View source for User:Pdepies

==Personal Information==
My name is Patrick Depies and I am a Math major with an emphasis in 'pure' mathematics, such as number theory and abstract algebra. I attended Marquette University for my first two years of college, and worked as a TA for Dr. Ruitenburg's Nature of Mathematics course first semester and Third Semester Calculus course second semester of this past year. I also competed in the Putnam Problem Solving Competition. I will be transferring to the University of Wisconsin-Madison to continue my education in the fall. I ultimately aim to earn a Ph.D. in mathematics and become a university professor (both hopefully on the west coast). During the Summer REU I will be working with [http://www.mscs.mu.edu/mscs/faculty/kfactor.html Dr. Kim Factor] researching graph theory and the effects of the BP oil spill on the ecosystem of the Gulf of Mexico.

==Pre-Orientation Work==
*Attended a talk by Dr. Sarah K. Merz of the University of the Pacific on her work in collaboration with Dr. Factor on the (1,2)-step competition graph.
*Read several sections of some biostatistical methods book that I will properly cite later.
*Did some basic background research on the oil spill

==Week 1==
===June 1===
*Attended the REU Orientation and Good Research Practices talk
*Met with Dr. Factor and discussed the general aim of the project and specific goals
===June 2===
*Began reading ''Digraphs: Theory, Algorithms, and Applications'' by Jorgen Bang-Jensen and Gregory Gutin. Material covered dealt mainly with notation and vocabulary in graph theory.
===June 3===
*Continued readin''g Digraphs: Theory, Algorithms, and Applications'' by Jorgen Bang-Jensen and Gregory Gutin. More terminology introduced along with several theorems and algorithms.
*Read an article by Carl Safina entitled 'We are all Gulf victims now'
===June 4===
*Requested several books by Joel E. Cohen, a noted Biologist and Graph Theorist, and acquired several articles that look like they will be very useful.
*Began searching for sources regarding the Gulf ecosystem. Placed a hold on one book at my local library and found another site that appears to have a thoroughly defined population of the Gulf Ecosystem but is limited to fish.
*Familiarized myself with the WIKI and how to edit it
==Week 2==
===June 7===
*Continued reading ''Digraphs: Theory, Algorithms, and Applications'' by Jorgen Bang-Jensen and Gregory Gutin. Worked through several exercises at the end of the chapter.
*Began defining the gulf ecosystem, starting with fish.
===June 8===
*Continued to define the gulf ecosystem.
===June 9===
*Attended the working lunch for REU students.
*Skimmed ''Food web patterns and their consequences'' by Stuart L. Pimm, John H. Lawton and Joel E. Cohen.
===June 10===
*Continued to define the gulf ecosystem.
*More thoroughly read ''Food web patterns and their consequences'' by Stuart L. Pimm, John H. Lawton and Joel E. Cohen.
===June 11===
*Continued to define the gulf ecosystem, I am beginning to notice the same potential sources of error and inaccuracy in food webs mentioned in ''Food web patterns and their consequences''.
==Week 3==
===June 14===
*Completed my catalogue of fishes in the gulf ecosystem. I've accumulated data for 147 separate species of fish. I will now look toward adding mammals and birds to the food web so that I can begin constructing the food web and competition graphs.
===June 15===
*Did some background research into how oil affects the organisms of an ecosystem.
*Read "Ratio of prey to predators in community food webs", an article from "Nature", Vol. 270, pp. 165-167, November 10, 1977.
*Read "Disturbances allow coexistence of competing species", by I Barradas and J. E. Cohen
===June 16===
*Read "Big Fish, Little Fish: The Search for Patterns in Predator-Prey Relationships" by Joel E. Cohen, originally published in the March/April 1989 issue of "The Sciences", published by The New York Academy of Sciences.
*Read "Recent Progress and Problems in Food Web Theory" by Joel E. Cohen, which also may have provided me with some good leads to sources regarding niche overlap, or competition, graphs.
===June 17===
*Read "A stochastic theory of community food webs: I. Models and aggregated data" by Joel E. Cohen and Charles M. Newman
**Identified several other articles that may be useful for the project utilized by Cohen his in "Recent Progress and Problems in Food Web Theory".
*Ordered a comprehensive survey of marine mammals in the Gulf of Mexico from my local library.
===June 18===
*Began populating the defined ecosystem with marine mammals, birds, and sea turtles
*Identified several high-risk species of fish, birds, and other marine life
==Week 4==
===June 21===
*Read "Digraphs: Theory, Algorithms, and Applications'' by Jorgen Bang-Jensen and Gregory Gutin.
*Continued to add species to the defined ecosystem.
*Began to graph the food web.
===June 22===
*Continued graphing the food web by hand, which seems like it will fail but patterns are emerging nonetheless. 
*Began searching for an appropriate program to digitize the food web.
===June 23===
*Attended the talk on good paper writing and presentation practices.
*Picked up two textbooks by Joel E. Cohen from inter-library loan
===June 24===
*Continued searching for a good di-graph program. Selected OmniGraffle Professional.
*Familiarized myself with OmniGraffle Professional, began digitizing the food web.
*Did additional research on several species' predators and prey in order to ascertain a more precise and complete model.
===June 25===
*Continued digitizing the food web and doing additional biological research as needed.
===June 26===
*Continued digitizing the food web and doing additional biological research as needed.
*Began planning a strategy to aid in constructing competition and (1,2)-step competition graphs.
===June 27===
*Continued digitizing the food web and doing additional biological research as needed.
==Week 5==
===June 28===
*Finished digitizing the food web and had two separate arrangements printed on poster size paper.
===June 29===
