Figure 1.

Simulated trait evolution under alternative evolutionary models. Illustration of accumulating trait variance assuming a model of phyletic gradualism (Brownian motion) (a) and a speciational model of punctuated evolution (b), in which trait change occurs in rapid bursts at speciation. Evolutionary time is on the x-axis and trait values on the y-axis. Lineages are represented by black lines and speciation events are indicated where a lineage splits in two. At origination, the ancestral lineage is assumed to have a trait value of 0. Lineages tend to diverge over time, following the assumed evolutionary model. However, because trait evolution is non-directional, the expected mean trait value at any point in time is that of the ancestor, but variance increases proportionally with time. Evolutionary convergences are illustrated when lineages cross on the y-axis; this can occur instantaneously at speciation for the model of punctuated evolution. Code for simulations kindly provided by T. Ingram (see also [72]).