October 29, 2011

Facilitated Variation (FV): a random (walk) tour

I have always been interested in the interface between complexity theory and evolutionary theory. Particularly, there is a lot to be learned from characterizing evolution as a complex, dynamic system. One central theme in the study of evolving systems is the ability of diverse populations to adapt to new environments. According to contemporary evolutionary theory, this should occur in a non-goal-directed (e.g. random) fashion, and seemingly presents a dilemma: how does variation get “shaped” towards adaptive ends when there is no centralized or deterministic control process? If it is true that evolutionary processes involve small, incremental changes that occur by chance, even in the presence of natural selection or genetic drift, then one might not expect highly-adaptive outcomes that contribute towards the evolution of complex traits.

Facilitated variation (hereafter FV) is a rather obscure concept proposed to explain how randomly-occurring variation in the genotype can end up producing adaptive, specialized phenotypes of high fitness. One of its proponents, a physiologist by the name of Marc Kirschner, has advanced this idea through publications[1], books[2], and conference talks. Kirschner's view is largely physiological, and so focuses on examples from biology (as opposed to computation). In the book “Plausibility of Life”, an example of FV is given that involves the rapid evolution of a double declaw morphology in dogs [2].

Figure 1. Figure 35, from Chapter 7 in “Plausibility of Life” [2]. Note that highly-specialized changes in the phenotype are determined by large-scale changes in the protein sequence.

FV depends on another concept called evolvability [3]. Evolvability, besides having a potentially recursive definition [4], defines the degree to which an organism or population can evolve towards new phenotypes given its current set of constraints and genetic background. According to the criteria of [1, 5], organisms and their phenotypes are evolvable if they exhibit one or more of the following characteristics: weak linkage, modularity, and exploratory behavior. In Gerhart and Kirschner [1], facilitated variation is conceptualized as a force of innovation in evolution resulting in events such as the emergence of RNA transcription, the specialization of cells towards differentiated phenotypes, and origins of morphogenetic patterning. I will now use examples from the evolution of nervous systems to demonstrate how these manifest themselves in the phenotype.

Weak linkage refers to the relaxed coupling of specific components that make up a trait. In the mammalian brain [6], linkage (or covariance) between all structures has been relaxed. This is the mechanism behind enlargement of certain structures relative to overall brain size. For example, structures such as mammalian isocortex are able to expand (or shrink) according to the demands of behavior, information processing, and/or energetics. However, it is important to note that linkage is never entirely disrupted, the importance of which is connected to modularity [7].

Modularity is also an important recipe for the evolution of structures such as the mammalian isocortex. The partitioning of information processing in a brain structure allows for things to proceed in parallel, which can facilitate “on-the-fly” adaptation as well as adaptive changes over evolutionary timescales. This distinction between evolutionary plasticity and life-history plasticity, and the ability to possess both, is a by-product of extensive modularity. In a more general phenotypic context, modularity allows for an organism to evolve specific evolutionary solutions. For example, if there is selective pressure on an organism for a certain type of locomotion, it does not make much sense for parts of the organism not directly involved in locomotion to be involved in the solution.

Exploratory behavior involves the relaxation of the brain or other phenotype’s “hard wiring”, whether it relates to connectivity or changes in structure. Again, isocortex and related structures seem to match this criterion. The combination of dense local connectivity with selective, sparse long-range connectivity (referred to in the literature as “scale-free” [8] connectivity) seems to have been a major evolutionary innovation in isocortex [9]. This type of architecture, seen in many highly adaptable complex networks (from social networks to protein-protein interaction networks), has allowed for myriad changes in the size and location of cortical maps across species.

Figure 2. Examples of brain connectivity. Nodes represent neurons or neural structures, while the arcs represent connections between nodes. A: whole-brain structural (synaptic) connectivity [8], B: example of a network with random connectivity [10], C: example of a network with scale-free (quasi-random) connectivity [10].

Another component of this facilitation mechanism concerns under what conditions FV acts on a population during the course of evolution. In their contribution to the literature on FV , Parter, Kashtan, and Alon [11] have characterized this in terms of RNA evolution and logical circuitry (e.g. a computational approach). These authors argue that many studies of evolution and evolvability examine the range and diversity without regard for the usefulness of the novel phenotypes produced in the course of evolution. Figure 3 demonstrates how this is also a matter of mapping between genotype and phenotype (across examples as diverse as animals, RNA structure, and boolean networks).

Figure 3. Animal, RNA structure, and boolean network example from Figure 1 as shown in [11].

Taking a more computational view than do Gerhart and Kirschner, Parter, Kashtan, and Alon characterize FV as an emergent phenomenon (e.g. the sum of a process being greater than its parts). Like Gerhart and Kirschner [1], they equate FV with the four characteristics of evolvability. Moreover, their view of FV has parallels with learning and memory mechanisms, particularly an idea originating from the turn of the last century called Baldwinian evolution [2]. This idea is based on the assumption that natural selection can be guided in part by the interaction between prior experience and current innovations [12]. While not usually a feature of mainstream evolutionary theory, it is often used in the evolutionary computation community (e.g. genetic algorithm design, behavioral simulations). However, this might also play a role in the evolvability of specific traits, allowing for complex solution to emerge from an otherwise random process.

This largely hypothetical idea (Baldwinian evolution)is the inspiration for Parter, Kashtan, and Alon’s conception of rapid adaptation, which results in the enhanced generation of novelty. In theory, an organism would learn (e.g. acquire mutations) from explorations of past environments, traces of which would then be retained in a population’s genomic diversity. In the context of subsequent environmental challenges, these genomic “memories” (likely instantiated as neutral mutations) would allow for rapid adaptation to seemingly novel environments. Dividing up the genotype and/or phenotype into modules, each component of which performing different tasks and evolving towards different fitness optima, seems to give the best results among their Boolean network examples. It is worth noting that this same research group (Uri Alon’s laboratory) has done work on a topic called environmental switching [13], or the rapid alteration between two environmental contexts. In bacterial and computational models, it has been observed that populations subject to switching are able to evolve solutions more rapidly than those remaining in a single environment.

