Monodominance in tropical forests: modelling reveals emerging clusters and phase transitions

Abstract

Tropical forests are highly diverse ecosystems, but within such forests there can be large patches dominated by a single tree species. The myriad presumed mechanisms that lead to the emergence of such monodominant areas is currently the subject of intensive research. We used the most generic of these mechanisms, large seed mass and low dispersal ability of the monodominant species, in a spatially explicit model. The model represents seven identical species with long-distance dispersal of small seeds, competing with one potentially monodominant species with short-distance dispersal of large seeds. Monodominant patches emerged and persisted only for a narrow range of species traits; these results have the characteristic features of phase transitions. Additional mechanisms may explain monodominance in different ecological contexts, but our results suggest that percolation-like phenomena and phase transitions might be pervasive in this type of system.

Keywords: criticality; dispersal; percolation; phase transitions; simulation; single-species dominance.

Figure 1.

The dependence of relative cluster size of the monodominant species on mortality at an intermediate seed mass of the monodominant species (SM = 9500) after 10 000 simulation years. The black horizontal lines in the boxes show the median, the boxes show the first and third quartiles and the vertical line shows the range of relative abundance, except extreme values (=points), in 1000 simulation runs for each combination of parameter values. The curve is hump-shaped, indicating that at mortalities between 1% and 2% the monodominant species can best be established.

Figure 2.

The relative abundance of the monodominant species plotted against its seed mass and representing different annual mortality rates for the trees (mortality rates are the same for all species). The boxes show the range of relative abundance in 1000 simulations of each parameter combination, and the circles mark outliers.

Figure 3.

Finite-size scaling of the percolation probability P_L (SM). The intersection of all system sizes indicates a critical point for the seed mass of the monodominant species at SM_c = 9488. The inset shows the same results after rescaling the x-axis; this analysis results in an estimate of 1.4 for the critical exponent v. Two thousand simulation runs were performed for small systems (<400 × 400 grid cells) and 1000 simulation runs for larger systems.

Figure 4.

Variation of dispersal range DR_i of the seven identical species. The dispersal radius of the seven identical species (default: DR_i = 20, i.e. 1256 grid cells in range) is changed: DR_i ∈ [1 … 30], whereas the dispersal radius of the monodominant species is kept constant with DR m ≡ 1 (four grid cells in range). For every time step, each tree invests a certain amount of energy into seeds, defined here as seed mass × dispersal area (in number of grid cells). The proportion of the energy a tree of the monodominant species and a tree of one of the identical species invests into its propagules is kept constant, independent of the dispersal radius. The critical seed masses SM_c (DR_i) are calculated as shown in figure 3 and electronic supplementary material, figures S1 and S2, and are plotted against the dispersal radii of the non-monodominant species. The value obtained for the case DR_i = DR_m = 1 (as in the neutral model case [16]) is set to 100%. One thousand simulation runs were performed for each parameter combination for small systems (<400 × 400 grid cells) and 500 simulation runs for larger systems.

Figure 5.

Simulations of 10 000 1-year time steps, with a seed mass of the monodominant species of SM = 9425 (close to the critical point SM_c 9488). The forest landscape consists of 512 × 512 grid cells, corresponding to 10 × 10 km. Black points symbolize the monodominant species, blue/grey/white colours show the non-monodominant tree species. The 20 squares show the simulated forest at different times, starting with one simulation year (top left) and proceeding in increments of 500 years to the bottom left. After some time, black clusters of the monodominant species formed and remained stable over the whole run time. In the areas where no clusters established, the density of the monodominant species decreased until in the final state no monodominant trees could be found outside a cluster.

Figure 6.

Aggregations of monodominant trees after 10 000 simulation years in a forest landscape of 512 × 512 grid cells, with monodominant seed mass at the critical point SM_c = 9488. Each cluster is defined by monodominant cells linked via the four direct neighbours and is represented by a different colour; white cells show mixed-forest areas. The centre of each aggregation is occupied by a single cluster; smaller clusters are found around the circumference of the central clusters.