How Can We Predict Inheritance?

Parents pass genetic information to their offspring through:

gametes.

Each gamete carries one allele for each gene, and fertilization combines alleles from:

two parents.

Because we understand how alleles are separated during meiosis and combined during fertilization, we can predict the:

probability of different genetic outcomes.

We can use:

• parent genotypes
• Punnett squares
• probabilities
• offspring phenotypes
• family information

to make predictions about:

inheritance.

These are predictions of probability, not guarantees about individual offspring.

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From Parents to Offspring

A useful way to think about inheritance is:

Parent genotypes

↓

Meiosis

↓

Gametes containing individual alleles

↓

Random fertilization

↓

Offspring genotype

↓

Offspring phenotype

Understanding this sequence allows us to predict how traits can pass from one generation to the:

next.

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A Simple Inheritance Example

Suppose fur colour in an imaginary animal is controlled by one gene.

Let:

B = black fur

b = brown fur

Suppose B is dominant over:

b.

The possible genotypes are:

BB

Bb

bb.

The corresponding phenotypes are:

BB → black

Bb → black

bb → brown.

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Genotype and Phenotype

Remember the important difference:

Genotype = allele combination

Phenotype = observable characteristic

For example:

Bb = genotype

Black fur = phenotype

Inheritance predictions often begin with genotypes and then use the dominance relationship to predict:

phenotypes.

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Predicting from Parent Genotypes

Suppose two heterozygous black animals reproduce.

Their genotypes are:

Bb × Bb.

Each parent can produce two types of gametes:

B

or:

b.

We can use a Punnett square to predict the possible:

offspring genotypes.

---

Constructing the Cross

Possible offspring genotypes are:

BB

Bb

Bb

bb.

---

Calculating Genotype Probabilities

From the cross:

Bb × Bb

we obtain:

1 BB

2 Bb

1 bb.

Therefore:

BB = 1/4 = 25%

Bb = 2/4 = 50%

bb = 1/4 = 25%

The expected genotype ratio is:

1 : 2 : 1.

---

Calculating Phenotype Probabilities

Because B is dominant:

BB → black

Bb → black

bb → brown

Therefore:

Black = 3/4 = 75%

Brown = 1/4 = 25%

The expected phenotype ratio is:

3 : 1.

---

Probability

Probability describes how likely an event is to occur.

Probability can be expressed as:

fraction

decimal

or:

percentage.

For example:

1/4 = 0.25 = 25%

1/2 = 0.50 = 50%

3/4 = 0.75 = 75%

1 = 100%

---

Probability Formula

A simple probability can be calculated using:

Probability = Number of desired outcomes ÷ Total number of possible outcomes

For example, suppose one of four equally likely Punnett-square outcomes is:

bb.

Then:

Probability of bb = 1 ÷ 4

= 1/4

= 25%.

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Why Is Inheritance Based on Chance?

During meiosis, alleles are separated into:

gametes.

Which sperm or pollen cell participates in fertilization is generally not determined by what trait would be useful to the:

offspring.

Similarly, which egg is fertilized is not selected to produce a particular:

genotype.

Fertilization therefore contains an important element of:

chance.

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Random Fertilization

Consider a heterozygous parent:

Aa.

Its gametes can carry:

A

or:

a.

Another Aa parent can also produce:

A

or:

a.

When gametes combine randomly, several combinations are possible:

AA

Aa

aa.

We can calculate the probability of each combination, but we cannot know with certainty which combination a particular fertilization will:

produce.

---

Probability Does Not Mean Certainty

Suppose a genetic cross predicts:

25% probability of aa.

Does this mean exactly one of every four offspring must be:

aa?

No.

Each offspring represents another genetic:

event.

Four offspring could theoretically include:

• zero aa offspring
• one aa offspring
• two aa offspring
• three aa offspring
• four aa offspring

The Punnett square tells us what is:

expected over many events,

not what must occur in a small family.

---

Think About Coin Tosses

A fair coin has a:

50% chance of heads

and a:

50% chance of tails.

