Lab 3

Stochastic Growth Model

Date: 01.25.2019

Population predictions

Last week we projected populations, but assumed

  • 'r' is constant

  • it does not change, ever

  • far from truth

Nature is unpredictable

Stochasticity

Stochasticity ~ 'the quality of lacking any predictable order'

  • Environmental- The unpredictable variation in population dynamics due to unpredictable variation in environment.

  • Demographic - The unpredicable variation in poulation dynamics due to random fluctuations in population growth rate, usually an issue of small populations

How should we predict the unpredictable?

By treating population parameters as random variable.

  • In our case, as of now, we are dealing with exponential growth model

  • So our population parameter is 'r'

  • We will treat 'r' as a random variable

Step 1: Random drawing of growth rate

Assume 'r' is normally distributed

#time = length(lambda) e.g., time=20

#sample a value of r for each time step

r_sim = rnorm(time, mean, sd)

Draw one value of 'r' from the distribution

'r' is normally distributed

plot of chunk unnamed-chunk-1

Project population from t to t+1 until tmax

for (i in 1:time) {

r_sim[i]

N_sim[i+1] = N_sim [i]* exp(r_sim[i])

}

3. Many simulations

##write the function

exp.stoch<- funtion(r_sim){

for(i in 1:time){

N_Sim[i+1]= N_sim[i]* exp(r_sim[i]) }

N_sim }

simulate hundreds or thousands of time

n_sims=no. of iterations

for(s in 1:n_sims){

r_sim=rnorm(time,r,sd)

N = exp.stoch (r_sim) stoch.out[,s]=N

}

Next week

Reading for quiz- Engen et al. 2001

Logistic growth model

Reading: Sibley & Hone 2002