Unit 5: Heredity

Meiosis and the Concept of Heredity

• Meiosis is a specialized type of cell division that reduces the chromosome number by half, producing four genetically unique haploid gametes from one diploid parent cell. This reduction is essential for maintaining chromosome stability across generations, as fertilization restores the diploid state. The process occurs in two main stages, meiosis I and meiosis II, each with its own phases that contribute to genetic diversity.
• Genetic variation in meiosis arises primarily through two mechanisms: crossing over and independent assortment. Crossing over occurs during prophase I when homologous chromosomes exchange segments, producing recombinant chromosomes with new allele combinations. Independent assortment in metaphase I shuffles maternal and paternal chromosomes randomly into gametes, creating vast genetic possibilities.
• The connection between meiosis and heredity lies in how gametes carry only one set of alleles for each gene, ensuring that offspring inherit half their genetic material from each parent. This explains why traits can reappear after skipping a generation — alleles are preserved in gametes even if they are not expressed in the parent. Without meiosis, sexual reproduction would double chromosome numbers each generation, disrupting genetic stability.
• Errors in meiosis, such as nondisjunction, can lead to abnormal chromosome numbers, causing conditions like Down syndrome (trisomy 21) or Turner syndrome (monosomy X). These events occur when homologous chromosomes or sister chromatids fail to separate properly, highlighting the importance of precise chromosome segregation. Such mistakes underline why meiosis is heavily regulated by checkpoints.
• Meiosis connects directly to evolutionary biology because the variation it produces fuels natural selection. Populations with higher genetic diversity have a greater capacity to adapt to environmental changes, resist diseases, and avoid extinction. Thus, meiosis is both a cellular process and a driver of biodiversity.

Mendelian Genetics

• Mendelian genetics is based on Gregor Mendel’s experiments with pea plants, which revealed that traits are inherited as discrete units called genes. Mendel’s work established the law of segregation and the law of independent assortment, which explain how alleles separate into gametes and how different genes are inherited independently. These principles form the foundation of classical genetics.
• The law of segregation states that each organism has two alleles for every gene, which separate during gamete formation so each gamete carries only one allele. This explains why offspring can inherit recessive traits even if the trait is not visible in either parent. Meiosis provides the biological basis for this principle, as homologous chromosomes separate during anaphase I.
• The law of independent assortment describes how alleles of different genes are distributed randomly into gametes, producing new genetic combinations. This principle applies to genes located on different chromosomes or far apart on the same chromosome. Crossing over can further randomize combinations, enhancing genetic variability beyond Mendel’s original observations.
• Monohybrid crosses track the inheritance of a single trait, producing a characteristic 3:1 phenotype ratio in the F2 generation when heterozygous parents are crossed. Dihybrid crosses, involving two traits, typically yield a 9:3:3:1 phenotypic ratio under complete dominance. These predictable ratios allow biologists to infer genotypes from observed phenotypes.
• Mendel’s principles remain essential for AP Biology because they apply broadly to many species, but students must recognize that they have limitations. Complex traits, linkage, gene interactions, and environmental factors can alter expected Mendelian ratios, making modern genetics a blend of Mendel’s laws and newer molecular insights.

Non-Mendelian Inheritance

• Non-Mendelian inheritance includes any genetic pattern that does not follow the classic Mendelian ratios of dominant and recessive traits. This category covers mechanisms like incomplete dominance, codominance, multiple alleles, polygenic traits, and pleiotropy. Understanding these patterns is essential because most traits in living organisms do not fit perfectly into Mendel’s original model.
• Incomplete dominance occurs when the phenotype of the heterozygote is intermediate between those of the two homozygotes. For example, crossing a red-flowered snapdragon with a white-flowered one produces pink flowers. This blending effect arises because neither allele is completely dominant, but the alleles remain distinct at the genetic level.
• Codominance describes situations in which both alleles in a heterozygote are fully expressed without blending. A common example is the ABO blood group system, where individuals with genotype IAIB express both A and B antigens on their red blood cells. This pattern shows that dominance relationships can vary by gene and context.
• Multiple alleles occur when a gene has more than two possible forms in a population, although any individual can carry only two alleles at a time. The ABO blood group again illustrates this, with three alleles (IA, IB, i) interacting in various combinations. This increases phenotypic diversity beyond the two-allele scenario Mendel studied.
• Polygenic traits, such as skin color, height, and eye color, are influenced by the additive effects of multiple genes. These traits display continuous variation rather than discrete categories, producing a bell-shaped distribution in populations. Pleiotropy, on the other hand, occurs when a single gene affects multiple traits, as seen in Marfan syndrome affecting connective tissue in many body systems.

