Surrounding aquatic organisms is a boundary layer across which molecules must move via diffusion. As the rate of water flow around an organism increases the size of the boundary layer shrinks. Using this information, determine how the rate of nutrient uptake in aquatic plants/algae change as water flow rates change.

### Theory

- Diffusion (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 552)

### References

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Microbes convert substrate through enzymatic reactions into products that are then converted into microbial biomass. Using this knowledge, determine microbial growth in a chemostat (substrate-limited growth) under varying enzyme and substrate concentrations.

### Theory

- Michaelis and Menten model for enzyme reactions (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 624; Stephen P. and John Guckenheimer. Dynamic Models in Biology. New Jersey: Princeton University Press, 2006. 8 )
- Enzyme kinetics (Stephen P. and John Guckenheimer. Dynamic Models in Biology. New Jersey: Princeton University Press, 2006. 8 )

### References

- Whitmore, A. P. 1996. Alternative kinetic laws to describe the turnover of the microbial biomass. Plant and Soil. 181(1): 169-173.
- Okpokwasili, G. C. and C. O. Nweke 2006. Microbial growth and substrate utilization kinetics. African Journal of Biotechnology. 5(4): 305-317.

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The mark recapture method involves capturing, marking, and then releasing a portion of individuals in a population. After a sufficient amount of time for the marked individuals to reintegrate back into the population has passed, another portion of the individuals from the population are captured. From the number of marked individuals that are recaptured the total population size can be estimated (e.g. if 10 individuals were tagged and released, and then 10 individuals are recaptured, 2 of which were tagged, the population can be estimated to be 50 individuals). Create a model/equation that describes how the mark recapture method works. From your equation/model, compute the probability of finding a certain number of marked individuals.

### Theory

- Mark recapture method (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 653)
- Equal likely outcomes (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 650)

### References

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The purpose of this project is to predict the time it takes for malaria to become potentially fatal. An equation will be used to calculate the proportion growth of parasitic cells within a micro-liter of blood. Two trials will be tested: 1)a small initial load of parasites, and 2)a large load of parasites. From these results, the probability of an average human to fight off the infection will be predicted.

### Theory

- exponential growth (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 21-23, 358-359)

### References

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Fish and trees continually grow, but their growth is restricted, so as they grow older they grow proportionately more slowly. Determine how long it would take for a pet shop goldfish (5cm in length) to reach the size of a whale shark (12m in length) with and without restricted growth constraints. Alternatively, determine how long it would take for the trunk of a Christmas tree (15cm trunk diameter) to reach the size of a giant sequoia (10m trunk diameter) with and without restricted growth constraints.

### Theory

- von Bertalanffy equation (Neuhauser, Claudia. Calculus for Biology and Medicine. New Jersey: Prentice Hall, 2000. 167, 359)

### References

- Fieber, L. A. et al. 2005. Von bertalanffy growth models for hatchery-reared Aplysia californica. Bulletin of Marine Science. 76(1): 95-104.
- Priestley, S.M., A.E. Stevenson, and L.G. Alexander. 2006. Growth Rate and Body Condition in Relation to Group Size in Black Widow Tetras (Gymnocorymbus ternetzi) and Common Goldfish (Carassius auratus). The Journal of Nutrition. 136: 2078S–2080S.
- Candy, S. G. et al. 2007. A von bertalanffy growth model for toothfish at heard island fitted to length-at-age data and compared to observed growth from mark-recapture studies. Ccamlr Science. 14: 43-66.
- Rumi, A. et al. 2007. Growth rate fitting using the von Bertalanffy model: analysis of natural populations of Drepanotrema spp. snails (Gastropoda : Planorbidae). Revista De Biologia Tropical. 55(2): 559-567.

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