James P. McDonald Week 2

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The Assignment

Part 1

  • When plugging in different numbers into the different constants I saw a consistent behavior when the growth rate was changed. At low growth rates the cell population would slowly increase and the nutrient concentration would slowly decrease and the cells used up nutrients at a slow pace. As the growth rate was increased the cells would grow more rapidly and nutrients would be depleted more rapidly. At a certain point the growth rates were so high that the cells would grow and the nutrients would be diminished almost instantaneously. After the point of maximum growth the cells slowly die off as there are no longer any nutrients available.

Part 2

  • As is the nature of logistic growth, the carrying capacity is important. In simulations of the system when the carrying capacity was very low the cells did not do well. The cells reached their carrying capacity almost immediately and died quickly as a result. Also, the nutrient concentration stayed high as they were not even living cells to take in the nutrients. As the carrying capacity was raised the cell populations increased and the nutrient levels decreased as the cells took in the nutrients. Once the carrying capacity got really high the cells would intake all of the nutrients before reaching their carrying capacity and the population would slow growing and eventually stop. The model behaves similarly to a logistic curve where the cells population initially increase rapidly as population is low and nutrients are high. As the cells grow they reach a point where they growth slows due to decreased nutrients, where eventually the cell growth will cease.
  • It is likely that yeast would produce a toxic waste product. If this is, it would have to be accounted for when looking at cell growth and death. The production of waste toxic to the yeast would cause the population to decrease due to increased death of the yeast. I would think the population of the yeast would fluctuate, as more yeast grow, more waste is produced and as a result the population of yeast will decline after the initial growth. Once the population of yeast declines the amount of waste will lessen and more yeast will then survive, causing another increase in the yeast population. The Malthus model would have to be altered to include the changing growth and death rates of the yeast.

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