# User:Andriab

## Contents

### Personal Information

My name is Andria Barraza. I am a senior at the University of the Pacific in Stockton, California majoring in Pure Math. I will be graduating next year and plan to continue on to get my masters degree in math.

**Week 1**(May 31st-June 3)

**Tuesday May 31**

- Met my mentor finally!
- Welcome/ Introductions to the program
- Tour of the campus
- Lunch with the mentors and grad students
- Paperwork
- How to use the wiki

**Wednesday June 1**

- Met with Dr. Factor to set up description and title for program
- Worked on Biomath Module packet completed packet up to pg. 35

-Read about food webs -Mathematical modeling -Basic Graph Theory Definition -Trophic levels/Energy Levels/Energy Transfer (Interesting!!) -Species importance and vulnerability -Redundancy and resiliency

**Thursday June 2**

- Worked on Module packet with Kenny in the morning

-Weighted arcs in food webs -Trophic status

- Had lunch with Dr. Factor, Kenny and Zac to discuss our goals and milestones for our research project
- Dr. Factor gave us a quick intro to graph theory and some basic definitions
- Went to talk "Good Research Practices, and the Art of Keeping Logs"
- Attended library orientation

**Friday June 3**

- Met with Kenny early in the morning to work on Graph Theory assignment
- Began working through the problem set in "Applied Combinatorics" by Alan Tucker

-Graph models - Basic definitions needed to begin working through the problem set

- Kenny and I worked through most of the set from this book. So far there have been few application to ecology but I am beginning to see how we will model the food webs using directed graphs
- Posted project name, milestones, and weekly log on the wiki today

**Week 2** (June 6 - June 10)

**Monday June 6**

- Worked through problems from various graph theory books
- Working on familiarizing myslef with definitions so that I can read through the graph theory papers I will begin looking through next week

**Tuesday June 7**

- Worked on the section about Isomorphisms. I underestimated how long it would take me to get through this section!
- Picked out the ecostytem I will be working with over the summer. The Sahara
- Met with Dr. Factor to discuss the graph theory Kenny and I have been studying so far
- Read through some of the Cohen material Dr. Factor assigned

**Wednesday June 8**

- Finished the last of the Isomorphism problems from one of the text books. I finally found a more efficient method I can use to identify isomorphic graphs.
- Continued reading the Cohen material
- Began reading the first paper on competition graphs

**Thursday June 9**

- Met with Dr. Factor to discuss the paper (Competition Graphs of Strongly Connected and Hamiltonian Digraphs)
- Participated in the luncheon
- Continued reading through the Cohen material paying special attention to the Cascade Model he uses to work with food webs
- Met with Zac and worked on going through the proofs from the paper we read this week

**Friday June 10**

- Began reading the second paper Dr. Factor assigned ( A Characterization of Competition Graphs)
- Finished reading through the Cohen material in the book
- I have been looking for information on the species found in the Sahara so that I can put together the food web and have not been able to find anything yet

**Week 3** (June 13-June 18)

**Monday June 13**

- Read through " A Characterization of Competition Graphs" and then met with Zac and Kenny to discuss and work through some of the theorems in the paper together
- Read various articles concerning food webs
- Picked the ecoregion I will be working on
- Found list of species in this region and began to do research to see what predator/prey relations there are among the species from the list

**Tuesday June 14**

- Finished going through the list of mammals.I have been listing what each animal preys on. I worked through 29 bird species out of 51 but then decided to leave them as one since group.
- Met with Dr. Factor to discuss how our research is going so far.
- Attended talk by Dr. Brylow. Learned about what makes a good research paper and what makes a good research talk.
- Finished going through the list of species. I wrote down what each one preys on.