Sex-Linked Inheritance and Pedigrees

• Sex-linked inheritance refers to traits controlled by genes located on sex chromosomes, most often the X chromosome in humans. Because males have only one X chromosome, they are more likely to express recessive X-linked traits like hemophilia or red-green color blindness. Females, with two X chromosomes, must inherit two copies of the recessive allele to express the trait.
• X-linked dominant traits are expressed in both sexes but often more severely in males, since they have only one copy of the gene. Fathers with an X-linked dominant trait will pass it to all their daughters but none of their sons, while mothers can pass it to both sons and daughters. This creates predictable patterns in pedigrees that can be used to identify inheritance type.
• Y-linked traits are much rarer because the Y chromosome contains fewer genes, mostly related to male sex determination and spermatogenesis. These traits are passed strictly from father to son, creating a unique vertical inheritance pattern in pedigrees. An example is certain types of male infertility linked to deletions on the Y chromosome.
• Pedigree analysis is a key tool for tracing inheritance patterns across generations. Circles represent females, squares represent males, and shading indicates the expression of the trait. Autosomal traits appear equally in both sexes, while sex-linked traits often show distinctive gender-related trends.
• Interpreting pedigrees requires understanding dominance relationships, carrier states, and how gene location affects inheritance. For AP Biology, students should be able to determine whether a trait is autosomal dominant, autosomal recessive, X-linked dominant, X-linked recessive, or Y-linked by analyzing the diagram’s structure and generational patterns.

Chromosomal Basis of Inheritance

• The chromosomal basis of inheritance links Mendel’s laws to the physical behavior of chromosomes during meiosis. Genes are located on chromosomes, and their segregation and independent assortment occur because of how chromosomes align and separate in meiosis I. This concept, proposed by Sutton and Boveri, unified genetics and cytology into a single theory of heredity.
• Homologous chromosomes carry the same genes but may have different alleles, and their separation in anaphase I explains Mendel’s law of segregation. Similarly, the random alignment of homologous pairs during metaphase I accounts for the law of independent assortment. Crossing over in prophase I adds another layer of variability, which Mendel’s laws did not originally explain.
• Linkage occurs when two genes are located on the same chromosome and tend to be inherited together. The closer the genes are on a chromosome, the less likely they are to be separated by crossing over. This violates the expected 9:3:3:1 ratio from dihybrid crosses, and linkage maps can be created using recombination frequencies to estimate distances between genes.
• Sex determination is another aspect of chromosomal inheritance, with different organisms using different systems (e.g., XY in humans, ZW in birds, XO in insects). The presence or absence of certain chromosomes, such as the Y chromosome carrying the SRY gene in humans, determines the development of sexual characteristics. This means inheritance patterns can be influenced by the specific chromosome involved.
• Chromosomal behavior during meiosis not only ensures genetic diversity but also plays a role in evolutionary processes. Natural selection can act on linked genes differently than on unlinked ones, affecting genetic variation in a population. Understanding chromosome dynamics helps explain both predictable inheritance patterns and exceptions to Mendel’s rules.

