Research Efforts in Mathematical Evolutionary
Developmental Biology: H. David Sheets, Dept. of Physics, Canisius
College
Ontogenetics refers to the pattern of growth or development of an organism, so from my point of view, it's just another type of dynamics. My contributions to the study of developmental processes in an evolutionary context have been in the development of software and mathematical methods to address various hypotheses. I've been working with Miriam Zelditch (Museum of Paleontology, University of Michigan, Ann Arbor) and William Fink (Museum of Zoology, Dept. of Biology, University of Michigan, Ann Arbor) on ontogeny in piranha.
The little fellow on the left here is an example of Pygocentris nattereri, showing the landmark configuration used in the work.
I've also been working with Keonho Kim and Chuck Mitchell at UB, and Mark Webster and Nigel Hughes at UC Riverside on developmental and evolutionary shape change in trilobites. Same mathematics, different organisms.
The features of a piranha can be mapped onto a thin plate spline decomposition, which is an orthogonal vector space, a method of morphometrics developed by Fred L. Bookstein (among others). Once this has been done, the ontogeny of a species can be thought of as motion through a high dimensional vector space (dynamics!).
So my role in this work has been to help analyze the dynamics in the vector space, and devise statistical tests based on resampling approaches to distinguish between developmental or evolutionary processes of shape change in the different species of piranha, or trilobite.
Papers on developmental processes in piranha:
Spatiotemporal reorganization of growth rates in the evolution of ontogeny,
Miriam L. Zelditch, H. David Sheets and William L. Fink, Evolution,August, 2000.
Heterochrony and heterotopy in the evolution of piranha body form, Miriam L.
Zelditch, H. David Sheets and William L. Fink, 2001 in The Evolution of Development, edited by Miriam L. Zelditch, John Wiley and Sons.
In trilobites:
Testing of Allometric Heterochrony in Trilobites, Mark Webster, H. David
Sheets, Nigel Hughes,2001, in The Evolution of Development, ed. by Miriam L. Zelditch, John Wiley and Sons.
Morphometric analysis of ontogeny and
allometry of the Middle Ordovician trilobite, Triarthrus becki.
Keonho Kim, H. David Sheets, Robert Haney, and Charles E. Mitchell, in submission, Paleobiology
For further reading see:
Fink, W.L. and M.L. Zelditch, Phylogenetic analysis of ontogenetic shape transformations: a reassessment of the piranha genus pygocentrus (Teleostei), Syst. Biol. 44(3):343-360, 1995
Zelditch,M.L., W.L. Fink and D.L.Swiderski, Morphometrics, Homology, and Phylogenetics: Quantified Characters as Synapomorphies, Syst. Biol. 44(2):179-189, 1995
Fink, W.L. and M.L. Zelditch,Shape Analysis and Taxonomic Status of Pygocentrus Piranhas (Ostariophysi, Characiformes) from the Paraguay and Parana River Basins of South America, Copeia, 1997(1):179-182
