Complexity Thoughts: Issue #58
Unraveling complexity: building knowledge, one paper at a time
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Foundations of network science and complex systems
Renormalization group (RG) methods have proven to be indispensable in understanding and classifying the aggregate behaviour of a wide range of physical systems with many degrees of freedom. Direct application of RG techniques devised for physical systems is problematic for complex networks, whether due to the absence of intrinsic notions of metric distance, or geometric or topological regularity.
In spite of these challenges, notable progress has been made in a number of restricted settings, which we survey in this Technical Review. Numerous open questions remain, and we summarize the case for a more broadly applicable network renormalization programme grounded on first principles, which we attempt to articulate.
[I should have to dedicate a whole post to this topic at some point]
The renormalization group (RG) is a powerful theoretical framework. It is used on systems with many degrees of freedom to transform the description of their configurations, along with the associated model parameters and coupling constants, across different levels of resolution. The RG also provides a way to identify critical points of phase transitions and study the system’s behaviour around them. In traditional physical applications, the RG largely builds on the notions of homogeneity, symmetry, geometry and locality to define metric distances, scale transformations and self-similar coarse-graining schemes. More recently, efforts have been made to extend RG concepts to complex networks. However, in such systems, explicit geometric coordinates do not necessarily exist, different nodes and subgraphs can have different statistical properties, and homogeneous lattice-like symmetries are absent — all features that make it complicated to define consistent renormalization procedures. In this Technical Review, we discuss the main approaches, important advances, and the remaining open challenges for network renormalization.
Evolution
It’s been a while since I have started exploring the concept of evolvability, and still I did not finish. Here some papers that I have (re)read, in this order.
More broadly, it is possible that using a multilevel “architecture” for evolution experiments could enable the evolution of many other adaptive modalities – E. Kussell in “Enabling evolvability to evolve”
Adaptive radiation in a heterogeneous environment
Successive adaptive radiations have played a pivotal role in the evolution of biological diversity1,2,3. The effects of adaptive radiation are often seen4,5,6, but the underlying causes are difficult to disentangle and remain unclear7,8,9. Here we examine directly therole of ecological opportunity and competition in driving genetic diversification. We use the common aerobic bacterium Pseudomonas fluorescens10, which evolves rapidly under novel environmental conditions to generate a large repertoire of mutants11,12,13. When provided with ecological opportunity (afforded by spatial structure), identical populations diversify morphologically, but when ecological opportunity is restricted there is no such divergence. In spatially structured environments, the evolution of variant morphs follows a predictable sequence and we show that competition among the newly evolved niche-specialists maintains this variation. These results demonstrate that the elementary processes of mutation and selection alone are suifficient to promote rapid proliferation of new designs and support the theory that trade-offs in competitive ability drive adaptive radiation14,15.
In yeast, a modified protein known as a prion generates variation in growth rate across diverse environments. Is this an example of an agent that has evolved in order to promote its possessor's adaptability?
Evolvability-enhancing mutations in the fitness landscapes of an RNA and a protein
Can evolvability itself be a product of adaptive Darwinian evolution?
Can evolvability—the ability to produce adaptive heritable variation—itself evolve through adaptive Darwinian evolution? If so, then Darwinian evolution may help create the conditions that enable Darwinian evolution. Here I propose a framework that is suitable to address this question with available experimental data on adaptive landscapes. I introduce the notion of an evolvability-enhancing mutation, which increases the likelihood that subsequent mutations in an evolving organism, protein, or RNA molecule are adaptive. I search for such mutations in the experimentally characterized and combinatorially complete fitness landscapes of a protein and an RNA molecule. I find that such evolvability-enhancing mutations indeed exist. They constitute a small fraction of all mutations, which shift the distribution of fitness effects of subsequent mutations towards less deleterious mutations, and increase the incidence of beneficial mutations. Evolving populations which experience such mutations can evolve significantly higher fitness. The study of evolvability-enhancing mutations opens many avenues of investigation into the evolution of evolvability.
