Antisymmetry, directional asymmetry, and dynamic morphogenesis
 John H. Graham,
 D. Carl Freeman,
 John M. Emlen
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Fluctuating asymmetry is the most commonly used measure of developmental instability. Some authors have claimed that antisymmetry and directional asymmetry may have a significant genetic basis, thereby rendering these forms of asymmetry useless for studies of developmental instability. Using a modified RashevskyTuring reactiondiffusion model of morphogenesis, we show that both antisymmetry and directional asymmetry can arise from symmetrybreaking phase transitions. Concentrations of morphogen on right and left sides can be induced to undergo transitions from phaselocked periodicity, to phaselagged periodicity, to chaos, by simply changing the levels of feedback and inhibition in the model. The chaotic attractor has two basins of attractionright sidedominance and left side dominance. With minor disturbance, a developmental trajectory settles into one basin or the other. With increasing disturbance, the trajectory can jump from basin to basin. The changes that lead to phase transitions and chaos are those expected to occur with either genetic change or stress. If we assume that the morphogen influences the behavior of cell populations, then a transition from phaselocked periodicity to chaos in the morphogen produces a corresponding transition from fluctuating asymmetry to antisymmetry in both morphogen concentrations and cell populations. Directional asymmetry is easily modeled by introducing a bias in the conditions of the simulation. We discuss the implications of this model for researchers using fluctuating asymmetry as an indicator of stress.
 Title
 Antisymmetry, directional asymmetry, and dynamic morphogenesis
 Journal

Genetica
Volume 89, Issue 13 , pp 121137
 Cover Date
 199302
 DOI
 10.1007/BF02424509
 Print ISSN
 00166707
 Online ISSN
 15736857
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 fluctuating asymmetry
 developmental stability
 chaos
 nonlinear dynamics
 Turing equations
 Industry Sectors
 Authors

 John H. Graham ^{(1)}
 D. Carl Freeman ^{(2)}
 John M. Emlen ^{(3)}
 Author Affiliations

 1. Department of Biology, Berry College, 30149, Mt. Berry, GA, USA
 2. Department of Biological Sciences, Wayne State University, 48202, Detroit, MI, USA
 3. US Fish and Wildlife, Building 204, Naval Station, 98115, Seattle, WA, USA