Figure 1

Adaptive radiation of mammals in the tertiary. (a) Total number of mammalian families and orders as function of time; redrawn from Ref. 25. (b) Animals and plants are classified in a hierarchical taxonomic system according to kingdom, phyla, class, order, family, genera, and species. The figure is redrawn from Ref. 26 and shows a graphical representation of the evolutionary relationships among orders of mammals (a so-called phylogenetic tree). The thickness of each group is proportional to the number of genera in that group. Notice the rapid establishment of basic lineages (here orders); taxa of lower systematic levels (e.g., families, genera) generally peak at later times compared to higher levels [27].Reuse & Permissions

Figure 2

Model schematics. Species are described by their coordinates in a two-dimensional morphospace defined with reference to two quantifiable phenotypic forms. Species compete with close-by species within a radius of $r<R$ through a short-range competition function and with species further away through a long-range competition function. New species originate as propagules of the parent species within the short-range competition radius.Reuse & Permissions

Figure 3

Species number and morphological disparity. (a) Number of species plotted as function of time; the inset shows the initial phase displaying steplike growth. The simulation is made using a constant short-range competition function with a power-law tail for long-ranges (model II). The constants are $\sigma =1$, $R=20\sigma$, $\beta =0.1$, $\epsilon =0.8$, $f_0=1$, $s=100$, $dt=0.005$, and $R_L=30\sigma$. (b) The mean square radius of the species density distribution $⟨r^2⟩=\sqrt{(x_j^2+y_j^2)}$ plotted as a function of time. The competition function and parameters are identical to the case described above.Reuse & Permissions

Figure 4

Phylogenetic tree and lineage dynamics. (a) A phylogenetic tree constructed by plotting the $y$ coordinate of all living species as function of time. (b) The number of lineages plotted as function of time. Note that the morphospace is bidimensional, and therefore the occupation patterns are partly masked by the superposition of lineages on the same line of sight.Reuse & Permissions

Figure 5

Lineage dynamics with different competition functions: The number of lineages plotted as a function of time. (a) Smoothed sphere competition with finite long-range competition (model I). Parameter values are $\sigma =1$, $R=20\sigma$, $\epsilon =0.8$, $s=100$, $dt=0.005$, $f_0=1$, $f_{\infty }=0.2$, and $a=2$. (b) Magnification of the first 12 000 time steps of same simulation. (c) Smoothed sphere competition with long-range competition dropping to zero (model I). Parameter values as in (a) except that $f_{\infty }=0$.Reuse & Permissions

Figure 6

Branching: Species distribution in morphospace at four different times. Top left, after 1000 time steps from the beginning of the simulation; top right, after 2000 time steps; bottom left, after 3000 time steps; bottom right, after 8000 time steps. The figure shows the dynamics of cluster fission during branching and the regular cluster distribution in morphospace. Model II with $\sigma =1$, $R=18\sigma$, $\beta =0.1$, $\epsilon =0.8$, $f_0=1$, $s=80$, $dt=0.005$, and $R_L=30\sigma$.Reuse & Permissions