If you toss it four times, you are not guaranteed:

two heads and two tails.

You might obtain:

four heads.

The probability is still 50% on each independent:

toss.

Genetic probability works in a similar way.

---

Each Offspring Is a New Event

Suppose two parents have a:

25% probability

of producing an offspring with a particular genotype.

Their first child has that genotype.

Does this mean their next child cannot have it?

No.

For the same parental genotypes, the probability for the next independent conception remains:

25%.

Previous outcomes do not use up genetic:

possibilities.

---

The Gambler's Fallacy in Genetics

A common mistake is thinking:

"The first three children did not inherit the trait, so the fourth one must."

This reasoning is:

incorrect.

If the probability for each conception is 25%, the probability remains:

25% for each independent conception.

Previous outcomes do not force the next:

outcome.

---

Larger Samples and Expected Ratios

Although small families may differ greatly from predicted ratios, larger numbers of offspring tend to produce proportions closer to expected:

probabilities.

Suppose:

Aa × Aa

predicts 25% aa.

Among four offspring, the actual proportion could vary widely.

Among 1,000 offspring, the proportion would generally be expected to be much closer to:

25%.

This is one reason Mendel studied large numbers of:

pea plants.

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Calculating Expected Numbers

Suppose a genetic cross predicts:

25% recessive phenotype.

There are 200 offspring.

Expected number:

0.25 × 200 = 50

So we would expect approximately:

50 offspring

to show the recessive phenotype.

---

Another Example

Suppose a cross predicts:

75% dominant phenotype.

A population produces 400 offspring.

Expected number:

0.75 × 400 = 300

Therefore, approximately:

300 offspring

would be expected to show the dominant phenotype.

The actual number may not be exactly:

300.

---

Predicting from a Recessive Phenotype

Phenotypes can provide clues about:

genotypes.

Suppose:

B = black

b = brown

with B dominant.

If an animal has brown fur, its genotype must be:

bb.

Why?

Because:

BB → black

Bb → black

bb → brown.

The recessive phenotype therefore provides strong evidence about the:

genotype.

---

Predicting from a Dominant Phenotype

Suppose an animal has black fur.

Can we determine its exact genotype?

No.

It could be:

BB

or:

Bb.

Therefore, a dominant phenotype often provides less information about genotype than a:

recessive phenotype.

---

Using Offspring as Genetic Evidence

Sometimes offspring phenotypes can reveal information about their parents':

genotypes.

Suppose two black animals produce a brown offspring.

Brown is recessive.

Therefore, the brown offspring must be:

bb.

Where did the two b alleles come from?

One came from:

each parent.

Therefore, both black parents must carry:

b.

Their genotypes must be:

Bb × Bb.

This is an example of using genetic evidence to make an inheritance:

prediction.

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Evidence-Based Genetic Reasoning

A strong genetic explanation should connect:

evidence → allele information → genotype → conclusion.

For example:

Evidence: Two dominant-phenotype parents produced a recessive-phenotype offspring.

Reasoning: The recessive offspring must have received one recessive allele from each parent.

Conclusion: Both parents must possess at least one recessive allele.

This type of reasoning is extremely useful when analyzing:

family inheritance patterns.

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Family Inheritance Patterns

Genetic traits can sometimes be followed through several generations of a:

family.

Scientists and genetic counselors can examine which individuals show a particular phenotype and use that information to investigate possible:

inheritance patterns.

A diagram used to represent genetic relationships within a family is called a:

pedigree.

---

What Is a Pedigree?

A pedigree is a diagram showing biological relationships and the occurrence of a particular trait across:

generations.

Pedigrees can help scientists investigate whether a trait might follow patterns such as:

• dominant inheritance
• recessive inheritance
• sex-linked inheritance

At this level, we will focus mainly on simple:

dominant and recessive patterns.

---

Reading a Simple Pedigree

Pedigrees use standardized:

symbols.

Traditionally:

Square = male

Circle = female

A filled symbol commonly indicates an individual showing the trait being:

studied.

