Wednesday - forage fish & cascades

Forage fish presentation

Some simulations exploring top-down & bottom up control concepts in simple models.

$$\frac{dN}{dt} = r N\left( 1 - \frac{N}{K} \right) - \alpha N P$$ $$\frac{dP}{dt} = \beta \alpha N P - \mu P$$ Note that at equilibrium, N depends only on predator dynamics, P on K and r. $$\hat N = \frac{\mu}{\alpha\beta}$$ $$\hat P = \frac{r}{\alpha}\left( 1 - \frac{N}{K} \right)$$

Saturating predator response:

$$\frac{dN}{dt} = r N\left( 1 - \frac{N}{K} \right) - \alpha N P$$ $$\frac{dP}{dt} = \beta \alpha \frac{N}{H+N} P - \mu P$$

Equilibrium:

$$\frac{\mu H}{ \alpha\beta-\mu}$$ $$\frac{r}{\alpha} \left(1- \frac{\hat N}{K}\right)$$

see code for saturating example.

Wainwright Lab Meeting presentation

• Presented rfishbase, rtreebase demos.