### Applet: The dynamics of a population with harvesting of a fixed number each time period

The population size $p_t$ in time period $t$ of a species that is being harvested (hunted) is plotted for 100 time periods. At time 0, the population size is $p_0$, which you can change by dragging the blue dot or typing a number in the box. In each time period, the population grows by a factor of $r$ but $a$ individuals are harvested and removed from the population, so that the dynamics of the population size follow $p_{t+1}-p_t = rp_t-a$. (You can change $r$ and $a$ by typing numbers in their boxes.) The equilibrium $p_t=E=a/r$ is plotted by the horizontal cyan line. You can explore how the evolution of the population size has very different behavior depending on the relationship between $p_0$ and $E$. To set the initial conditions to be exactly the equilibrium, you can enter $E$ in the box for $p_0$. You may notice something that doesn't make sense with this model. You can zoom the vertical axis in and out by clicking the buttons with arrows.

Applet file: population_with_harvesting_fixed_number.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.