The Lotka Volterra Predator Prey Model

Predators/prey relationships play a big role in animal populations. If the balance between predators and prey is changed, populations are changed. The white- tailed deer populations in some areas has grown too large because there are no natural predators.

model and multiple nuclei model. The first model was created by sociologist E.W. Burgess and

Different characteristics of species allows for the types of niches that can be occupied and whether or not they can be coexisted for example a food specialist will have anatomical and physiological adaptations that allow it to acquire and extract energy and nutrients from one food source extremely well, but will be at a disadvantage if that food source runs low. A food generalist may not acquire as much energy from the specialist’s preferred food, but will be able to make up for that by consuming other kinds of food. We can easily envision circumstances in which either species might outcompete the other. To achieve coexistence of species the carrying capacities of certain species must not be overshot and remain

The equation is dz/dx=ky(1-z/A). dz/dx is increasing rate of zombie, z is the population and A is the capacity (50). The k value we use is the average of the k values of the second to the fourth data point, k=1.0603. The function represent z in term of t is z=A-A/(B*e^kt+1). B is another constant. The B value we use is the average of each B value of each data point, B=0.0211. So z=50-50/(0.000256*e^(2.7477t)+1).

Plot a family of curves (use at least 20 values of K; you will probably need to use more) of P_(steady state) against iteration number to illustrate your findings.

The givens and assumptions are all of the values included in the above equation. The equation above also highlights what we needed to find, the discrete dynamical system, and the plan was to make assumptions, analyze the givens, and substitute all the given values into the general discrete dynamical system equation.

The “predators” in this experiment were three different types of tools, a tweezer, a wooden clothespin, and a clothes clip. At the start of the first round, there were ten beans for each different type of bean. Nearly all the white beans were taken out of the first round, only one survived. This was because the white beans were large, non slippery, and easy to catch. Red beans and green beans were not as easy to catch. Based on the data and the graph, the tweezers captured the most beans in this round and the clothes clip had the least (w/ only one white bean).

number of animals in an area surpasses the available food supply? More often than not, the

c.Population-all the organisms belonging to the same species within an area at the same time

now find the range of values which Kc can take for the overall system to be stable.

Survival of the fittest does limit both competing species, albeit there are times when the sheer population overwhelms that evolutionary mechanism. “...So many rabbits loose in Australia that even though about two million were shot or trapped each year, it didn’t make a dent in their population. Over time, the rabbits have caused untold damage…” (Semmler, para. 2). Rabbits took over their ecosystem and managed to stay put as part of the food web because of the size of their population.

The exact scenario changes in each example, but the central idea remains that through a chain of interactions, a non-abundant species has an outsized impact on ecosystem functions.

All three of the organism will have a spike in population growth due to the extinction of the coyotes. But there won’t be any more dramatic change in population after the first couple years after the death of the coyote population. This is because the black raspberry have 3 other species consuming them as food. The population will increase but not as much compared to the other organisms population growth. Rabbits has the least amount of predators. After the extinction of coyote only human consume rabbits which result dramatic increase in the rabbit population. All three will reach a plateau stage after each species get use to the change in the number of species that consume

When I was trying to think on a paper to write, it came to my mind something I read a long time ago about Yellowstone. When wolves started to get hunted in Yellowstone and got eliminated of the equation, Coyotes were the species that occupied the main predators in the area. However, there is a small difference between coyotes and wolfs. When it comes to hunting, coyotes hunt anything that they can kill from small species to big one, they don’t follow any pattern. In the Yellowstone ecosystem were many species depended on the small pray, coyotes eliminated their food. This was a huge problem for more than a century. Now, when they introduced wolfs into the ecosystem again, they rapidly eliminated the coyotes that were overpopulated and fixed

In the paper\cite{DeAl2011}, they have introduced a predator interference term into the Holling type I functional response. Since the resulting system shows a much richer dynamical behavior to the Holling type I functional response with predator mutual interference. They have shown that these dynamical properties do not result from the lack of smoothness but rather from subtle differences in the functional responses. Ko and Ryu\cite{Koan2006} studied a prey-predator model with Holling type II functional response by incorporating a prey refuge. In the Honors Program Project by Rachel\cite{VArb2013}, he has considered the basic Lotka-Volterra model with two-predator and one-prey model as well as a ratio-dependent model. He has described the uses