The Tree of Life: Challenges for Discrete Mathematics and Theoretical Computer Science

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The Tree of Life Challenges for Discrete
Mathematics and Theoretical Computer Science
Fred S. Roberts DIMACS Rutgers University
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The tree of life problem raises new challenges
for mathematics and computer science just as it
does for biological science.
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• For math. and CS to become more effectively
  utilized, we need to
• develop new tools
• establish working partnerships between
  mathematical scientists and biological
  scientists
• introduce the two communities to each others
  problems, language, and tools
• .

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• introduce outstanding junior researchers from
  both sides to the issues, problems, and
  challenges of problems arising from the tree of
  life

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• involve biological and mathematical scientists
  together to define the agenda and develop the
  tools of this field.

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These are some of the motivations for this
meeting. I will lay out some of the challenges
for math and CS, with emphasis on discrete math
and theoretical CS.
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What are DM and TCS?

• DM deals with
• arrangements
• designs
• codes
• patterns
• schedules
• assignments

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TCS deals with the theory of computer algorithms.

• During the first 30-40 years of the computer age,
  TCS, aided by powerful mathematical methods, had
  a direct impact on technology, by developing
  models, data structures, algorithms, and lower
  bounds that are now at the core of computing.

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DM and TCS have found extensive use in many areas
of science and public policy, for example in
Molecular Biology. These tools seem
especially relevant to problems of the tree of
life
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DM and TCS Continued

• These tools are made especially relevant to the
  tree of life problem because of
• Geographic Information Systems

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DM and TCS Continued

• Availability of large and disparate computerized
  databases on subjects relating to species and the
  relevance of modern methods of data mining.

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Outline

• Phylogenetic Tree Reconstruction
• Database Issues
• Nomenclature
• Setting up a Species Bank
• Digitization of Natural History Collections
• Interoperability
• The Many Applications of Research on the Tree of
  Life

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Phylogenetic Tree Reconstruction
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Phylogeny (continued)

• New methods of phylogenetic tree reconstruction
  owe a significant amount to modern methods of
  DM/TCS.
• Trees, supertrees, consensus trees will all be
  discussed at length in this meeting
• I will only make a few brief remarks about them.

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Phylogenetic Challenges for DM/TCS

• Tailoring phylogenetic methods to describe the
  idiosyncracies of viral evolution -- going beyond
  a binary tree with a small number of
  contemporaneous species appearing as leaves.
• Dealing with trees of thousands of vertices, many
  of high degree.
• Making use of data about species at internal
  vertices (e.g., when data comes from serial
  sampling of patients).

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Phylogenetic Challenges for DM/TCS Continued

• Network representations of evolutionary history -
  if recombination has taken place.
• Modeling viral evolution by a collection of trees
  -- to recognize the quasispecies nature of
  viruses.
• Devising fast methods to average the quantities
  of interest over all likely trees.
• Thanks to Eddie Holmes and Mike Steel for ideas.
• DIMACS Working Group on Phylogenetic Trees and
  Rapidly Evolving Diseases, Sept. 3-6, 2003

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Database Issues

• Assembling the tree of life requires collecting
  massive amounts of data about the worlds
  scientific species.
• Making it a collaborative project requires making
  such data universally available.
• There are great challenges for Math and CS,
  specifically DM and TCS.
• Thanks to the Global Biodiversity Information
  Facility (GBIF) for many of the following ideas.

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Complexity of Data

• In many ways, data about the worlds species are
  far more complex than genetic or protein sequence
  data. (GBIF)

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Complexity of Data (contd)

• There are databases of images, databases in
  numerous forms, etc.
• Data is heterogeneous.
• Data has errors and inconsistencies.

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Nomenclature

• There are some 1.75M named species
• By some estimates, there are up to 10M actual
  species.

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Nomenclature (contd)

• The same species is often named more than once.
• On the average, each species has two additional
  names (synonyms) besides its own name. (GBIF)

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Nomenclature (contd)

• Thus, there is need to assemble names in an
  electronic catalogue, with synonyms and common
  misspellings.
• This would be of fundamental importance in aiding
  research on biodiversity.

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Nomenclature (contd)

• Because of errors, one major challenge for TCS is
  data cleaning.

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Nomenclature (contd)

• Another challenge is to search a database to see
  if two entries are similar.
• This is a standard problem in database theory.
• TCS algorithms involving k-nearest neighbor and
  other methods are very helpful here.

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Setting up a Species Bank
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Setting up a Species Bank (contd)

• A species bank would provide not only names, but
  also data about a species
• Type
• Distribution
• Ecological role
• Phylogenetic history
• Physiology
• Genomics
• This involves issues about huge datasets.

