Monohybrid Inheritance Virtual Lab

A monohybrid cross follows the inheritance of a single gene that has two versions, called alleles. Two parents that differ in that one gene are crossed, and the offspring are counted by type. The pattern of the counts, and what it tells us about how genes are passed on, is the foundation of genetics. It was first worked out by Gregor Mendel, who bred garden peas in the 1850s and 1860s and published his results in 1866.

The topic is more than a set of ratios to memorise. It combines three skills that appear throughout science: building a model (genes are inherited as separate units), turning the model into a prediction (a Punnett square gives probabilities), and testing the prediction against noisy data (a chi-squared test asks whether the gap between observed and expected counts could be chance). This laboratory lets you practise all three on virtual organisms, with as many offspring as you like.

The notes work in three layers. Material marked Foundation needs only fractions and the idea of probability. Core material matches typical secondary courses and the first years of university biology, and uses Punnett squares, ratios, the multiplication and addition rules and the chi-squared test. Extension material goes further, with binomial probabilities, conditional probability for test crosses, the continuity correction and the limits of the statistics.

The simulation starts with two heterozygous parents (Rr and Rr) from complete dominance, a batch of 200 offspring and a random draw each time. Before you press the button, write down what you expect. Then compare. The difference between your prediction and the result is the main teaching point of this page.

Learning outcomes

Foundation

• Define gene, allele, genotype, phenotype, homozygous, heterozygous, dominant and recessive.
• Explain that an offspring receives one allele from each parent, and that each parent passes on one of its two alleles by chance.
• Complete a Punnett square for a cross between two parents of known genotype.
• State the expected 3 : 1 phenotype ratio when two heterozygotes are crossed under complete dominance.
• Explain why real results rarely match the expected numbers exactly.

Core (A-level, IB, AP, WAEC and first-year university)

• Predict genotype and phenotype ratios and probabilities for any monohybrid cross, for complete dominance, incomplete dominance and codominance.
• State Mendel's law of segregation and explain it in terms of meiosis.
• Use the multiplication and addition rules to find probabilities for several offspring.
• Describe a test cross and use it to find an unknown genotype.
• Carry out a chi-squared test: expected counts, the statistic, degrees of freedom, the p-value and a conclusion in words.
• Describe how sample size affects how closely observed counts follow the expected ratio.

Extension (IB HL, AP, university)

• Use the binomial distribution to find the probability of a particular number of offspring of one type.
• Combine prior probability and test-cross evidence to find the probability that an unknown parent is homozygous.
• Apply the Yates continuity correction and check the conditions for the chi-squared approximation.
• Estimate a probability from a line of best fit through the origin and state its standard error.
• Describe why the real world departs from simple Mendelian ratios: lethal alleles, linkage, penetrance and small families.

Terminology Foundation

A gene is a stretch of DNA that influences a trait. Its position on a chromosome is its locus. Different versions of a gene are alleles. Body cells of most animals and plants are diploid: they carry two copies of each chromosome, one inherited from each parent, so each individual has two alleles of each gene (one on each of the pair of homologous chromosomes). Sex cells, or gametes, are haploid and carry just one allele of each gene.

The pair of alleles an individual carries is its genotype. The observable result is its phenotype. An individual with two identical alleles is homozygous (for example RR or rr). An individual with two different alleles is heterozygous (Rr), and is sometimes called a hybrid for that gene, which is where the word monohybrid comes from. A heterozygote that hides a recessive allele is also called a carrier when the recessive allele causes a condition.

In complete dominance, the heterozygote looks like one of the homozygotes. The allele that shows is dominant (written with a capital letter, R), the one that is hidden is recessive (r). Dominant does not mean common or stronger. It describes only how the two alleles combine in the phenotype.

Mendel's experiments Foundation

Mendel chose the garden pea because it grows quickly, has clear either-or traits and can be crossed by hand. He studied seven traits, including seed shape (round or wrinkled), seed colour, flower colour and plant height. He first spent two years making sure his parent plants were true-breeding, meaning that self-pollination always gave offspring like the parent. He then crossed true-breeding round-seeded plants with true-breeding wrinkled-seeded plants.

The parental generation is written P. All the offspring of the first generation, the F1, had round seeds. The wrinkled trait had vanished. When Mendel allowed the F1 plants to self-pollinate, the second generation, F2, contained both kinds, and about three quarters were round and one quarter wrinkled. For seed shape he reported 5,474 round and 1,850 wrinkled seeds, a ratio of about 2.96 to 1. Mendel realised that the wrinkled trait had not been lost in the F1: it had been hidden, and then reappeared.

Mendel's laws Core

Textbooks state the results as laws, and the numbering varies between books. Check which version your course uses.

