NIMBioS Working Group on Cross-Topology Registration
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| (Back row, L to R): John Stinchcombe, Fang Yao, Benedikt Halgrimsson, Daniel Gervini, Mark Kirkpatrick, Joel Kingsolver, Steve Marron; (Front row, L to R): Eladio Marquez, Patrick Carter, Jay Beder, Karin Meyer, Washington Mio, Nancy Heckman, Richard Gomulkiewicz; (Kneeling, L to R): David Houle and Sarang Joshi |
Darwinian Morphometics and the Problem of Shape
Biologists have a rich array of quantitative tools for analyzing the genetics and evolution of traits, especially when the traits can be described by one or a few measurements. But describing some traits, such as gene expression profiles or life history patterns, is far more complex, often defined as a mathematical function of some other variable, such as body size as a function of age.
A group of statisticians, mathematicians and biologists have formed a Working Group at the National Institute for Mathematical and Biological Synthesis to address the questions arising from the problem of analyzing complex evolutionary traits. The Darwinian Morpometrics: Cross-Topology Registration of Shape Working Group held its first meeting, Jan. 10-12, at NIMBioS on the University of Tennessee, Knoxville campus. Working Group co-organizers are Patrick A. Carter, associate professor of biology at Washington State University; Richard Gomulkiewicz, professor of biology and mathematics at Washington State University; David Houle, professor of biology at Florida State University; and J. Stephen Marron, professor of statistics at University of North Carolina, Chapel Hill.
One fundamental challenge to understanding the evolution of function-valued traits is properly registering, or aligning, them while accounting for variation among individuals or taxa. This challenge is especially acute when considering morphological shapes, such as changes in form of fly wings. In Drosophila wings, for example, the shape the wing develops from a single sheet of cells on which self-perpetuating patterns of gene expression draw at least three separate types of functions. Each of the different functions occurs at a different time in development. To fully understand the evolution of the wings, it is necessary to understand what combination of these processes leads to differences in form.
The group's goal is to develop a deeper understanding of the actual biological processes that underlie differences in form. Over the course of several years, the group plans to synthesize the development of appropriate hypotheses with new methods of registration to produce logical and systematic methods of analysis.
NIMBioS Working Groups are comprised of 10-15 invited participants and focus on specific questions related to mathematical biology. Each group typically meets two to three times over the course of two years at the Institute.
The National Institute for Mathematical and Biological Synthesis (NIMBioS) brings together researchers from around the world to collaborate across disciplinary boundaries to investigate solutions to basic and applied problems in the life sciences. NIMBioS is funded by the National Science Foundation in collaboration with the U.S. Department of Homeland Security and the U.S. Department of Agriculture, with additional support from The University of Tennessee, Knoxville.
NIMBioS Working Group: Cross-Topology Registration
Topic: Darwinian Morphometrics: Cross-Topology Registration of Shape
Organizers: Patrick A. Carter (School of Biological Sciences, Washington State University); Richard Gomulkiewicz (Department of Mathematics and School of Biological Sciences, Washington State University); David Houle (Department of Biological Science, Florida State University); J. Stephen Marron (Department of Statistics and Operations Research, University of North Carolina, Chapel Hill).
Meeting dates: January 10-12, 2010; January 8-10, 2011
Project summary: Many complex traits of central importance in biology are defined by mathematical functions, and the variation, selection and evolution of these "function-valued traits" are of increasing interest. One fundamental challenge to understanding the evolution of function-valued traits is properly registering (or aligning) them while accounting for variation among individuals or taxa. This challenge is especially acute when considering morphological shapes, such as fly wings, but also occurs for other types of traits, such as ontogenies and reaction norms. Our view is that the problem of registration is not separate from analysis of the functions themselves, but rather is an essential part of the analysis. However, existing methods used by evolutionary biologists are not explicitly based on hypotheses about the nature of variation, but rather on convenient geometric properties that allow a general approach to be developed. We propose developing much deeper understanding of the actual biological processes that underlie differences in form, by the novel approach of integrating biological hypotheses directly into the geometric operation of registration and the resulting statistical analysis. Our proposed working group activities will synthesize the development of appropriate hypotheses with methods of registration not previously considered by evolutionary biologists, such as point distribution models, voxel based space warps, and medial models, to produce logical and systematic methods of analysis. We anticipate that our work will lead to multiple data analysis and theory papers, at least one summary paper describing the problem and its solutions, and computer program modules for general distribution and use. Four 3-day meetings are planned over the next 2 years.
NIMBioS Working Group on Cross-Topology Registration:
Summary of Meeting 1, January 10-12, 2010
Participants: Jay Beder (Univ. of Wisconsin, Milwaukee); Patrick Carter (Washington State Univ.); Daniel Gervini ( Univ. of Wisconsin, Milwaukee); Richard Gomulkiewicz (Washington State Univ.); Benedikt Halgrimsson (Univ. of Calgary); Nancy Heckman (Univ. of British Columbia); David Houle (Florida State Univ.); Sarang Joshi (Univ. of Utah); Joel Kingsolver (Univ. of North Carolina); Mark Kirkpatrick (Univ. of Texas); Eladio Marquez (Florida State Univ.); Steve Marron (Univ. of North Carolina); Karin Meyer (Univ. of New England); Washington Mio (Florida State Univ.); John Stinchcombe (Univ. of Toronto); Fang Yao (Univ. of Toronto)
During the first meeting, empiricists described systems with which they work and specific and general statistical challenges for which they need solutions, while the statisticians described the types of problems central to their research and their general approach to solving those problems. Breakout groups were formed to focus on solving specific problems. Three major areas discussed included using Bayesian approaches to improve estimates of genetic parameters of function-valued phenotypes, incorporating the genetic relationship of individuals into methods of aligning curves, and developing computational and bioinformatic infrastructure necessary for the study of variation in morphology at a genome-wide scale.
NIMBioS Working Groups are chosen to focus on major scientific questions at the interface between biology and mathematics. NIMBioS is particularly interested in questions that integrate diverse fields, require synthesis at multiple scales, and/or make use of or require development of new mathematical/computational approaches. NIMBioS Working Groups are relatively small (10-12 participants, with a maximum of 15), focus on a well-defined topic, and have well-defined goals and metrics of success. Working Groups will typically meet 2-4 times over a two-year period, with each meeting lasting 3-5 days; however, the number of participants, number of meetings, and duration of each meeting is flexible, depending on the needs and goals of the Group.