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Setting up a Species Bank (contd)

• NASA earth science satellites alone beam home
  image data at the rate of 1.2 terabytes a day.
• By 2010, this is expected to grow to 10 petabytes
  a day. (Kathleen Bergen, U. Michigan)

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Name Equal to Size in Bytes
Bit 1 bit 1/8
Nibble 4 bits 1/2 (rare)
Byte 8 bits 1
Kilobyte 1,024 bytes 1,024
Megabyte 1,024 kilobytes 1,048,576
Gigabyte 1,024 megabytes 1,073,741,824
Terrabyte 1,024 gigabytes 1,099,511,627,776
Petabyte 1,024 terrabytes 1,125,899,906,842,624
Exabyte 1.024 petabytes 1,152,921,504,606,846,976
Zettabyte 1,024 exabytes 1,180,591,620,717,411,303,424
Yottabyte 1,024 zettabytes 1,208,925,819,614,629,174,706,176
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Setting up a Species Bank (contd)

• The problem is even worse We need to combine
  information from many databases.
• There is no known way to catalogue all species of
  plants in one place given current database
  systems techniques. (Jessie Kennedy, Napier
  University, Edinburgh)

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Setting up a Species Bank (contd)

• One possible approach Tree and graph methods to
  support overlapping classifications as directed
  acyclic graphs or with complex objects (taxa or
  specimens) as nodes. (Jessie Kennedy)

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Digitizing Natural History Collections

• It has been estimated that there are between 1.5
  and 3 Billion specimens in the worlds natural
  history collections, including herbaria, living
  microorganism stock centers, and other
  repositories (GBIF).

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Digitizing Natural History Collections (contd)

• If we could digitize information about these
  specimens, and make them available, we would
  have a treasure trove of information about the
  worlds biota. (GBIF)
• Pilot projects have shown that utilizing
  digitized data from several institutions
  databases can be a powerful tool. (GBIF)

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Digitizing Natural History Collections (contd)

• Challenge digitization and reference of
  non-standard data (photos, sonograms, field
  notes)

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Digitizing Natural History Collections (contd)

• Challenge Develop methods for visualizing the
  data (e.g., species distributions)

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Digitizing Natural History Collections (contd)

• Challenge Develop search engines for real-time
  searching of such extremely large data sets.

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Digitizing Natural History Collections (contd)

• Challenge Make information access on the web
  more knowledge-based so humans and intelligent
  software can work together. (Susan Gauch, U.
  Kansas)

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Digitizing Natural History Collections (contd)

• Challenge Use intelligent agents to organize
  and present relevant information on the web.
  (Susan Gauch)

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Digitizing Natural History Collections (contd)

• Challenge Use partial information as training
  data for classification algorithms (Susan Gauch)
• One approach Use training data and
  classification algorithms with learning
  capabilities.
• (See DIMACS project on Monitoring Message
  Streams)

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Digitizing Natural History Collections (contd)

• Another approach to problems posed by
  digitization Use tools of knowledge
  inferencing (Yannis Ioannidis, University of
  Wisconsin)
• Still another approach Use methods of
  spatio-temporal data mining (Ioannidis see work
  of Muthukrishnan at Rutgers)

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Interoperability

• Goal Devise standards for datasets so as to
  allow researchers to collaborate across datasets
  develop standards leading to database
  interoperability. (GBIF)

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Interoperability

• Challenge How do we develop ways to more
  accurately represent observational or
  experimental data so that others may use them?
  (Jessie Kennedy)
• Challenge Deal with issues of inconsistency and
  scalability.
• Challenge Formalize issues of policy with regard
  to others databases.
• Challenge Interoperability over a diversity of
  users and types of equipment.

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Interoperability

• One approach Semantic Web the idea used to
  express the growing desire to make information
  access on the Web more knowledge-based so humans
  and intelligent software can work together.
  (Susan Gauch)

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Interoperability

• Another approach Make use of languages such as
  XML developed to aid interoperability in business
  and military collaborations.

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The Many Applications of Research on the Tree of
Life

• Side benefits in many fields
• Agriculture
• Biomedicine
• Biotechnology
• Natural resource management
• Pest control
• Control of emergent diseases
• Sustainable use of biodiversity resources
• Global climate change

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The Many Applications of Research on the Tree of
Life

• Lets say youre importing bananas from South
  America

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The Many Applications of Research on the Tree of
Life

• A camera in the hold of the ship sees a spider.
• What kind of spider is it?
• Is it safe to unload your cargo of bananas?

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The Many Applications of Research on the Tree of
Life

• Luckily, you have a digitized natural history
  database.
• With an efficient search feature.
• (Thanks to Diana Lipscomb for this example)

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The Many Applications of Research on the Tree of
Life