This project will look at home range estimation for wildlife, which involves estimating the area that an animal occupies from satellite tracking data. The goal is to look at how home ranges can be estimated using concave hulls in a geographic information system (GIS). More specifically, this project will show how areas of the concave hulls are computed in a GIS (using a trapezoid-based algorithm) and how the area could be computed using calculus-based integrals.

Theory

• integration techniques and computational methods (Neuhauser, Claudia. ‘Calculus for Biology and Medicine’. New Jersey: Prentice Hall, 2000. 282-348)

References

Growth rate

Food chains/webs describe feeding relationships and energy flow within ecosystems. As one organism is consumed by another there is substantial losses in production as energy passes from one trophic level to the next. Choose a simple food chain that you wish to investigate and create a model that describes energy flow from one trophic level to the next. The ratio of production at one trophic level to production at the next higher trophic level is called the conversion efficiency. Determine the conversion efficiency of your food chain.

Theory

• Compartment models (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 587; DMB pg. 7)

References

For fisheries it is imperative for managers to understand the population dynamics of the fishery they are trying to manage. Create a model to describe the recruitment of fish into a population as a function of the size of the parent stock. What happens to recruitment as you increase or decrease the parent stock? What are the management implications of changes in the parent stock?

Theory

• Derivatives of exponential function (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 131)

References

It is known that the test used to identify a very rare disease or the presence of a performance enhancing drug results gives a positive result 98% of the time when the disease or drug is actually present and a false positive 0.5% of the time. What is the probability of a positive test result when a random individual is tested? Negative result?

Theory

• Approximation and local linearity (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 146)
• Error propagation (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 149)
• Law of total probability (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 658)

References

• Welsh, M. et al. 1997. Sexually transmitted disease risk assessment used among low-risk populations in East/Central Africa: A review. East African Medical Journal. 74(12): 764-771.
• Jorgensen, L. G. M. et al. 2004. Should we maintain the 95 percent reference intervals in the era of wellness testing? A concept paper. Clinical Chemistry and Laboratory Medicine. 42(7): 747-751.
• Lloyd, C. J. and D. Frommer 2004. Estimating the false negative fraction for a multiple screening test for bowel cancer when negatives are not verified. Australian & New Zealand Journal of Statistics. 46(4): 531-542.