At large but finite magnetic field, opposite-spin admixtures in approximate product eigenstates let nominally spin-forbidden electric-dipole channels borrow intensity. Their amplitudes scale as spin-orbit interaction energy divided by Zeeman energy; their intensities therefore vanish quadratically in that ratio.

A spread of particle or molecular dimensions rather than a single size. A quantitative measure must state the weighting and statistic; particle-size variation and polymer chain-length variation are related examples but use different common indices.

The radial null integral from the Big Bang is ${\chi }_p=c{\int }_0^{t}d{t}^{\prime }/R(t^{\prime })=c{t}^{1-p}/[A(1-p)]$. Multiplication by the scale factor gives the proper radial horizon distance. It is $3ct$ for a flat matter-only model and $2ct$ for a flat radiation-only model. A finite initial time different from zero or an earlier expansion era changes the result.

In the standard single-seed model, individual particles execute random walks until first contact with a growing cluster, where they stick irreversibly. Exposed tips intercept more particles than screened inner regions, producing branched clusters. This differs from diffusion-limited cluster aggregation, in which whole existing clusters move and join one another. The two models need not share the same mass fractal dimension.

Association of dispersed particles into larger clusters, often after repulsive stabilization is weakened. Salt screening, reduced surface charge, polymer bridging or depletion force can promote it. Clusters may sediment rapidly; preventing aggregation and preventing gravitational separation are distinct stability requirements.

Information concerning the probability that offspring are genetically sired by a male. Its effect on care depends on detection, future mating opportunities and effects on offspring, not only average extra-pair paternity.

Reproductive allocation is the distribution of resources and effort among reproductive activities, offspring and future opportunities. Investing more in one component can reduce resources for another. An allocation trade-off concerns limited resources rather than an assumption that every observed correlation is causal.

An apicomplexan parasite belongs to an evolutionary lineage containing organisms such as Plasmodium and Cryptosporidium. Plastid retention and metabolic requirements vary among lineages and life-cycle stages.

Plasmodium falciparum is an apicomplexan parasite with stage-dependent metabolic requirements. Blood-stage chemical-rescue experiments identify an essential apicoplast output under defined culture conditions.

Cryptosporidium parvum is an apicomplexan parasite lacking an apicoplast. Its organelle and metabolic inventory provides a comparison for lineages retaining a plastid.

A corallicolid is a member of a coral-associated apicomplexan lineage. Retention of chlorophyll-biosynthesis genes without photosystem genes illustrates why a partial pigment pathway is not evidence for complete photosynthesis; its physiological role requires further testing.

An avian palatal arrangement with extensive bracing among the vomer, pterygoid bone, palatine bone and skull base. It is associated with Palaeognathae; the name does not establish evolutionary primitiveness.

An avian palatal arrangement with more mobile pterygoid–palatine articulation and reduced bracing compared with the palaeognathous palate. Mobility varies among species and cannot be read from the group name alone.

A measured magnetic field component or magnitude after subtraction of a reference field. Source geometry, magnetization direction and observation height affect its sign and amplitude; an anomaly is not a direct map of rock polarity.

magnetization retained as magnetic minerals cool through blocking temperatures in an ambient field. Subsequent alteration, reheating and remagnetization can change the record.

A paired anterior fin associated with the pectoral girdle.

A paired more posterior fin associated with the pelvic girdle.

The proposal that paired appendages evolved through modification of branchial structures. Evidence for a pharyngeal contribution to the shoulder is distinguishable from evidence that the whole fin arose by conversion of a gill arch.

The proposal that discrete paired fins evolved through differentiation and regional restriction of an earlier continuous ventrolateral appendage field.

The proposal that developmental mechanisms first operating in median fins were redeployed in paired appendages. Shared mechanisms do not by themselves specify the anatomical precursor or migration route.