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ARS Home » Plains Area » Miles City, Montana » Livestock and Range Research Laboratory » Research » Publications at this Location » Publication #153036
Title: MATHEMATICAL MODELS: POPULATION DYNAMICS

Author
item Macneil, Michael
item CRONIN, M - ENTRIX, INC.

Submitted to: Encyclopedia of Animal Science
Publication Type: Book / Chapter
Publication Acceptance Date: 2/1/2004
Publication Date: 1/31/2005
Citation: Macneil, M.D., Cronin, M.A. 2005. p. 609-311. In Mathematical models: population dynamics. Encyclopedia of Animal Science. Marcel Dekker, Inc.

Interpretive Summary: Many variables affect census numbers and allele frequencies of populations. Therefore, a model is often necessary to focus on the most important variables. Using a model facilitates predictions or inferences about the natural system that are both consistent and objective. Models of population dynamics are widely used in studying human demographics, epidemiology, and wildlife management. Modeling census numbers has been less valuable in domestic animal agriculture. However, detailing factors affecting reproductive rate, survival, and gene flow have important ramifications on present and future efficiency of animal production. This paper provides a brief review of 1) how mathematical models may be used in understanding population dynamics and 2) how many of the same underlying phenomena are examined in the animal sciences. The intended audience for this work is students and others having limited familiarity with mathematical modeling, agricultural production systems or population dynamics.

Technical Abstract: The goal of this paper is to provide a brief review of mathematical models of population dynamics and applications of related methodology in the animal sciences. The basic function of any model is to represent something in abstract form simplifying the complex conditions encountered in nature. Because there are many variables that affect populations of animals, a model is often necessary to focus on the most important variables. A model allows the mathematical description of a population by considering a few important and estimable variables, and consists of equations that represent assumptions about how a system works in nature. Solving the equations allows predictions or inferences about the natural system. Classical models of census number and genotypic frequency are reviewed. Models of population dynamics have only rarely been used in animal science. However, reproductive rate, survival, and gene flow are important issues in the animal sciences and are also discussed. We conclude mathematical models are valuable tools to increase understanding of population dynamics. In natural populations, formal applications of classical models of population dynamics provide insight into changes in census numbers and facilitate prediction of future inventories. Modeling census numbers has been less valuable in domestic animal agriculture. However, detailing factors affecting reproductive rate, survival, and gene flow have important ramifications on present and future efficiency of animal production.