Due Wed Mar 11
10 points total
1. Competition for resources (4 points). We have discussed (in Lecture 3 and elsewhere) growth that depletes a resource. A simple model is shown below.
a. Explain how this model combines several components (as discussed in Lecture 14) including flow control, positive feedback and constant flow.
b. Draw an expanded view of this model that shows competition of two species for a single resource ONLY through depletion of a common resource.
c. In a competition situation like this, it is possible for one plant to do well initially (at high resource) but then the other plant do well and take over when the resources are depleted. For example, consider two species with different Vmax and Km as shown below. Species 1 has a Vmax = 20 and a Km=5, and species 2 has Vmax = 40 and Km =40. Describe the mechanism of species shift that takes place as the plants deplete the resource. Refer to this graph to explain how this works.
2. Alternative hypotheses (2 points). An alternate model for competition between organisms can include direct interactions (instead of indirectly thorough a shared resource pool). Draw an alternative model diagram that would show this. These two models (from part 1 and part 2) represent alternative hypothesis for plant-plant interaction. What would you observe or measure (what experiment could you perform) to tell the difference between these two mechanisms, i.e. how would you tell which mechanism is operating in any specific case?
3. Succession based on competition (2 points). One model for succession is that plant replace each other based on their competitive ability to use resources (as shown in part 1). Create a model diagram for 4 species that rely on a single resource and sketch the relative Michaelis-Menten curves that would result in Species A doing well at first, followed by SpeciesB, SpeciesC and finally (at low resources) SpeciesD.
4. Succession and competition based on two resources (2 points). As a increase in complexity to the model in part 3, create a model that has two nutrients supplied to 4 species and show how the populations would compete for both of those resources, leading to the same sort of outcome (i.e. succession of Species A to Species D). This model will have to track both resources separately. Sketch a model diagram and explain how it works and in what domains of resource 1 and resource 2, each species would dominate.
March 7, 2009
