Figure 1. Simpson's three primary modes of evolution. The bell-shaped curves are meant to suggest the distribution of morphology at any given time, and the dashed lines the ancestor–descendant pathways. The solid parallel lines indicate ‘adaptive zones’. (a) Speciation: population differentiation, race formation, and formation of species without significant change in ecological niche. (b) Phyletic evolution: the transformation of whole lineages by slow and progressive evolution – phyletic gradualism is shown, but Simpson also included stasis under this heading (see text). (c) Quantum evolution: the rapid transition from one adaptive zone to another. Similar to punctuated equilibrium, except that for Simpson this occurred only in cases where major niche shifts were involved. After Simpson (1944), figure 31.

Figure 2. Schematic representation of evolutionary patterns in lower molar tooth area in species of the small Eocene mammal, Hyopsodus, from northwestern Wyoming. A total of three species lineages are shown (lineages represented by only one sample have been omitted). Shaded regions indicate intervals of intensive sampling at 6 m intervals in the section of sediments that spans a total of 500 m. Width of the lineages indicates the observed range of variation in morphology, and the thin dashed lines track the means of samples from successive levels. The thick horizontal dashed line in the centre of the section represents a species transition in a poorly sampled interval. After Gingerich PD (1977) Patterns of evolution in the mammalian fossil record. In: Hallam A (ed.) Patterns of Evolution, pp. 469–500. Elsevier, Amsterdam.

Figure 3. Punctuated equilibrium and phyletic gradualism. The evolution of six lineages involving approximately the same range and sequence of morphological change, according to the two theories. Under punctuated equilibrium (a), the species are in morphological stasis throughout their durations, and the rise and establishment of new, descendant species (dashed lines) is so rapid as to be unobserved. Under phyletic gradualism (b), evolutionary change is happening constantly in all lineages, at varying (but usually slow) rates, and new species are formed by gradual transitions, at rates similar to those observed within species lineages.