Allele copies are identical by descent if they derive from the same specified ancestral copy. Identical observed states need not imply this ancestry. Two diploid individuals are 2-IBD when both of their allele copies can be paired as identical by descent; autozygous individuals carrying two copies of the same ancestral copy are mutually 2-IBD when that ancestor is shared.

A genetic marker is an observed inherited genomic state used to track chromosomes, test genetic association, or perform genetic linkage analysis. Genetic marker alleles need not themselves cause the phenotype. Several genetic markers on one nonrecombining region form a single observed haplotype.

In ordinary diploid meiosis, the two copies at a genetic locus separate: each gamete receives one copy. With fair transmission, a heterozygote $Aa$ produces gametes carrying $A$ or $a$ with probability $1/2$ each. This is a transmission mechanism conditional on a parental genotype, rather than a statement about how common either allele is in a population.

For the one-locus cross $Aa\times Aa$, assume independent parental transmissions, no new mutation, and no differences in fertilization or survival between the resulting genotypes. Multiplying the two gamete probabilities gives four equally likely ordered outcomes: $AA,Aa,aA,aa$, each with probability $1/4$. Combining the two orders of the heterozygote givesOnly under the additional ideal model of complete dominance of $A$, complete penetrance, and no environmental changes to the scored characteristic do $AA$ and $Aa$ share the dominant phenotype. Its probability is then $0.25+0.50=0.75$. The inheritance calculation alone does not determine a phenotype or predict a generic disease risk.

These are probabilities, not a requirement that every four offspring contain one $AA$, two $Aa$ and one $aa$. For 100 independent offspring under the ideal model, the expected values of the three counts are $25,50,25$; the $aa$ count has a binomial distribution with standard deviation $\sqrt{100(0.25)(0.75)}\approx 4.33$. Each new transmission keeps the same conditional probabilities given the parental genotypes.

In his paper published in 1866, Mendel reported 5,474 round and 1,850 wrinkled pea seeds: $5474/7324\approx 0.7474$ round, close to the ideal $0.75$. Following descendants also distinguished two inherited classes within the round phenotype, illustrating why genotype cannot always be read from appearance.^[ref] At several genetic loci, transmission patterns additionally depend on genetic linkage and genetic recombination.

Meiosis reduces two sets of chromosomes to one. In the ordinary diploid life cycle, this makes it possible for fertilization of two haploid gametes to restore the diploid state rather than double the number of sets in every generation. Its two divisions perform different tasks: meiosis I separates homologous chromosomes, whereas meiosis II separates sister chromatids. One round of DNA replication precedes both divisions; there is no second round between them. See ^[ref].

Two homologous chromosomes carry corresponding genetic loci, potentially with different alleles; two sister chromatids originate by DNA replication of one chromosome. After chromosomal crossover between nonsister chromatids, the sister chromatids need not carry identical alleles everywhere. Separating the two relationships explains why a haploid product of meiosis I still contains replicated chromosomes.

The two divisions explain Mendelian segregation; variable orientation of different homologous chromosome pairs connects it to independent assortment. Genetic recombination adds another source of allele combinations. These mechanisms reshuffle inherited material without requiring a new mutation.

The symmetric diagram is useful for counting, but human oogenesis produces one functional ovum rather than four. The polar bodies receive discarded chromosomes and little cytoplasm. See Human Reproductive Anatomy and Gametogenesis (§43.3, Oogenesis and Figure 43.13: unequal divisions and polar bodies).

Ascertainment in a genetic study specifies how individuals or families enter a genetic study. If $A$ is the event of inclusion, then $P(X\mid A)=P(X)P(A\mid X)/P(A)$. Selection on disease phenotype can change an unconditional pedigree likelihood. When comparing genetic marker probabilities conditional on a specified disease pattern, selection depending only on that pattern cancels from the linkage likelihood ratio.

A gene is an inherited functional unit of genetic material. In cellular organisms, a gene is a region of DNA whose information produces a functional RNA or contributes to a protein. This connects inheritance to cellular chemistry: a change in a gene can alter the amount or activity of a protein, and thereby a phenotype. See NHGRI: gene.

