Mendelian Inheritance Calculator: Understanding Genetic Inheritance Patterns

Mendel's Laws of Inheritance

Mendel's experimental work with Pisum sativum led to three foundational principles that govern how genetic traits pass from parents to offspring. Although originally described for discrete plant characteristics, these laws apply directly to single-gene (monogenic) disorders in humans.

The Law of Segregation

Every individual carries two alleles for each autosomal gene—one inherited from each parent. During the formation of gametes (meiosis), these two alleles separate so that each gamete carries only one allele. This means that each parent transmits exactly one of their two alleles to each offspring, with equal probability. The law of segregation is the basis for Punnett square analysis and for calculating the 50% transmission probability that underpins virtually all Mendelian risk assessments.

The Law of Independent Assortment

Alleles for different genes assort independently of one another during gamete formation, provided the genes are located on different chromosomes (or are sufficiently far apart on the same chromosome). In clinical genetics, this principle means that the inheritance of one condition does not, in general, influence the inheritance of another. Exceptions occur when genes are closely linked on the same chromosome, which is exploited in linkage analysis for gene mapping and carrier detection.

The Principle of Dominance

When two different alleles are present in a heterozygous individual, one allele (dominant) may mask the expression of the other (recessive). In the context of human disease, this determines whether a single mutant allele is sufficient to produce the phenotype (dominant inheritance) or whether two mutant alleles are required (recessive inheritance). It is worth noting that dominance is a property of the phenotype, not the allele itself: the same allele may behave as dominant for one trait and recessive for another, depending on the molecular mechanism involved.

These three principles, together with our understanding of sex-linked inheritance (genes carried on the X or Y chromosomes), form the framework within which all Mendelian inheritance calculators operate. The challenge in clinical genetics is that real families rarely present textbook patterns. Reduced penetrance, variable expressivity, de novo mutations, and genetic heterogeneity all complicate the analysis—which is precisely why rigorous probabilistic calculation matters.

Autosomal Dominant Inheritance

In autosomal dominant inheritance, a single copy of the disease-causing allele is sufficient to produce the phenotype. The gene is located on one of the 22 autosomes (non-sex chromosomes), so the condition affects males and females with equal frequency. A heterozygous affected individual partnered with an unaffected homozygous individual has a 50% probability of transmitting the mutation to each offspring.

Recognising Autosomal Dominant Patterns in Pedigrees

The hallmarks of autosomal dominant inheritance in a pedigree include: the condition appears in every generation (vertical transmission); affected individuals have at least one affected parent (barring de novo mutations or reduced penetrance); approximately half of the offspring of an affected individual are affected; unaffected individuals do not transmit the condition to their children; and both sexes are affected in roughly equal proportions. Male-to-male transmission is possible, which distinguishes autosomal dominant from X-linked dominant inheritance.

Penetrance and Age-Dependent Expression

Not all autosomal dominant conditions exhibit complete penetrance. Penetrance is the proportion of individuals carrying the disease genotype who manifest the phenotype. A condition with 80% penetrance means that 20% of mutation carriers remain unaffected. This has profound implications for pedigree interpretation: an apparently unaffected individual in a dominant pedigree may still carry the mutation and transmit it to offspring.

Many dominant conditions also show age-dependent penetrance—the probability of manifesting the phenotype increases with age. Huntington disease, for example, has near-zero penetrance before age 20 but approaches complete penetrance by age 70. A Mendelian inheritance calculator must account for the current age of each individual when estimating their probability of carrying the mutation: a 25-year-old unaffected individual from a Huntington family has a very different residual risk than a 65-year-old unaffected individual.

Anticipation

In conditions caused by trinucleotide repeat expansions (such as Huntington disease and myotonic dystrophy), the mutation may expand in successive generations, leading to earlier onset and more severe disease—a phenomenon called anticipation. Inheritance calculators that model anticipation must consider not only the probability of transmitting the mutation but also the likelihood of repeat expansion during transmission, which can depend on the sex of the transmitting parent.

Clinical Examples

Common autosomal dominant conditions include Huntington disease (trinucleotide repeat expansion in HTT, with age-dependent penetrance and anticipation), Marfan syndrome (FBN1 mutations, with significant variable expressivity), hereditary breast and ovarian cancer due to BRCA1 and BRCA2 mutations (with sex-dependent, age-dependent penetrance), familial hypercholesterolaemia (LDLR, APOB, or PCSK9 mutations), and neurofibromatosis type 1 (NF1 mutations, with almost complete penetrance but marked variable expressivity). Each of these conditions illustrates why a simple 50% transmission risk is insufficient for clinical counselling—penetrance, expressivity, and modifying factors must all be integrated.