Evolution takes multiple paths to evolvability when facing environmental change
That all the diversity of life constitutes what Erasmus Darwin called “a single living filament”—an unbroken chain of descent from the last universal common ancestor—is evidence of life’s fundamental adaptability. However, the evolutionary processes that shape this ability to adapt (evolvability) remain elusive because of the required resolution and timespan of observations. Using evolving, self-replicating computer programs, we find that multiple pathways to increased evolvability emerge concurrently and distinctly aid adaptation. One pathway (evolved mutational landscapes) allows rapid adaptation to previously seen environments, while the other (higher mutation rates) allows rapid adaptation to entirely new environments. This multifaceted picture of evolvability helps us understand how organisms deal with ever-changing conditions and relentlessly explore nature’s opportunities for innovation.
Life at all scales is surprisingly effective at exploiting new opportunities, as demonstrated by the rapid emergence of antimicrobial resistance and novel pathogens. How populations acquire this level of evolvability and the various ways it aids survival are major open questions with direct implications for human health. Here, we use digital evolution to show that changing environments facilitate the simultaneous evolution of high mutation rates and a distribution of mutational effects skewed toward beneficial phenotypes. The evolved mutational neighborhoods allow rapid adaptation to previously encountered environments, whereas higher mutation rates aid adaptation to completely new environmental conditions. By precisely tracking evolving lineages and the phenotypes of their mutants, we show that evolving populations localize on phenotypic boundaries between distinct regions of genotype space. Our results demonstrate how evolution shapes multiple determinants of evolvability concurrently, fine-tuning a population’s adaptive responses to unpredictable or recurrent environmental shifts.
The causes of evolvability and their evolution
Evolvability is the ability of a biological system to produce phenotypic variation that is both heritable and adaptive. It has long been the subject of anecdotal observations and theoretical work. In recent years, however, the molecular causes of evolvability have been an increasing focus of experimental work. Here, we review recent experimental progress in areas as different as the evolution of drug resistance in cancer cells and the rewiring of transcriptional regulation circuits in vertebrates. This research reveals the importance of three major themes: multiple genetic and non-genetic mechanisms to generate phenotypic diversity, robustness in genetic systems, and adaptive landscape topography. We also discuss the mounting evidence that evolvability can evolve and the question of whether it evolves adaptively.
In recent years, biologists have increasingly been asking whether the ability to evolve — the evolvability — of biological systems, itself evolves, and whether this phenomenon is the result of natural selection or a by-product of other evolutionary processes. The concept of evolvability, and the increasing theoretical and empirical literature that refers to it, may constitute one of several pillars on which an extended evolutionary synthesis will take shape during the next few years, although much work remains to be done on how evolvability comes about.
Still, it seems that it’s possibile to evolve evolvability in the lab!
The mutation matrix and the evolution of evolvability
Evolvability is a key characteristic of any evolving system, and the concept of evolvability serves as a unifying theme in a wide range of disciplines related to evolutionary theory. The field of quantitative genetics provides a framework for the exploration of evolvability with the promise to produce insights of global importance. With respect to the quantitative genetics of biological systems, the parameters most relevant to evolvability are the G-matrix, which describes the standing additive genetic variances and covariances for a suite of traits, and the M-matrix, which describes the effects of new mutations on genetic variances and covariances. A population's immediate response to selection is governed by the G-matrix. However, evolvability is also concerned with the ability of mutational processes to produce adaptive variants, and consequently the M-matrix is a crucial quantitative genetic parameter. Here, we explore the evolution of evolvability by using analytical theory and simulation-based models to examine the evolution of the mutational correlation, rμ, the key parameter determining the nature of genetic constraints imposed by M. The model uses a diploid, sexually reproducing population of finite size experiencing stabilizing selection on a two-trait phenotype. We assume that the mutational correlation is a third quantitative trait determined by multiple additive loci. An individual's value of the mutational correlation trait determines the correlation between pleiotropic effects of new alleles when they arise in that individual. Our results show that the mutational correlation, despite the fact that it is not involved directly in the specification of an individual's fitness, does evolve in response to selection on the bivariate phenotype. The mutational variance exhibits a weak tendency to evolve to produce alignment of the M-matrix with the adaptive landscape, but is prone to erratic fluctuations as a consequence of genetic drift. The interpretation of this result is that the evolvability of the population is capable of a response to selection, and whether this response results in an increase or decrease in evolvability depends on the way in which the bivariate phenotypic optimum is expected to move. Interestingly, both analytical and simulation results show that the mutational correlation experiences disruptive selection, with local fitness maxima at –1 and +1. Genetic drift counteracts the tendency for the mutational correlation to persist at these extreme values, however. Our results also show that an evolving M-matrix tends to increase stability of the G-matrix under most circumstances. Previous studies of G-matrix stability, which assume nonevolving M-matrices, consequently may overestimate the level of instability of G relative to what might be expected in natural systems. Overall, our results indicate that evolvability can evolve in natural systems in a way that tends to result in alignment of the G-matrix, the M-matrix, and the adaptive landscape, and that such evolution tends to stabilize the G-matrix over evolutionary time.