Alternative inherited versions at a genetic locus are alleles. The distinction matters: two parents can carry the same gene but different alleles, and a genetic locus can have variation outside a gene. Neither the word gene nor a change in DNA alone specifies the resulting phenotype.

// Target: biology.bigb

A chromosome carries genes and other genetic material. A haplotype records the alleles carried on one chromosome at specified genetic loci.

In a typical eukaryotic cell nucleus, an unreplicated chromosome comprises one long double-stranded DNA molecule with associated proteins; a replicated chromosome comprises two associated sister chromatids. It need not be X-shaped: that familiar outline depicts a condensed, replicated state.^[ref]

For these ordinary centromere-bearing chromosomes, count by centromere units before separation: the paired sister centromere regions count together as one replicated chromosome. Once sister chromatids separate in anaphase of mitosis or meiosis II, each becomes a daughter chromosome. Thus the undivided anaphase biological cell in the $2n=6$ mitotic example transiently contains twelve daughter chromosomes, but each pole receives six and each completed daughter cell nucleus remains diploid. State the counting compartment and stage; summing both poles is not the ploidy of one daughter.

A mutation changes inherited genetic sequence. Under an infinite sites mutation model, every mutation occurs at a previously unmutated position, so mutations below the sample's common ancestor correspond to segregating sites.

More precisely, a mutation changes a genetic nucleotide sequence; in cellular organisms this is a DNA sequence. An altered sequence can be copied by DNA replication into descendant biological cells, changing their genotype whether or not an observable phenotype changes. Inheritance along a cell lineage does not require transmission to an offspring organism. In animals, germline mutations can enter offspring through gametes, whereas somatic mutations remain in body-cell lineages.^[ref]

A DNA lesion is damage to the physical DNA molecule, such as a damaged nucleobase or a broken strand. It need not become a lasting mutation: DNA repair can restore the original sequence. Conversely, a copied nucleotide substitution can leave an ordinary, correctly paired DNA duplex whose sequence differs from the ancestor. The distinction is between a damaged template and a changed inherited message, not simply between harmful and harmless effects.^[ref]

Small mutations include nucleotide substitutions and indels. Larger changes can remove a gene, duplicate a chromosome region or rearrange its order. Genetic recombination can bring existing alleles together without creating a new nucleobase at the exchanged positions; the mechanism and the resulting sequence change are different questions. A molecular description of a mutation, its effect on a gene product and its effect on a phenotype are likewise three separate statements.

For an original consequence ledger, choose the coding strand segment $5^{\prime }\text{-}\mathrm{ATG}\mathrm{TTT}\mathrm{GAA}\mathrm{TAA}\text{-}{3}^{\prime }$ with initiation at the first displayed codon. Use the standard genetic code, the same reading frame and suitable gene expression context throughout. Its messenger RNA has U in place of T, and the predicted amino acid chain is methionine–phenylalanine–glutamic acid residue, followed by a stop codon. This is a constructed coding segment, not an experimentally measured gene.

In the second row, position 6 changes from T to C, replacing TTT by TTC. Both corresponding RNA codons specify phenylalanine, so the predicted chain is unchanged. Changing position 5 from T to C instead gives TCT, whose RNA codon specifies serine. Changing position 7 from G to T gives TAA and therefore a stop codon before the original glutamic acid residue. Each is one nucleotide substitution, but their coding consequences differ. Even preservation of the amino acid chain does not guarantee unchanged gene expression or phenotype.

Insert GGA after ATG to add a glycine codon, or remove the complete TTT codon to remove phenylalanine. Both indels preserve the downstream reading frame because their lengths are three nucleotides. A one-nucleotide insertion at that location instead produces a frameshift mutation; the positional explanation and a worked regrouping appear under frameshift mutation. The ledger illustrates why interpreting a genetic variant requires its position and context, rather than just the label mutation.

Mutation supplies new inherited variation on which natural selection can act. The Luria-Delbrück experiment makes the distinction unusually visible: natural selection reveals resistant descendants, while the timing of a prior mutation determines how many descendants are available to reveal. This connects an invisible change in one biological cell to a visible pattern across cell cultures.

