Specialization Can Drive the Evolution of Modularity

Organismal development and many cell biological processes are organized in a modular fashion, where regulatory molecules form groups with many interactions within a group and few interactions between groups. Thus, the activity of elements within a module depends little on elements outside of it. Modularity facilitates the production of heritable variation and of evolutionary innovations. There is no consensus on how modularity might evolve, especially for modules in development. We show that modularity can increase in gene regulatory networks as a byproduct of specialization in gene activity. Such specialization occurs after gene regulatory networks are selected to produce new gene activity patterns that appear in a specific body structure or under a specific environmental condition. Modules that arise after specialization in gene activity comprise genes that show concerted changes in gene activities. This and other observations suggest that modularity evolves because it decreases interference between different groups of genes. Our work can explain the appearance and maintenance of modularity through a mechanism that is not contingent on environmental change. We also show how modularity can facilitate co-option, the utilization of existing gene activity to build new gene activity patterns, a frequent feature of evolutionary innovations.     

The Evolutionary Origins of Hierarchy

Hierarchical organization—the recursive composition of sub-modules—is ubiquitous in biological networks, including neural, metabolic, ecological, and genetic regulatory networks, and in human-made systems, such as large organizations and the Internet. To date, most research on hierarchy in networks has been limited to quantifying this property. However, an open, important question in evolutionary biology is why hierarchical organization evolves in the first place. It has recently been shown that modularity evolves because of the presence of a cost for network connections. Here we investigate whether such connection costs also tend to cause a hierarchical organization of such modules. In computational simulations, we find that networks without a connection cost do not evolve to be hierarchical, even when the task has a hierarchical structure. However, with a connection cost, networks evolve to be both modular and hierarchical, and these networks exhibit higher overall performance and evolvability (i.e. faster adaptation to new environments). Additional analyses confirm that hierarchy independently improves adaptability after controlling for modularity. Overall, our results suggest that the same force–the cost of connections–promotes the evolution of both hierarchy and modularity, and that these properties are important drivers of network performance and adaptability. In addition to shedding light on the emergence of hierarchy across the many domains in which it appears, these findings will also accelerate future research into evolving more complex, intelligent computational brains in the fields of artificial intelligence and robotics.     

From Caenorhabditis elegans to the human connectome: a specific modular organization increases metabolic,functional and developmental efficiency

The connectome, or the entire connectivity of a neural system represented by a network, ranges across various scales from synaptic connections between individual neurons to fibre tract connections between brain regions. Although the modularity they commonly show has been extensively studied, it is unclear whether the connection specificity of such networks can already be fully explained by the modularity alone. To answer this question, we study two networks, the neuronal network of Caenorhabditis elegans and the fibre tract network of human brains obtained through diffusion spectrum imaging. We compare them to their respective benchmark networks with varying modularities, which are generated by link swapping to have desired modularity values. We find several network properties that are specific to the neural networks and cannot be fully explained by the modularity alone. First, the clustering coefficient and the characteristic path length of both C. elegans and human connectomes are higher than those of the benchmark networks with similar modularity. High clustering coefficient indicates efficient local information distribution, and high characteristic path length suggests reduced global integration. Second, the total wiring length is smaller than for the alternative configurations with similar modularity. This is due to lower dispersion of connections, which means each neuron in the C. elegans connectome or each region of interest in the human connectome reaches fewer ganglia or cortical areas, respectively. Third, both neural networks show lower algorithmic entropy compared with the alternative arrangements. This implies that fewer genes are needed to encode for the organization of neural systems. While the first two findings show that the neural topologies are efficient in information processing, this suggests that they are also efficient from a developmental point of view. Together, these results show that neural systems are organized in such a way as to yield efficient features beyond those given by their modularity alone.     