• Law of segregation. Each individual carries two alleles for a gene. When gametes form, the two alleles separate, so each gamete receives one allele, and each of the two is equally likely to end up in any given gamete. Fertilisation then restores the pair. This is the law that matters for monohybrid crosses.
• Law of dominance (sometimes the principle of uniformity). When two true-breeding parents with different alleles are crossed, the F1 all show the same phenotype, the dominant one in complete dominance. The recessive phenotype returns in the F2.
• Law of independent assortment. Alleles of different genes are distributed into gametes independently of each other. This applies to two or more genes, so it belongs to dihybrid crosses, and it has exceptions when genes lie close together on the same chromosome (linkage).

Segregation has a physical explanation that Mendel could not know. In meiosis the homologous chromosomes of a pair separate into different gametes. If a parent is Rr, half of its gametes carry the chromosome with R and half carry the chromosome with r.

Three ways two alleles can combine Core

In incomplete dominance and in codominance, each genotype has its own phenotype, so the phenotype ratio equals the genotype ratio. In complete dominance two genotypes (RR and Rr) share one phenotype, which is why the 1 : 2 : 1 genotype ratio becomes a 3 : 1 phenotype ratio. In incomplete dominance the heterozygote is a blend, such as pink from red and white. In codominance both alleles are fully expressed side by side, as in a roan coat with red and white hairs.

Probability and the Punnett square Core

Genetics is applied probability. For a heterozygous parent, each gamete carries R with probability 1/2 and r with probability 1/2. The two parents' gametes combine independently. A Punnett square lists the gamete types of one parent along the top, the other down the side, and fills each box with the resulting genotype. When each gamete type is equally likely, each box has probability 1/4.

Two rules cover most calculations. The multiplication rule: the probability that two independent events both happen is the product of their probabilities (probability of R from parent 1 and R from parent 2 is 1/2 × 1/2 = 1/4). The addition rule: the probability that either of two mutually exclusive events happens is the sum (Rr arises as R then r, or r then R: 1/4 + 1/4 = 1/2). Probability describes each offspring. It is the chance behind each one, and it does not guarantee that a family of four contains exactly one wrinkled seed. Each offspring is independent, with no memory of earlier ones.

Gametes and genotype probabilities Core

Let a parent produce gametes carrying the second allele with probability a (0 for AA, 1/2 for Aa, 1 for aa) and the other parent with probability b. For one offspring:

P(AA) = (1 − a)(1 − b)    P(Aa) = a(1 − b) + (1 − a)b    P(aa) = ab

For two heterozygotes a = b = 1/2, so P(AA) = 1/4, P(Aa) = 1/4 + 1/4 = 1/2 and P(aa) = 1/4. This is the 1 : 2 : 1 genotype ratio. Under complete dominance the dominant phenotype has probability P(AA) + P(Aa) = 3/4 and the recessive phenotype has 1/4, the 3 : 1 ratio.

Expected counts and the size of chance variation Core

If the probability of a type is p and a batch has n offspring, the expected count is E = np. The actual count varies from batch to batch. For independent offspring the count follows a binomial distribution, with standard deviation:

σ = √(n p (1 − p))

About 95% of batches fall within two standard deviations of the expected count. The share of offspring of the type has standard error:

SE = √(p (1 − p) / n)

SE falls as 1/√n. A batch four times larger is only twice as precise, and to cut the uncertainty tenfold you need a hundred times as many offspring.

Binomial probability Extension

The probability that exactly k of n independent offspring have a type of probability p is:

P(k) = C(n, k) p^k (1 − p)^{n − k}    where C(n, k) = n! / (k! (n − k)!)

The chi-squared test Core

To test whether observed counts O fit a ratio, find the expected count E in each category from the ratio, then add up the scaled squared gaps:

χ² = Σ (O − E)² / E

The sum runs over all categories (two for a 3 : 1 ratio, three for 1 : 2 : 1). The degrees of freedom are the number of categories minus 1, because once all but one count is known the last is fixed by the total n. The null hypothesis H0 says the data follow the ratio. The p-value is the probability, if H0 were true, of a χ² at least as large as the one found. A small p (below 0.05 by the usual convention) means the data would be surprising under H0, so H0 is rejected. A large p means the data are consistent with H0. That does not prove the ratio: it only says the data give no good reason to doubt it. Critical values at the 5% level are 3.84 for 1 degree of freedom, 5.99 for 2 and 7.81 for 3.

Two conditions matter. The counts must be actual counts, not percentages or proportions. And each expected count should be at least 5, otherwise the χ² distribution is a poor approximation. With 1 degree of freedom, some courses apply the Yates continuity correction, replacing |O − E| by |O − E| − 0.5 in each term, which makes the test slightly more cautious for small samples Extension.

