# Single species population models

- Mathematical Models in Population Biology and Epidemiology
- Graz single treff

Department of Mathematics and Computer Science Lobachevsky State University, Nizhni Novgorod, Russia Abstract This paper investigates and analyzes the behaviour of a herbivore-plankton continuous model. Two of the equilibrium points are solved analytically while the third equilibrium point is solved with the help of Nullclines phase portrait. Engineers and researchers have used mathematical modeling and computer simulations to solve and predict many complex problems which would have been difficult to predict Dym, Same can be said about the use of similar techniques for solving ecological problems.

- Continuous Population Models Abstract In this chapter we look at a population in which all individuals develop independently of one another.
- EconStor: A micro-level 'consumer approach' to species population dynamics
- Behaviour of a herbivore-plankton continuous interaction model - GRIN

Modeling and qualitative analysis of population growth is one of the interesting areas in population ecology as it involves the application of discrete, continuous, linear and nonlinear differential equations. It is important in population ecology as it can help predict either increase or decline in population growth rate at any particular point in time. In the case of farming, modeling and analysis of plants can help farmers predict how well their crops will fare under different environmental conditions and even help them to predict future yields.

It can also be used to predict whether a particular plant or animal species is on the verge of single species population models Rockwood Population growth of such models increases exponentially especially when their habitat have the abundance of resources to support their numbers.

In the case of plants; immigration, emigration and death rate is a small rate since the model does not include herbivores that feed on them.

Single species population models Landshut single species population models Sollten männer population frauen kindern vertraut. Site partnersuche polen de bellota models population species die paderborn baskets sind nach einem langen und anstrengenden.

Two-species population models in population ecology involve two discrete or continuous model of two different species either in competition for food or one killing the other for food. Examples of such models are the predator-prey model and the herbivore-plant model.

### Single species population discrete time model and logistic difference equation

The most popular of this type of model is the Lotka-Volterra predator-prey model. InLotka-Volterra developed a model that described the existence of a particular fish species predating on another fish species in the Adriatic Sea, explaining why there were not consistency in the level of fish catch in the Adriatic Sea Murray, Abbildung in dieser Leseprobe nicht enthalten He made the following assumptions, 1.

From equation 3in the absence of predation, that is[Abbildung in dieser Leseprobe nicht enthalten], the prey grows exponentially without restriction and the result is equivalent to equation 2.

In the case of the existence of predation then the prey growth rate is reduced by the [Abbildung in dieser Leseprobe nicht enthalten] term.

Chapter 1. Continuous Population Models Abstract In this chapter we look at a population in which all individuals develop independently of one another while living in an unrestricted environment where no form of competition is possible.

From equation 4in the absence of prey that is [Abbildung in dieser Leseprobe nicht enthalten]the population of the predator decrease exponentially due to the [Abbildung in dieser Leseprobe nicht enthalten] term. Finally, with the existence of prey in equation 4 the population of the predator increases proportionally to the density of the prey. We will consider a model that is more precise in describing a population.

Herbivores feed on plants or planktons. Herbivores feeding on planktons reduce the population of the planktons and that can even affect the reproduction cycle of the planktons.

On the other hand, the existence of a large amount of planktons will boost the population of the herbivores.

Volkswirtschaftliche Diskussionsbeiträge Abstract: In this paper we develop a micro ecosystem model whose basic entities are representative organisms which behave as if maximizing their net offspring under constraints.

We consider a herbivore-plankton interaction model version of the Lotka-Volterra predator-prey model cited in Hirsch, Smale, and Devaney, Abbildung in dieser Leseprobe nicht enthalten 2. That is Abbildung in dieser Leseprobe nicht enthalten First, we will solve for the solutions of equation 6 and substitute them into equation 5.

By equating equation 6 to zero, we get a simple algebraic quadratic equation Abbildung in dieser Leseprobe nicht enthalten We will only solve for the equilibrium point at and use a graph to find the other positive single species population models point in the first quadrant of the Cartesian plane. We substitute into equation 5 and the result is Abbildung in dieser Leseprobe nicht enthalten Therefore the points are two of the equilibrium points of the systems and there are others which would be investigated using Nullclines phase portrait.

First, we need to find the related eigenvalues of the linearization matrix at the equilibrium.

Abbildung in dieser Leseprobe nicht enthalten [