I would now like to present my own ideas regarding potential mechanisms behind FV, based on insights from complexity theory. Let’s consider the aggregate effect of mutations across individuals in a population as a diffusive process (e.g. driven by noise). Mutations, being largely random, should be distributed across a population in a way that favors no particular portion of the phenotype space. In other words, changes to the variety of phenotypes due to mutations across a population should result in solutions that are distributed in a uniform manner around the current solution (mean phenotype). While this may or may not be a fair assumption, we can envision this as a random walk across the phenotype space. A random walk [14] is a model typically used to describe the fluctuation of particles from a central point that explore a given space both incrementally and randomly. These step sizes (e.g. fluctuations) are drawn from a Gaussian distribution (a.k.a. Brownian motion or white noise), which has a uniform variance about the mean value (see Figure 4).

Figure 4. Left: an instance of a Gaussian random walk. Right: the distribution of step lengths about the mean.

However, random walks and their associated noise need not be based on a Gaussian distribution. There is a class of random walks called Levy flights (or Drunkard's walks) [15], which are based on a 1/f noise distribution and may allow for large-scale jumps across phenotype space using a random (e.g. noise-driven) mechanism (see Figure 5). Levy fights have a behavior similar to avalanches and other power law behaviors in that they exhibit a few very large magnitude events embedded in a vast number of more uniform events. In terms of phenotype space, these large jumps towards phenotypes that exhibit novel adaptations of high fitness may occur due to mutations in genes of large effect, or mutations in the regulatory regions of a gene. In addition, Levy flights (e.g. 1/f random walks) seem to have the right timescale characteristics -- as major evolutionary innovations are quite rare [16] -- to serve as a driving mechanism for evolutionary innovation.

Figure 5. Left: an instance of the Levy flight (1/f random walk). Right: the distribution of step lengths about the mean.

I will not attempt to reconcile all of these ideas here with one grand statement. Nevertheless, I will say that FV is a potentially powerful mechanism for explaining the open-ended nature of evolutionary innovation. Ideas from complexity theory may also help us resolve this ongoing dilemma, in addition to sojourns into high-throughput data. References for further reading can be found below.

[1] Gerhart, J. and Kirschner, M. (2007). The theory of facilitated variation. PNAS, 104(1), 8582–8589.

[2] Kirschner, M. and Gerhart, J. (2005). Plausibility of Life. Yale University Press, New Haven.

[3] Wagner, A. (2005). Robustness and Evolvability in Living Systems. Princeton University Press, Princeton, NJ.

[4] Pigliucci, M. (2008). Is evolvability evolvable? Nature Reviews Genetics, 9, 75-82.

[5] Streidter, G. (2006). Principles of Brain Evolution. Sinauer Press, Sunderland, MA.

[6] Darlington, R.B. and Finlay, B.L. (1995). Linked regularities in the development and evolution of mammalian brains. Science, 268, 1578-1584.

[7] Schlosser, G. and Wagner G. (2004) Modularity in Development and Evolution. Harvard University Press, Cambridge, MA.

[8] Bullmore, E. and Sporns, O. (2009). Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Reviews Neuroscience, 10, 186-198.

[9] Jehee, J.F.M. and Murre, J.M.J. (2008). The scalable mammalian brain: emergent distributions of glia and neurons. Biological Cybernetics, 98, 439–445.

[10] Sporns, O. (2011). Networks of the Brain. MIT Press, Cambridge, MA.

[11] Parter, M., Kashtan, N., and Alon, U. (2008). Facilitated Variation: How Evolution Learns from Past Environments To Generalize to New Environments. PLoS Computational Biology, 4(11), e1000206.

[12] Baldwin, J.M. (1896). A New Factor in Evolution. American Naturalist, 30(354), 441-451.

[13] Kashtan, N., Noor, E., and Alon, U. (2007). Varying environments can speed up evolution. PNAS USA, 104, 13711–13716.

[14] Antonelli, P.L. and Sammarco, P.W. (2009). Evolution Via Random Walk on Adaptive Landscapes. Open Systems & Information Dynamics, 6(1), 47-68.

[15] Reynolds, A. M., and C. J. Rhodes. 2009. The Lévy flight paradigm: random search patterns and mechanisms. Ecology, 90, 877–887.

[16] Lowe, C.B., Kellis, M., Siepel, A., Raney, B.J., Clamp, M., Salama, S.R., Kingsley, D.M., Lindblad-Toh, K., and Haussler, D. (2011). Three Periods of Regulatory Innovation During Vertebrate Evolution. Science, 333, 1019-1024.

Additional References (or, things that shaped my thinking when writing this post that are not directly cited)
Hayden, E.J., Ferrada, E., and Wagner, A. (2011). Cryptic genetic variation promotes rapid evolutionary adaptation in an RNA enzyme. Nature, 474, 92-95.

Rutherford, S.L. (2000). From genotype to phenotype: buffering mechanisms and the storage of genetic information. BioEssays, 22, 1095-1105.

Wagner, G. P. and Altenberg, L. (1996). Complex adaptations and the evolution of evolvability. Evolution, 50, 967–976.

Weinreich, D.M., Delaney, N.F., Depristo, M.A., and Hartl, D.L. (2006). Darwinian evolution can follow only very few mutational paths to fitter proteins. Science, 312, 111–114.

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