Autosomal Recessive Inheritance

Autosomal recessive conditions require two copies of the disease-causing allele for the phenotype to manifest. Carriers—individuals heterozygous for one normal and one mutant allele—are typically unaffected. When two carriers reproduce, the probability for each pregnancy is: 1/4 affected, 2/4 carrier, 1/4 non-carrier. This 1:2:1 genotype ratio is the foundation of recessive inheritance calculations.

Carrier Frequency and Hardy-Weinberg Equilibrium

To estimate the probability that an individual from the general population is a carrier for a recessive condition, we use the Hardy-Weinberg equilibrium. If the disease incidence is q² (where q is the frequency of the disease allele), then the carrier frequency is 2pq, where p = 1 − q. For example, cystic fibrosis affects approximately 1 in 2,500 individuals of Northern European ancestry, so q = 1/50, and the carrier frequency is approximately 2 × (49/50) × (1/50) ≈ 1 in 25. This is a critical input for any inheritance calculator: when a partner has no family history of the condition, the prior probability that they are a carrier is derived from population carrier frequency.

Population-Specific Carrier Frequencies

Carrier frequencies vary significantly between populations due to founder effects, genetic drift, and selective pressures. Cystic fibrosis carrier frequency is approximately 1 in 25 in Northern Europeans but much lower in East Asian populations. Sickle cell disease has carrier frequencies as high as 1 in 4 in parts of Sub-Saharan Africa, reflecting the heterozygote advantage against malaria. Tay-Sachs disease has a carrier frequency of approximately 1 in 30 in Ashkenazi Jewish populations compared to 1 in 300 in the general population. A clinically useful inheritance calculator must allow the user to specify or select the relevant population to ensure accurate carrier probability estimation.

Consanguinity and Increased Recessive Risk

Consanguinity—the union of individuals descended from a common ancestor—increases the probability that both partners carry the same recessive allele inherited identical by descent. The coefficient of inbreeding (F) quantifies this risk. First cousins, for example, have F = 1/16. For a rare recessive condition with disease allele frequency q, the risk to offspring of first cousins is approximately q/16 + q²(15/16), which for rare alleles is dominated by the q/16 term—potentially many times higher than the general population risk of q². This is why consanguineous families have a disproportionately higher incidence of rare autosomal recessive conditions.

Recognising Autosomal Recessive Patterns in Pedigrees

In pedigrees, autosomal recessive conditions characteristically affect siblings rather than parents (horizontal pattern); the condition appears to skip generations; parents of affected children are usually unaffected carriers; consanguinity in the parents increases suspicion; and both sexes are affected equally. A key rule for interpreting recessive pedigrees: an unaffected sibling of an affected individual (when both parents are confirmed carriers) has a 2/3 probability of being a carrier, not 1/2. This is because we condition on the observation that they are unaffected, eliminating the 1/4 probability of being homozygous affected.

X-Linked Inheritance

X-linked inheritance involves genes located on the X chromosome. Because males have only one X chromosome (hemizygous), a single mutant allele on the X chromosome is sufficient to produce the phenotype in males. Females, with two X chromosomes, are typically carriers when heterozygous for the mutant allele and are usually unaffected (though manifesting carriers do exist, owing to skewed X-inactivation or other mechanisms).

X-Linked Recessive Inheritance

X-linked recessive is the most common X-linked inheritance pattern encountered in clinical genetics. The key features are: predominantly males are affected; there is no male-to-male transmission (fathers transmit their Y chromosome to sons, not their X); carrier females transmit the mutation to 50% of sons (who will be affected) and 50% of daughters (who will be carriers); affected males transmit the carrier state to all of their daughters and none of their sons.

Bayesian Updating for Carrier Status in X-Linked Pedigrees

One of the most powerful applications of Bayesian analysis in genetics is the updating of X-linked carrier risk based on family observations. Consider a woman whose mother is a confirmed carrier of haemophilia A. Her prior probability of being a carrier is 1/2. If she has three unaffected sons, each son provides conditional evidence against her being a carrier. The posterior probability of her being a carrier, given three unaffected sons, is calculated as:

Her carrier risk drops from 50% to approximately 11%. Each additional unaffected son further reduces the risk. This is a routine calculation in genetic counselling, and an inheritance calculator automates it across the entire pedigree.