**Wednesday June 15**

- Read through various encyclopedia entries to find out more about trophic levels, ecological communities, and food web theory.
- Put together entire food web. I grouped various animals together and my food web now includes 25 species.
- Updated wiki

**Thursday June 15**

- Finished compiling food web. When I looked over it again I realized I had missed some arcs.
- Met with Dr. Factor to discuss a paper we read through this week and to show her the food web.
- Attended weekly luncheon
- Attended NSF talk about ethical research

**Friday June 16**

- Put together competition graph.
- Wrote a draft sysnopsis what the backgroud material I have studied to date.
- Began reading through "Weighted Competition Graphs"

**Week 4** (June 20-June 24)

**Monday June 20**

- Met with Zac to discuss the paper about weighted competition graphs.
- I spent a great deal of time today revising my food web.I am going to begin working on the (1,2)-step competion graph so I want to make sure that I make all the necessary changes before I go on. I took out a few species after checking various sources and finding that they might not be a part of the ecoregion I am working with. I also divided the birds into two groups. Aves and birds, the Aves are omnivores.

**Tuesday June 21**

- Used sketchpad to draw my food web and competition graph.
- Met with Dr. Factor to show her what I have done in the past week. My synopsis was a little bit too short. Remember to go back and rewrite it!
- I began working on the (1,2)-Step competition graph. I decided to look at what specices will not (1,2) compete since it seems that most species WILL (1,2) compete.

**Wednesday June 22**

- I drew out the (1,2) Step competition graph using sketch pad and I have to find a better way of grouping the species together. There are way too many edges, so many that the graph is basically useless.
- I decided to switch over to working with matrices. I made the adjacency matrix for the food web and put together the competition matrix. I began working on the (1,2)-Step competition matrix. Basically I printed out the one used to represent the competition matrix but deleted all of the zeroes since they can potentially be ones in the (1,2) step graph.

**Thursday June 23**

- I finished working on the matrix the represents the (1,2)- Step competition graph. Finally!! (on paper)
- Met with Dr. Factor to discuss what direction we would like to go with the research.
- Attended the luncheon.

**Friday June 24**

- Completed the matrix using excell so that. I went back and corrected a few errors in the other matrices.
- I spent the day compiling (1,2)-Step competition graphs based on the foodwebs found in the back of the Cohen book "Community Food Webs:Data and Theory." I would like to find why there are edges missing since most of the graphs are complete. I am only using the commmunity webs that have 10-13 species because anything bigger becomes hard to work with and extremely time consuming. It would be helpful if we could write a matlab program that will produce the matrix that corresponds to the competition graph and the (1,2)-Step competiion graph.

**Week 5 ** (June 27-July 1)

**Monday June 27**

- Put together (1,2)-Step competition graphs for a few more community webs from Cohen's book
- I came up with a few more propositions about the completeness of (1,2)-Step competition graphs that I will present to Dr. Factor tomorrow
- Brainstormed ideas for which directon I would like my research to go in

**Tuesday June 28**

- Made outline for what my talk is going to be about this Thursday
- Met with Dr. Factor to discuss my work
- Continued preparing for my presentation.... took a long time to find some source of information that would help motivate the research area that we are working in. I finally found it in the Cohen book!!

**Wednesday June 29**

- Prepared powerpoint slides for presentation. Making the diagrams in sketchpad is very time consuming but Word is not much better.
- Sent it to Dr. Factor and had to make a lot of revisions, mostly I had to add background information and more diagrams.

**Thursday June 30**

- Practiced presentation a few times to work on the timing.
- Made final changes to slides
- Presentations Today!!!!

**Friday July 1**

- Continued trying to find what there must be in the digraph in order to have a (1,2)-Step Competion graph that is NOT complete.... I'm thinking this may not be an idea worth pursuing because of the limited amount of time we have this summer.
- Some of the different aspects of the webs that I am looking at are the insets/ outsets, trophic levels, and chains in the food webs

**Week 6 **(July 4- July 8)

** Tuesday July 5**

- Met with Dr. Factor and discussed presentation- I need to work on motivating problem but we decided that I will mention in the next presentation that we are working on developing a tool that can be applied we are not focused on applying it ourselves!!!
- Continued working on Characterizing digraphs of complete (1,2)-Step Competition graphs.... Dr. Factor gave me some new idease to pursue.

