Question

In: Advanced Math

Suppose you have been asked to develop a simple model for the movement of ants in...

Suppose you have been asked to develop a simple model for the movement of ants in the presence of a food source. Discuss how you could simulate this model. Your answer should include any simplifying assumptions, some parameters that you’d need, and the interaction rules you would set up.

Solutions

Expert Solution

WITHOUT USER INTERACTION

On setup, two ant colonies (one of red ants and one of black ants) and a number of flowers are created in the world. Ants are spawned in the ant colony and then wander until they find food, represented as flowers in the model. When they find food, they personally gain energy through eating nectar, then they return to the colony while laying down a pheromone, represented as pink trails in this model to feed the young inside the nest. Ants near pheromone trails are attracted to the strongest chemical trail. As the ants exhaust a food source, they once again begin to wander until they find another food source or another pheromone trail to follow.

When two or more ants of opposing colonies encounter each other, they fight or scare each other away also leaving chemicals that attract more ants. For the winner, this works to protect the food source from competing colonies. The ant queen reproduces when the ants in her colony collect enough food, set by the create cost for each colony. Flowers periodically grow up around the map, resupplying food in the game. Ants die if they get too old, cannot find food, or sometimes when they lose a fight. Nests die if they have no more ants living in them.

When the ants have enough surplus food, they release male and female winged ants to reproduce. When these winged ants meet they make a new colony.

USER INTERACTION

Users can interact with the model, setting parameters for their colony and ants. Ideally each colony color would be played by an individual or team. Only a single input will be registered at any time - so teams will need to determine turn-taking practices.

The colony teams interact with this complex system in two ways. First, they can adjust the characteristics of their colony and its ants. Second, they can add or remove certain environmental features from the world.

Colony teams can decide how large and aggressive their ants are. When the size of ants increases, they become slightly faster and stronger in a fight. When players make their ants more aggressive, it increases the likelihood that ants detect opposing ants and thus the probability that they will attack. The START-ENERGY sliders set the amount of energy a new born ant has when it leaves the nest for the first time. This determines how far it can walk before finding food.

Increases in size, aggressiveness or start-energy reduces the expected population of the colony, by increasing the the cost of creating more ants, displayed in the "Create Cost" widget. The changes also increases their likelihood of fighting and winning through emergent interactions of parameters (size and aggressiveness) and agent actions (collecting food, leaving trails, and fighting).

Colony teams can adjust the environment by adding chemical trails, adding flowers, and erasing chemical trails with vinegar.

HOW TO USE IT

There are five widgets in the center of the screen that control functions for both the red and black colony teams. As shown in the diagram above, marked 4 above, PLAY and STOP control the model’s time measured in ticks. Marked 5 in the diagram, RESTART sets the model back to initial conditions. The ADD drop down menu, marked 6 above, allows you to choose to place flowers, chemical pheromone trails, or erase trails with vinegar. To use it, select one of them, then click on the view. The EVAPORATION-RATE slider, marked 7 above, controls the evaporation rate of the chemical.

Each team decides how large and aggressive their ants are with the sliders to the left and right of the view, marked 2 in the diagram above. Then they each select how much food each new ant starts with. Once teams have decided, they should agree to click the RESTART button to set up the ant nests (with red and black flags) and the food-flowers. Clicking the PLAY button starts the simulation.

If you want to change the size, aggressiveness or starting food move your team's sliders either before pressing RESTART, or after to affect newly born ants.

Marked 1, monitors Red and Black ants at the top, counts the ants’ population named BLACK ANTS on the left, and RED ANTS on the right. Marked 2, the three sliders at the bottom left and right are sliders players can use to adjust their ant’s size, aggressiveness, and the maximum amount of energy, or basically how long ants can walk without eating. Adjusting any of these sliders will change the Create Cost. These sliders can be adjusted at any time during the game to experiment with different settings. Marked 3, in the middle, Ant Adaptation provides a monitor CREATE COST. The CREATE COST monitor shows the total value that it currently costs to produce one more ant. Specifically, the colony produces a new ant when the stored food is greater than the CREATE COST. The cost is calculated by a function of the three sliders.

THINGS TO NOTICE

The ant colony generally exploits the food sources in order, starting with the food closest to the nest, and finishing with the food most distant from the nest. It is more difficult for the ants to form a stable trail to the more distant food, since the chemical trail has more time to evaporate and diffuse before being reinforced.

Once the colony finishes collecting the closest food, the chemical trail to that food naturally disappears, freeing up ants to help collect the other food sources. The more distant food sources require a larger "critical number" of ants to form a stable trail.

The population of each of the two colonies is shown in the plot. The line colors in the plot match the colors of the colonies.

Changing a team's AGGRESSIVENESS, or SIZE, changes ant behavior. It also changes the depiction of the ant in the widget marked 8 above.

Notice how proximity of food to the colony affects population growth.

Notice if too much chemical causes problems.

This model operates at two levels, both representing the individual ant, and the colony. This makes it an agent-based model of a super-organism.


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