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1-039-StochasticPopModels-ModelingScenario

Author(s): Daniel Flath

Macalester College, St. Paul Mn USA

Keywords: Probability population dynamics Variance Mean stochastic deterministic

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Abstract

Resource Image We develop strategies for creating a population model using some simple probabilistic assumptions. These assumptions lead to a system of differential equations for the probability that a system is in state (or population size) n at time t.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

We go further and compare the mean population levels to the deterministic models from direct differential equations development.

We will develop stochastic or probabilistic models; for the probability that a population is size N at time t. In actual populations there is a random component to the growth that may not

be captured in simpler differential equations models. We examine this approach in a straightforward way.

We are going to describe the population by an infinite sequence of functions.

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Authors

Author(s): Daniel Flath

Macalester College, St. Paul Mn USA

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