Falling towards forgetfulness: synaptic decay prevents spontaneous recovery of memory

Long after a new language has been learned and forgotten, relearning a few words seems to trigger the recall of other words. This "free-lunch learning" (FLL) effect has been demonstrated both in humans and in neural network models. Specifically, previous work proved that linear networks that learn a set of associations, then partially forget them all, and finally relearn some of the associations, show improved performance on the remaining (i.e., nonrelearned) associations. Here, we prove that relearning forgotten associations decreases performance on nonrelearned associations; an effect we call negative free-lunch learning. The difference between free-lunch learning and the negative free-lunch learning presented here is due to the particular method used to induce forgetting. Specifically, if forgetting is induced by isotropic drifting of weight vectors (i.e., by adding isotropic noise), then free-lunch learning is observed. However, as proved here, if forgetting is induced by weight values that simply decay or fall towards zero, then negative free-lunch learning is observed. From a biological perspective, and assuming that nervous systems are analogous to the networks used here, this suggests that evolution may have selected physiological mechanisms that involve forgetting using a form of synaptic drift rather than synaptic decay, because synaptic drift, but not synaptic decay, yields free-lunch learning.     

Anatomical Network Analysis Shows Decoupling of Modular Lability and Complexity in the Evolution of the Primate Skull

Modularity and complexity go hand in hand in the evolution of the skull of primates. Because analyses of these two parameters often use different approaches, we do not know yet how modularity evolves within, or as a consequence of, an also-evolving complex organization. Here we use a novel network theory-based approach (Anatomical Network Analysis) to assess how the organization of skull bones constrains the co-evolution of modularity and complexity among primates. We used the pattern of bone contacts modeled as networks to identify connectivity modules and quantify morphological complexity. We analyzed whether modularity and complexity evolved coordinately in the skull of primates. Specifically, we tested Herbert Simon’s general theory of near-decomposability, which states that modularity promotes the evolution of complexity. We found that the skulls of extant primates divide into one conserved cranial module and up to three labile facial modules, whose composition varies among primates. Despite changes in modularity, statistical analyses reject a positive feedback between modularity and complexity. Our results suggest a decoupling of complexity and modularity that translates to varying levels of constraint on the morphological evolvability of the primate skull. This study has methodological and conceptual implications for grasping the constraints that underlie the developmental and functional integration of the skull of humans and other primates.     

Challenges in identifying and interpreting organizational modules in morphology

Form is a rich concept that agglutinates information about the proportions and topological arrangement of body parts. Modularity is readily measurable in both features, the variation of proportions (variational modules) and the organization of topology (organizational modules). The study of variational modularity and of organizational modularity faces similar challenges regarding the identification of meaningful modules and the validation of generative processes; however, most studies in morphology focus solely on variational modularity, while organizational modularity is much less understood. A possible cause for this bias is the successful development in the last twenty years of morphometrics, and specially geometric morphometrics, to study patters of variation. This contrasts with the lack of a similar mathematical framework to deal with patterns of organization. Recently, a new mathematical framework has been proposed to study the organization of gross anatomy using tools from Network Theory, so‐called Anatomical Network Analysis (AnNA). In this essay, I explore the potential use of this new framework—and the challenges it faces in identifying and validating biologically meaningful modules in morphological systems—by providing working examples of a complete analysis of modularity of the human skull and upper limb. Finally, I suggest further directions of research that may bridge the gap between variational and organizational modularity studies, and discuss how alternative modeling strategies of morphological systems using networks can benefit from each other.     