Chromosomal Mutations and Disorders

• Chromosomal mutations involve changes in chromosome structure or number, which can have major effects on phenotype. Structural mutations include deletions, duplications, inversions, and translocations, each altering the arrangement of genetic material. These changes can disrupt gene function or regulation, sometimes leading to serious health conditions.
• Deletions remove a segment of DNA, potentially eliminating essential genes, as seen in Cri-du-chat syndrome caused by deletion on chromosome 5. Duplications repeat a segment, increasing gene dosage and potentially causing developmental abnormalities. Inversions reverse the orientation of a chromosome segment, which can disrupt meiosis if crossing over occurs in the inverted region.
• Translocations occur when a segment of one chromosome is transferred to another nonhomologous chromosome. Balanced translocations may not cause symptoms in carriers but can lead to infertility or genetic disorders in offspring due to unbalanced gametes. Chronic myelogenous leukemia is associated with a specific reciprocal translocation known as the Philadelphia chromosome.
• Numerical abnormalities, called aneuploidies, result from nondisjunction during meiosis, where chromosomes fail to separate properly. Trisomy conditions like Down syndrome (trisomy 21) and sex chromosome disorders like Klinefelter syndrome (XXY) or Turner syndrome (XO) illustrate how extra or missing chromosomes affect development. The severity often depends on which chromosome is involved.
• Polyploidy, the presence of more than two complete sets of chromosomes, is rare in animals but common in plants, often producing larger and more robust individuals. While lethal in most animals, polyploidy can drive rapid speciation in plants. This shows that not all chromosomal changes are harmful — some can be evolutionary advantages in certain contexts.

Linkage and Gene Mapping

• Genetic linkage occurs when two or more genes are located close together on the same chromosome and tend to be inherited together. Because crossing over during meiosis is less likely to separate genes that are close together, linked genes do not follow the independent assortment ratios predicted by Mendel. This phenomenon was first observed in fruit flies by Thomas Hunt Morgan, who studied the inheritance of eye color and wing shape.
• Recombination frequency measures how often crossing over separates two linked genes, expressed as a percentage. A recombination frequency of 1% corresponds to one map unit (centimorgan) of distance between genes. This allows scientists to create linkage maps, which are diagrams showing the relative positions of genes on a chromosome.
• Complete linkage means genes are so close together that no recombination is observed between them, and they are inherited as a single unit. In contrast, partial linkage allows for some recombinant offspring, with recombination rates increasing as the genes are farther apart. The maximum observable recombination frequency is 50%, which occurs when genes are far apart on the same chromosome or on different chromosomes.
• Mapping experiments often involve test crosses between heterozygotes for linked genes and homozygous recessives. The phenotypes of offspring are counted to determine recombination frequencies. By combining data from multiple gene pairs, scientists can construct more comprehensive chromosome maps.
• Although linkage maps are useful, they are not physical maps — they show relative positions based on recombination rather than exact DNA sequence distances. Advances in molecular genetics, such as genome sequencing, have confirmed and refined linkage map data. Understanding linkage helps explain why certain traits are inherited together more often than expected.

Patterns of Inheritance in Populations

• Patterns of inheritance at the population level are studied through population genetics, which examines how allele frequencies change over time. The Hardy–Weinberg equilibrium model provides a baseline for predicting genetic variation in an idealized, non-evolving population. This model assumes random mating, no mutation, no migration, no selection, and a large population size.
• The Hardy–Weinberg equation, \( p^2 + 2pq + q^2 = 1 \), describes the expected genotype frequencies in a population, where \( p \) is the frequency of the dominant allele and \( q \) is the frequency of the recessive allele. If observed frequencies differ significantly from predicted values, it indicates that one or more of the equilibrium conditions have been violated. This is a powerful tool for detecting evolutionary forces acting on a population.
• Gene flow, mutation, genetic drift, and natural selection are major forces that can change allele frequencies. Genetic drift, which is more significant in small populations, includes effects like the bottleneck effect (sharp population reduction) and the founder effect (new population established by a small group). These random changes can reduce genetic diversity and increase the prevalence of rare alleles.
• Non-random mating, such as assortative mating or inbreeding, can also shift genotype frequencies without necessarily changing allele frequencies. Inbreeding increases homozygosity, which can expose harmful recessive traits. Assortative mating for certain phenotypes can influence how traits are distributed in a population.
• Studying inheritance in populations helps biologists understand both microevolutionary changes and long-term evolutionary patterns. For example, the persistence of harmful alleles like sickle-cell anemia in certain populations can be explained by heterozygote advantage, where carriers have increased fitness in malaria-endemic regions. This demonstrates that inheritance patterns are shaped by both genetic rules and environmental pressures.

