Practice_demography.Rmd

---
title: "Practice_Demography_Change"
author: "Meng-Hsin, Wu"
date: "2021/11/25"
output: html_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

According to the equations in this model, let's create our own function call osc3.

Creating new function
---
```{r new function}
osc3<-function(r1,alpha12,r2,alpha21,
               N1_start,N2_start,t){
  N1<-rep(1,t)
  N2<-rep(1,t)
  N1[1]<-N1_start
  N2[1]<-N2_start
  K1<-100
  K2<-100
  for(i in 2:t){
    N1[i]<-N1[i-1]+N1[i-1]*r1*((K1-N1[i-1]-alpha12*N2)/K1)
    N2[i]<-N2[i-1]+N2[i-1]*r2*((K2-N2[i-1]-alpha21*N1)/K2)
  }
  generation<-c(1:t)
  par(las=1, lwd=2, lty=2,
      xlim=c(0,100),
      ylim=c(0,100))
  
  if(N1[1]==0){plot(N2~generation,
    type='l', 
    col='red')
    title(main='N2 only' )}else{
      if(N2[1]==0){plot(N1~generation,
      type='l', col='blue')
        title(main='N1 only')}else{
  plot(N1~generation,
  type='l', col='blue')
  lines(N2~generation, col='red')
  title(main='Both species competing')
  legend(x=80, y=60,
         legend=c('N1','N2'),
         col=c('blue', 'red'),
         lty=1,
         lwd=2,
         cex=1
         )
        }
    }
}
```

Now, let's check this finction by defining parameters in it.

Set parameters
---
```{r parameters}
osc3(r1=1,
     alpha12=1,
     r2=1,
     alpha21 = 2,
     N1_start = 2,
     N2_start = 2,
     t=100)


```

Let's change the parameters, forecasting what will happen to the two population overtime.

Change parameters
---
```{r change parameters}
osc3(1,2,2,3,2,2,100)


```

Now, let's check what will the plot look like when there is only one species exists.

Situation will only one species
---
```{r one species}

osc3(1,1,1,1,2,0,100)
osc3(1,1,1,1,0,2,100)


```

In addition, I'd like to use another package specified in stability and demography analysis.

Package phaseR
---
```{R phaseR package}
library(phaseR)
```
Let's create another function called osc2

Creating new function
---
```{R osc2}
osc2<- function(t, y, parameters){
  N1<-y[1]
  N2<-y[2]
  r1<-parameters[1]
  alpha1<-parameters[2]
  r2<-parameters[3]
  alpha2<-parameters[4]
  K1<-100
  K2<-100
  dy<-numeric(2)
  dy[1]<- r1*N1*(K1-N1-alpha1*N2)/K1
  dy[2]<- r2*N2*(K2-N2-alpha2*N1)/K2
  list(dy)
}

```

We can apply function in the package to check the oscillation between two competing species.

Show oscillation
---
```{R show oscillation}
numericalSolution(osc2, 
          y0=c(2,2),
          tlim=c(1,100),
          parameters=c(1,1,1,2),
          type='one',
          col=c('red','blue'),
          add.grid = T,
          add.legend = T,
         state.names=c('N1','N2')
                  )

```