Lesson 5 of 10 / Inheritance
Expected ratios are probabilities
Why might five offspring fail to match a 3:1 prediction?
In this lesson: Explain chance differences between expected and observed inheritance ratios, especially in small samples.
About 5 min
The key ideaRandom gamete combinations can make an observed ratio differ from its expected probability. Small samples show larger proportional fluctuations.
Both illustrative samples use Rr x Rr with an expected 3 round : 1 wrinkled ratio.
| Phenotype | Expected | Observed |
|---|---|---|
| Round | 9 | 7 |
| Wrinkled | 3 | 5 |
Expected 9 round and 3 wrinkled; observed 7 and 5. A small sample can deviate substantially by chance. The next offspring still has probability 1/4 of being wrinkled under the model.
Green: round. Gold: wrinkled. Bar widths show proportions, and the table gives counts. These are fixed illustrative datasets, not a random biological simulation.
Explanation
A Punnett square lists possible allele combinations and their probabilities under a model. It does not predict the order of births or require a family to contain every box exactly once. Each fertilisation combines gametes as a separate chance event.
For Rr x Rr, a recessive offspring has probability 1/4 each time under the model. If the first three offspring show the dominant phenotype, the fourth still has probability 1/4 of being recessive. The earlier outcomes do not use up dominant combinations or force a recessive one next.
In a small sample, one additional offspring makes a large difference to the observed proportion. Larger samples usually give proportions closer to the expected probabilities, although an exact ratio is still not guaranteed.
Report observations separately from expectations. For example, 5 recessive offspring among 12 gives an observed recessive proportion of 5/12, about 42%, while the model expects 25%. This difference alone in a small sample does not show the inheritance model is wrong. Repeated large, systematic differences would need further investigation.
Step by step
- 1
Calculate the expectation
Use the cross to find the probability, then multiply by the sample size.
- 2
State the observation
Use the actual counts and avoid relabelling them as predictions.
- 3
Explain the difference
Random gamete combinations and a small sample can produce chance deviations.
Worked example
Twelve offspring
Rr x Rr produces 7 round and 5 wrinkled offspring. State the expected numbers and explain the difference.
One way to explain it
The expectation is 12 x 3/4 = 9 round and 12 x 1/4 = 3 wrinkled. The observed 7:5 ratio differs because random fertilisation in a small sample can produce chance fluctuations.
Why this answer works
- Expected and observed counts are different kinds of information.
- The total remains 12 in both comparisons.
- Do not change the probability of the next offspring to compensate.
Is this true? "After three dominant offspring, the next one must be recessive to complete 3:1."
The model gives the same probability at each fertilisation. Previous outcomes do not force the next outcome.