Gene–Environment Interactions

• Gene–environment interactions describe how the expression of genetic traits can be influenced by environmental conditions. Even individuals with identical genotypes can show different phenotypes depending on environmental factors like temperature, nutrition, stress, or exposure to toxins. This explains why traits are not solely determined by DNA but are also shaped by life experiences.
• Classic examples include coat color in Himalayan rabbits, which turns darker in colder body regions, and hydrangea flowers changing color depending on soil pH. In humans, height is influenced by both genes and nutritional availability, while predispositions for certain diseases may only manifest under specific environmental triggers. These cases demonstrate that environment can modulate the penetrance and expressivity of genes.
• Some environmental effects occur during critical developmental windows, meaning timing can be as important as the nature of the exposure. For example, prenatal exposure to alcohol can cause fetal alcohol spectrum disorders even if the genetic background is healthy. Conversely, a favorable environment can buffer the effects of certain harmful alleles.
• Epigenetic changes — chemical modifications to DNA or histones that alter gene activity without changing the sequence — are a major mechanism through which environment influences genes. Diet, stress, and environmental toxins can induce epigenetic changes, which sometimes persist across generations. This adds complexity to inheritance beyond simple Mendelian rules.
• Understanding gene–environment interactions is essential for fields like personalized medicine and public health. It allows scientists to identify at-risk individuals and design interventions that minimize harmful environmental influences or maximize beneficial ones. This knowledge also helps explain why genetically similar individuals can have very different health outcomes.

Probability Rules in Genetics

• Probability rules in genetics are used to predict the likelihood of offspring inheriting specific traits. Mendelian genetics applies the same basic probability principles found in mathematics, particularly the multiplication and addition rules. These predictions are essential for solving monohybrid and dihybrid cross problems accurately.
• The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities. For example, if the probability of inheriting a dominant allele from one parent is ½ and from the other parent is also ½, the probability of being homozygous dominant is \( \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \). This is used for calculating the chance of combined genotypes.
• The addition rule applies when determining the probability of one event OR another occurring. For example, the probability of being heterozygous (Aa) from a cross between Aa × Aa is the sum of the probabilities of inheriting A from one parent and a from the other (¼) plus a from one parent and A from the other (¼), totaling ½. This is important for calculating phenotypic ratios.
• When traits follow independent assortment, probabilities from different genes can be multiplied. However, linked genes require adjusted methods because their inheritance is not independent. Recognizing when to apply each probability rule is critical for solving genetic problems correctly.
• Probability calculations can also be extended to more complex genetic situations such as multiple alleles, incomplete dominance, and polygenic traits. Using these rules allows scientists and breeders to predict inheritance patterns and make informed decisions in research, agriculture, and medicine.

Chi-Square Analysis in Genetics

• Chi-square (\( \chi^2 \)) analysis is a statistical test used in genetics to determine whether observed results differ significantly from expected results based on a hypothesis. It is particularly useful for testing whether experimental data fit Mendelian inheritance ratios. This allows scientists to distinguish between random variation and genuine deviation from expected outcomes.
• The formula for chi-square is \( \chi^2 = \sum \frac{(O - E)^2}{E} \), where \( O \) is the observed frequency and \( E \) is the expected frequency. Each category’s difference is squared to remove negative values, then divided by the expected value to standardize the contribution. The sum of all these values is compared against a chi-square distribution table.
• The degrees of freedom (df) for chi-square in genetics are calculated as the number of categories minus 1. Using the calculated \( \chi^2 \) value and the degrees of freedom, a p-value is obtained to determine statistical significance. A common threshold is p = 0.05, meaning there is only a 5% chance that observed deviations are due to random variation.
• If the chi-square test shows no significant difference between observed and expected values (p > 0.05), the null hypothesis that the data fit the expected ratio is accepted. If p ≤ 0.05, the null hypothesis is rejected, suggesting that factors like linkage, experimental error, or incorrect assumptions may be affecting the results. This is an essential step in validating genetic models.
• Chi-square analysis is widely used in both classical genetics and modern molecular studies. It helps researchers verify inheritance patterns, test predictions, and identify when traits deviate from expected Mendelian ratios. Mastery of this method ensures more accurate interpretation of experimental data.