*Determined and documented trophic levels of all species in the food web.
*Went through more up to date statistics regarding the oil spill.
===June 30===
*Began reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Read the introduction by Hiroya Kawanabe and Keiji Iwasaki and "Individual variation, social structure, community organization, and hierarchical views in the marine context" by Keiji Iwasaki.
===July 1===
*Began classifying trophic links in the ecosystem.
===July 2===
*Continued classifying trophic links in the ecosystem.
===July 3===
*Finished classifying and tabulating trophic links. Compared ratios of links to species and link types to total links with expected ratios according to Cohen. The quantity of links is accurate, but there is error in the ratios of types of links to total links.
===July 4===
*Investigated possible sources of error in the food web. The simplest explanation for the error was a mis-classification of a keystone species, and upon further biological research this proved to be the case. Recalculated ratios and compared them again, there is error present still but to a much lesser and more believable extent which can be accounted for in several ways.
==Week 6==
===July 5===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Read "Discussion: community and social organization -- morphology and function of linkages between organisms" by Yasuo Ezaki.
*Began work on presentation.
===July 6===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Read "Predatory behaviour of the intertidal snail, Nucella Lapillus, and its effect on community structure" by Roger N. Hughes and Michael T. Burrows, "Discussion: predators, preation, and community structure: patterns and processes" by David L. B. Noakes, and "Mode of competition and interspecific competitive outcomes" by Koichi Fujii and Yukihiko Toquenaga.
===July 7===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Began reading "Discussion: understanding indirect effects: is it possible?" by Stuart L. Pimm. This has been, by far, the most insightful and useful essay I've read to date on food web theory.
*Constructed niche subgraph and niche competition graph for the Blue Fin Tuna, analyzed graphs in order to make a pulse, or short-term, prediction on the effect that a decrease in population of the tuna would have on the rest of the organisms in the sub-graph.
===July 8===
*Continued to work on  and finalize presentation, practiced presenting.
===July 9===
*Attended the presentation session for the REU and presented my work thus far.
*Met with Dr. Factor regarding possible directions for the rest of the project.
==Week 7==
===July 13===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Finished reading "Discussion: understanding indirect effects: is it possible?" by Stuart L. Pimm.
*Began looking at the underlying competition graphs and patterns that are beginning to make themselves apparent.
===July 14===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Read "Cost-Benefit model for the evolution of symbiosis" by Hiroyuki Matsuda and Masakazu Shimada and "Discussion: mutualism as a pattern and process in ecosystem organization" by Thomas P. Burns.
===July 15===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
** Read "Modelling indirect effects of predation on community structure" by Osamu Tsumura, Kohkichi Kawasaki, and Nanako Shigesada.
*Constructed some more species subgraphs from the comprehensive food web.
===July 16===
*Continued reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Read "An extension of niche theory for complex interactions" by Masahiko Higashi, "Discussion: promoted coexistence through indirect effects: need for a new ecology of complexity" by Bernard C. Patten, and "On the ecological importance of direct versus indirect effects in ecological communities" by Thomas W. Schoener.
===July 17===
*Constructed more species subgraphs.
===July 18===
*Constructed more species subgraphs and began constructing their corresponding competition graphs.
==Week 8==
===July 19===
*Finished constructing subgraphs and competition graphs of the species I've chosen, making sure to select from various trophic levels.
===July 20===
*Finished reading essays from "Mutualism and Community Organization: Behavioral, Theoretical, and Food Web Approaches".
**Read "Concluding remarks" by Joel E. Cohen
*Began analyzingthe nature of certain relationships in food webs and their effect on overall web stability and effects in the short term.
===July 21===
*Downloaded and installed LaTeX for Mac (MacTeX).
*Began analyzing the species subgraphs qualitatively.
*Continued analyzing the nature of certain relationships in food webs and their effect on overall web stability and effects in the short term.
===July 22===
*Continued analyzing the nature of certain relationships in food webs and their effect on overall web stability and effects in the short term.
===July 24===
*Continued analyzing the nature of certain relationships in food webs and their effect on overall web stability and effects in the short term.
==Week 9==
===July 26===
*Wrote the rough draft of the section of my paper on error (4 pages thus far)
===July 27===
*Finished analysis of what I'm calling the 'Competitive Predator-Prey Pair'. I now plan on looking at the implications of increasing the number of intermediate species, creating a 'Competitive Predator-Prey n-tuple'.
===July 28===
*Attended working lunch at Marquette.
*Began looking at other relationships in the food web and their effect on overall stability in the long term.
===July 29===
*Finished analyzing simple model of competition under a shared predator.
*Began work on poster by reading poster literature provided by Dr. Brylow.
===July 30===
*Finished analyzing 'Competitive Predator-Prey n-tuples'.
*Continued work on poster.
===July 31===
*Continued work on poster.
===August 1===
*Continued work on poster.
*Read another article on newfound effects of oil dispersant.
==Week 9==
===August 2===
*Finished rough draft of poster.
===August 3===
*Double checked poster for errors, finished works cited, added illustrations.
*Began work on bibliography for paper.