An unfilled symbol commonly indicates an individual who does not show the:

trait.

Horizontal lines connect reproductive partners, while vertical lines connect parents to:

offspring.

---

Generations in a Pedigree

Generations are commonly labeled using Roman numerals:

I

II

III

Individuals within a generation are numbered from:

left to right.

For example:

II-3

means:

the third individual in generation II.

This allows scientists to discuss individuals in a pedigree precisely.

---

Recognizing a Recessive Pattern

Suppose two parents do not show a trait but produce an offspring who:

does.

Under a simple autosomal dominant-recessive model, this can provide evidence that the trait is:

recessive.

If the affected offspring is:

aa,

then each parent must have contributed:

a.

If the parents themselves do not show the recessive phenotype, they could be:

Aa.

Therefore:

Aa × Aa

can produce:

aa offspring.

---

Recognizing a Dominant Pattern

For a simple dominant trait, an individual showing the trait usually has at least one:

dominant allele.

The genotype could be:

AA

or:

Aa.

If an affected heterozygous individual reproduces with an unaffected aa individual:

Aa × aa

the expected phenotype probabilities are:

50% dominant phenotype

50% recessive phenotype.

However, actual family sizes are often small, so real pedigrees may not show these ratios exactly.

---

Worked Family Example 1

Suppose attached earlobe type in an imaginary species follows simple inheritance.

Let:

E = dominant phenotype

e = recessive phenotype.

Two individuals show the dominant phenotype.

They produce an offspring showing the recessive phenotype.

What can we conclude?

The offspring must be:

ee.

Therefore, each parent contributed:

e.

Because the parents show the dominant phenotype, each must also possess E.

Therefore:

Parent 1 = Ee

Parent 2 = Ee.

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Worked Family Example 2

Suppose a recessive condition is represented by:

r.

An individual showing the condition has genotype:

rr.

This individual has a child with someone who is:

RR.

Cross:

rr × RR.

All offspring receive:

r from one parent

and:

R from the other.

Therefore:

100% Rr.

Under complete dominance, none would show the recessive phenotype, but all would carry the recessive:

allele.

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Worked Family Example 3

Now suppose:

rr × Rr.

The rr parent produces only:

r gametes.

The Rr parent produces:

R or r.

Therefore:

50% Rr

50% rr.

The probability of the recessive phenotype is:

50%.

---

Using Unknown Genotypes

Inheritance problems sometimes include an unknown:

genotype.

Suppose a dominant-phenotype organism could be:

AA

or:

Aa.

How might we determine which genotype is more likely?

We can examine:

offspring.

If the organism produces an aa offspring, then it must have contributed an:

a allele.

Therefore, it cannot be:

AA.

It must be:

Aa.

---

Test Crosses as Evidence

A test cross can be used to investigate an unknown dominant-phenotype genotype.

The unknown individual is crossed with a:

homozygous recessive individual.

Suppose the unknown genotype is:

A_

where the underscore means the second allele is not yet known.

It could be:

AA

or:

Aa.

---

If the Unknown Parent Is AA

Cross:

AA × aa

All offspring are:

Aa.

All show the:

dominant phenotype.

---

If the Unknown Parent Is Aa

Cross:

Aa × aa

Possible offspring are:

Aa

and:

aa.

Therefore, recessive-phenotype offspring are:

possible.

If recessive offspring appear, this provides evidence that the unknown parent was:

heterozygous.

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Genetic Evidence Can Rule Out Possibilities

Good genetic reasoning does not always tell us exactly what a genotype:

is.

Sometimes it tells us what the genotype:

cannot be.

For example, if an individual produces a recessive offspring, that parent cannot be homozygous dominant under the simple inheritance model.

Why?

Because a homozygous dominant parent has no recessive allele to:

contribute.

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Genetic Evidence and Certainty

It is important to distinguish between:

possible

probable

and:

certain.

For example, an organism showing a dominant phenotype could be:

AA or Aa.