Inferring an unknown genotype Extension

In a test cross, an individual with the dominant phenotype but unknown genotype (AA or Aa) is crossed with a homozygous recessive (aa). If it is AA, all offspring show the dominant phenotype. If it is Aa, half the offspring show the recessive phenotype. A single recessive offspring proves Aa. If n offspring are all dominant, the probability of that happening for an Aa parent is (1/2)ⁿ. By Bayes' theorem, with a prior probability q that the parent is AA:

P(AA | n dominant, none recessive) = q / [q + (1 − q)(1/2)ⁿ]

A dominant-phenotype child of an Aa × Aa cross is AA with probability 1/3 and Aa with probability 2/3, so q = 1/3. Then P(AA) = 1 / (1 + 2^{1 − n}): 0.941 after 5 dominant offspring, 0.970 after 6 and 0.998 after 10. Learners often quote the simpler figure that 5 offspring give a one-in-32 chance of error. That figure is the chance an Aa parent would fool you, which is a different thing from the probability that the parent is AA.

Line of best fit through the origin Extension

If you plot the count N of one type against batch size n for several batches of the same cross, the points lie near a straight line through the origin, N = m n, where the gradient m estimates the probability p. The least-squares gradient is m = Σ n_i N_i / Σ n_i², and the analysis tool in this lab reports its standard error from the scatter of the points about the line.

Every number below was checked by computation. Round only at the end.

The simulator draws four graphs. Learn to read each one as evidence.

Share against batch size Core

Each red point is one batch, with batch size across and the share of the first phenotype up. The black line is the expected share, and the grey dashed funnel marks 2 standard errors either side of it. The points scatter widely on the left and tighten on the right. About 19 in 20 points should lie inside the funnel. A point outside is not an error, only a rare event.

Observed and expected counts Foundation

Blue bars show what you got and gold bars show what the Punnett square predicted for your batch size. Compare heights. Differences of a few offspring are ordinary. The chi-squared statistic puts a number on whether the overall difference is larger than chance would usually give.

The p-values of your batches Core

If every batch really follows its expected ratio, the p-values are scattered evenly between 0 and 1, with about 5% below the red 0.05 line. Seeing one or two points under the line out of twenty is exactly what chance predicts. Seeing most points below the line suggests the model is wrong. This graph is a good reminder that a p-value is a measure of surprise, not of correctness.

Running total Core

The pooled share is the total number of the first type divided by the total offspring so far. It wanders at first, then settles at the true probability as more offspring are pooled. This is the law of large numbers: random fluctuations in proportions shrink as n grows. It does not mean that the numbers even out in the short run. After a lucky run of dominant offspring, the next offspring still has probability 3/4 of being dominant, and the surplus is diluted by new data, not cancelled.

The chi-squared distribution Extension

The p-value is the area in the tail of a chi-squared curve beyond your χ². The curve has a different shape for each number of degrees of freedom. The diagram shows 2 degrees of freedom (the 1 : 2 : 1 test) and 4. The shaded tail beyond 5.99 has area 0.05 for 2 degrees of freedom.

Line of best fit in the Analyse section Extension

The count of one phenotype is plotted against batch size, with a least-squares line through the origin. The gradient is the estimated probability, shown with its standard error and compared with the Punnett-square prediction. Points far from the line at large batch size are the ones that deserve a second look.

The ratios 3 : 1 and 1 : 2 : 1 are idealised. They assume a long list of conditions that real organisms often break. Knowing the conditions lets you recognise when a surprising result is a clue rather than an error.

Assumptions behind the ratios Core

• Equal gametes. The two alleles of a heterozygote are passed on with equal probability. Some real genes break this rule, an effect called segregation distortion or meiotic drive.
• Random fertilisation. Any egg is as likely to meet any sperm or pollen grain as any other. Some matings are preferred or avoided.
• Equal survival. All genotypes survive and are counted equally. If one genotype is less likely to survive to be scored, the observed ratio shifts.
• One gene, two alleles. The trait is controlled by a single gene with two alleles. Many traits depend on several genes, or on multiple alleles of one gene (the ABO blood groups have three).
• Clear classification. Each offspring can be assigned to exactly one phenotype without error.

When the ratios change Core

Small families and selection Core

Human families are small. With two carrier parents and four children, the chance that exactly one child is affected is only 42%, and about 32% of such families have no affected child at all (Example 3). A family with no affected child is not evidence against the model. Human geneticists also face ascertainment bias: families usually come to attention because they already have an affected child, so families with no affected children are missing from the sample, and the apparent proportion affected is too high. Special methods correct for this.

