around 1.84 m, and in 1860 they were among the shorter populations in Europe. Twenty centimetres in a century and a half is far too fast for the gene pool to have changed much — what changed was nutrition, public health and childhood disease. The same shift has happened in South Korea and Japan within living memory, and it has stalled or reversed in a few countries where nutrition got worse. This is the clearest evidence there is that height is genuinely both: the ranking within a population is largely inherited, and the level the whole population sits at is set by the environment. It also explains a fact you can check in any old building — Tudor doorways and the bunks in Nelson's navy were not built for shorter people out of some quirk of taste.
Before this lesson
Connects to
At GCSE this becomes
- Normal distributions, polygenic inheritance, and separating genetic from environmental causes using twin and adoption studies.
Where to next
- Next: Chromosomes, genes and DNA
- Previous: Sampling an ecosystem
Ecosystems and interdependence
Ask Mr Badmus AI
Want to sort a characteristic the bench does not cover?
The sixty-student data set is invented for this lesson, shaped to be realistic rather than taken from a real survey. Blood group frequencies are approximate UK values. Eye colour is treated as three categories here, which is a simplification: eye colour is influenced by several genes and real eyes grade into one another more than this bench suggests.
Lesson content © MrBadmusAI.