||Competition Graph and Food Webs
My project involves analyzing the competition graphs of food webs. Statistically, the competition graphs of most of the actual food webs are found to be interval graphs but most directed graphs do not have interval competition graphs. So, it's interesting to investigate this characteristic of food webs. The main goal of my project is to characterize the directed graphs whose competition graphs are interval graphs.
- Week 1:
- I arrived at Rutgers, met with other REU participants and my mentor. My mentor assigned some readings which helped me get more familiar with my research project and create a brief introductory presentation about my project.
- Week 2:
- I gave the presentation on Monday (slides included below). This week I worked on modeling random food webs computationally using Java and implemented their competition graphs. I also got a few questions to work on next week from my mentor.
- Week 3:
- This week I investigated on properties of chordal graphs and interval graphs. For the chordal graphs, I read some papers on their transitive orientation and for the interval graphs I researched on the clique incidence matrix and the consecutive ones property. My next task will be to come up with an implementation of these on real food web data.
- Week 4:
- This week I computed competition graphs from real food web data and analyzed transitive orientation in both competition graphs and their complements. I also read some articles on occurence of cliques in real communities.
- Week 5:
- This week I improvised the food web model by adding weights on the edges, which represents the diet percentage of the predator. There has been previous research done where weights represents the common number of preys but the idea of predator's diet is not explored.
- Week 6:
- This week I explored the weighted model of food web. The idea of putting weights on the edges and assigning a threshold to compute the competition graph seemed to be very interesting and a better way to model the competition in a real food web.
- Week 7:
- This week was mostly experimenting with the threshold value on the edges which essentially determines if a edge should be discounted when computing the competition graph. Also, I prepared slides for my second presentation (slides included below) and gave the presentation on Friday.
- Week 8:
- This week I found an interesting result while analyzing the YellowStone Park food web data. The competition graph of the yellowstone park had a forbidden subgraph of interval graph, the asteroidal triple. But using the weighted model of the food web with a threshold of 0.2, the competition graph was an interval graph.
- Week 9:
- This is the last week of the REU program and I will spend this week on completing my final report.