May 20, 2012

A Constructal Approach to Evolution: how "physical" is descent with modification?

I have been reading a book by Adrian Bejan (Mechanical Engineering professor at Duke) called "Design in Nature" [1] which summarizes his work on something called "constructal theory" for a mass audience. This is not a argument for creationism, but an ambitious attempt at unifying the evolution of biological, social, and earth systems under a single set of principles.

Constructal theory (Bejan's pet concept) is an attempt to apply the principles of thermodynamics to complex systems, and is inspired by the work of Ilya Prigogine [2] and others [3]. In his book (which is a tour-de-force of previously-published journal articles), Bejan has attempted to extend constructal law to the "design" of natural systems. Of course, natural systems (ranging from river basins and mountain ranges to trees and animals) are very diverse. In a reductionist sense, very are also very dissimilar. Plants and animals have different units of heredity and modes of action than do river basins and mountain ranges. Yet Bejan is not interested in the smallest possible unit of biological mechanism (e.g. genes, replicators). Instead, he is interested in the self-organization of these phenomena, and unifies the evolution of all natural systems under the framework of energy flow and networks that diffuse this energy.

While Bejan is admittedly not an evolutionary biologist, and some of his ideas do not square away with Darwinian and/or phylogenetic theory (see Figure 34 for an example of this), the notion of self-organization being at the heart of evolution is an intriguing one that I have blogged about here before. To get at this somewhat elusive phenomenon, Bejan relies on unifying insights from animal biomechanics, allometric scaling, and energetics into a set of general principles that can be used to understand why animals move and look the way they do [4]. 

Bejan's design principle for evolution can be stated as "the time needed to move fast over long distances should be the same as the time it takes to move slowly over short distances". This implies that the while modes of locomotion should vary widely across phylogeny, there should be proportional changes in the locomotory apparatus across animals of different sizes. As body size increases, so should neuromuscular output (force, power, and torque). Bejan collaborated with Jim Marden of Penn State to investigate this issue (with very intriguing results as shown in Figure 1).

Figure 1. Exponential scaling laws predict the speed, stroke frequencies, and muscular output across a variety of organisms. COURTESY: Figure 2 in [5].

The constructal principle (as applied across natural systems) can be defined as one of maximizing the flow of energy in a system over time such that these flows become maximally efficient [6]. What does this mean in the context of natural systems? Consider a river basin. Water that randomly diffuses (flows) from higher to lower elevations does not transfer and consolidate energy very efficiently. Over time, there is a spontaneous organization of these flows into a series of channels. This system might further evolve hierarchical structure where smaller channels flowing into larger ones.

I use this example as an analogue of how networks of vasculature and peripheral nervous system fibers may have emerged in the evolution of complex organisms. In the case of vasculature, the self-organization of vessels and their networks is not spontaneous, but dependent on the amount of target tissue present and the local activity of VEGF and other factors.

Figure 2. Cartoon demonstrating the principle of organismal design as a minimization of flows. A: effects of Newtonian environmental parameters (e.g. gravity, resistance) on animal morphology (a Square oozer* used for illustration purposes), B: changes in shape to morphology of the Square oozer over time. C: changes in flows inside Square oozer over time from laminar to turbulent to something resembling a vasculature. Adapted from figures and text in [1].

Even though he is an engineer, Bejan views evolution not as an optimizing process, but as a process in which nature produces "good enough" designs that are refined over time in accordance with physical law. This is a subtle but important difference. If we think of evolutionary change in terms of maximizing reproductive fitness or the necessity of climbing peaks on a fitness landscape, Bejan's model suggests that fitness is only one aspect of what is actually driving evolutionary change. It also lends support to the idea that evolution is guided by heuristics (e.g. good enough local information that can lead to adaptive outcomes, for an example, from behavioral decision-making, see [7].)

In Bejan's conception, flow systems should improve over time by reducing friction or some other objective. In the case of flows, laminar flows can evolve over time into turbulent flows, which allow for the formation of structure and more localized diffusion. Typically, the transition from laminar to turbulent flows is described by a dimensionless parameter called the Reynolds' number.

While the Reynolds' number is not a analogue of fitness, it could be an alternate means of assessing the evolution and/or complexity of a given flow. This may seem as anathema to many evolutionary biologists. Yet as a heuristic indicator, describing evolution in terms of energy flows might not be so unorthodox after all [8].

What does this have to do with phenotypic organization? As I mentioned before, Bejan is interested in self-organization, which requires one to think about biological systems from a top-down perspective. One aspect of biological development involves the integration of phenotypes over evolutionary time [9]. This can be understood by thinking about groups of traits that are functionally and/or developmentally integrated.

Phenotypic integration is usually defined as multivariate variance components which map to traits that function as a unit. The question is: does the interaction of an organism with physical forces in the environment help to select how traits are associated or directly select upon morphology in any significant way? It is not clear from the work presented in Bejan’s book, but the work on universal scaling laws [see 5] suggests that physical interactions between the organism and environment (via behavior) acts as a universal constraint on morphological design.