Phenotype alone does not tell us which.

However, if that organism produces an aa offspring, then we know it contributed:

a.

That provides stronger evidence that it is:

Aa.

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Multiplication Rule for Independent Events

Sometimes we want to calculate the probability of several independent genetic events occurring:

together.

Suppose each child has a 25% probability of genotype aa.

What is the probability that two consecutive children are both aa?

Multiply the probabilities:

1/4 × 1/4 = 1/16

Therefore:

Probability = 1/16 = 6.25%.

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Another Probability Example

Suppose each offspring has a:

50% probability

of a particular phenotype.

What is the probability that two consecutive offspring both show that phenotype?

1/2 × 1/2 = 1/4

Therefore:

25%.

This works because we are considering independent:

events.

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Three Consecutive Outcomes

Suppose the probability of a recessive phenotype is:

1/4.

What is the probability that three consecutive offspring all show the recessive phenotype?

1/4 × 1/4 × 1/4

= 1/64

≈ 1.56%

This outcome is unlikely, but it is still:

possible.

---

Probability of Either Outcome

Sometimes several outcomes satisfy a question.

For:

Aa × Aa

suppose we want the probability of a homozygous offspring.

The possible homozygous genotypes are:

AA

and:

aa.

Probability of AA:

1/4

Probability of aa:

1/4

Add them:

1/4 + 1/4 = 1/2

Therefore:

50% of offspring are expected to be homozygous.

---

Probability of a Heterozygous Offspring

For:

Aa × Aa

the Punnett square contains:

AA, Aa, Aa, aa.

Two of the four outcomes are:

Aa.

Therefore:

P(Aa) = 2/4

= 1/2

= 50%.

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Probability of the Dominant Phenotype

Again consider:

Aa × Aa.

Dominant phenotype genotypes are:

AA

and:

Aa.

Therefore:

P(dominant phenotype)

= P(AA) + P(Aa)

= 1/4 + 2/4

= 3/4

= 75%.

---

Probability of the Recessive Phenotype

The recessive phenotype requires:

aa.

Therefore:

P(recessive phenotype)

= 1/4

= 25%.

---

Experimental Results vs Predicted Results

Imagine a cross predicts:

75% purple flowers

and:

25% white flowers.

A researcher grows 100 offspring and observes:

72 purple

28 white.

Does this mean the Punnett-square prediction was wrong?

Not necessarily.

The predicted values are:

probabilities.

Random variation can cause observed results to differ somewhat from the expected:

ratio.

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Using Evidence from Larger Samples

Suppose another researcher grows:

10,000 offspring.

If the inheritance model is correct, the observed proportion would generally be expected to lie relatively close to the predicted:

3 : 1 ratio.

Large samples provide stronger evidence for identifying inheritance patterns because random fluctuations tend to have a smaller proportional:

effect.

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When Evidence Does Not Fit the Prediction

Suppose a simple model predicts:

75% dominant phenotype

and:

25% recessive phenotype.

But a very large experiment consistently produces a very different:

pattern.

Scientists should not simply ignore the:

evidence.

Instead, they might ask:

• Is the assumed genotype correct?
• Is the trait actually controlled by one gene?
• Is dominance complete?
• Are environmental factors involved?
• Is another inheritance pattern operating?

Scientific predictions should always be tested against:

evidence.

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Limitations of Simple Inheritance Predictions

Punnett squares are powerful, but simple crosses make several:

assumptions.

Real traits may involve:

• multiple genes
• multiple alleles
• codominance
• incomplete dominance
• sex-linked inheritance
• gene interactions
• environmental effects

Therefore, not every characteristic can be accurately predicted using a simple:

2 × 2 Punnett square.

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Real Human Traits

Many familiar human characteristics are sometimes incorrectly taught as simple dominant-recessive:

traits.

Characteristics such as:

• eye colour
• hair colour
• height
• skin pigmentation

are generally more genetically complex than a simple:

A/a model.

When learning Punnett squares, it is often better to use clearly defined model traits or well-established single-gene examples.

