Heredity

A gene is a hereditary unit associated with a DNA sequence; an allele is a variant. Homologous chromosomes carry corresponding gene locations but need not carry identical alleles. Probability multiplication requires the appropriate independence or conditional-probability assumptions.

One DNA replication is followed by two divisions. Homologous chromosomes pair and then separate in meiosis I; sister chromatids usually separate in meiosis II. The result is haploid products with one chromosome from each homologous pair. Fertilization restores the diploid number. Homologs carry the same types of genes but can have different alleles.

Crossing over between nonsister chromatids of homologs can create new allele combinations. Independent assortment results from the orientation of homologous pairs at meiosis I. Random fertilization adds variation. These processes reshuffle existing alleles; mutation is the ultimate source of new alleles.

For an Aa × Aa cross with complete dominance and equal survival, the genotype probabilities are 14 AA, 12 Aa, and 14 aa. The phenotype ratio is 3 dominant to 1 recessive, not 3 AA to 1 aa. A ratio gives an expectation across many offspring, not a fixed schedule for each family.

Multiply probabilities for independent events that must occur together; add probabilities for mutually exclusive alternatives. A dihybrid 9:3:3:1 phenotype ratio requires suitable independent assortment, complete dominance at both loci, and other assumptions. Linkage, epistasis, differential survival, or sampling can produce other observed patterns.

Dominance describes a heterozygote’s phenotype relative to the homozygotes. A dominant allele need not be common, beneficial, or molecularly more abundant. In incomplete dominance, the heterozygote has a distinct intermediate phenotype. In codominance, both allele-associated products or traits are detectable.

Multiple genes can contribute to one phenotype, and one gene can affect multiple traits. Environmental conditions can also influence gene expression and phenotype. A continuous trait distribution often reflects combined genetic and environmental effects rather than a single simple dominant–recessive pair.

Genes on the same chromosome can be inherited together more often than an independent-assortment model predicts. In a testcross, offspring classes can reveal the gametes produced by the heterozygous parent. The more frequent classes usually identify parental combinations when the design meets the standard linkage assumptions.

Recombination frequency is recombinant offspring divided by total offspring. For relatively short intervals, a percentage approximates map distance in centimorgans. A frequency near 50% does not establish that genes lie on different chromosomes: widely separated loci on the same chromosome can also appear unlinked because multiple crossovers hide some recombination events.

Pedigrees constrain possible genotypes but do not always uniquely identify inheritance mode. Small families can fit more than one model. In typical X-linked recessive inheritance, a male receives his X chromosome from his mother; father-to-son transmission of an X-linked allele does not occur.

A chi-square goodness-of-fit comparison measures deviations from a stated expected distribution. Expected counts come from the model and total sample size, not from rounding observations into a convenient ratio. A large P-value means insufficient evidence to reject the model, not proof that it is true. Nondisjunction and extranuclear inheritance require models beyond simple Mendelian segregation.

Crossing over exchanges DNA between nonsister chromatids of homologous chromosomes during prophase I. Independent assortment reflects the random orientation of homologous pairs at metaphase I. Random fertilization combines independently produced gametes. These processes reshuffle alleles; mutation is the ultimate source of new allele sequences. Saying that meiosis “creates new genes” confuses reshuffling with mutation.

In meiosis I, homologous chromosomes separate while sister chromatids ordinarily remain together. In meiosis II, sister chromatids separate. One DNA replication followed by two divisions reduces chromosome-set number. Nondisjunction can occur when homologs or sister chromatids fail to separate, producing gametes with abnormal chromosome numbers. Follow the specific division in a diagram instead of memorizing one universal outcome.

Start with the parental genotypes and list the gametes each parent can produce. For Aa × Aa, each parent contributes A or a with probability one-half, so the offspring probabilities are one-quarter AA, one-half Aa, and one-quarter aa. The phenotype ratio depends on the relationship between alleles. Complete dominance, incomplete dominance, and codominance can produce different phenotype patterns from the same genotype probabilities.

