Preserving and restoring biodiversity is becoming a great challenge as we face a world where planetary boundaries will likely be crossed over the following decades. Such challenge needs to consider multiple scales of complexity, both in space and time. A common thread in most cases is the presence of nonlinear phenomena generating shifts among alternative states. These breaking points imply a new perception of risk and different management strategies. A broad range of phenomena affect the preservation of healthy communities and constrain the ways to deal with conservation, from local features associated with habitat loss or facilitation to mesoscale or global network-level ecological complexity and the role played by extreme events. How are these scales connected? How can the emergent properties associated with ecosystem dynamics be exploited? Here a synthesis of ideas is presented, with a complex systems view of the different scales involved, the emergent phenomena separating them, and the universal properties that allow defining simple models on each scale.

Leigh Van Valen was an American evolutionary biologist who made major contributions to evolutionary theory and is particularly remembered by his groundbreaking paper "A New Evolutionary Law" (1973) where he provided evidence from fossil record data that this law maintains that the probability of extinction within any group remains es­sentially constant through time. In order to explain such unexpected result, Van Valen formulated a very influential idea that he dubbed the "Red Queen hypothesis". It states that the constant decay must be a consequence of evolutionary interactions among connected species within ecological networks. In Van Valen's picture, species do not merely evolve: they also coevolve with other species. As a consequence, when thinking in adaptation to an external environment, the other species must be considered as part (may be a major part) of such external world. Van Valen's law provided the first complex systems theory of coevolutionary dynamics and inspired a whole range of theoretical and experimental developments and scholars from very diverse fields, from economics to physics. In that respect, Leigh Van Valen's contribution percolated far beyond its original formulation. Red Queen arms races are nowadays considered a widespread feature of complex adaptive systems.

The possibility of abrupt transitions threatens to poise ecosystems into irreversibly degraded states. Recently, it has been proposed the use of engineered microbiomes in endangered ecosystems to prevent them to cross tipping points and avoid collapse. Potential targets for such interventions include some of the most prominent life-support systems in the biosphere: drylands and coral reefs. Since engineering can require the introduction of microorganisms not present in resident communities, how can we weight the potential outcomes? One way is to use general models of species interactions where the "synthetic" strain is incorporated into a standard multispecies model. Here we follow this approach by modelling a resource-consumer community where one of the species is a modified one that acts by preserving some key resource. We show how the indirect effect of damping the decay of shared resources results in biodiversity increase, and last but not less, the successful incorporation of the synthetic within the ecological network. Further extensions and implications for future restoration and terraformation strategies are discussed.

When computers start to become a dominant part of technology around the 1950s, fundamental questions about reliable designs and robustness were of great relevance. Their development gave rise to the exploration of new questions such as what made brains reliable (since neurons can die) and how computers could get inspiration from neural systems. In parallel, the first Artificial Neural Networks came to life. Since then, the comparative view between brains and computers has been developed in new, sometimes unsuspected directions. With the rise of deep learning and the development of connectomics, an evolutionary look at how both hardware and neural complexity have evolved or designed is required. In this paper, we argue that important similarities have resulted both from convergent evolution (the inevitable outcome of architectural constraints) and inspiration of hardware and software principles guided by toy pictures of neurobiology. Moreover, dissimilarities and gaps originate from the lack of major innovations that have paved the way to biological computing (including brains) that are completely absent within the artificial domain. As it occurs within synthetic biocomputation, we can also ask whether alternative minds can emerge from A.I.\ designs. Here we take an evolutionary view of the problem and discuss the remarkable convergences between living and artificial designs and what are the pre-conditions to achieve artificial intelligence.

While rapidly becoming a main thread in the development of new therapies, the rise of synthetic biology is also tied to concerns about the potential impact on ecosystems. That is particularly relevant in the of deployment in natural habitats, including the human microbiome. These concerns have boosted the analysis of diverse strategies of containment, from engineered cell death to xenobiology to the creation of Xeno nucleic acids. However, little attention has been paid to the potential containment implicit in nonlinear ecological interactions and the lessons provided by the population dynamics models used in community ecology. If we consider synthetic strains as some class of "species" embedded within an ecological context, it is possible to show that some network interaction patterns and their associated nonlinear responses can offer a reliable source of containment. Here we present and discuss some simple examples of these "ecological firewalls" that could help provide a self-regulating biocontainment. Our firewall designs can help to ensure that engineered organisms have a limited spread while, when required, preventing their extinction. The basic synthetic designs and their dynamical behaviour are presented, each one inspired in a given ecological class of interaction. Their possible applications are discussed and the broader connection with invasion ecology outlined.

