Stochastic models in seed dispersals: random walks and birth–death processes

Figures & data

Figure 1. Flowchart for simulating two competing plant species.

Figure 2. The deterministic and stochastic IBMs for two competing plant species $N_1$ and $N_2$ for arbitrary parameters: $N_1\left(0\right)=20$, $N_2\left(0\right)=25$, ${\beta }_1=2$, ${\beta }_2=1.78$, ${\psi }_1=0.02$, ${\psi }_2=0.02$, ${\alpha }_1=0.03$ and ${\alpha }_2=0.03$. The deterministic model is the solution of Equations (13(13) $\begin{array}{r}\frac{\mathrm{d}{N}_1\left(t\right)}{\mathrm{d}t}={\beta }_1{N}_1\left(t\right)-{\psi }_1{N}_1\left(t\right)-{\alpha }_2{N}_1\left(t\right)N_2\left(t\right)\end{array}$(13) ) and (14(14) $\begin{array}{r}\frac{\mathrm{d}{N}_2\left(t\right)}{\mathrm{d}t}={\beta }_2{N}_2\left(t\right)-{\psi }_2{N}_2\left(t\right)-{\alpha }_1{N}_1\left(t\right)N_2\left(t\right).\end{array}$(14) ) while the stochastic simulation is obtained by one realization of the Gillespie algorithm.

Figure 3. Flowchart for the simulation of a $2\mathrm{D}$ symmetric random walks.

Figure 4. Flowchart for simulation of a $2\mathrm{D}$ intermittent random walks.

Figure 5. The paths and mean cover time of a $2\mathrm{D}$ symmetric and a $2\mathrm{D}$ intermittent walks. (a) First 50 steps of a $2\mathrm{D}$ symmetric random walks. (b) An agent, performing a $2\mathrm{D}$ symmetric random walks, takes 4336 steps to visit the domain of N=400. (c) First 20 steps of a $2\mathrm{D}$ intermittent random walks. (d) When performing a $2\mathrm{D}$ intermittent walks, the agent takes 2417 steps to visit N=400.

Figure 6. Cover time distributions for a $2\mathrm{D}$ symmetrical and $2\mathrm{D}$ intermittent walks nearly approximate the Gumbel distribution in different domain sizes for $\rho =20,{\mathrm{\Lambda }}_1=10,{\mathrm{\Lambda }}_2=5$.