For unlinked loci, multiplication can combine separate probabilities. Linked loci require gamete frequencies that reflect recombination rather than an automatic one-quarter for every gamete type. In X-linked inheritance, identify the sex chromosomes carried by each gamete and distinguish the probability among all offspring from the probability conditional on being a son or daughter. A probability is an expected long-run frequency, not a guarantee for a small family.

A pedigree can rule out simple inheritance models when a required pattern is impossible under the stated assumptions. Unaffected parents with an affected child can fit recessive inheritance; father-to-son transmission argues against a simple X-linked model. But incomplete penetrance, new mutations, and small families can complicate real pedigrees. Use the model specified in the question and explain the decisive relationship rather than guessing from visual frequency.

A chi-square statistic compares observed and expected counts under a model. Larger differences contribute more, but each squared difference is divided by its expected count. State the null hypothesis and use the appropriate degrees of freedom. Failing to reject the null means the data are not sufficiently inconsistent with the model; it does not prove the model true. A significant result indicates poor fit, not which alternative mechanism is correct.

Homologous chromosomes carry corresponding gene loci and can carry different alleles. In a diploid organism, one homolog usually came from each parent. Sister chromatids are the copies made when a chromosome replicates. Before recombination, they are ordinarily nearly identical copies of the same homolog. A homologous pair and a pair of sister chromatids are therefore different structures, even when a simplified drawing makes both look like paired rods.

Ploidy counts complete chromosome sets. Replication copies DNA without adding a new set of homologous chromosomes. A diploid cell remains diploid after S phase, although its DNA amount doubles. Counting chromosomes by centromeres gives the same chromosome count before and after replication while sisters remain joined. After sister separation, each former chromatid is counted as a chromosome. Always specify whether you are counting the whole cell, one nucleus or one future daughter.

For a species with 2n=6, a diploid cell has three homologous pairs. After replication it has six duplicated chromosomes and twelve chromatids. A normal final gamete has one member of each pair: three chromosomes. The letter n describes the set number, not a universal number of chromosomes. A species with a different karyotype can have a different n while obeying the same logic.

DNA replication precedes meiosis I. Homologous chromosomes pair, and the members of each pair are separated into different daughter nuclei during the first division. Because each daughter receives one homolog from each pair, the number of sets is reduced. The chromosomes are still duplicated at this stage. Meiosis II separates sister chromatids without another round of DNA replication between the two divisions.

Imagine a maternal homolog carrying allele A and a paternal homolog carrying allele a. Before replication there are two chromosomes. After replication each has two sisters. Meiosis I separates the A-bearing homolog from the a-bearing homolog, ignoring crossing over for this simple model. Meiosis II separates each homolog’s sisters. Each final nucleus contains one allele at that locus, not the original pair. Fertilization can restore a diploid combination.

After meiosis I, a nucleus is haploid even though each chromosome still has two chromatids. A common mistake is to label it diploid simply because duplicated structures are visible. State which homologs are present, rather than judging ploidy from the amount of DNA. In many animals the divisions produce cells that undergo further development into functional gametes; the four nuclei need not become four equivalent eggs.

The orientation of one homologous pair at metaphase I can be independent of another pair. Different orientations generate different combinations of maternal and paternal homologs in gametes. Ignoring crossing over, n independently assorting pairs allow 2ⁿ chromosome-origin combinations. This calculation counts combinations under its assumptions; it is not the number of alleles, genes or offspring a parent must produce.

During prophase I, nonsister chromatids of homologous chromosomes can exchange corresponding DNA segments. A chromosome can therefore contain a new combination of alleles already present in the parental homologs. Crossing over is not the same as mutation: ordinary reciprocal recombination rearranges existing information rather than requiring a new allele to arise. Sisters can differ after a crossover involving one of them.

Which gametes unite introduces further combinations. Independent assortment, recombination and fertilization contribute to variation, but their effects should not be added as if they were identical counts. Nearby loci on the same chromosome may remain associated more often than independently assorting loci. To predict a cross, first identify whether the question gives independent assortment, linkage or a measured recombination frequency.

A genotype records alleles at the loci being considered. A phenotype is a measurable feature produced by genotype interacting with biological and environmental conditions. In a simple complete-dominance model, AA and Aa share the dominant phenotype, while aa shows the recessive phenotype. The model does not say the two genotypes have identical molecular activity or that every trait follows complete dominance.