Multicellular life forms have evolved many times in our planet, suggesting that this is a common evolutionary innovation. Multiple advantages have been proposed for multicellularity (MC) to emerge. In this paper we address the problem of how the first precondition for multicellularity, namely "stay together" might have occurred under spatially limited resources exploited by a population of unicellular agents. Using a minimal model of evolved cell-cell adhesion among growing and dividing cells that exploit a localised resource with a given size, we show that a transition occurs at a critical resource size separating a phase of evolved multicellular aggregates from a phase where unicellularity (UC) is favoured. The two phases are separated by an intermediate domain where where both UC and MC can be selected by evolution. This model provides a minimal approach to the early stages that were required to transition from Darwinian individuality to cohesive groups of cells associated with a physical cooperative effect: when resources are present only in a localised portion of the habitat, MC is a desirable property as it helps cells to keep close to the available local nutrients.

Phenotypic switching in cancer cells has been found to be present across tumor types. Recent studies on Glioblastoma report a remarkably common architecture of four well-defined phenotypes coexisting within high levels of intra-tumour genetic heterogeneity. Tumours grown from any cell type recapitulate the original phenotypic composition. Similar dynamics have been shown to occur in breast cancer, melanoma and likely across further cancer types. Given the adaptive potential of phenotypic switching (PHS) strategies, understanding how it drives tumour evolution and how to break down these architectures is a major priority. Here we model the ecological dynamics behind PHS. The model is able to reproduce experimental results, and specific conditions for cancer progression and clearance reveal novel features of plastic tumours and its direct consequences on therapy resistance. Following our results we discuss \textit{transition} therapy as a novel scheme to target not only combined cytotoxicity but also the rates of phenotypic switching.

Viruses have established symbiotic relationships with almost every other living organism on Earth and at all levels of biological organisation, from other viruses up to entire ecosystems. In most cases, peacefully coexisting with their hosts, but in most relevant cases, parasitising them and inducing diseases. Viruses are playing an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organisation, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as it occurs with temperatures separating phases in a liquid, define sharp qualitative types of behaviour. These {\em phase transitions} are very well known in Physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing to understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known examples of transition phenomena in virology and their simplest mathematical modelling approaches. We suggest that the advantages of abstract, simplified pictures used in Physics are also the key to properly understand the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across levels and their evolutionary and clinical implications are outlined.

Ordinary computing machines prohibit self-reference because it leads to logical inconsistencies and undecidability. In contrast, the human mind can understand self-referential statements without necessitating physically impossible brain states. Why can the brain make sense of self-reference? Here, we address this question by defining the Strange Loop Model, which features causal feedback between two brain modules, and circumvents the paradoxes of self-reference and negation by unfolding the inconsistency in time. We also argue that the metastable dynamics of the brain inhibit and terminate unhalting inferences. Finally, we show that the representation of logical inconsistencies in the Strange Loop Model leads to causal incongruence between brain subsystems in Integrated Information Theory.

The idea that the Earth system self-regulates in a habitable state was proposed in the 1970s by James Lovelock, who conjectured that life plays a self-regulatory role on a planetary-level scale. A formal approach to such hypothesis was presented afterwards under a toy model known as the Daisyworld. The model showed how such life-geosphere homeostasis was an emergent property of the system, where two species with different properties adjusted their populations to the changing external environment. So far, this ideal world exists only as a mathematical or computational construct, but it would be desirable to have a real, biological implementation of Lovelock's picture beyond our one Biosphere. Inspired in the exploration of synthetic ecosystems using genetic engineering and recent cell factory designs, here we propose such a living, microbial Daisyworld. This is based on a synthetic microbial ecosystem using pH as the external, abiotic control parameter. Several case studies are considering, including two, three and multiple species assemblies. Despite that oscillatory dynamics and chaos emerge in the latter case, it is shown that global regulation is also achieved in most cases as species diversity increases. The alternative implementations and their implications of this model in other synthetic biology scenarios, including ecosystem engineering, are outlined.

