Question

Problems Chapter 3 / Page 103 Q. 4 Investigate the model for density dependence due to Hassell given by $N_{t+1} = \lambda N_t (1 + aN_t)^{-b}$ for $\lambda, a, b$ positive constants. 1. What are the effects of the three parameters, $\lambda$, $a$, and $b$? Do increased values of these parameters strengthen or weaken the growth of the population? 2. For certain parameter ranges, this equation has a biologically meaningful nonzero steady state. Show that this steady state is given by $\bar{N} = \frac{\lambda^{1/b} - 1}{a}$ and discuss the appropriate param- eter constraints. (Hint: Recall that $\bar{N}$ has to be positive.)

          Problems Chapter 3 / Page 103
Q. 4 Investigate the model for density dependence due to Hassell given by
$N_{t+1} = \lambda N_t (1 + aN_t)^{-b}$ for $\lambda, a, b$ positive constants.
1. What are the effects of the three parameters, $\lambda$, $a$, and $b$? Do increased values of these
parameters strengthen or weaken the growth of the population?
2. For certain parameter ranges, this equation has a biologically meaningful nonzero steady
state. Show that this steady state is given by $\bar{N} = \frac{\lambda^{1/b} - 1}{a}$ and discuss the appropriate param-
eter constraints. (Hint: Recall that $\bar{N}$ has to be positive.)

Problems Chapter 3 / Page 103
Q. 4 Investigate the model for density dependence due to Hassell given by
Nt+1 = λ Nt (1 + aNt)^-b for λ, a, b positive constants.
1. What are the effects of the three parameters, λ, a, and b? Do increased values of these
parameters strengthen or weaken the growth of the population?
2. For certain parameter ranges, this equation has a biologically meaningful nonzero steady
state. Show that this steady state is given by N̅ = (λ^1/b - 1)/(a) and discuss the appropriate param-
eter constraints. (Hint: Recall that N̅ has to be positive.)

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