How to Use Chi-Square Analysis in Genetics

When and Why to Use \(\chi^2\) in Genetics

• Use the chi-square (\(\chi^2\)) test to decide whether your observed offspring counts are consistent with an expected Mendelian ratio (e.g., 3:1, 1:1, 9:3:3:1). It answers, “Are the differences just sampling error, or do they suggest a real biological effect like linkage or selection?” This moves you beyond eyeballing percentages and gives a formal, quantitative decision.
• \(\chi^2\) compares each category’s observed count \((O)\) to its expected count \((E)\) under a genetic hypothesis you specify first. The test sums the standardized differences across all categories so one big mismatch or many small ones both contribute. Because it uses counts, it fits Punnett-square predictions perfectly.
• Typical AP Bio uses include monohybrid and dihybrid crosses, testcrosses, and independence (linkage) checks. If a dihybrid cross deviates strongly from 9:3:3:1, \(\chi^2\) helps evaluate whether genes may be linked rather than independently assorting. It also applies to 1:1 or 1:2:1 expectations from testcrosses and incomplete dominance scenarios.
• Always choose your expected ratio based on a clear hypothesis tied to meiosis: segregation predicts 1:2:1 genotypes; independent assortment predicts 9:3:3:1 phenotypes for two genes. If your hypothesis changes (e.g., “genes are linked”), you must update the expected proportions accordingly. The test evaluates the fit to the hypothesis you state, not whether your data are “good” in general.
• The decision rule uses a p-value (commonly \( \alpha = 0.05 \)) with degrees of freedom \(df=\text{#categories}-1\). If \(p>0.05\) (or \(\chi^2\) is below the critical value), you fail to reject the null: deviations likely come from chance. If \(p\le 0.05\), you reject the null and consider biological explanations like linkage, selection, or scoring errors.

Step-by-Step Procedure (Exam-Ready)

• 1) State the null hypothesis \(H_0\): “Observed counts fit the expected genetic ratio.” For example, for a monohybrid phenotype cross of two heterozygotes, \(H_0\): 3 tall : 1 short. The alternative hypothesis \(H_a\) is that the data do not fit that ratio.
• 2) Compute expected counts from your total \(N\) using the ratio fractions. For a 3:1 model and \(N=160\), the expectations are \(E_{\text{tall}}=0.75\times160=120\) and \(E_{\text{short}}=0.25\times160=40\). Expectations must be in counts, not just proportions.
• 3) Use the chi-square formula: \[ \chi^2=\sum \frac{(O-E)^2}{E} \] Do this for each phenotype category and then sum. Show your work clearly to earn method points on FRQs.
• 4) Find \(df\) as \(\text{#categories}-1\). A 3:1 test has 2 categories \(\Rightarrow df=1\); a 9:3:3:1 has 4 categories \(\Rightarrow df=3\). The df must match exactly how many categories you tested.
• 5) Decision: compare your \(\chi^2\) to the critical value at \(p=0.05\) and your \(df\), or compute a p-value. If \(\chi^2\) is smaller than the critical value, the deviation is not significant and you keep \(H_0\); if larger, you reject \(H_0\) and investigate causes (e.g., linkage).