Clinical Examples

Well-known X-linked recessive conditions include haemophilia A (factor VIII deficiency, F8 gene) and haemophilia B (factor IX deficiency, F9 gene), Duchenne muscular dystrophy (DMD gene, with approximately one-third of cases arising from de novo mutations), red-green colour blindness (OPN1LW/OPN1MW genes), and glucose-6-phosphate dehydrogenase (G6PD) deficiency. The high de novo mutation rate in Duchenne muscular dystrophy is particularly important for inheritance calculations: a mother of a single affected son with no other family history has a carrier probability of approximately 2/3 (not 1), because one-third of cases are de novo.

Beyond Simple Mendelian: Complex Inheritance

While Mendel's laws provide the framework, human genetics is rarely as straightforward as a textbook Punnett square. Several phenomena complicate the simple Mendelian picture, and a robust inheritance calculator must account for as many of these as possible.

Reduced Penetrance and Variable Expressivity

Reduced penetrance means that some individuals who carry a disease genotype never develop the associated phenotype. Variable expressivity means that among those who do manifest the condition, the severity and specific features can vary widely. Both phenomena make pedigree interpretation more challenging: an apparently unaffected individual in a dominant pedigree may carry the mutation (reduced penetrance), and two affected family members may have very different clinical presentations (variable expressivity). Neurofibromatosis type 1, for example, shows almost complete penetrance but striking variable expressivity—even within the same family.

Germline Mosaicism

Germline (gonadal) mosaicism occurs when a mutation arises during early embryonic development and is present in a proportion of the individual's germ cells but not in somatic cells. The parent may be clinically unaffected (the mutation is not detectable in blood) yet have a recurrence risk that is substantially higher than the general population de novo rate. Germline mosaicism is documented for Duchenne muscular dystrophy (where maternal blood VAF is often far below germline VAF), osteogenesis imperfecta (where two lethal OI neonates from unaffected parents is the classic counselling case), achondroplasia (strong paternal-age effect with measurable sperm VAF), tuberous sclerosis, and the severe epileptic encephalopathies such as Dravet syndrome.

A mosaicism-aware calculator computes a posterior probability distribution over the competing hypotheses — parental germline mosaicism, inherited with reduced penetrance, and true de novo — and a recurrence risk integrated across them. When a somatic variant allele fraction (VAF) from blood, sperm, or saliva sequencing is available, recurrence risk for the next pregnancy is approximately VAF × 0.5 × penetrance for autosomal dominant conditions. Joint-parent logic ensures that confirming mosaicism in one parent properly exonerates the other, rather than leaving both under residual co-suspicion. For the full model and worked scenarios, see our germline mosaicism calculator guide.

De Novo Mutations

De novo mutations are new genetic changes that arise in a gamete or early embryo and are not present in either parent's germline. They are a significant source of autosomal dominant conditions: approximately 50% of neurofibromatosis type 1 cases and approximately one-third of Duchenne muscular dystrophy cases arise de novo. The importance for inheritance calculators is twofold. First, the absence of family history does not rule out a genetic condition. Second, when a de novo mutation is confirmed in a child, the recurrence risk for siblings is low (typically 1–5%, reflecting the possibility of germline mosaicism) rather than the 50% risk that would apply if a parent carried the mutation constitutionally.

Anticipation and Parent-of-Origin Effects

Anticipation—the tendency for certain conditions to become more severe or present at an earlier age in successive generations—is a hallmark of trinucleotide repeat disorders. The direction of anticipation can depend on the sex of the transmitting parent: large expansions in Huntington disease tend to occur during paternal transmission, whereas congenital myotonic dystrophy almost exclusively results from maternal transmission of a greatly expanded repeat.

Genomic imprinting is a separate parent-of-origin effect in which the expression of certain genes depends on whether they were inherited from the mother or the father. The classic examples are Prader-Willi syndrome (loss of paternally expressed genes at 15q11-q13) and Angelman syndrome (loss of the maternally expressed UBE3A gene at the same locus). These conditions do not follow standard Mendelian patterns and require specialised inheritance models.