Dominant does not mean common, beneficial, stronger or evolutionarily superior. It describes how alleles relate to the phenotype in a heterozygote for the trait being measured. A rare allele can be dominant, and a common allele can be recessive. A capital letter is notation chosen to represent a stated relationship; it is not experimental evidence for that relationship.

An individual with a dominant phenotype could be AA or Aa. Crossing it with aa makes the offspring informative because the tester contributes only a. Recessive offspring demonstrate that the unknown parent supplied a, under the simple model. A finite sample containing only dominant offspring supports but does not prove AA: an Aa parent can produce such a sample by chance.

For independent events, multiply probabilities to find the probability they occur together. In Aa×Aa, a particular offspring receives a from each parent with probability 12×12=14. Independent births under the same model do not “use up” that probability. After three dominant-phenotype offspring, the next offspring is not owed the recessive phenotype.

For mutually exclusive routes to the same event, add their probabilities. A heterozygote can receive A from the first parent and a from the second, or the reverse. Each route has probability 14, so the total is 12. Adding is appropriate because a single offspring cannot follow both distinct allele-origin routes simultaneously. For overlapping events, direct addition would double-count the overlap.

The probability that an offspring is Aa is not the same as the probability that it is Aa given a dominant phenotype. In Aa×Aa, the surviving possibilities after conditioning on dominant phenotype are AA, Aa and aA, so the conditional heterozygote probability is 23. The condition changes which outcomes are in the denominator; it does not change how meiosis occurred.

For an AaBb individual whose loci assort independently, AB, Ab, aB and ab gametes each have probability 14. These symbols describe gametes, not diploid offspring. Combining gametes from both parents produces offspring genotypes. A frequent error is to write Aa as a gamete from a standard diploid parent: normal meiosis gives one allele per locus to each haploid gamete.

For AaBb×AaBb with independent assortment, complete dominance at both loci, no interacting phenotype classification and equal survival, the two dominant phenotypes occur together with probability 34×34=916. The other phenotype classes have probabilities 316, 316 and 116. Linkage, gene interactions or differential survival can change this pattern. A ratio is the output of a model, not a replacement for its assumptions.

A test cross AaBb×aabb can reveal the gametes of the heterozygous parent because the tester supplies ab. With independent assortment and equal viability, four offspring classes are expected equally. Large departures may motivate a linkage model, but phenotype scoring or survival differences are alternatives to consider. Keep raw counts and biological mechanisms separate until the evidence connects them.

In incomplete dominance, a heterozygote can have a phenotype intermediate between the two homozygotes. In codominance, distinct contributions from both alleles can be detected in the heterozygote. Neither pattern requires alleles to stop segregating. An Rr×Rr cross still predicts a 1:2:1 genotype ratio under normal segregation; whether that is also the phenotype ratio depends on how genotypes are expressed.

An intermediate phenotype does not mean parental alleles permanently merge. If a red homozygote and a white homozygote produce pink heterozygotes, crossing heterozygotes can recover both parental phenotypes. The discrete alleles persist even though the heterozygote’s phenotype is intermediate. Molecular dose, enzyme activity and pathway behavior can connect genotype with the measured phenotype.

A population may contain more than two alleles at a locus, but a typical diploid individual still carries at most two copies of that locus. In the ABO model, Iᴬ and Iᴮ are codominant and each is dominant over i. An IᴬIᴮ individual is AB, not an intermediate halfway between A and B. Always use the allele relations provided for the trait.

Use Xᴬ and Xᵃ to keep the allele attached to the chromosome carrying it. In the standard XX/XY model for a locus absent from Y, an XY individual has one copy of the X-linked locus. A recessive allele on that X can therefore be expressed without a second recessive copy. This is hemizygosity, not proof that the allele became dominant. These are model assumptions, not a claim that all organisms use the same sex-determination system.

An XY father transmits his X to daughters and his Y to sons in this model. An XX mother can transmit either X to offspring of either sex. For XᴬXᵃ×XᴬY, half the sons are expected to receive Xᵃ and show a fully penetrant recessive trait. Daughters receive the father’s Xᴬ, so none are expected to show that recessive phenotype under the simple model.

