Foundations

If migrants form a specified fraction of a population's allele pool, the post-migration allele frequency is a weighted average of resident and migrant frequencies.

Recurrent mutation can replenish a deleterious allele that purifying selection removes.

In the ideal neutral diploid population, a new single-copy allele has eventual fixation probability 1/(2N).

Under equal constant lineage-specific substitution rates, the expected substitutions separating two descendant lineages accumulate over both branches since their common ancestor.

Coordination compounds can share composition while differing in ligand connectivity or spatial arrangement.

Neutral-fragment and oxidation-state counting consistently allocate ligand and metal electrons when their conventions are used throughout.

Dissociative ligand substitution loses a ligand before addition, while an associative route adds an incoming ligand before loss.

Ligand-field MO models combine metal and ligand orbitals with compatible symmetry, adding covalent interactions beyond a point-charge crystal field.

Hydrogen in an ionic hydride is formally H− and can act as a strong base or reducing species; proton transfer with water produces hydrogen gas and hydroxide.

Boron trihalides have trigonal-planar molecular reference structures and can accept donor electron pairs; BF3 and fluoride form BF4−.

Nitrogen forms oxides with several formal oxidation states.

Phosphorus(III) and phosphorus(V) oxides have different oxygen content and formal oxidation states.

Oxide O²−, peroxide O₂²− and superoxide O₂− contain different numbers and arrangements of oxygen atoms and electrons.

Halogens and halides have distinct oxidizing and reducing roles; for example, chlorine can oxidize bromide under suitable solution conditions.

In the elementary alkene hydroboration model, C–H and C–B bonds form together from the same face without a free carbocation intermediate.

Adding hydration equivalents to an alkyne initially produces an enol, which can tautomerize to a carbonyl compound.

A nucleophile can add to an activated aryl system, forming an anionic intermediate before leaving-group elimination restores aromaticity.

An amine's basicity can be described by the acidity of its conjugate ammonium species under specified conditions.

In chain-growth polymerization, monomer addition regenerates a growing active centre.

Step-growth polymerization joins compatible functional groups on monomers and oligomers rather than requiring all growth at one persistent chain centre.

For a reversible one-to-one receptor/ligand interaction at equilibrium, the dissociation constant relates free receptor, free ligand and complex concentrations.

Ligand binding at one site can alter affinity or activity at another through coupling of protein states.

Coulometry infers reacting amount from integrated charge and electron stoichiometry.

Voltammetry records current while controlling the working-electrode potential relative to a reference; a counter electrode carries the balancing current.

Fluorescence emission follows optical excitation while competing with nonradiative relaxation.

Mitochondrial and plastid ancestry is supported by bacterial affinities in molecular machinery and genes, organelle reproduction and transfer of many organelle-derived genes into nuclear genomes.

Mosses, liverworts and hornworts illustrate gametophyte-dominant land-plant life cycles.

Lycophytes and fern-related lineages have vascular sporophytes and life cycles that produce gametophytes through spores.

Gene lineages need not coalesce at a population or species split.

Species traits can be correlated because related lineages share evolutionary history.