Cranial modularity and sequence heterochrony in mammals

Heterochrony, the temporal shifting of developmental events relative to each other, requires a degree of autonomy among those processes or structures. Modularity, the division of larger structures or processes into autonomous sets of internally integrated units, is often discussed in relation to the concept of heterochrony. However, the relationship between the developmental modules derived from studies of heterochrony and evolutionary modules, which should be of adaptive importance and relate to the genotype-phenotype map, has not been explicitly studied. I analyzed a series of sectioned and whole cleared-and-stained embryological and neonatal specimens, supplemented with published ontogenetic data, to test the hypothesis that bones within the same phenotypic modules, as determined by morphometric analysis, are developmentally integrated and will display coordinated heterochronic shifts across taxa. Modularity was analyzed in cranial bone ossification sequences of 12 therian mammals. A dataset of 12-18 developmental events was used to assess if modularity in developmental sequences corresponds to six phenotypic modules, derived from a recent morphometric analysis of cranial modularity in mammals. Kendall's tau was used to measure rank correlations, with randomization tests for significance. If modularity in developmental sequences corresponds to observed phenotypic modules, bones within a single phenotypic module should show integration of developmental timing, maintaining the same timing of ossification relative to each other, despite differences in overall ossification sequences across taxa. Analyses did not find any significant conservation of developmental timing within the six phenotypic modules, meaning that bones that are highly integrated in adult morphology are not significantly integrated in developmental timing.     

Formation and Maintenance of Robust Long-Term Information Storage in the Presence of Synaptic Turnover

A long-standing problem is how memories can be stored for very long times despite the volatility of the underlying neural substrate, most notably the high turnover of dendritic spines and synapses. To address this problem, here we are using a generic and simple probabilistic model for the creation and removal of synapses. We show that information can be stored for several months when utilizing the intrinsic dynamics of multi-synapse connections. In such systems, single synapses can still show high turnover, which enables fast learning of new information, but this will not perturb prior stored information (slow forgetting), which is represented by the compound state of the connections. The model matches the time course of recent experimental spine data during learning and memory in mice supporting the assumption of multi-synapse connections as the basis for long-term storage.     

Analysis of a hyper-diverse seed dispersal network: modularity and underlying mechanisms

Mutualistic interactions involving pollination and ant-plant mutualistic networks typically feature tightly linked species grouped in modules. However, such modularity is infrequent in seed dispersal networks, presumably because research on those networks predominantly includes a single taxonomic animal group (e.g. birds). Herein, for the first time, we examine the pattern of interaction in a network that includes multiple taxonomic groups of seed dispersers, and the mechanisms underlying modularity. We found that the network was nested and modular, with five distinguishable modules. Our examination of the mechanisms underlying such modularity showed that plant and animal trait values were associated with specific modules but phylogenetic effect was limited. Thus, the pattern of interaction in this network is only partially explained by shared evolutionary history. We conclude that the observed modularity emerged by a combination of phylogenetic history and trait convergence of phylogenetically unrelated species, shaped by interactions with particular types of dispersal agents.     

Self-assembly of neural networks viewed as swarm intelligence

While self-assembly is a fairly active area of research in swarm intelligence, relatively little attention has been paid to the issues surrounding the construction of network structures. In this paper we extend methods developed previously for controlling collective movements of agent teams to serve as the basis for self-assembly or “growth” of networks, using neural networks as a concrete application to evaluate our approach. Our central innovation is having network connections arise as persistent “trails” left behind moving agents, trails that are reminiscent of pheromone deposits made by agents in ant colony optimization models. The resulting network connections are thus essentially a record of agent movements. We demonstrate our model’s effectiveness by using it to produce two large networks that support subsequent learning of topographic and feature maps. Improvements produced by the incorporation of collective movements are also examined through computational experiments. These results indicate that methods for directing collective movements can be adopted to facilitate network self-assembly.     

Varieties of modules: kinds, levels, origins, and behaviors

This article began as a review of a conference, organized by Gerhard Schlosser, entitled "Modularity in Development and Evolution." The conference was held at, and sponsored by, the Hanse Wissenschaftskolleg in Delmenhorst, Germany in May, 2000. The article subsequently metamorphosed into a literature and concept review as well as an analysis of the differences in current perspectives on modularity. Consequently, I refer to general aspects of the conference but do not review particular presentations. I divide modules into three kinds: structural, developmental, and physiological. Every module fulfills none, one, or multiple functional roles. Two further orthogonal distinctions are important in this context: module-kinds versus module-variants-of-a-kind and reproducer versus nonreproducer modules. I review criteria for individuation of modules and mechanisms for the phylogenetic origin of modularity. I discuss conceptual and methodological differences between developmental and evolutionary biologists, in particular the difference between integration and competition perspectives on individualization and modular behavior. The variety in views regarding modularity presents challenges that require resolution in order to attain a comprehensive, rather than a piecemeal and fragmentary, evolutionary developmental biology. J. Exp. Zool. (Mol. Dev. Evol.) 291:116-129, 2001.     

