LauraTerada Individual Journal Assignment Week 2
- I simulated the given system with different values for the different variables in the equation such as the growth rate, initial concentration of nutrients, and the initial concentration of the cells. More specifically, I focused on changing the growth rate and how that affects the concentration of cells and nutrients. When setting the growth rate to a lower number, the the cell population increased while the concentration of nutrients decreased. As I increased the value of “r,” or the growth rate, the concentration of cells increased as well, along with the a decrease in nutrient concentration. As the nutrients were being used up by the cells, the nutrient concentration consequently decreased. The concentration of cells developed a carrying capacity, which was shown through a more horizontal slope.
- As shown in the equation and stated in the assignment, the carrying capacity increases linearly with the nutrient level. As I simulated the system with different carrying capacity values, I made a few observations in regards to how this new system behaves. When I set the carrying capacity variable to a low number, the cell population reached its capacity relatively quickly, then decreased. However, when I increased the value of the carrying capacity, the cell concentration increased. Consequently, the nutrient level decreased as the cell concentration reached its carrying capacity. Once the nutrients were used up, the cell concentrtion then began to decrease as a result. Thus, graphing the logistic growth model allowed me to understand how carrying capacity can affect a population's growth requirements.
- The Malthus model is a simple model that explains the rate of change of the population. The model states that the rate of change is equal to the death rate being subtracted from the birth rate. However, the model can further be adjusted to include nutrient levels and population size. In order to account for true cell functions, the Malthus model should be further adjusted. For example, if the yeast produces waste, this waste may be toxic. These toxic compounds can then affect the growth rate of the entire population. Firstly, when the yeast cells proliferate, more waste will be produced. Thus, yeast cells will die off. This decrease in population, due to waste production, should be accounted for in the Malthus equation. Secondly, one might consider the nutrient dependent growth rate in the model. The nutrients in the chemostat may react with the waste products of yeast, thus decreasing the concentration of usable nutrients. However, is just an assumption that the waste products may react with the nutrients. If this is true, the equation should account for the relationship between growth rate and nutrient/waste levels.