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First published online November 17, 2006
Journal of Experimental Biology 209, 4732-4746 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02559

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Biomimetic evolutionary analysis: testing the adaptive value of vertebrate tail stiffness in autonomous swimming robots

J. H. Long, Jr^1,*, T. J. Koob², K. Irving¹, K. Combie¹, V. Engel¹, N. Livingston³, A. Lammert⁴ and J. Schumacher⁵

¹ Department of Biology, Program in Cognitive Science, and the Interdisciplinary Robotics Research Laboratory, Vassar College, Poughkeepsie, NY 12604, USA
² Skeletal Biology, Shriners Hospital for Children, Tampa, FL 33612, USA
³ Department of Electrical Engineering and Computer Science, Case Western Reserve University, Cleveland, OH 44106, USA
⁴ Speech and Hearing Research, VA Medical Center and East Bay Institute for Research and Education, Martinez, CA 94553, USA
⁵ Department of Neurology, Columbia University, New York, NY 10032, USA

^* Author for correspondence (e-mail: jolong{at}vassar.edu)

Accepted 21 September 2006

For early vertebrates, a long-standing hypothesis is that vertebrae evolved as a locomotor adaptation, stiffening the body axis and enhancing swimming performance. While supported by biomechanical data, this hypothesis has not been tested using an evolutionary approach. We did so by extending biomimetic evolutionary analysis (BEA), which builds physical simulations of extinct systems, to include use of autonomous robots as proxies of early vertebrates competing in a forage navigation task. Modeled after free-swimming larvae of sea squirts (Chordata, Urochordata), three robotic tadpoles (`Tadros'), each with a propulsive tail bearing a biomimetic notochord of variable spring stiffness, k (N m^-1), searched for, oriented to, and orbited in two dimensions around a light source. Within each of ten generations, we selected for increased swimming speed, U (m s^-1) and decreased time to the light source, t (s), average distance from the source, R (m) and wobble maneuvering, W (rad s^-2). In software simulation, we coded two quantitative trait loci (QTL) that determine k: bending modulus, E (Nm^-2) and length, L (m). Both QTL were mutated during replication, independently assorted during meiosis and, as haploid gametes, entered into the gene pool in proportion to parental fitness. After random mating created three new diploid genotypes, we fabricated three new offspring tails. In the presence of both selection and chance events (mutation, genetic drift), the phenotypic means of this small population evolved. The classic hypothesis was supported in that k was positively correlated (r²=0.40) with navigational prowess, NP, the dimensionless ratio of U to the product of R, t and W. However, the plausible adaptive scenario, even in this simplified system, is more complex, since the remaining variance in NP was correlated with the residuals of R and U taken with respect to k, suggesting that changes in k alone are insufficient to explain the evolution of NP.

Key words: vertebrae, axial skeleton, notochord, stiffness, swimming, navigation, robots, evolution

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