# Single species population models, Introduction to Population Modeling | J.C. Frauenthal | Springer

Continuous Population Models Abstract In this chapter we look at a population in which all individuals develop independently of one another. For this situation to occur these individuals must live in an unrestricted environment where no form of competition is possible.

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If the population is small then a stochastic model is more appropriate, as the likelihood that the population becomes extinct due to chance must be considered.

However, a deterministic model singlebörse dillingen provide a useful way of gaining sufficient understanding about the dynamics of a population whenever the population is large enough.

Furthermore, perturbations to populations at equilibrium often generate on short time scales independent individual responses, which are appropriately modeled by deterministic models. For example, the propagation of a disease in a large population via the introduction of a single infected individual single species population models to the generation of secondary cases.

In short, the spread of disease in a large population of susceptibles may be thought of as an invasion process via independent contacts with a few infectious individuals.

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

Discrete Population Models Abstract In this chapter we shall consider populations with a fixed interval between generations or possibly a fixed interval between measurements. The underlying assumption will always be that population size at each stage is determined by the population sizes in past generations, but that intermediate population sizes between generations are not needed.

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 single species population models said about the use of similar techniques for solving ecological problems.

Usually the time interval between generations is taken to be a constant. However, single species population models are situations in which the growth rate does not single species population models instantaneously to changes in population size.

Other causes of response delays which have been mentioned in the biological literature include differences in resource consumption with respect to age structure, migration and diffusion of populations, gestation and maturation periods, delays in behavioral response to environmental changes, and dependence single species population models a population on a food supply that requires time to recover from grazing.

In deriving a mathematical model to reflect a particular biological delay mechanism one must consider carefully how this mechanism affects the growth rate.

### Behaviour of a herbivore-plankton continuous interaction model

One approach to modeling delays that has been used is formulation of a discrete model or difference equation and consideration of the delay in the time between steps. While this is appropriate for populations with a discrete reproduction cycle, such as many fish populations, it does not accurately model populations with continuous growth and time lags. The metered models studied in Section 2.