Panmixia is random mating within a breeding population, without systematic choice by genotype or phenotype. In a homogeneous genetic model it makes the two parental gamete draws independent, yielding the Hardy-Weinberg equilibrium genotype probabilities $p_i^2$ and $2p_i{p}_j$. It is a modelling assumption; assortative mating and population stratification are distinct ways a population can depart from it.

// Target: causal-inference.bigb

Ploidy counts complete sets of chromosomes in a cell nucleus. Write $n$ for the number of chromosomes in one set: haploid means one set, diploid two. DNA replication produces sister chromatids without changing ploidy.^[ref]

Consider an illustrative species with $2n=6$, hence $n=3$. One set contains three distinguishable chromosome types, $A,B,D$; the diploid cell nucleus contains two homologous chromosomes of each type. Labels describe chromosome identity, not particular alleles. Let $C$ be the Nuclear DNA content of one unreplicated set. All entries below refer to one completed product of division, or the starting cell nucleus, rather than the sum over products. Here “chromatid count” includes the single DNA copy in each unreplicated chromosome.

The arithmetic follows the allocation rules. DNA replication replaces each of six single copies with two associated sister chromatids: $6\times 2=12$ copies still grouped as six chromosomes. Meiosis I allocates one homologous chromosome of every type to each product: three replicated chromosomes, with $3\times 2=6$ copies. Meiosis II allocates one copy from each pair of sister chromatids to each final product: three single-copy chromosomes. Compare meiotic DNA content for the general symbolic bookkeeping. Chromosomal crossover can change the alleles on a chromatid without changing these counts when exchanges preserve material.

Keeping ploidy, chromosome count and Nuclear DNA content separate makes the beauty of meiosis explicit: copying supplies material for two divisions, while sorting determines which complete sets each product inherits. It also prevents interpreting a doubled DNA signal as evidence of an extra homologous chromosome set.

Functional complementation is restoration of a specified function or phenotype by introducing a gene into a deficient recipient. In the yeast cross-species complementation experiment, the restored property is growth without supplied methionine, under the assay conditions. Rescue need not restore every property of the original genotype.

The genetic background is the rest of the genotype against which a focal allele or gene deletion is studied. Other genes can influence the resulting phenotype, so comparisons should specify which background is held fixed.

A biological strain is a maintained variant or lineage within a species. Naming the species alone does not specify a laboratory genotype or its genetic background.

An analytical form of gel electrophoresis using an anionic surfactant and a polymer gel to separate proteins predominantly by chain size under denaturing conditions. Western blot separation often uses SDS-PAGE; the resulting apparent mass and subsequent antibody binding provide complementary, incomplete evidence about identity.

Under controlled staining and detector settings, integrated fluorescence can be approximately proportional to nuclear DNA amount. A histogram of accepted single-cell events then separates a $2C$ region, an intermediate region and a $4C$ region. These are ordinarily assigned to G0 phase/G1 phase, S phase, and G2 phase/M phase respectively in the stated diploid model.

A Cornell protocol fixes a single-cell suspension by adding cold 70% ethanol dropwise while mixing, reducing clumping. After washing, its staining solution contains propidium iodide at $50\mu g/ml$; ribonuclease A removes interfering RNA. It specifies excitation at $488\mathrm{nm}$ and emission around $600\mathrm{nm}$. The resulting readout is fluorescence per event, not a direct count of chromosomes. ^[ref]

Useful controls include an unstained sample for background and a reference population with known nuclear DNA amount, processed with identical settings. Two attached $2C$ biological cells can mimic one $4C$ event. Comparing signal integral with pulse height or width helps exclude such doublets; a gate selecting intact single particles also limits debris. These are proposed assay checks, not measurements underlying the illustration.

A $4C$ peak cannot distinguish G2 phase from mitosis; a $2C$ peak cannot distinguish G1 phase from G0 phase. Mixed ploidy, uneven staining and aggregates can invalidate phase assignments. Peak areas describe the accepted sample at collection, and do not by themselves establish phase durations, division rates or a particular arrest mechanism. A treatment comparison needs matched handling and another readout appropriate to the claimed mechanism.

A file header is leading information describing how to interpret the following data. Dimensions and a choice of compression method are examples. The two toy image compression examples explicitly count these fields.