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Mathematics in Conservation

The Case of the Endangered Florida Panther



Co Authors:

Geffrey F. Stopper
Department of Biology
Sacred Heart University
stopperg@sacredheart.edu

Andrew G. Lazowski
Department of Mathematics
Sacred Heart University
lazowskia@sacredheart.edu

Abstract:

This interrupted case study teaches probability theory and transmission genetics through their application to the conservation of the endangered Florida panther. An endangered population is unlikely to survive simply due to its small population size. But a basic understanding of probabilities and transmission/population genetics reveals two additional problems with small population size: (1) lost genetic variation due to genetic drift decreases adaptability of the population and (2) increased homozygosity due to obligate inbreeding increases the expression of deleterious recessive alleles (inbreeding depression). These factors combine to create the phenomenon known as the extinction vortex--as a population size gets smaller and smaller, the likelihood of the population surviving decreases faster than the population size decreases, and the population is drawn ever-more strongly towards extinction. The case was developed as an interdisciplinary lesson in mathematics and biology for use in an introductory college-level probability and statistics course, but could also be used effectively in an introductory biology course in college (for non-majors or majors) or an advanced high school course in biology or probability.

Objectives:
  • Articulate some of the basic terms and concepts of transmission genetics, population genetics, and inbreeding.
  • Understand how probability theory is essential in transmission genetics and population genetics.
  • Apply probability to solve real-world problems.
  • Write meaningful statements about probability.
Keywords: Conservation; population genetics; transmission genetics; extinction; preservation; Florida panther; inheritance; inbreeding; probability
Topical Area: Policy issues, Regulatory issues
Educational Level: High school, Undergraduate lower division, Undergraduate upper division, Graduate, Professional (degree program), Faculty development
Formats: PDF
Type/Method: Analysis (Issues), Dilemma/Decision, Discussion, Interrupted
Language: English
Subject Headings: Biology (General)   Ecology   Environmental Science   Evolutionary Biology   Genetics / Heredity   Interdisciplinary Sciences   Mathematics   Natural Resource Management   Mathematics   Statistics   Wildlife Management   Zoology  
Date Posted: 8/15/2013
Date Modified:
Copyright: Copyright held by the National Center for Case Study Teaching in Science, University at Buffalo, State University of New York. Please see our usage guidelines, which outline our policy concerning permissible reproduction of this work.

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