- Suppose a population is growing according to a logistic model at rmax=0.2 and K =5000.
- Plot sustainable yield (SY) vs. population size
- What is the population size associated with maximum sustainable harvest (MSY)?
- What is the harvest (yield) obtained at this population size?
- What is the rate (harvest per capita) at which the population can be sustainably harvested to obtain maximum yield?
- Suppose a population is growing as above but K is stochastic (mean=5000, sd=500, Normal distribution)
- Simulate yield over 50 years when harvest is maintained at the above MSY rate and the population starts at N0=2500.
- Compare the yield and abundance averaged over 50 years of these simulated populations (replicate!) to that obtained under the deterministic MSY model.
- Try increasing the sd of K to 1500. How does this affect average N and yield?
- Simulate stochastic population growth for 100 years and report the mean and sd of persistence for 100 replicated population trajectories, given that population growth is according to a stochastic birth-death process as follows:
- N[t+1]=N[t]-D[t]+F[t]
- D[t]~Binom(N[t], d=0.4)
- F[t]~Poisson(f*N[t]), f=0.6
- Initial abundance N0=10
- Modify the above simulation to include a density-dependent term for recruitment, with all other assumptions as before:
- F[t]~Poisson(f[t]*N[t]), f[t]=(1-N[t]/K)*fmax ;K=50, fmax=0.6
- Repeat the simulations in 3 and 4 but with d=0.5 and f=0.5 (fmax=0.5 in density dependent case)
- Use R to produce a table showing the mean and sd of persistence for the 4 combinations of
- Density dependent and independent recruitment
- d=0.4, f (or fmax=0.6 ; d=f (or fmax)=0.5