==Sources==
*Cohen, Joel E. 1989 [http://lab.rockefeller.edu/cohenje/PDFs/159CohenBigFishLittleFishTheSciences1989.pdf Big Fish, Little Fish: The Search for Patterns in Predator-Prey Relationships]. The Sciences (New York Academy of Sciences) 29(2):37-42, March-April.
*Cohen, Joel E. 1983 [http://lab.rockefeller.edu/cohenje/PDFs/104CohenCurrentTrendsFoodWebTheory1983.pdf Recent Progress and Problems in Food Web Theory]. In: Current Trends in Food Web Theory ed. D. L. DeAngelis, W. M. Post & G. Sugihara. ORNL-5983:17-24. Oak Ridge, TN: Oak Ridge National Laboratory.
*Stuart L. Pimm, John H. Lawton, and Joel E. Cohen. 1991 [http://lab.rockefeller.edu/cohenje/PDFs/181PimmLawtonCohenNature1991.pdf Food web patterns and their consequences]. Nature 350:669-674, 25 April.
*Ignacio Barradas and Joel E. Cohen. 1994 [http://lab.rockefeller.edu/cohenje/PDFs/217BarradasCohethBiol19941.pdf Disturbances allow coexistence of competing species]. Journal of Mathematical Biology 32:663-676.
*Cohen, Joel E. 1977 [http://lab.rockefeller.edu/cohenje/PDFs/058CohenRatioPreyPredatorCommFoodWebsNature1977.pdf Ratio of prey to predators in community food webs]. Nature 270:165-167, 10 November.
*J. E. Cohen & Charles M. Newman. 1985 [http://lab.rockefeller.edu/cohenje/PDFs/123CohenNewmanproRSocLondB1985.pdf A stochastic theory of community food webs: I. Models and aggregated data.] Proceedings of the Royal Society (London) series B 224:421-448.
*Seattle Audobon Society. (2008). BirdWeb. Retrieved (2010, June 17) from http://www.seattleaudubon.org/birdweb/index.aspx

==Goals==
*Gather thorough background information on Food Webs and Competition Graphs in General
**Read Bang-Jensen's text on di-graphs
**Read and disseminate several applicable works by Joel E Cohen
*Research the Gulf Ecosystem
**Identify species particularly affected by the oil spill disaster
**Construct a food web and pertinent competition graphs
**Interpret graphs and results
*Extend this to (1,2)-step competition graphs
**Employ various techniques to examine the nature of a relationship between two organisms (positive or negative)