Biological Systems
Collective behaviour, social interactions and leadership in animal groups are often driven by individual differences. However, most studies focus on same-species groups, in which individual variation is relatively low. Multispecies groups, however, entail interactions among highly divergent phenotypes, ranging from simple exploitative actions to complex coordinated networks. Here we studied hunting groups of otherwise-solitary Octopus cyanea and multiple fish species, to unravel hidden mechanisms of leadership and associated dynamics in functional nature and complexity, when divergence is maximized. Using three-dimensional field-based tracking and field experiments, we found that these groups exhibit complex functional dynamics and composition-dependent properties. Social influence is hierarchically distributed over multiscale dimensions representing role specializations: fish (particularly goatfish) drive environmental exploration, deciding where, while the octopus decides if, and when, the group moves. Thus, ‘classical leadership’ can be insufficient to describe complex heterogeneous systems, in which leadership instead can be driven by both stimulating and inhibiting movement. Furthermore, group composition altered individual investment and collective action, triggering partner control mechanisms (that is, punching) and benefits for the de facto leader, the octopus. This seemingly non-social invertebrate flexibly adapts to heterospecific actions, showing hallmarks of social competence and cognition. These findings expand our current understanding of what leadership is and what sociality is.
A Markovian dynamics for Caenorhabditis elegans behavior across scales
Are you ready for the Markov worm? Yes, that worm.
Complex phenotypes, such as an animal’s behavior, generally depend on an overwhelming number of processes that span a vast range of scales. While there is no reason that behavioral dynamics permit simple models, by subsuming inherent nonlinearities and memory into maximally predictive microstates, we find one for Caenorhabditis elegans foraging. The resulting “Markov worm” is effectively indistinguishable from real worm motion across a range of timescales, and we can decompose our model dynamics both to recover and reveal behavioral states. Finally, we connect postures to trajectories, illuminating how worms explore the environment in different behavioral states.
How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm Caenorhabditis elegans, we show that a single dynamics connects posture-scale fluctuations with trajectory diffusion and longer-lived behavioral states. We take short posture sequences as an instantaneous behavioral measure, fixing the sequence length for maximal prediction. Within the space of posture sequences, we construct a fine-scale, maximum entropy partition so that transitions among microstates define a high-fidelity Markov model, which we also use as a means of principled coarse-graining. We translate these dynamics into movement using resistive force theory, capturing the statistical properties of foraging trajectories. Predictive across scales, we leverage the longest-lived eigenvectors of the inferred Markov chain to perform a top–down subdivision of the worm’s foraging behavior, revealing both “runs-and-pirouettes” as well as previously uncharacterized finer-scale behaviors. We use our model to investigate the relevance of these fine-scale behaviors for foraging success, recovering a trade-off between local and global search strategies.
Top: the Markov worm. Bottom: the real worm.