Were Mendel's results too good? Extension

Several later statisticians, notably R. A. Fisher in the 1930s, pointed out that when all of Mendel's published experiments are combined, they sit closer to the expected ratios than chance would usually allow. The reasons are still debated. Suggestions include unconscious bias in classifying seeds, stopping counts when they looked right, or the way different experiments were reported. The discussion does not change the validity of Mendel's laws, which have been confirmed by countless later experiments. It does illustrate a lesson for any experimenter: results that are too perfect deserve the same scrutiny as results that are too surprising. In this laboratory you will often see the opposite pattern: random batches that fall outside the funnel one time in twenty.

Limits of any statistical test Extension

A chi-squared test cannot prove a ratio is correct, only fail to reject it. It tests one hypothesis at a time, it is sensitive to sample size (Example 7), and a very large sample can flag a tiny and biologically unimportant difference. For a rigorous investigation, plan the sample size before collecting data and decide in advance how a result will be judged.

Start with a question Foundation

A good investigation begins with a question that can be answered with data. Three suit this laboratory.

1. Do the offspring of two heterozygotes follow a 3 : 1 ratio under complete dominance, and a 1 : 2 : 1 ratio under incomplete dominance?
2. How does the number of offspring in a batch affect how closely the observed ratio matches the expected one?
3. Can a test cross show whether a dominant-phenotype parent is homozygous or heterozygous, and how many offspring are enough?

Variables Core

Hypotheses and predictions Core

Write the null hypothesis H0 as a statement about the underlying probability: 'the offspring of Rr × Rr follow a 3 : 1 ratio'. The alternative H1 is that they do not. Then write numerical predictions before you collect data. For question 2, a reasonable prediction is that the batches of 10 will vary by roughly ±0.14 around the expected share 0.75 (the standard error is √(0.75 × 0.25 / 10) = 0.137) and the batches of 640 by roughly ±0.017. Notice that a prediction states what you expect and how large the scatter should be.

A protocol using the simulator Core

1. Choose the mode of inheritance and the genotypes of both parents. Check the Punnett square drawn for you and write down the predicted ratio.
2. Decide the batch size and the number of repeats before you start. Ten or more batches per condition give a useful picture of the scatter.
3. Press Breed a batch. Wait for the batch to finish. It is recorded automatically in the table.
4. Repeat. For a strictly repeatable record, tick 'Repeatable batch' and note the seed. Using the same seed again reproduces the same offspring, which is useful for checking your counting.
5. Download the CSV file if you want to analyse the data in a spreadsheet.
6. Analyse: the chi-squared tool, the line of best fit and the graphs.
7. Conclude: state whether H0 is rejected for each condition, and what the pattern across batch sizes shows.

Designing a real experiment Extension

Living organisms differ in how practical they are for teaching genetics. Garden peas give large clear traits but take months per generation and need space. The fruit fly Drosophila melanogaster completes a generation in around ten to fourteen days at room temperature, produces dozens of offspring per cross and has many easy-to-score mutants, but needs virgin females and careful handling. Rapid-cycling Brassica plants complete a life cycle in roughly five to six weeks. Maize cobs are a classic classroom choice, because one cob carries a few hundred kernels, each of which is one offspring, and kernels can be counted by colour or shape on a single day. Whichever organism you use, check the plan with your teacher, record the organism's source and decide in advance how phenotypes will be classified.

From counts to conclusions Core

Genetics data are counts. Record the actual number of each phenotype and the total n. Convert counts to shares (count ÷ n) when comparing batches of different sizes, but always use the raw counts in the chi-squared test.

Chi-squared checklist

1. State H0 and H1 in words, with the ratio.
2. Find the expected counts E from the ratio and n. Check that each E is at least 5.
3. Calculate each term (O − E)² / E and add them up to get χ².
4. Find the degrees of freedom: categories − 1.
5. Compare with the critical value at the 5% level (3.84 for 1 degree of freedom, 5.99 for 2, 7.81 for 3), or find the p-value.
6. Conclude in words: whether the data are consistent with the ratio, and what that implies about the genotypes or the model.

When there are only two categories, χ² equals the square of the familiar z-score: z = (observed share − expected share) / SE. For 389 round of 500 seeds against 3 : 1, the observed share is 0.778, SE = √(0.75 × 0.25 / 500) = 0.0194, so z = 0.028 / 0.0194 = 1.45 and z² = 2.09, which is the χ² for those counts (389 and 111 against 375 and 125).

Interpreting the p-value Core

A p-value of 0.15 means that if the 3 : 1 ratio were exactly right, a gap at least this large would occur in about 15% of batches. It does not mean the ratio is 85% likely to be right, and it does not measure how big or important the departure is. The 5% level is a convention, not a law of nature. Reporting the exact p-value and the χ² gives the reader more than the bare words 'significant' or 'not significant'.

Uncertainty Core

Two kinds of uncertainty affect genetics data.

• Sampling (random) uncertainty. Even with perfect counting, a finite batch will not match the probabilities. This is described by the standard error and falls as 1/√n. You cannot remove it, only reduce it by increasing n. The simulation shows it directly.
• Classification (systematic) error. Phenotypes may be misjudged: a pink flower scored as red, a poorly formed seed counted as round, an escaped fly not counted. This error does not average out and can shift a ratio. Reduce it with clear written criteria, blind scoring by a second person and recounting.

Report a share with its uncertainty, for example 0.778 ± 0.019 (one standard error, using the observed share 0.778 gives √(0.778 × 0.222 / 500) = 0.0186). A rough 95% range is the share ± 2 standard errors.

Pooling data Extension

Combining batches from the same cross into one large sample gives a more powerful test, but only if the batches agree with each other. Suppose three batches give 71 : 29, 55 : 25 and 148 : 52 (dominant : recessive). Pooled, they are 274 : 106, χ² = 1.70 against 3 : 1. A fuller analysis (a heterogeneity test) checks that the individual batch values of χ² are not larger than expected as well. If one batch comes from a different cross or was classified differently, pooling hides the problem.

Line of best fit and its uncertainty Extension

The Analyse section fits N = m n through the origin. The gradient m is the estimate of the probability and its standard error, SE(m) = √[ Σ(N_i − m n_i)² / ((k − 1) Σ n_i²) ], where k is the number of batches. Compare m ± 2 SE with the Punnett-square probability. If the prediction lies inside the range, the data agree with the model. If many data sets are analysed this way, about 1 in 20 will miss by chance alone.

Presenting results Core

• Give a table with the cross, n, counts, expected counts, χ², degrees of freedom and p.
• Choose graphs that match the question: the funnel for sample size, bars for observed against expected.
• Keep sensible precision: 3 significant figures for χ² and share, 2 to 3 decimal places for p.
• Say what you would change: more batches, larger n, independent scoring.

In the virtual laboratory Foundation

The random choices come from the browser's random number generator, or from a seeded generator when you tick the box. These are pseudo-random numbers: they behave statistically like random events and are suitable for teaching. Your table is kept only in your own browser, so it will be there when you return on the same device, and clearing site data removes it.

With living organisms Core

• Scoring. Decide the classes before you start and write the criteria down. For seed shape: smooth and round or visibly wrinkled when dry. For fly eye colour: under a stereo microscope or hand lens with a consistent light.
• Counting. Use a tally sheet, mark each individual once (for example by moving it into a counted tray), and count twice. A second person who does not know the expected ratio can score blind.
• Sampling. Count a whole cob or a complete vial, not a convenient part. Choosing which to count after looking at the colours introduces bias.
• Records. Record the date, the parent stock and every offspring count, including any that did not fit a class or were lost.

Handling data Core

Download the CSV file and open it in a spreadsheet to calculate expected counts and χ² for yourself, then compare with the tool. The file records the cross, n, each phenotype count, the expected ratio, χ², degrees of freedom, p and the seed, if one was used.

Safety with real organisms Foundation

The simulation is entirely safe. If you go on to a real genetics practical, your teacher or supervisor will give the risk assessment for your equipment and organisms. Points that commonly arise are listed here for awareness, and your own school or institution's rules override anything on this page.

• Plants. Wash hands after handling soil and plants. Some people react to pollen or to mould on stored seed. Use only seed sold for growing or teaching, and do not eat it, as some seed is treated with chemicals.
• Fruit flies. Flies are usually immobilised with an approved anaesthetic. Follow the supplier's instructions, work in a ventilated place and keep flies from escaping. Dispose of flies as your institution instructs, for example by freezing.
• Hygiene and waste. Keep food and drink away from work areas. Wash hands. Dispose of cultures and bedding as instructed.
• Welfare. Living organisms should be handled gently, kept in suitable conditions and not left unattended for long periods.

Ethics with human genetics Core

Examples about inherited human conditions are sensitive. Genetic information is personal and can affect other family members. A classroom should not ask learners to reveal their own or their family's genetic conditions, and should not use well-known human traits, such as tongue rolling or earlobe attachment, as examples of simple dominance. Those traits are not controlled by a single dominant gene as once taught, and family patterns do not follow the simple ratios. Use pedigrees that are clearly made up, and remember that real genetic counselling needs trained professionals.

Limits of the simulation Core

• The simulation teaches the logic of inheritance and statistics. It does not train you in handling living organisms, scoring phenotypes or recording a real notebook.
• Random batches will sometimes look unusual. That is a feature of the topic and not a fault.
• Marks in the examination section are for learning and are not an official grade. This page is an original teaching resource and is not endorsed by, and does not replace the materials of, any examination board.

Each of these costs marks every year. Check your work against the list.

Layout of a genetics answer Core

Genetics questions reward a clear, ordered answer. Whatever the format, the following layout earns method marks even if a later step slips.