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Evidence-Based Prediction

A strong inheritance prediction should include:

1. The allele definitions

Example:

B = dominant allele

b = recessive allele

2. The parent genotypes

Example:

Bb × bb

3. The possible gametes

Example:

B or b × b

4. The Punnett square

5. The genotype probabilities

6. The phenotype probabilities

7. A conclusion supported by the genetic evidence

This makes the reasoning clear and:

testable.

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Worked Investigation

Suppose a plant species has:

R = red flowers

r = white flowers.

R is dominant.

A red plant is crossed with a white plant.

Their offspring include:

48 red plants

and:

52 white plants.

What can we infer?

---

Step 1: Determine the White Parent

White is recessive.

Therefore, the white parent must be:

rr.

---

Step 2: Consider the Red Parent

The red parent could initially be:

RR

or:

Rr.

We need evidence to decide between these possibilities.

---

Step 3: Use the Offspring

Some offspring are:

white.

White offspring must be:

rr.

The white parent contributes one r.

The red parent must therefore also contribute:

r.

Therefore, the red parent cannot be:

RR.

It must be:

Rr.

---

Step 4: Test the Prediction

The predicted cross is:

Rr × rr.

This predicts:

50% Rr → red

50% rr → white.

The observed results:

48 red : 52 white

are reasonably close to the predicted:

1 : 1 ratio.

The evidence therefore supports the proposed simple inheritance:

model.

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Why Genetic Predictions Matter

Understanding inheritance probabilities has applications in:

• plant breeding
• animal breeding
• conservation biology
• genetic research
• medicine
• agriculture

Genetic predictions help scientists understand how alleles can move through:

populations and generations.

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Common Mistake: Probability Means Guarantee

A probability of:

25%

does not mean exactly one of every four offspring will show the:

trait.

It means each independent offspring has the predicted chance under the assumptions of the:

model.

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Common Mistake: Previous Children Change the Next Probability

Suppose a couple's genetic cross gives a 25% probability for a particular genotype.

They have three children without that genotype.

The probability for the fourth child does not automatically become:

higher.

Each conception is a new:

event.

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Common Mistake: Dominant Means More Likely to Be Inherited

A dominant allele is not automatically more likely to enter a:

gamete.

A heterozygous:

Aa

individual normally has a 50% probability of passing A and a 50% probability of passing:

a.

Dominance affects expression, not allele:

segregation.

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Common Mistake: Phenotype Always Reveals Genotype

A recessive phenotype can often identify genotype under simple complete dominance.

A dominant phenotype usually:

cannot.

For example:

A_

could mean:

AA or Aa.

Additional genetic evidence may be required.

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Common Mistake: A Pedigree Proves an Inheritance Pattern

A small pedigree can suggest an inheritance:

pattern.

However, small families provide limited data, and chance can produce patterns that resemble other inheritance:

models.

Scientists therefore consider the amount of evidence and alternative explanations before drawing strong:

conclusions.

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Common Mistake: Every Human Trait Is Mendelian

Many human traits are influenced by multiple genes and environmental:

factors.

Simple Punnett-square models should only be used when the underlying inheritance pattern supports those:

assumptions.

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Check Your Understanding

1. What information is needed to predict a simple genetic cross?

2. Explain the difference between genotype and phenotype.

3. Why does each gamete normally carry only one allele for each gene?

4. Why is fertilization described as involving chance?

5. Cross Bb × Bb using a Punnett square.

6. What is the probability of BB?

7. What is the probability of Bb?

8. What is the probability of bb?

9. If B is dominant, what is the probability of the dominant phenotype?

10. What is the probability of the recessive phenotype?

11. Why does a 25% probability not mean exactly one of four offspring must show the trait?

12. If the first offspring has genotype bb, what is the probability that the next offspring from Bb × Bb will also be bb?

13. Explain why previous offspring do not change the genetic probability for the next independent conception.

14. A cross predicts 75% tall offspring. If 200 offspring are produced, approximately how many would you expect to be tall?

