John Long - Darwin’s Devices

You can see the original pictures of the fossils in this paper: D.-G. Shu, S. Conway Morris, J. Han, Z.-F. Zhang, K. Yasui, P. Janvier, L. Chen, X.-L. Zhang, J.-N. Liu, Y. Li, and H.-Q. Lui, “Head and Backbone of the Early Cambrian Vertebrate Haikouichthys ,” Nature 421, no. 6922 (January 2003): 526–529.

Sindre Grotmol, Harald Hryvi, Roger Keynes, Christel Krossøy, Kari Nordvik, and Geir K. Totland, “Stepwise Enforcement of the Notochord and Its Intersection with the Myoseptum: An Evolutionary Path Leading to Development of the Vertebra?” Journal of Anatomy 209, no. 3 (2006): 339–357.

“Stiffness” by itself is an ambiguous term. Many different kinds of stiffness exist. What they have in common is that they are all a proportionality constant between an applied force, stress, or torque and the resulting change in length, strain, or curvature, respectively. Flexural stiffness is defined as the proportionality constant between a torque and the resulting curvature. Flexural stiffness assumes that this relationship is the same all along the length of the structure that you are bending. If you want to describe the stiffness of the whole structure, a physicist would talk about “spring constant” or a “spring stiffness.” I prefer the term “structural stiffness.” In the case of a cantilevered beam with a weight hung off the end, the structural stiffness is the ratio of the flexural stiffness to the cube of the beam’s length. This means that you can have beams of constant flexural stiffness but different structural stiffness if you vary their lengths.

For reconstructions of the skeletons and their partial vertebrae, see J. A. Long and M. S. Gordon, “The Greatest Step in Vertebrate History: A Paleobiological Review of the Fish-Tetrapod Transition,” Physiological and Biochemical Zoology 77, no. 5 (2004): 700–719.

The use of the term “biomimetic” varies across engineering, bioengineering, and biomedical engineering. Here I use “biomimetic” to mean a system built to resemble, as much as possible, the biological target.

Rolf Pfeifer, and Christian Scheier, Understanding Intelligence (Cambridge, MA: MIT Press, 1999).

Hou Xian-Guang, Richard J. Aldridge, Jan Bergstron, David J. Siveter, Derek J. Siveter, and Feng Xiang-Hong, The Cambrian Fossils of Chengjiang, China: The Flowering of Early Animal Life (Malden, MA: Wiley-Blackwell, 2007).

Yes, I’m referencing the television show Survivor on CBS. Their logo reads, “Outwit, outplay, outlast.” I in no way mean to imply that reproduction is or should be part of this show.

Cameron K. Ghalambor, Jeffrey A. Walker, and David N. Reznick, “Multi-trait Selection, Adaptation, and Constraints on the Evolution of Burst Swimming Performance,” Integrative and Comparative Biology 43, no. 3 (2003): 431–438. Also see R. B. Langerhans, “Predicting Evolution with Generalized Models of Divergent Selection: A Case Study with Poeciliid Fish,” Integrative and Comparative Biology 50, no. 6 (2010): 1167–1184.

Barbara Webb, “Can Robots Make Good Models of Biological Behaviour?” Behavioural and Brain Sciences 24, no. 6 (2001): 1033–1050. Also see Webb, “Validating Biorobotic Models,” Journal of Neural Engineering 3, no. 3 (September 2006): R25–R35. I use my rephrased terms of Webb’s dimensions in my paper “Biomimetic Robotics: Self-Propelled Physical Models Test Hypotheses about the Mechanics and Evolution of Swimming Vertebrates,” Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science 221, no. 10 (2007): 1193–1200.

Plagiarism detector alert: a thank you to Lewis Carroll.

This single number that measures feeding behavior is a composite from the fitness function that we developed in Chapter 3. We defined better “relative fitness” for an individual in a given generation, relative to other individuals in that generation, as the sum of their scaled values for increased swimming speed, decreased time to the light target, reduced distance from the light target over the course of the whole experiment, and reduced wobble as they moved. These relative fitness values only make sense within a generation relative to other competing individuals at that time and place: they can’t be compared across generations. To make those cross-generation comparisons for Figure 4.1, we compared any individual’s performance to the average of all individuals over all ten generations scaled by the standard deviation of the particular sub-behaviors, speed, time, distance, and wobble. In statistical terms, we summed up the z-scores of each sub-behavior for each individual.

In statistics one standard deviation, which changes in value depending on the situation, is a measure of how far away from the average most numbers in a group of numbers fall. A small standard deviation means that most numbers in the group are close to the average of the group.

If you are interested in the mathematics of the mating that we used, you can find the details in our paper on the evolution of Tadro3: J. H. Long Jr., T. J. Koob, K. Irving, K. Combie, V. Engel, N. Livingston, A. Lammert, and J. Schumacher, “Biomimetic Evolutionary Analysis: Testing the Adaptive Value of Vertebrate Tail Stiffness in Autonomous Swimming Robots,” Journal of Experimental Biology 209, no. 23 (December 2006): 4732–4746.

In John Gillespie’s Population Genetics: A Concise Guide, 2nd ed. (Baltimore: Johns Hopkins University Press, 2004), he speaks of “demographic stochasticity” as this source of small-number randomness. He also points out a second such source, the segregation of the different parental alleles into separate gametes. Both sources together he calls genetic drift. In our robotic simulation segregation is not a factor because our quantitative characters are, by design, split evenly between chromosomes.

Students and scholars of evolutionary theory will be quick to interject, what about sexual selection, gene flow, genetic drift, epistasis, mating, and developmental processes as evolutionary mechanisms? True. Those are other identifiable mechanisms of evolutionary change. Lenski’s point, which I follow here, is that any mechanism fits into a category of either being deterministic or random. Natural selection is deterministic in that once you identify all of Brandon’s information (see Chapter 2), you can predict evolutionary outcome. Random factors like mutation or assortative mating have outcomes that are not predictable. I continue to be influenced by this fascinating and illuminating paper: M. Travisano, J. A. Mongold, F. Bennett, and R. E. Lenski, “Experimental Tests of the Roles of Adaptation, Chance, and History in Evolution,” Science 267, no. 5194 (1995): 87–90. Also, you may be interested in the Neutral Theory of molecular evolution, which is based on the idea that most random genetic changes have no effect on selection. In the face of genomic data, this idea is rapidly changing: Matthew W. Hahn, “Toward a Selection Theory of Molecular Evolution,” Evolution 62, no. 2 (2007): 255–265.

For completeness, I should tell you that the variable I (in units of meters to the fourth power) is called the “second moment of area.” The second moment of area is a geometric property of how the structure’s material is arranged and clustered in cross-section, the plane perpendicular, to, in this case, the long axis of our beam that we measure with the variable L .