1. Key. Choose a letter and state which allele is which: 'R = round (dominant), r = wrinkled (recessive)'.
2. Parental phenotypes and genotypes. Write each parent and its genotype.
3. Gametes. Show the gametes of each parent, one allele each, often circled.
4. Offspring genotypes. Use a Punnett square or a branching diagram.
5. Offspring phenotypes. Convert genotypes to phenotypes using the key.
6. Ratio or probability. Give it in simplest terms (3 : 1, 1/4, 25%). Say what was asked: a ratio is not the same as a probability.

Command words Foundation

Check the command words your own course uses, since each body defines them in its own guidance.

Chi-squared answers Core

• State H0 as a sentence and name the ratio you are testing.
• Show E for every category, then every term, then the total. Method marks are given for correct working even if the arithmetic slips.
• State the degrees of freedom and the critical value or p-value you are using. If a table is provided in the exam, read the correct column, the 0.05 level.
• Finish with a conclusion in words, linked to the context: 'The seed shapes are consistent with a 3 : 1 ratio, so the data support a single gene with complete dominance'.
• Do not say 'accept' or 'prove'. Use 'reject' or 'do not reject' for H0.

Probability questions Core

• Decide whether the question asks for 'and' (multiply) or 'or' (add) before you start.
• For 'at least one', use 1 − P(none), as in Example 3.
• For parents who are unaffected but have an affected child, both must be carriers (Aa × Aa). If a further unaffected child is asked about, the probability that it is a carrier is 2/3, since the possible unaffected genotypes AA and Aa have probabilities 1/4 and 1/2.

General advice Foundation

• Read the whole question first, including any family tree or data table, and underline numbers.
• Use the marks as a guide: two marks usually means two distinct points or one step of working.
• If you have time, check totals: offspring counts add to n, probabilities sum to 1.
• Practise under timed conditions with the examination section of this laboratory, then read the explanation for every question you miss. Marks in this lab are for learning, not an official grade.

The table lists the topic names under which monohybrid inheritance usually appears. Names, order and depth change between editions, so use it to find your place, then check your own current specification or course guide for the exact requirements, the equations you are given and the statistics expected. This page does not quote specification codes and does not claim to match any particular board's wording.

Level guide Foundation

• Foundation: terminology, dominance, Punnett squares for simple crosses, 3 : 1 and 1 : 1.
• Core: incomplete dominance and codominance, probability rules, test crosses, chi-squared, sampling variation.
• Extension: binomial probability, Bayesian reasoning about test crosses, the Yates correction, regression through the origin, and limits of simple Mendelian models.

When your course adds a topic that is not here, such as dihybrid crosses, linkage or sex-linked inheritance, the logic of this lab still applies: list the gametes, combine them in a grid, convert genotypes to phenotypes, and test the prediction against counts.

Plant and animal breeding Foundation

Breeders select parents to produce desirable offspring. A breeder who wants a true-breeding line for a recessive trait can choose only individuals that show the trait, because every recessive-phenotype individual is homozygous. A dominant trait is harder, because AA and Aa look the same. The test cross is the standard answer: cross the individual with a homozygous recessive and count the offspring. Breeders balance the cost of the test (the number of offspring needed, the time) against the confidence they need, which is why the result of Example 8, six offspring for 95% confidence, matters in practice.

Genetic counselling and carriers Core

Several well-known conditions follow the simple patterns. Cystic fibrosis and sickle cell disease are inherited as autosomal recessive conditions: two carrier parents have a 1 in 4 chance of an affected child with each pregnancy, a 1 in 2 chance of a carrier child and a 1 in 4 chance of a child with neither the condition nor the allele. Huntington's disease is an autosomal dominant condition, so one affected heterozygous parent has a 1 in 2 chance of passing the allele on to each child. Counsellors translate these probabilities into plain language. They stress that each child is independent and that probabilities describe the chance, not what will happen in a given family.

Pedigrees, or family trees, show who is affected. A recessive condition often skips generations and appears in children of unaffected parents. Two unaffected parents with an affected child must both be carriers. In a dominant condition, every affected person has an affected parent (unless there is a new mutation or incomplete penetrance).

Intermediate and codominant traits Core

• Familial hypercholesterolaemia. Individuals with one faulty allele have raised blood cholesterol, and those with two are usually more severely affected, a pattern like incomplete dominance.
• MN blood groups. The M and N forms of a surface molecule on red blood cells are codominant: heterozygotes carry both, so the three genotypes give three phenotypes.
• ABO blood groups. The A and B alleles are codominant to each other and both dominant to O. The gene has three alleles, an extension beyond the two-allele model.
• Sickle cell trait. A carrier has some sickle haemoglobin and some normal haemoglobin. At the molecular level the alleles are codominant, while the whole-body phenotype can seem recessive. Where malaria is common, carriers have an advantage, which helps explain why the allele remains frequent.

