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Consortium for Mathematics and its Applications

Product ID: 99688
Supplementary Print
Undergraduate

Time Resources in Animals (UMAP)

Author: Kevin Mitchell and Steven Kolmes


This unit presents an alternative to the classical optimal foraging models in behavioral ecology. The model presented in this reading is concerned with a time-budgeting process dependent only upon whether an animal is hungry or satiated at a given moment. The analysis of the model is carried out using simple Markov chains.

Table of Contents:

TIME RESOURCES
The Daily Pie
Key Concepts

THE THERMOSTAT MODEL OF FEEDING
The Activity and Appetite Functions
Changing Activities

MODEL I: AN OVERSIMPLIFIED EXAMPLE
Putting the Model Together: Catepillars
Keeping Track of Changing States
Western Tent Catepillars
Generating Data by Computer Simulation
The Relationship Between d and Resting Time
The Relationship Between b, d, and Resting Time
Eastern Tent Catepillars

LAZINESS

MODEL II: VARYING PREY VALUES
The Heron as Forager
The Assumptions about Herons
Two Special Cases
The Relationship Between c, d, and Rest Time (b = 0)
Combining the Results

A DIFFERENT ANALYSIS: RATES OF CHANGE

MODEL III: ENERGY LOSS DURING FORAGING
The Cat as Forager
The Mathematical Assumptions
A Single Simplification
A Comment on Desperation

MODEL IV: THE POSSIBILITY OF STARVATION
The Changes of State for the Stressed Cat
New Questions: Surviving the Winter
Improving the Rate of Successful Foraging
The Effect of Lowered Energy Loss at Rest
Moderating Winter
Tentative Conclusions

CONCLUSION

ANSWERS TO SELECTED EXERCISES

REFERENCES

ACKNOWLEDGMENT

ABOUT THE AUTHORS

APPENDIX: COMPUTER PROBLEMS

©1989 by COMAP, Inc.
UMAP Module
59 pages

Mathematics Topics:

Algebra , Discrete & Finite Mathematics , Abstract & Linear Algebra

Application Areas:

Life Sciences & Medicine , Biology

Prerequisites:

High School Algebra

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