15. Why might the actual number differ from the expected number?

16. What genotype must an individual with a recessive phenotype have under complete dominance?

17. Why can an individual showing the dominant phenotype have two possible genotypes?

18. Two dominant-phenotype parents produce a recessive-phenotype offspring. What does this tell you about their genotypes?

19. What is a pedigree?

20. What information can a pedigree provide?

21. How might unaffected parents produce an offspring with a recessive trait?

22. Explain how offspring can provide evidence about an unknown parent genotype.

23. What is a test cross?

24. Why is a homozygous recessive individual useful in a test cross?

25. If each offspring has a 50% probability of a trait, what is the probability that two consecutive offspring both show the trait?

26. If each offspring has a 25% probability of genotype aa, what is the probability that two consecutive offspring are both aa?

27. Explain why larger samples often match predicted genetic ratios more closely than small samples.

28. What should scientists do if experimental results repeatedly disagree with a genetic prediction?

29. Give two reasons why a simple Punnett square might not accurately model a real trait.

30. Explain how genetic evidence can be used to support an inheritance prediction.

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Key Terms

• Inheritance: Transmission of genetic information from parents to offspring.
• Allele: Alternative version of a gene.
• Genotype: Allele combination possessed by an organism.
• Phenotype: Observable characteristic of an organism.
• Gamete: Haploid reproductive cell carrying one allele for each gene.
• Fertilization: Fusion of gametes to produce a new genetic combination.
• Probability: Measure of the likelihood of an outcome.
• Genetic cross: Analysis of parental genotypes to predict offspring.
• Punnett square: Diagram used to predict possible offspring genotypes.
• Dominant allele: Allele expressed in a heterozygote under complete dominance.
• Recessive allele: Allele whose phenotype is normally expressed when two recessive copies are present.
• Carrier: Heterozygous individual carrying a recessive allele associated with a trait or condition.
• Pedigree: Diagram showing biological relationships and inheritance of a trait across generations.
• Test cross: Cross involving a homozygous recessive individual used to investigate an unknown genotype.
• Expected ratio: Proportion predicted by a genetic model.
• Observed ratio: Proportion actually found in experimental or family data.

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Key Takeaways

• Inheritance can be predicted using knowledge of alleles, meiosis, fertilization, and probability.
• Parents pass alleles to offspring through gametes.
• Each gamete normally carries one allele for each gene.
• Fertilization combines alleles from two parents.
• Punnett squares predict possible offspring genotypes and phenotypes.
• Genetic predictions describe probabilities, not certainties.
• 1/4 = 25%, 1/2 = 50%, and 3/4 = 75%.
• For Bb × Bb, the expected genotype ratio is 1 BB : 2 Bb : 1 bb.
• Under complete dominance, Bb × Bb produces an expected 3:1 phenotype ratio.
• Each independent conception represents a new genetic event.
• Previous offspring do not change the probability for the next offspring when the parental genotypes remain the same.
• Small families may differ greatly from predicted ratios because of chance.
• Larger samples generally provide stronger evidence for expected inheritance patterns.
• A recessive phenotype often provides strong information about genotype.
• A dominant phenotype may correspond to more than one genotype.
• Offspring phenotypes can provide evidence about parental genotypes.
• Two dominant-phenotype parents can produce a recessive offspring if both carry the recessive allele.
• Pedigrees can be used to investigate inheritance across generations.
• A test cross can provide evidence about an unknown genotype.
• Genetic evidence can sometimes rule out possible genotypes.
• Good genetic reasoning connects evidence, alleles, genotypes, probabilities, and conclusions.
• Expected results and observed results do not have to be exactly identical.
• Large, consistent differences between prediction and evidence may indicate that the genetic model needs to be reconsidered.
• Not every trait follows simple Mendelian inheritance.
• Many real traits involve multiple genes, different allele relationships, or environmental influences.
• Inheritance predictions are strongest when they are supported by clear genetic evidence and appropriate probability reasoning.