Human language is a prime example of a complex system characterized by multiple scales of description. Understanding its origins and distinctiveness has sparked investigations with very different approaches, ranging from the Universal Grammar to statistical analyses of word usage, all of which highlight, from different angles, the potential existence of universal patterns shared by all languages. Yet, a cohesive perspective remains elusive. In this paper we address this challenge. First, we provide a basic structure of universality, and define recursion as a special case thereof. We cast generative grammars of formal languages, the Universal Grammar and the Greenberg Universals in our basic structure of universality, and compare their mathematical properties. We then define universality for writing systems and show that only those using the rebus principle are universal. Finally, we examine Zipf's law for the statistics of word usage, explain its role as a complexity attractor, and explore its relation to universal writing systems as well as its similarities with universal Turing machines. Overall, we find that there are two main kinds of universality, termed {\it mechanistic} and {\it emergent}, and unveil some connections between them.

Complex dynamical fluctuations, from molecular noise within cells, collective intelligence, brain dynamics or computer traffic have been shown to display noisy behaviour consistent with a critical state between order and disorder. Living close to the critical point can have a number of adaptive advantages and it has been conjectured that evolution could select (and even tend to) these critical states. One way of approaching such state is by means of so-called self-organized criticality (SOC) where the system poises itself close to the critical point. Is this the case of living cells? It is difficult to test this idea given the enormous dimensionality associated with gene and metabolic webs. In this paper, we present an alternative approach: to engineer synthetic gene networks displaying SOC behaviour. This is achieved by exploiting the presence of a saturation (congestion) phenomenon of the ClpXP protein degradation machinery in E. coli cells. Using a feedback design that detects and then reduces ClpXP congestion, a {\em critical motif} is built from a two-gene network system, where SOC can be successfully implemented. Both deterministic and stochastic models are used, consistently supporting the presence of criticality in intracellular traffic. The potential implications for both cellular dynamics and designed intracellular noise are discussed.

Cognitive networks have evolved to cope with uncertain environments in order to make reliable decisions. Such decision making circuits need to respond to the external world in efficient and flexible ways, and one potentially general mechanism of achieving this is grounded in critical states. Mounting evidence has shown that brains operate close to such critical boundaries consistent with self-organized criticality (SOC). Is this also taking place in small-scale living systems, such as cells? Here we explore a recent model of engineered gene networks that have been shown to exploit the feedback between order and control parameters (as defined by expression levels of two coupled genes) to achieve a SOC state. We suggest that such SOC motif could be exploited to generate adaptive behavioral patterns and might help design fast responses in synthetic cellular and multicellular organisms.

What is the potential for synthetic biology as a way of engineering, on a large scale, complex ecosystems? Can it be used to change endangered ecological communities and rescue them to prevent their collapse? What are the best strategies for such ecological engineering paths to succeed? Is it possible to create stable, diverse synthetic ecosystems capable of persisting in closed environments? Can synthetic communities be created to thrive on planets different from ours? These and other questions pervade major future developments within synthetic biology. The goal of engineering ecosystems is plagued with all kinds of technological, scientific and ethic problems. In this paper we consider the requirements for Terraformation, i. e. for changing a given environment to make it hospitable to some given class of life forms. Although the standard use of this term involved strategies for planetary terraformation, it has been recently suggested that this approach could be applied to a very different context: ecological communities within our own planet. As discussed here, this includes multiple scales, from the gut microbiome to the entire biosphere.

The study of ecosystems, both natural and artificial, has historically been mediated by population dynamics theories. In this framework, quantifying population numbers and related variables (associated with metabolism or biological-environmental interactions) plays a central role in measuring and predicting system-level properties. As we move towards advanced technological engineering of cells and organisms, the possibility of bioengineering ecosystems (from the gut microbiome to wildlands) opens several questions that will require quantitative models to find answers. Here, we present a comprehensive survey of quantitative modelling approaches for managing three kinds of synthetic ecosystems, sharing the presence of engineered strains. These include test tube examples of ecosystems hosting a relatively low number of interacting species, mesoscale closed ecosystems (or ecospheres), and macro-scale, engineered ecosystems. The potential outcomes of synthetic ecosystem designs and their limits will be relevant to different disciplines, including biomedical engineering, astrobiology, space exploration and fighting climate change impacts on endangered ecosystems. We propose a space of possible ecosystems that captures this broad range of scenarios and a tentative road map for open problems and further exploration.

Multicellularity is one of the major evolutionary transitions, and its rise provided the ingredients for the emergence of a biosphere inhabited by complex organisms. Over the last decades, the potential for bioengineering multicellular systems has been instrumental in interrogating nature and exploring novel paths to regeneration and disease, as well as cognition and behaviour. Here, we provide a list of open problems that encapsulate many of the ongoing and future challenges in the field, and we suggest conceptual approaches that may facilitate progress.