Question

The Lotka-Volterra model produces consistently identical cycles because it is deterministic. The lynx and hare simulation on the right does not, because it is stochastic. Run the simulation again now with the controls below, paying attention to the animals in the enclosure at the top. Given the differences between these two types of models, why would it be difficult to determine accurate values for the four parameters in the Lotka-Volterra predator-prey model (a, rprey, m, b) for animals in the real world?
A. In the real world, individual predators do not differ in their ability to search for prey.
B. In the real world, random and unpredictable events occur, so the Lotka-Volterra parameters vary over time
C. In the real world, prey population sizes constantly change, and the Lotka-Volterra model fails to account for this.
D. In the real world, biological interactions are so complex and dynamic that models have no relevance.

Answer 1

Answer:

B. In the real world, random and unpredictable events occur, so the Lotka-Volterra parameters vary over time

Explanation:

Lotka-Volterra equations are mathematical models that explain biological prey-predator interactions among two species, considering the following assumptions,      

• The ecosystem is isolated and closed. There is no migration.
• The whole individuals are reproductively equivalent.

• In the absence of the predator, prey shows an exponential growth rate. The prey is in the ideal environment.

• In the absence of the prey, the predator population decreases exponentially.  The predator environment is also ideal, but it is limited by the prey density.  
• The predation rate is proportional to the encounters rate, which also depends on density.

• The predators affect the prey populations, making it decrease proportionally to the number of prey and predators present.

• The prey population also influence the predator population, proportionally to the number of encounters between the two species.

In these equations, the variable D is the number of predators, and P the number of preys.

The parameters are always constant:  

• r1: prey growth rate.

• a1: predator hunting success.

• r2: predator growth rate.

• a2: the success of the predator in hunting and feeding.

In nature, there are many factors affecting interactions. Dense-dependent factors and dense-independent factors. Also in reality there are stochastic factors. Stochasticity refers to the variability in the system involving those factors that are affecting or influencing the population growth. Stochasticity might be related to good years and bad years for population growth.

In a real situation, the compliance of the whole assumptions does not occur. The previously mentioned constants might vary, changing continuously the interaction among the predator and the prey. These parameters change in different degrees, resulting in different circumstances for both species.