Worked Example — Monohybrid 3:1 (Tall vs. Short)

• Setup: Cross \(Tt \times Tt\); expect 3 tall : 1 short. Observed in \(N=160\): 130 tall, 30 short. Null hypothesis: “Data fit a 3:1 ratio.” This is the classic single-trait chi-square scenario.
• Expected counts: \(E_{\text{tall}}=0.75\times160=120\), \(E_{\text{short}}=0.25\times160=40\). Writing both expected counts is essential to show your ratio translation. Keep totals consistent (\(120+40=160\)).
• Compute \(\chi^2\): Tall: \(\frac{(130-120)^2}{120}=\frac{100}{120}\approx0.833\). Short: \(\frac{(30-40)^2}{40}=\frac{100}{40}=2.5\). Sum: \(\chi^2\approx0.833+2.5=3.333\).
• Degrees of freedom: \(df=2-1=1\). Critical value at \(p=0.05\) and \(df=1\) is \(3.841\). You can memorize common critical values (e.g., \(df=1\Rightarrow3.841\); \(df=3\Rightarrow7.815\)) to move fast.
• Decision & conclusion: \(3.333<3.841\Rightarrow\) fail to reject \(H_0\). The data are consistent with a 3:1 Mendelian ratio; observed deviations are likely sampling error. State your conclusion in context: “Tall vs. short fits 3:1 at \(\alpha=0.05\).”

Dihybrid Crosses, Linkage, and Expected Ratios

• For two independently assorting genes in a dihybrid cross (\(AaBb \times AaBb\)), the expected phenotypic ratio is \(9:3:3:1\) across four categories. Translate that to proportions (0.5625, 0.1875, 0.1875, 0.0625) and multiply by \(N\) to get each \(E\). Use all four categories in your \(\chi^2\) sum (so \(df=3\)).
• If genes are linked, the 9:3:3:1 expectation is wrong; parental phenotypes will be over-represented and recombinants under-represented. A large \(\chi^2\) (small p) against 9:3:3:1 suggests non-independence and motivates a linkage hypothesis. You can then compute recombination frequency to estimate map distance (not part of \(\chi^2\) itself, but a common follow-up).
• In testcrosses (\(AaBb \times aabb\)), expect 1:1:1:1 if genes assort independently. Mark observed counts for each phenotype class, compute \(E=N/4\) for all four, and proceed with \(df=3\). Significant deviation suggests linkage or selection bias.
• If any expected count drops below 5, \(\chi^2\) assumptions weaken. Combine sparse categories logically (e.g., combine both recombinant classes) or increase sample size to keep \(E\ge5\). AP graders expect you to note this limitation if it appears.
• Always align your categories with your biological hypothesis first (independent assortment vs. linkage). The statistic only tests consistency with the model you chose; it doesn’t pick the model for you. Clear hypothesis → correct expected ratios → valid inference.

Interpreting p-Values, Degrees of Freedom, and Writing Conclusions

• Degrees of freedom reflect how many independent categories you’re testing: \(df=\text{#categories}-1\). Monohybrid (2 cats) → \(df=1\); dihybrid (4 cats) → \(df=3\). If you collapse categories, recalculate \(df\) accordingly.
• Decision rule: compare \(\chi^2\) to the critical value at \(p=0.05\) for your \(df\), or report the p-value if provided. \(\chi^2\) smaller than the threshold → “fail to reject \(H_0\)” (fits the ratio); larger → “reject \(H_0\)” (does not fit). Never say “prove” or “accept” — stick to “reject” or “fail to reject.”
• Contextual conclusion is crucial for full credit: name the cross, ratio, and what your result means biologically. Example: “Our dihybrid data do not fit 9:3:3:1 at \(\alpha=0.05\), suggesting the two genes are not assorting independently and may be linked.”
• Direction of deviation can hint mechanism: excess parentals + deficit recombinants → linkage; systematic excess of one phenotype → selection or viability differences. The \(\chi^2\) test flags significance; your genetics reasoning explains why.
• Replication & sample size matter: small \(N\) inflates sampling noise and can hide real effects. Larger, replicated samples stabilize expected counts and strengthen conclusions on AP investigations and FRQs.