### Applet: Equilibria when harvesting natural populations

A plot showing the equilibria for logistic growth with harvesting. The updating function $f(x)=x+r(1-x)-hx$ is shown by the red curve along with the diagonal line $x=y$ in blue. The two equilibria, which are the intersections between the curves, are shown by the blue and green points. The green point corresponds to the equilibrium $E_1=0$. As you can observe by the slope of $f$ at the equilibria, as long as the harvesting rate $h$ is less than the low density growth rate $r$, the equilibrium $E_2$ corresponding to the blue point is positive and stable, and the equilibrium $E_1=0$ is unstable. If the harvest rate is larger than the low density growth rate, then the second equilibrium $E_2$ becomes negative an unphysical. The only physically relevant equilibrium is $E_1=0$, which is stable. You can change $r$ and $h$ by typing values in their boxes. To display the sustainable harvest, which is the stable equilibrium multiplied by the harvest rate $h$,check the “show harvest” box.

Applet file: harvest_natural_populations_equilibria.ggb

#### Applet links

This applet is found in the pages

#### General information about Geogebra Web applets

This applet was created using Geogebra. In most Geogebra applets, you can move objects by dragging them with the mouse. In some, you can enter values with the keyboard. To reset the applet to its original view, click the icon in the upper right hand corner.

You can download the applet onto your own computer so you can use it outside this web page or even modify it to improve it. You simply need to download the above applet file and download the Geogebra program onto your own computer.