**In this lab the basic concept of optimal foraging and the behavior of a sit-and-wait (ambush) predator whose optimal foraging strategy is to maximize the energy are explained using mathematical simulator. The steps for working out the simulator are discussed in the following sections.**

- While clicking the ÃƒÂ¢Ã¢â€šÂ¬Ã…â€œSimulator ÃƒÂ¢Ã¢â€šÂ¬Ã…â€œtab one will get a page as shown below.

- The ÃƒÂ¢Ã¢â€šÂ¬Ã…â€œvariablesÃƒÂ¢Ã¢â€šÂ¬Ã¢â€žÂ¢ in the simulator window are default values. User can change the values according to the data to be tested.

Using this menu, the user can set the desired values for the variables mentioned in the menu, according to which the corresponding graph will get plotted in the simulator window.

**Reciprocal Proportion**

The variables include: Abundance of prey (a) and Cut-off Radius. For example, if there is an abundance of 1 prey in every 100 seconds, a = 0.01. In this exercise we assume the possible foraging area of the predator as a semicircle. The outer boundary of the semicircle is referred as the cut-off radius.

**Average Time**

The average pursuit time is the time taken by the predator to pursue a prey in all parts of its foraging area. The parameters include: Abundance of prey (a), Velocity (v) and Cut-off radius.

**Energy Gain**

This allow the user to calculate the net energy gain. The average rate of energy gain from foraging in a particular area (we assume it as a semicircle) is the average energy per prey divided by the average time spent getting it.

The parameters are, Abundance of prey (a), Velocity (v), Energy content of each prey item (e), Energy burned (ew), which means the energy burned by a predator while waiting for the prey, Flying speed of predator (v), Energy burned while predation (ep) and Cut-off radius.

**Control Menu:**

**Table 1 shows the importance of each tab in the Run ÃƒÂ¢Ã¢â€šÂ¬Ã¢â‚¬Å“ Control Menu**

Table 1: Parameters of Control menu of the simulator

**Sample Problem: **

In nature it is observed that, the density of different prey can vary among habitats and regions. Does a change in abundance of prey affect the optimal distance of prey pursuit? Create a plot with total energy gained on y axis and plot the result by increasing the abundance of prey to 0.95, velocity to 80, energy content to 800, energy burned to 1.5 and flying speed to 40. What is the relationship between net energy gain and distance to the prey item? Assume that the cut-off radius of the foraging area is 5 with a fraction of 4 and end value as 60.

When the given data is provided in the specific boxes of the variable tabs, click on Plot graph on the Control Menu.

The graph will be displayed on the Simulator Viewable window.

Each value can be observed in the plot.

## Result Interpretation:

The net gain of energy of a sit and wait predator is calculated using mathematical simulator. Here, in this example, it is plotted that the net energy gain of the predator is 95038.166 (kilocalories per second) in an area of 54.33 meters (radius).