Foundations

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.

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.

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.

Characteristic archaeal membrane lipids contain branched isoprenoid chains ether-linked to a glycerol-1-phosphate backbone, compared with the common bacterial/eukaryotic fatty-acyl ester-linked glycerol-3-phosphate model.

Plasmogamy joins fungal cytoplasm without immediately fusing the nuclei.

Diatoms provide a photosynthetic eukaryotic example with silica-rich cell walls.

Epistasis means that the phenotypic effect associated with a locus depends on another locus, including masking effects in a biochemical pathway.

For an X-linked locus without a corresponding Y allele in the standard XX/XY model, an XY individual is hemizygous, and reciprocal crosses can yield different genotype distributions.

A cohort life table follows individuals born together.

In a fixed density-independent age model, the growth factor λ satisfies Σ_{x≥1}λ^(−x)l_xm_x=1.

A simple internally colonized metapopulation tracks the occupied fraction p of equivalent habitat patches.

Failure to detect a species does not establish absence.

For a collection containing N individuals with N_i in each observed species, the expected species count in a uniformly drawn subset of n individuals without replacement is E[S_n]=Σ_i[1−C(N−N_i,n)/C(N,n)].

A genetic perturbation tests a causal prediction when the intended change and relevant phenotype are measured against appropriate controls.

The D statistic compares two discordant allele-sharing patterns in an ordered four-sample test.

Reaction stoichiometry relates species-amount changes to reaction and exchange fluxes.

GUIDE-seq detects tagged double-strand-break locations by oligonucleotide integration and sequencing.

EmptyDrops tests barcode expression against an ambient-RNA null rather than relying solely on total-count thresholds.

UMIs help distinguish amplified reads from captured molecules, but barcode errors and finite capture affect estimated counts.

In Lecuit’s nondimensional two-cell example, the isolated reaction Jacobian has eigenvalues −1, whereas an antisymmetric spatial mode can become unstable after unequal diffusive coupling.

Dupont and colleagues altered substrate rigidity and cell geometry and tested actomyosin/Rho and YAP/TAZ responses in specified cultured mammalian cells.

A local alignment score is evaluated against an explicit random-sequence null and search space.

HaplotypeCaller assembles candidate haplotypes in active regions and compares reads with them through PairHMM likelihoods before genotype inference.

Phylogenetic substitution models differ in equilibrium frequencies, transition rates and among-site mixtures.