Linear Motif-Mediated Interactions Have Contributed to the Evolution of Modularity in Complex Protein Interaction Networks

The modular architecture of protein-protein interaction (PPI) networks is evident in diverse species with a wide range of complexity. However, the molecular components that lead to the evolution of modularity in PPI networks have not been clearly identified. Here, we show that weak domain-linear motif interactions (DLIs) are more likely to connect different biological modules than strong domain-domain interactions (DDIs). This molecular division of labor is essential for the evolution of modularity in the complex PPI networks of diverse eukaryotic species. In particular, DLIs may compensate for the reduction in module boundaries that originate from increased connections between different modules in complex PPI networks. In addition, we show that the identification of biological modules can be greatly improved by including molecular characteristics of protein interactions. Our findings suggest that transient interactions have played a unique role in shaping the architecture and modularity of biological networks over the course of evolution.     

Emergence of symmetric, modular, and reciprocal connections in recurrent networks with Hebbian learning

While learning and development are well characterized in feedforward networks, these features are more difficult to analyze in recurrent networks due to the increased complexity of dual dynamics – the rapid dynamics arising from activation states and the slow dynamics arising from learning or developmental plasticity. We present analytical and numerical results that consider dual dynamics in a recurrent network undergoing Hebbian learning with either constant weight decay or weight normalization. Starting from initially random connections, the recurrent network develops symmetric or near-symmetric connections through Hebbian learning. Reciprocity and modularity arise naturally through correlations in the activation states. Additionally, weight normalization may be better than constant weight decay for the development of multiple attractor states that allow a diverse representation of the inputs. These results suggest a natural mechanism by which synaptic plasticity in recurrent networks such as cortical and brainstem premotor circuits could enhance neural computation and the generation of motor programs. Received: 27 April 1998 / Accepted in revised form: 16 March 1999     

Ecological,historical and evolutionary determinants of modularity in weighted seed‐dispersal networks

Modularity is a recurrent and important property of bipartite ecological networks. Although well‐resolved ecological networks describe interaction frequencies between species pairs, modularity of bipartite networks has been analysed only on the basis of binary presence–absence data. We employ a new algorithm to detect modularity in weighted bipartite networks in a global analysis of avian seed‐dispersal networks. We define roles of species, such as connector values, for weighted and binary networks and associate them with avian species traits and phylogeny. The weighted, but not binary, analysis identified a positive relationship between climatic seasonality and modularity, whereas past climate stability and phylogenetic signal were only weakly related to modularity. Connector values were associated with foraging behaviour and were phylogenetically conserved. The weighted modularity analysis demonstrates the dominating impact of ecological factors on the structure of seed‐dispersal networks, but also underscores the relevance of evolutionary history in shaping species roles in ecological communities.     

Avoiding catastrophic forgetting by coupling two reverberating neural networks

Gradient descent learning procedures are most often used in neural network modeling. When these algorithms (e.g., backpropagation) are applied to sequential learning tasks a major drawback, termed catastrophic forgetting (or catastrophic interference), generally arises: when a network having already learned a first set of items is next trained on a second set of items, the newly learned information may completely destroy the information previously learned. To avoid this implausible failure, we propose a two-network architecture in which new items are learned by a first network concurrently with internal pseudo-items originating from a second network. As it is demonstrated that these pseudo-items reflect the structure of items previously learned by the first network, the model thus implements a refreshing mechanism using the old information. The crucial point is that this refreshing mechanism is based on reverberating neural networks which need only random stimulations to operate. The model thus provides a means to dramatically reduce retroactive interference while conserving the essentially distributed nature of information and proposes an original but plausible means to ‘copy and paste’ a distributed memory from one place in the brain to another.     

