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When moisture is available, it is taken up by the fungus leading to a mechanical change which allows more light to get through, triggering algal photosynthesis; new food and new tissue are then made.

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flowers and ferns, grow early in the spring with long, quick-growing leaves so gather as much sunlight before the trees block them

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trees grow large leaves to absorb the most possible light during the growing season.

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Since winter is so cold they tend to have thicker coats for warmth

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grow thicker pelts in the fall to protect the animals during the cold winter months.

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At Florida Tech, math is a large part of many student's curriculum and many students make a career out of it.

Applied math major Greta Polo's student design project deals with understanding and modeling a prey and predator and a control population to find their ideal number of meetings while simultaneously maximizing their total numbers.

According to Polo, the project provides a solution to model the meetings of potential populations.

"Say you have an invasive bacteria in the ocean," Polo said. "You can model how it would affect the fish and what control, like fishing, you would use to solve this problem and at what periods of time you would allow this to happen to help the overall population."

For example, take a rabbit, a fox and a hunter. Without the fox, the rabbits would multiply infinitely many times; without rabbits, the foxes would die out as they do not have anything to eat, and without hunters, the foxes would eat all the rabbits.

However, most populations cannot be modeled in a continuous manner, as a real-life setting is discontinuous and non-linear. This is what makes the process more complicated and where the math comes in. Polo used a space called L 2, which is the space of discontinuous functions to help model this relationship.

Additionally, when something is not continuous, it is hard to know whether it has a derivative in order to proceed. That is why Polo used the method of Frechet Differentiation.

"When we do this, we prove uniqueness and the existence of a solution which allows us to proceed within our process," Polo said. "Solving our adjoint system backwards, from a terminal time, allowed us to solve the original system in the normal forward method to proceed to formulate a gradient."

The gradient method is a method that shows the direction to move in, in order to find the optimal solution. Iterating this and using numerical approximations, Polo modeled how certain conditions would affect the population and when the best hunting seasons would be in order to maximize the numbers of foxes and rabbits.

Polo was inspired to pursue this project because math at a higher level can become very abstract and many people fail to see the applications it has to something in the real world.

"I think this project was very applicable to a real world situation and I was also happy to see it myself as sometimes when doing theoretical math, I find it myself harder to see and understand it," Polo said.

Polo was very surprised to see how math in infinite dimensions could apply to fully understandable real-life situations.

"This project helped me see how the math you do in theory is fully applicable to something in the real world and without it, it would be a lot harder to properly understand and find a solution," Polo said. "It will definitely help me in my career if I wanted to go into modeling and controlling certain variables."

Polo advises students to choose a research topic they like and have the ability to explain it to people.

"Its important to love what you are doing or else you will never get it done in the best way you can," she said. "This is definitely an important part of your college experience as it allows you to find a way to put together all the things you have learned throughout the years into a project which ties it all together."

Polo received "Best in Show for Mathematical Sciences" at the 2016 Northrop Grumman Engineering and Science Student Design Showcase.

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Solving the Predator and Prey Equation | Florida Tech eCurrent

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At Florida Tech, math is a large part of many student's curriculum and many students make a career out of it. Applied math major Greta Polo's student design project deals with understanding and modeling a prey and predator and a control population to find their ideal number of meetings while simultaneously maximizing their total numbers.

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Larger mammals, such as deer, are smaller and have shorter antlers than deer in other biomes. This adaptation gives them the ability to move freely in the underbrush.

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the bird and the deer-the bird eats the insects off of the deer ,so the bird gets a meal and the deer is insect free.

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he tapeworm and animal-the animal(host) gets harmed by the tapeworm(parasite) when the tapeworm eats the animals food.

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A squirrel uses the tree for protection and food but the tree isn't harmed

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A-Located in the eastern United States, Canada, Europe, China , Japan, and parts of Russia
B- Quick change in seasons all the time and more commonly are mild summers no higher than 70 and cold winters
C- mountains, valleys, rolling hills, and flat plateaus. In the Southern Hemisphere, dry deciduous forests tend to occur near grasslands where the land is rolling or more nearly level.