Locus Heterogeneity and Multifactorial Inheritance

Locus heterogeneity occurs when the same clinical phenotype can be caused by mutations in different genes. Hereditary hearing loss, for example, can result from mutations in any of over 100 genes. This complicates recurrence risk calculation: two affected individuals from different families may carry mutations in different genes, meaning their offspring would be obligate carriers for both but affected for neither (assuming recessive inheritance at each locus). A comprehensive inheritance calculator considers the differential diagnosis and allows the user to specify or test for specific loci.

Many common conditions—heart disease, type 2 diabetes, most cancers—result from the combined effects of multiple genes and environmental factors (multifactorial or polygenic inheritance). These conditions do not follow simple Mendelian patterns. While Mendelian inheritance calculators are not designed for polygenic risk, they remain essential for the subset of families in which a high-penetrance single-gene variant is responsible. For hereditary cancer syndromes, empirical models such as BRCAPRO and MMRpro blend Mendelian genetics with population-level data to provide accurate risk estimates.

How to Calculate Inheritance Probabilities

Mendelian inheritance calculations fundamentally rely on two techniques: Punnett square analysis for determining genotype probabilities in straightforward crosses, and Bayesian updating for incorporating additional evidence (such as phenotypic observations, test results, or reproductive history) to refine those probabilities.

Punnett Squares

A Punnett square is a grid that maps all possible combinations of parental alleles in offspring. For a cross between two carriers of an autosomal recessive condition (genotype Aa × Aa):

The result: 1/4 (25%) probability of being homozygous normal (AA), 2/4 (50%) carrier (Aa), and 1/4 (25%) affected (aa).

Bayesian Updating: A Worked Example

One of the most frequently encountered questions in genetic counselling is: “If both parents are carriers for cystic fibrosis, what is the probability that their unaffected child is a carrier?”

From the Punnett square, the unconditional genotype probabilities for each child are:

• AA (non-carrier): 1/4
• Aa (carrier): 2/4
• aa (affected): 1/4

We know the child is unaffected, which eliminates the aa outcome. We apply Bayes' theorem by conditioning on the observation “unaffected”:

The answer is 2/3 (approximately 67%). This result is counterintuitive to many patients (and some clinicians): the probability of being a carrier is higher than the naive 50% because we have excluded the possibility of being affected but not the possibility of being a carrier. This type of Bayesian updating is central to genetic counselling and is one of the most common operations a Mendelian inheritance calculator performs.

Integrating Genetic Test Results

Bayesian analysis becomes even more powerful when molecular test results are available. If an individual's carrier probability is 2/3 based on pedigree analysis, and they then undergo a carrier screening test with 95% mutation detection rate that returns negative, the posterior carrier probability can be updated:

The negative test result dramatically reduces the carrier probability from 67% to about 9%. This illustrates why inheritance calculators that integrate both pedigree data and molecular results are far more useful than either approach alone.

How Evagene Models Mendelian Inheritance

Evagene is a web-based clinical-grade pedigree management system that integrates Mendelian inheritance calculations directly into the pedigree. Rather than requiring clinicians to perform manual Bayesian calculations or use separate probability tools, Evagene runs the models automatically across the family structure, propagating probabilities from known genotypes and phenotypes to every individual in the pedigree.

Three Built-In Mendelian Models

Evagene includes three Mendelian inheritance models, each configurable to the specific condition under evaluation:

Differential Diagnosis Mode

When the inheritance pattern is uncertain, Evagene's differential diagnosis mode allows clinicians to evaluate multiple inheritance models simultaneously against the same pedigree data. This is particularly useful in families with limited pedigree information, where it may not be clear whether a condition follows autosomal dominant with reduced penetrance, autosomal recessive, or X-linked inheritance. The models can be compared side by side, helping guide further investigation and testing.

Cancer-Specific Empirical Models

For hereditary cancer syndromes, Mendelian models alone may not capture the full complexity of risk. Evagene integrates the BayesMendel suite of empirical models: BRCAPRO for hereditary breast and ovarian cancer (BRCA1/BRCA2), MMRpro for Lynch syndrome (mismatch repair gene mutations), and PancPRO for familial pancreatic cancer. These models combine Mendelian transmission genetics with population-level cancer incidence data, sensitivity/specificity of molecular tests, and phenocopy rates to produce calibrated carrier and cancer risk predictions. For more on hereditary cancer risk assessment, see our guide to hereditary cancer risk assessment.

For detailed documentation on Evagene's risk analysis capabilities and how to configure inheritance models within pedigrees, visit the Evagene help centre.

Frequently Asked Questions

Related Resources