**Wednesday July 6**

- COntinued my pursuit of characterizing the digraph
- Also put together a handout of the conjectures I have made so far, including diagrams and I also worked on proofs for these statements

**Thursday July 7**

- Finished handout this morning before meeting with Dr. Factor
- Met with Dr. Factor today to discuss progress
- Discussed new direction for my work. I will be looking at the connectedness of (1,2)-Step Competition graphs and characterizing the corresponding digraphs. This will probably take up the remaining weeks of research that are left.

**Friday July 8**

- In attempting to characterize the digraphs I have found that there are too many variables to work with! There is the number of species in the foodweb, the number of basal species, top predators and the number of trophic levels.
- Spent most of the day looking at different combination of these variables and trying to find a systematic way of working with all of the different food webs we can consider.
- It seems that because of all of the variables that there are in this problem it is going to be very difficult to come up with definite conclusions.

** Week 7 **( July 11-July 15)

** Monday July 11**

- Inputted data for about 30 food webs from the Cohen web. My plan is to find what the average number of basal species are for a web as well as top predators so that there can be some constraints set on these variables.
- Found the average percentage of basal species and top predators in a foodweb
- Continued working on characterizing the digraphs using the percentages from the data
- Met with Zac and installed LaTeX on my laptop

**Tuesday July 12**

- Met with Dr. Factor and discussed my work with her
- Wrote out some background info that will be useful for my research paper
- It looks like I may not have to look at so many individual webs and that I only have to consider the trophic levels of the foodwebs!!

**Wednesday July 13**

- Came up with a few conjectures this morning but then I found that I was able to disprove almost every single one... disappointing.
- I finally came up with a few conjectures concerning the connectednes of species that are found in the 2nd and 3rd trophic level but I have yet to prove them

**Thursday July 14**

- I have continued working on coming up with a counterexample for the conjectures I have but I have not been able to produce one. I will probably begin working on proving them soon.
- I am working on digraphs with 1 trophic level and only varying the number of species in the first trophic level. Looking to see if any work has been done concerning the connectedness of the competition graphs for foodwebs, but I haven't been able to find anything yet.

** Friday July 15**

- I have decided to begin to look for specific cases where there is going to be an edge in the (1,2)-Step comepetition graph and when it is going to be missing... smaller steps.
- Finally came up with a conjecture concerning the connectedness of the first trophic level! I had made things too complicated before.

**Week 8**(July 18-July 22)

**Monday July 18**

- Wrote out a few proofs for some of the conjectures I had
- Continued working on what I can say about the connectedness of the (1,2)-Step Competition graph

**Tuesday July 19**

- Met with Zac to go over the proofs I have
- Disscussed what other topics I may be able to look at this week

**Wednesday July 20**

- I worked on proving a statement that had many cases to consider....after spending hours working on it I was able to find a case that disproved the statement!
- Rewrote some of the proofs I had done before

**Thursday July 21**

- Met with Zac to go over proofs
- I continued working on characerizing the digraph that corresponds to the nearly connected (1,2)-step competition graph

**Friday July 22**

- My intuition led me astray. I had a few statements I thought might be true but I was able to disprove all of them!
- Worked on my poster for the presentations

**Week 9**(July25-July 29)

**Monday July 25**

- Met with Dr. Factor to show her my poster
- Edited my poster
- Coninued working on some proofs

**Tuesday July 26**

- Continued working/editing my poster
- Began to work on my presentation

**Wednesday July 27**

- Edited my poster some more and submitted the final copy to Dr. Factor
- Worked on identifying relationships between connected digraph and the nearly connected (1,2)-step competition graph

**Thursday July 28**

- Attended Luncheon
- Met with Dr. Factor to disucss the plans for our last week of work
- Wrote out a rough draft of the research paper on Word

**Friday July 29**

- Worked on presentation

**Week 10**(August 1-5)

**Monday August 1**

- Met with Dr. Factor to show her my presentation
- Edited my presentation
- Began working on the graphics for my research paper

**Tuesday August 2**

- Poster presentation
- Worked on research paper...in Word

** Wednesday August 3**

- Mini presentations
- Continued working on paper

**Thursday August 4**

- Mini presentations
- Continued working on paper
- Submitted research paper to Dr. Factor

**Friday August 5**

- Edited research paper
- Attended final meeting....lots of surveys!
- Submitted final research paper