Figure 3. An example of phenotypic integration, in this case the development of a trait under sexual selection. Along the bottom edge of the diagram are the input parameters e, m, and g, which serve as the genetic components of variance. While the contributions of Newtonian physics are not shown, one can imagine how it might fit into this scheme. COURTESY: Figure 3.1 of [10].

Another similarity is between Bejan's prediction that energy flows will eventually form channels and the canalization of developmental pathways predicted by Waddington [11]. While Waddington predicted that developmental processes are buffered along "channels" or common pathways, his mechanism was vague. Constructal theory might be able to explain development in the context of biocomplexity. In the book, Bejan places the development of chicken embryos in the same framework as the evolution of river channels and social hierarchies. In constructal theory, hierarchies emerge by the formation of an elemental construct, and then replication of these constructs at many size scales.

In the case of a river channel, a rivulet (flow channel) forms by overcoming a threshold of resistance, and serves as the elemental construct. As the system evolves, new channels form at a variety of size scales, which occurs through coalescence with other rivulets. In the end, the distribution of rivulets becomes exponential, where a few large rivulets rely on inputs from many smaller ones. Perhaps the same can be said for developmental landscapes, in which the most common pathways are those that represent development in most (but not all) contexts.

Figure 4. A picture of a self-organized river system (left) evolved over geologic time contrasted with Waddington's developmental landscape (right).

So has Bejan discovered a new aspect of the evolutionary process? Some of the ideas he explores are quite well understood (such as allometric scaling), while others (the spontaneous formation of hierarchies) are not much considered in the realm of evolution. There are two major contributions to the scientific literature on evolution. One is to advance the role of biomechanics as a major evolutionary force. While biomechanics is central to animal (and plant) behavior, it is generally not treated as a major component of selection. The other contribution is to recognize the role of spontaneous organization guided by energetic constraints in producing diversity. Self-organization provides a top-down mechanism that may complement the effects on genes and proteins. These components might be added to studies on biological evolution and evolutionary computation alike to potentially reveal new insights into evolutionary change, phenotypic variation, and biomimetic design.


* Square oozer (Quadratus exsudares) is a theoretical organism I have used for illustrative purposes. It's motility resembles that of a slime mold.


[1] Bejan, A. and Zane, P.D. (2012). Design in Nature. How the constructal law governs evolution in biology, physics, technology, and social organization. Doubleday Books, New York.

For good overviews of constructal theory, please see:
BOOK: Bejan, A. (2000). Shape and Structure: from engineering to nature. Cambridge University Press, Cambridge, UK.

PAPER: Bejan, A.D. and Lorente, S. (2011). The constructal law and the evolution of design in nature. Physics of Life Reviews, 8.


[2] Father of the dissapative structures concept. For more information, see Prigogine, I. and Stengers, I. (1984). Order out of Chaos. Bantam Books, New York.

[3] These are not completely novel ideas. See books by R. McNeil Alexander (Elastic Mechanisms in Animal Movement), Steven Vogel (Life in Moving Fluids: the physical biology of flow), and E.R. Weibel (Symmorphoses: on form and function in shaping life) for related work.

[4] For some interesting work on the universal scaling of metabolic rate across phylogeny and ecological conditions, see:

Brown, J.H., Gillooly, J.F., Allen, A.P., Savage, V.M., and West, G.B. (2004). Toward a metabolic theory of ecology. Ecology 85(7), 1771–1789.

[5] Bejan, A. and Marden, J.H. (2006). Unifying constructal theory for scale effects in running, swimming and flying. Journal of Experimental Biology, 209, 238-248.

[6] For application to ecological systems, see the maximum power principle of H.T. Odum and the system ecology community:

Odum, H.T. and Brown, M.T. (2007). Environment, Power and Society for the Twenty-First Century: The Hierarchy of Energy. Columbia University Press.

[7] Gigerenzer, G. (2001). The Adaptive Toolbox: towards a Darwinian rationality. IN "Evolutionary Psychology and Motivation" J.A. French, A.C. Kamil, and D.W. Leger, eds. pgs. 113-143, University of Nebraska Press, Lincoln.

[8] I have been working on a model (an alternative to fitness landscapes) that treats evolutionary "space" as a flow field, and utilizes a tool called Lagrangian Coherent Structures as a potential way to quantify this.

For more information: Alicea, B. (2011). Lagrangian Coherent Structures (LCS) may describe evolvable frontiers in natural populations. arXiv, arXiv:1101.6071.

[9] Schlichting, C.D. and Pigliucci, M. (1998). Phenotypic Evolution: a reaction norm perspective. Sinauer, Sunderland, MA.

[10] Pigliucci, M. and Preston, K. (2004). Phenotypic Integration: studying the ecology and evolution of complex phenotypes. Oxford University Press, Oxford, UK.

[11] Waddington, C.H. (1962). New Patterns in Genetics and Development. Columbia University Press, New York.

1 comment:

  1. For the geometries behind these behaviours from an architect's perspective, please refer to research first published in AD Magazine in 1995, amended and republished last year, in 2011: