---
title: "Rosenzweig-MacArthur predator-prey model (Pineda-Krch et al., 2007)"
output: rmarkdown::html_vignette
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%\VignetteIndexEntry{Rosenzweig-MacArthur predator-prey model (Pineda-Krch et al., 2007)}
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%\VignetteEngine{knitr::rmarkdown}
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---
```{r, setseed, echo=FALSE}
set.seed(1)
knitr::opts_chunk$set(fig.width = 8, fig.height = 6)
```
Rosenzweig-MacArthur predator-prey model (Pineda-Krch et al., 2007, Pineda-Krch, 2008)
```
dN/dt = r(1-N/K - alpha/(1+wN))NP
dP/dt = c*alpha/(1+wN))NP
```
This model has five reactions with the following per capita rates,
```
prey birth: b
prey death: d+(b-d)N/K
predation: alpha/(1+wN)
predator birth: c*alpha/(1+wN)N
predator death: g
```
Propensity functions:
```
a1 = b * N
a2 = (d+(b-d)N/K) * N
a3 = alpha/(1+wN) * N * P
a4 = c*alpha/(1+wN) * N * P
a5 = g * P
```
Load package
```{r}
library(GillespieSSA)
```
Define parameters
```{r}
parms <- c(b=2, d=1, K=1000, alpha=0.005,
w=0.0025, c=2, g=2)
tf <- 10 # Final time
simName <- "Rosenzweig-MacArthur predator-prey model" # Name
```
Define initial state vector
```{r}
x0 <- c(N=500, P=500)
```
Define state-change matrix
```{r}
nu <- matrix(c(+1, -1, -1, 0, 0,
0, 0, 0, +1, -1),
nrow=2,byrow=TRUE)
```
Define propensity functions
```{r}
a <- c(
"b*N",
"(d+(b-d)*N/K)*N",
"alpha/(1+w*N)*N*P",
"c*alpha/(1+w*N)*N*P",
"g*P"
)
```
Run simulations with the Direct method
```{r direct}
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.d(),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```
Run simulations with the Explict tau-leap method
```{r etl}
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.etl(tau = .01),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```
Run simulations with the Binomial tau-leap method
```{r btl}
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.btl(),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```
Run simulations with the Optimized tau-leap method
```{r otl}
set.seed(1)
out <- ssa(
x0 = x0,
a = a,
nu = nu,
parms = parms,
tf = tf,
method = ssa.otl(),
simName = simName,
verbose = FALSE,
consoleInterval = 1
)
ssa.plot(out, show.title = TRUE, show.legend = FALSE)
```