**In this lab the basic concept of pest population invasion and the spread of pest population 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.

**Table 1 shows the importance of each tab in the Variable Menu**

Tabe 1: Parameters in the variable menu of the simulator

**Run-Control Menu:**

**Table 2 shows the importance of each tab in the Run ÃƒÂ¢Ã¢â€šÂ¬Ã¢â‚¬Å“ Control Menu**

Table 2: Parameters of Run-Control menu of the simulator

**Sample Problem:**

- Consider the example of spread of Asian long horned beetle in a new area within North America with initial population density 100. Due to the favourable environmental condition there is a dramatic increase in the population growth rate of the pest and it rapidly spreads in the hardwood of deciduous forest. There were no known natural predators for this beetle except for the limited biotic and abiotic factors within the temperate zone of North America. Let the rate at which this population grows be 8 and the rate of dispersal be 0.4 in the size of the habitat where the population is located be 200 kilometers. Consider the minimum number of individuals required to establish a population is 20. Find out the spread of the invasive species in kilometers after 75 years in the habitat after its introduction.

To find the spread of invasive species in the ecosystem, one should apply the provided parameters in the specific boxes in the simulation tab.

**[Initial population of pest = 100, Population growth rate = 8, Disperse Rate = 0.4, Length of habitat = 200, Establishment number = 20, Number of years = 75]**

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

The graph will be displayed on the Simulator Viewable window.

On the peak of each plot, the population of the pest at the specific time period is displayed.

## Result Interpretation:

The invasion of the pest in the ecosystem is calculated using the mathematical simulator. In this example, invasive species, Asian long horned beetle, spreads 77 kilometers in the given habitat after 75 years.