Statistics in genetics Core

The chi-squared test used here is a general tool. Geneticists use it to check Mendelian ratios in crosses, to look for departures from expected genotype frequencies in populations, and to compare allele counts between groups of people in association studies. In each case the reasoning is the one in this lab: expected counts from a model, observed counts from data, and a p-value for how surprising the gap is.

Research, conservation and agricultural uses Foundation

Genetic ratios guide seed production, the planning of animal breeding programmes, conservation of small populations and the interpretation of crosses in research on model organisms such as fruit flies, roundworms and yeast. Understanding the ratios is also the basis for understanding how new genetic tools work.

Two genes: the dihybrid cross Extension

When two genes assort independently, a cross between double heterozygotes (AaBb × AaBb) gives a 9 : 3 : 3 : 1 ratio of the four phenotype classes, since 9/16 = 3/4 × 3/4, 3/16 = 3/4 × 1/4, and 1/16 = 1/4 × 1/4. The multiplication rule applies independently to each gene. For Mendel's round yellow, round green, wrinkled yellow and wrinkled green seeds, the counts 315, 108, 101 and 32 (n = 556) give expected counts 312.75, 104.25, 104.25 and 34.75, χ² = 0.47, 3 degrees of freedom and p = 0.93. The data fit very well (p = 0.93). A single close fit is unremarkable. The question raised in section F concerns the pattern across all of Mendel's experiments taken together.

Linkage and sex linkage Extension

Genes that lie close together on the same chromosome tend to be inherited together, so the 9 : 3 : 3 : 1 ratio is distorted. Genes on the X chromosome give different ratios in males and females, because males have one X. Recognising a ratio that fails the monohybrid model is the first step to recognising a more complicated one.

Multiple alleles and lethal alleles Extension

A population can carry more than two alleles of a gene, although each individual has at most two. A lethal allele changes the observed ratio. If one homozygous genotype (say AA) dies before scoring, a cross between two heterozygotes leaves surviving offspring in the ratio 2 Aa : 1 aa, which is 2 : 1 by phenotype. A χ² test against 3 : 1 will then reject, which is a clue to look for a lethal effect rather than an error.

Allele frequencies in populations Extension

For a population with allele frequencies p and q (p + q = 1) that mates at random and has no selection, mutation or migration, genotype frequencies are p², 2pq and q²: the Hardy-Weinberg relationship. It is the population-level version of the Punnett square. If 1 in 10,000 individuals is homozygous recessive, q² = 0.0001, so q = 0.01 and the carrier frequency is 2pq = 2 × 0.99 × 0.01 = 0.0198, about 1 in 50.

From ratio to molecule Extension

Genes are stretches of DNA, and alleles differ in sequence. Mendel's round and wrinkled seeds correspond to a gene for an enzyme involved in starch branching: the wrinkled allele disrupts the enzyme, so the seed stores sugars and loses water as it dries, giving the wrinkled surface. Dominance is not a property of the allele alone but of the pathway. With enough working enzyme from one allele the heterozygote looks round, which is why complete dominance is common for alleles that lose function. Incomplete dominance arises when a half dose of the product gives an intermediate result.

Better statistics Extension

• Exact tests. For small samples, the exact binomial test or Fisher's exact test gives exact probabilities and avoids the chi-squared approximation.
• Likelihood. The likelihood of the data under each hypothesis can be compared directly, as in the test-cross posterior. The G-test is a related alternative to χ².
• Effect size and confidence intervals. Report the estimated probability with an interval, not only a yes-or-no decision.
• Multiple testing. If twenty independent batches are each tested at the 5% level, about one will appear to fail by chance. The p-value graph in this lab shows this.

• A gene has alleles. Each diploid individual has two alleles of a gene, one from each parent, and passes on one of them in each gamete, at random.
• Genotype is the pair of alleles. Phenotype is the observable trait. Different genotypes can share a phenotype.
• Under complete dominance, Rr × Rr gives genotypes 1 RR : 2 Rr : 1 rr and phenotypes 3 dominant : 1 recessive.
• Under incomplete dominance or codominance, the heterozygote has its own phenotype, so Aa × Aa gives 1 : 2 : 1 for both genotypes and phenotypes.
• A test cross with a homozygous recessive reveals an unknown genotype. A single recessive offspring proves the parent heterozygous. A run of dominant offspring only makes homozygous more likely.
• Probabilities describe each offspring, not the family. Offspring are independent. Use the multiplication rule for 'and' and the addition rule for 'or'.
• Expected counts are E = n × p. Counts vary by about σ = √(n p (1 − p)) around them.
• The share of a type has standard error √(p (1 − p) / n), so larger samples follow the ratio more closely. Four times the sample halves the uncertainty.
• χ² = Σ (O − E)² / E, with degrees of freedom equal to categories minus 1. Use counts, not percentages, and check that E is at least 5.
• The p-value is the chance of a gap this large or larger if the ratio is right. p ≥ 0.05 means the data are consistent with the ratio, and p < 0.05 means reject H0 at the 5% level. About 1 in 20 correct models will be rejected by chance.
• Real organisms depart from simple ratios because of lethal alleles, linkage, penetrance, environment and small samples.
• Marks in this laboratory are for learning, not an official grade. Check your own specification for what you must know.

