Evolution of distinct species during geographic separation. Persistence of isolation after renewed contact is a further test.

Origin of distinct species without initial geographic separation at the relevant scale. Current sympatry alone does not establish this historical route.

Secondary contact is renewed geographic contact between biological populations that diverged during an interval of separation. The resulting interaction can involve gene flow, a hybrid zone or continued reproductive isolation.

Present-day sympatry therefore does not alone establish sympatric speciation: the populations may have become distinct elsewhere before meeting again. Historical inference needs evidence about both the earlier separation and the later exchange.

Evolution of increased premating isolation because interpopulation mating has fitness costs. Ecological divergence without such selection is not sufficient evidence.

Origin of a reproductively distinct lineage through hybridization. A surviving hybrid individual alone is not a new species.

The rest energy of a body is $E_0=m{c}^2$. A body emitting energy $dE$ and no net momentum in its rest frame loses mass $dE/c^2$. For a radiating source of luminosity $L$, the corresponding radiative mass-loss rate is $L/c^2$.

Angular concentration and Doppler enhancement of radiation from a relativistically moving emitter. Frequency, photon arrival rate and apparent solid angle transform together; inferred brightness depends on viewing angle and the emission geometry.

Patience sorting processes values into piles by putting each next value on the leftmost pile whose top is at least that value, creating a new pile when none qualifies. The pile tops stay increasing, so binary search finds the destination. The number of piles equals the length of a longest increasing subsequence: each pile is nonincreasing in arrival order, while predecessor links across piles construct an increasing subsequence of that length. For 3,1,2,4, the tops evolve to 1,2,4, giving length three. Changing the comparison changes whether equality is allowed in the subsequence. Merging the completed piles can then produce a full sorted output.^[ref]

A long-range regulatory element contributing to limb expression of Sonic hedgehog. Evolutionary changes in its activity provide a testable example of altered developmental deployment.

A regular solution keeps the ideal combinatorial entropy of mixing while allowing a nonzero energetic preference for unlike contacts. For a symmetric binary mixture with equal molecular sizes, the displayed free energy per site combines mixing entropy with a contact penalty $\chi \varphi (1-\varphi )$. Its spinodal satisfies $1/\varphi +1/(1-\varphi )-2\chi =0$. At the symmetric thermodynamic critical point, the third composition derivative also vanishes, giving ${\varphi }_c=1/2$ and ${\chi }_c=2$. If $\chi =A/T$, the critical temperature is $A/2$. This is the equal-size limit of Flory–Huggins solution theory.

The distribution of an element among chemical forms distinguished by oxidation state, complexation or association with phases. Speciation affects solubility and partitioning.

Sample rotation about an axis at approximately $54.74^{\circ }$ to the field, averaging appropriate second-rank anisotropic interactions when spinning and pulse conditions are suitable.

A solid solution adjoining a pure-component end of a composition phase diagram. Its solute content can be small but need not be zero. A phase label such as (Bi) therefore does not by itself mean exactly pure bismuth.

Replacement of a lattice ion by another of the same formal charge. charge neutrality alone does not ensure unlimited solubility; size and coordination preferences also matter.

Coupled changes in ions, oxidation states or vacancies that preserve charge balance when a lattice substitution changes formal charge.

The composition boundary beyond which one homogeneous phase cannot accommodate additional solute under the stated conditions. Phase separation or a new structure can appear beyond that range.

An approximate linear interpolation of a substitutional solid solution's lattice parameter with atomic composition. Converting the inferred atomic fraction to mass fraction requires molar masses. Ordering, nonideal mixing, strain and multiple phases can invalidate a simple two-endpoint interpolation.

Resistance to dislocation motion caused by substitutional or interstitial solutes and their interactions with the dislocation strain field and core.

Testing a small software component against a specified expected behavior.

Testing interactions between software components, including data formats, units and ordering.