Question

Answer questions 1-5

1. Compare and contrast the underlying causes of time delays in predator-prey interactions.
2. What is the Lotka-Volterra Model? What is the relationship that exists between predators and prey? How is this model affected by time?
3. Compare functional and numerical response. What are the different types of functional responses related to prey consumed to prey density? Are predators affected by these changes in density? Is there a pattern?
4. Compare and contrast lethal and nonlethal effects of predation. Give examples to explain your reasoning.
5. How can organisms other than plants avoid negative (harmful) interactions?

Answer 1

In order to prove and maintain their existence the species compete, evolve and disperse. Predator prey model is thus the building block of the ecosystem. The predator- prey interaction can be of various forms depending on the ecosystem resource-consumer, plant-herbivore, parasite-host, tumor cells (virus)-immune system, susceptible-infectious interactions, etc.

The Predator-prey Model may have application outside the ecosystem as they deal with the general loss -win interactions. Competitive interactions when observed closely are found to be some forms of predator-prey interaction in disguise.

The simplest of all predator-prey interaction is the Lotka-Volterra model. The model was developed independently by Lotka (1925) and Volterra (1926).

Vito Volterra, an Italian Mathematician proposed a differential equation model in 1926, that explained the observed increased in predator fish population and corresponding decrease in the prey fish population in Adriatic Sea during World War I. Parallelly in the United States, the equations were derived independently by Alfred Lotka (1925) to describe a hypothetical chemical reaction in which the chemical concentrations oscillate.

dxdt=αx-βxy,

= αχ – βαy,

dydt=δxy-γy

* = 8xy - Vy dt

where

x is the number of prey (for example, deer);

y is the number of predator (for example, Lions);

dx/dt , and dy/dt represent the instantaneous growth rates of the two populations;

t represents time;

α, β, γ, δ are positive real parameters describing the interaction of the two species.

As differential equations are used in the Lotka-Volterra model, the relationship between Predator and Prey is Deterministic and Continuous. The linearization of the equation lead to the simple harmonic motion wherein the population of the predator trails the population of prey by 90 degrees.

Red reperesents Prey ; $1585660968932_blob.png$

Grey represents Predator

X axis is Time ; Y axis is Population of Prey and Predators

The rate of predation upon the prey is assumed to be proportional to the rate at which the predators and the prey meet which is represented by βxy.

The model shows an linear relationship with time.

There are three types of Functional Response

Type I: The functional response rises in proportional to the increase in availability of the food (prey density) and their become liner after reaching a maximum limit.

Type II: The attack rate increases at a decreasing rate with prey density until it becomes constant at satiation. Type II responses are typical of predators that specialise on one or a few prey

Type III: The attack rate accelerates at first and then decelerates towards satiation. Type III is a Sigmoid response, these are typical of generalists that switch from one prey species to another and/or increase their feeding when resources are abundant