Figure 1.
Simple control flow diagram of the simulation algorithm.
Ecological processes that have been incorporated into the algorithm to specify the life cycle of a plant species, including the interaction with secondary seed dispersers. After an initial map (year 0) of plant number per occupied cell is determined, the simulation starts by letting adult plants (top of the diagram) produce seeds which may then follow different paths through the algorithm. They may end up either as predated seeds (which are simply eliminated from the model) or as unremoved, dropped or rejected seeds, all of which may germinate and, eventually, give rise to adult plants again. In the diagram these processes are equivalent to going from top to bottom and, then, back up to the top again. That represents one time step (i.e. one year) in the model, and one whole model run consists of simulating a time period of five years. The simulation follows the fate of every plant and seed individually, both in time (yearly) and space (in each cell).
Figure 2.
Theoretical models of plant population dynamics responses to the dual effect of seed harvesting ants.
Graphical representation of the main four different theoretical models of plant population dynamics (A, Ants-independent model; B, Ant predation-dependent model; C, Ant dispersal-dependent model; and D, Ant-dependent model) in response to the uncoupled effects of seed predation and seed dispersal by ants which are determined by the comparison of four different scenarios in which each is the result of the cross combination of the two antagonistic effects (‘dual effect’ scenario, Predation+Dispersal+; ‘predator’ scenario, Predation+Dispersal−; ‘disperser’ scenario, Predation−Dispersal+; and ‘no-ant’ scenario, Predation−Dispersal−). Minus and plus represent the absence or existence of an effect, respectively. Note that the “dual effect” scenario was used as the reference scenario and, thus, it was settled with constant values thorough time and models.
Table 1.
Model parameterization.
Figure 3.
Spatial occupation and plant density predicted by the simulations model run.
(A) Proportion of cells occupied, and (B) plant density per cell (0.25 m2) of C. minima, F. ericoides and D. pentaphyllum predicted by the simulations model run under the four different scenarios (‘dual effect’, ‘predator’, ‘disperser’, and ‘no-ant’) and for each simulation year. The black circles indicate where the observed occupation values fall five years after the beginning of the study (validation data).
Figure 4.
Pair correlation functions calculated from mean Ripley's
curves (see text for details) from simulated plant presence-absence maps. Shown are results corresponding to C. minima (A), F. ericoides (B) and D. pentaphyllum (C) after the simulation algorithm ran for 5 years. For the sake of comparison, the corresponding
curves for the initial scenario (i.e. the observed spatial distribution of presence-absence of plants for each species) are also included and are labeled as ‘initial’. The gray curve (‘no-ant’) has been drawn but is barely visible in the figures. It is under the red curve (‘predator’) in A and B, and under the green curve (‘disperser’) in C.
Figure 5.
Occupancy and colonization rates calculated from simulations.
(A) Proportion of cells occupied each year of simulation in relation to all cells that were occupied in the initial scenario (occupancy rate), and (B) proportion of cells unoccupied each year of simulation in relation to all cells that were unoccupied in the initial scenario (colonization rate) of C. minima, F. ericoides and D. pentaphyllum predicted by the simulations model run under the four different scenarios (‘dual effect’, ‘predator’, ‘disperser’, and ‘no-ant’).
Table 2.
Summary of the theoretical models of plant population dynamics in response to seed predation and seed dispersal followed for each plant species and output of the model.