How Lateral Connections and Spiking Dynamics May Separate Multiple Objects Moving Together

Over successive stages, the ventral visual system of the primate brain develops neurons that respond selectively to particular objects or faces with translation, size and view invariance. The powerful neural representations found in Inferotemporal cortex form a remarkably rapid and robust basis for object recognition which belies the difficulties faced by the system when learning in natural visual environments. A central issue in understanding the process of biological object recognition is how these neurons learn to form separate representations of objects from complex visual scenes composed of multiple objects. We show how a one-layer competitive network comprised of ‘spiking’ neurons is able to learn separate transformation-invariant representations (exemplified by one-dimensional translations) of visual objects that are always seen together moving in lock-step, but separated in space. This is achieved by combining ‘Mexican hat’ functional lateral connectivity with cell firing-rate adaptation to temporally segment input representations of competing stimuli through anti-phase oscillations (perceptual cycles). These spiking dynamics are quickly and reliably generated, enabling selective modification of the feed-forward connections to neurons in the next layer through Spike-Time-Dependent Plasticity (STDP), resulting in separate translation-invariant representations of each stimulus. Variations in key properties of the model are investigated with respect to the network’s ability to develop appropriate input representations and subsequently output representations through STDP. Contrary to earlier rate-coded models of this learning process, this work shows how spiking neural networks may learn about more than one stimulus together without suffering from the ‘superposition catastrophe’. We take these results to suggest that spiking dynamics are key to understanding biological visual object recognition.     

Evolution of complex modular biological networks

Biological networks have evolved to be highly functional within uncertain environments while remaining extremely adaptable. One of the main contributors to the robustness and evolvability of biological networks is believed to be their modularity of function, with modules defined as sets of genes that are strongly interconnected but whose function is separable from those of other modules. Here, we investigate the in silico evolution of modularity and robustness in complex artificial metabolic networks that encode an increasing amount of information about their environment while acquiring ubiquitous features of biological, social, and engineering networks, such as scale-free edge distribution, small-world property, and fault-tolerance. These networks evolve in environments that differ in their predictability, and allow us to study modularity from topological, information-theoretic, and gene-epistatic points of view using new tools that do not depend on any preconceived notion of modularity. We find that for our evolved complex networks as well as for the yeast protein–protein interaction network, synthetic lethal gene pairs consist mostly of redundant genes that lie close to each other and therefore within modules, while knockdown suppressor gene pairs are farther apart and often straddle modules, suggesting that knockdown rescue is mediated by alternative pathways or modules. The combination of network modularity tools together with genetic interaction data constitutes a powerful approach to study and dissect the role of modularity in the evolution and function of biological networks.     

A neuron-like network with the ability to learn coordinated movement patterns

A model calculation is presented simulating the coordinated interaction between the walking legs of a multi-legged animal. The neural network consists of separate modules with oscillatory capabilities. It has the ability to adjust the necessary parameters for producing a coordinated interaction between the modules in a self-organizing fashion. Some sort of reinforcement comparison learning is used to train the network. It starts oscillations in a completely uncoupled state. After about 100 learning steps, the generation of a stable alternating pattern is usually terminated. Then, the network is able to maintain synchronization, even when disturbances are applied to single agents or to the network as a whole.     

Chipping away at memory

Inverse power-law behavior is known to be characteristic of adaptation, learning, and memory. Herein, we propose a phenomenological model of forgetting based on renewal theory that introduces a new psychophysical concept, chipping; discrete events that chip away at chunks of memory and thereby produce forgetting. The neural mechanism producing these chips is the 1/f-noise that is generically produced in complex neuronal networks.