Allele

One of the alternative versions of a gene.

Autosome

A chromosome that is not a sex chromosome.

Carrier

A heterozygous individual who has one copy of a recessive allele and usually does not show its effect.

Chi-squared test

A statistical test that compares observed counts with the counts expected from a hypothesis.

Codominance

A pattern in which both alleles of a heterozygote are fully expressed at the same time.

Complete dominance

A pattern in which the heterozygote looks like one of the homozygotes.

Degrees of freedom

The number of independent categories in a chi-squared test, equal to the number of categories minus 1 here.

Diploid

Having two sets of chromosomes, one from each parent.

Dominant allele

An allele whose effect shows in the heterozygote.

Expected count

The count predicted by a hypothesis: the sample size times the probability.

F1, F2

The first and second filial generations: the offspring of the parental cross, and the offspring of the F1 crossed among themselves.

Gamete

A haploid sex cell, such as an egg or a sperm, that carries one allele of each gene.

Gene

A section of DNA that influences a trait.

Genotype

The alleles an individual carries for a gene or genes.

Haploid

Having one set of chromosomes.

Heterozygous

Having two different alleles of a gene.

Homozygous

Having two identical alleles of a gene.

Incomplete dominance

A pattern in which the heterozygote has a phenotype between those of the two homozygotes.

Law of segregation

The principle that the two alleles of a gene separate into different gametes, each equally likely to be passed on.

Locus

The position of a gene on a chromosome.

Meiosis

The cell division that produces haploid gametes from a diploid cell.

Monohybrid cross

A cross that follows the inheritance of a single gene.

Null hypothesis

The statement, such as 'the data follow a 3 : 1 ratio', that a test tries to reject.

Observed count

The count actually obtained in an experiment.

p-value

The probability, if the null hypothesis is true, of a result at least as extreme as the one observed.

Pedigree

A diagram of a family showing the inheritance of a trait.

Penetrance

The proportion of individuals with a genotype who show its phenotype.

Phenotype

The observable characteristics of an individual.

Punnett square

A grid showing every combination of the gametes of two parents.

Recessive allele

An allele whose effect is hidden in the heterozygote under complete dominance.

Standard error

A measure of how much a sample statistic, such as a share, varies from sample to sample.

Test cross

A cross of an individual of unknown genotype with a homozygous recessive individual.

True-breeding

Producing offspring identical to the parents for the trait when self-pollinated or bred among themselves, because the parents are homozygous.

Yates correction

An adjustment to chi-squared for 1 degree of freedom that subtracts 0.5 from each absolute difference.

These are titles and publishers for further reading, listed without links. Find current editions through the publisher's home page or your library. No quotation from them is reproduced here.

• Mendel, G. (1866). Versuche über Pflanzen-Hybriden, Verhandlungen des naturforschenden Vereines in Brünn. Many English translations exist under the title Experiments on Plant Hybridization.
• Fisher, R. A. (1936). 'Has Mendel's work been rediscovered?', Annals of Science. Publisher: Taylor & Francis (tandfonline.com).
• Griffiths, A. J. F. and colleagues, Introduction to Genetic Analysis. Publisher: W. H. Freeman, Macmillan Learning (macmillanlearning.com).
• Reece, J. B. and colleagues, Campbell Biology. Publisher: Pearson (pearson.com).
• Hartl, D. L., Essential Genetics and Genomics. Publisher: Jones & Bartlett Learning (jblearning.com).
• NIST/SEMATECH e-Handbook of Statistical Methods. Publisher: National Institute of Standards and Technology (nist.gov).
• Scitable, genetics articles. Publisher: Nature Education, Springer Nature (nature.com).
• Specification and syllabus documents for your own course, from the body that sets your examination: Cambridge University Press & Assessment (cambridgeinternational.org), the West African Examinations Council (the website of your country's office), the International Baccalaureate Organization (ibo.org) and the College Board (collegeboard.org).

This laboratory is an original teaching resource by Specialty Digest. It has not been endorsed or reviewed by any examination board or publisher named above, and its marks are for learning, not an official grade.