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One of the main properties of biological systems is modularity, which manifests itself at all levels of their organization, starting with the level of molecular genetics, ending with the level of whole organisms and their communities. In a…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting…
Inspired from human cognition, machine learning systems are gradually revealing advantages of sparser and more modular architectures. Recent work demonstrates that not only do some modular architectures generalize well, but they also lead…
The evolution of structure in biology is driven by accretion and change. Accretion brings together disparate parts to form bigger wholes. Change provides opportunities for growth and innovation. Here we review patterns and processes that…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
Most biological systems are formed by component parts that to some degree are inter-related. Groups of parts that are more associated among themselves and are relatively autonomous from others are called modules. One of the consequences of…
Noise is a ubiquitous feature of the physical world. As a result, the first prerequisite of life is fault tolerance: maintaining integrity of state despite external bombardment. Recent experimental advances have revealed that biological…
A central biological question is how natural organisms are so evolvable (capable of quickly adapting to new environments). A key driver of evolvability is the widespread modularity of biological networks--their organization as functional,…
Metabolic networks consist of linked functional components, or modules. The mechanism underlying metabolic network modularity is of great interest not only to researchers of basic science but also to those in fields of engineering. Previous…
The increasing volume of ecologically and biologically relevant data has revealed a wide collection of emergent patterns in living systems. Analyzing different datasets, ranging from metabolic gene-regulatory to species interaction…
In this review, we discuss modularity and hierarchy in biological systems. We review examples from protein structure, genetics, and biological networks of modular partitioning of the geometry of biological space. We review theories to…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations.…
Biological and social systems are structured at multiple scales, and the incentives of individuals who interact in a group may diverge from the collective incentive of the group as a whole. Mechanisms to resolve this tension are responsible…
Direct reciprocity is a powerful mechanism for evolution of cooperation based on repeated interactions between the same individuals. But high levels of cooperation evolve only if the benefit-to-cost ratio exceeds a certain threshold that…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…
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…
Microbial communities are ubiquitous in nature and come in a multitude of forms, ranging from communities dominated by a handful of species to communities containing a wide variety of metabolically distinct organisms. This huge range in…