Half of the sons is not half of all offspring. If the sex probability is one-half, the probability of an affected son among all offspring is 12×12=14. If the question already states that the offspring is a son, do not multiply by the sex probability again. State whether the denominator includes all offspring or only one group.

A simple pedigree problem may assume full penetrance, no new mutation and an autosomal or X-linked single-locus trait. Under an autosomal recessive model, two unaffected parents can both be carriers and have an affected child. Under a fully penetrant autosomal dominant model without a new mutation, two unaffected parents would not produce an affected child. Changing these assumptions can change which models remain plausible.

An affected individual in an autosomal recessive model is aa. An unaffected parent of an affected child must supply a and also have A, so Aa is justified. An unaffected sibling could be AA or Aa; do not fill in a unique genotype without evidence. Conditional probabilities can resolve some questions even when the exact genotype remains uncertain. Keep unknowns explicit rather than letting a neat diagram imply certainty.

A pattern appearing only in males in one small pedigree does not prove X linkage. Chance can produce a sex imbalance for an autosomal trait. Father-to-son transmission is inconsistent with direct transmission of a paternal X-linked allele under the standard model, but family phenotypes alone may still have alternative explanations. Use multiple informative relationships and explain which model each observation constrains.

For a simple Aa×Aa cross with complete dominance and equal viability, the null phenotype probabilities are 34 and 14. In 160 offspring, expected counts are 120 and 40. Expected counts come from the null model and the total sample size; they are not the observed counts rounded into a convenient ratio. Categories should be mutually exclusive and observations independent for the usual goodness-of-fit procedure.

Calculate χ²=Σ((O−E)²E). If observations are 112 dominant and 48 recessive, the contributions are 64120 and 6440, totaling about 2.13. Squaring prevents positive and negative departures from canceling, while dividing by E scales each discrepancy. With two categories and no parameters estimated from these data, degrees of freedom are one. Small expected counts can undermine the usual approximation.

Using a stated significance level and reference threshold, decide whether to reject the null model. Failing to reject means the evidence is insufficient to detect a departure at that threshold; it does not prove the biological model true. Rejecting a ratio does not uniquely identify linkage, viability differences or scoring error. Statistical evidence motivates a biological explanation and follow-up.

Temperature, nutrition, light and other environmental conditions can change the expression of a phenotype. Genotypes can differ in how they respond to the same environmental change. A reaction norm describes a genotype’s phenotype across environments. Environmental effects do not imply that genes are irrelevant, and genetic effects do not imply that a phenotype is fixed in every environment.

Compare multiple genotypes in each of the same environments. Replicate individuals and assign environments appropriately rather than growing one genotype only in bright light and another only in shade. That confounded design cannot separate genotype from light. A common-garden comparison holds environment more constant; a factorial comparison can test whether environmental responses differ among genotypes.

Suppose genotype A grows 10 cm in shade and 20 cm in sun, while B grows 12 cm in shade and 13 cm in sun. Both genotype and environment may matter, and the response to light differs between genotypes. These example means need replication and uncertainty information before strong statistical claims. A change in growth does not by itself show a heritable change in DNA sequence.

Mitochondria and chloroplasts contain genetic material. Their transmission can differ from the typical nuclear chromosome pattern because gametes contribute cytoplasm and organelles unequally. Maternal transmission is common in many systems but is not a universal rule for every species or organelle. Reciprocal crosses can reveal a parent-of-origin pattern, though further evidence is needed to establish its mechanism.

A polygenic trait depends on variation at multiple loci and can also be influenced by environment. Continuous variation does not require alleles to blend or stop segregating. Combining many genetic contributions and environmental effects can produce a broad distribution. A single-gene Punnett square is then an incomplete description of the phenotype, even though chromosome segregation still operates.

At one locus an enzyme may produce a pigment precursor, while another locus affects a later step. If the first step is absent, differences at the later step may be masked. Such interactions can alter phenotype ratios without changing allele segregation. To explain an unusual ratio, connect genotypes to a pathway rather than merely naming a memorized exception.