Habitat loss causes long extinction transients in small trophic chains

Transients in ecology are extremely important since they determine how equilibria are approached. The debate on the dynamic stability of ecosystems has been largely focused on equilibrium states. However, since ecosystems are constantly changing due to climate conditions or to perturbations driven by the climate crisis or anthropogenic actions (habitat destruction, deforestation, or defaunation), it is important to study how dynamics can proceed till equilibria. This article investigates the dynamics and transient phenomena in small food chains using mathematical models. We are interested in the impact of habitat loss in ecosystems with vegetation undergoing facilitation. We provide a dynamical study of a small food chain system given by three trophic levels: primary producers, i.e., vegetation, herbivores, and predators. Our models reveal how habitat loss pushes vegetation towards tipping points, how the presence of herbivores in small habitats could promote ecosystem's extinction (ecological meltdown), or how the loss of predators produce a cascade effect (trophic downgrading). Mathematically, these systems exhibit many of the possible local bifurcations: saddle-node, transcritical, Andronov-Hopf, together with a global bifurcation given by a heteroclinic bifurcation. The associated transients are discussed, from the ghost dynamics to the critical slowing down tied to the local and global bifurcations. Our work highlights how the increase of ecological complexity (trophic levels) can imply more complex transitions. This article shows how the pernicious effects of perturbations (i.e., habitat loss or hunting pressure) on ecosystems could not be immediate, producing extinction delays. These theoretical results suggest the possibility that some ecosystems could be currently trapped into the (extinction) ghost of their stable past

Dynamics, evolution and information in nonlinear dynamical systems of replicators

En aquesta tesi he investigat diversos camps de la biologia que podrien englobar-se en la disciplina general dels sistemes no lineals de replicadors. Els treballs presentats en aquesta tesis investiguen diversos fenomens dinàmics i processos evolutius per virus de RNA, pels anomenats hipercicles i per models generals de replicadors antagonistes. Específicament he investigat les anomenades quasiespècies, utilitzades per a modelitzar poblacions de RNA. Els treballs sobre hipercicles exploren diversos fenomens previs a l'origen de la vida i a l'aparició de la primera cèl.lula vivent. Mitjançant models ecològics com també utilitzant diferents eines computacionals he estudiat l'anomenada hipòtesi de la Reina Roja per entitats replicadores simples amb mutació. Aquests estudis tenen un interès en el contexte de l'evolució prebiòtica i l'ecologia teòrica.In this thesis I have investigated several fields of biology that can be classified in the general subject of replicator nonlinear systems. The works presented in the thesis investigate several dynamical phenomena and evolutionary processes for RNA viruses, for hypercycles and for general models on antagonistic replicator dynamics. I have specifically investigated the dynamics of so-called quasispecies, used for the modelization of RNA populations. The works on hypercycles explore several phenomena related to previous events to the origin of life and to the appearance of the first living cell. By means of some ecologically-based mathematical models as well as of some computational models we also investigate the so-called Red Queen hypothesis for small, replicating-mutating entities. These studies are of interest in the context of prebiotic evolution and theoretical ecology.Programa de doctorat en Biomedicin

Simple genomes, complex interactions: epistasis in RNA virus

Owed to their reduced size and low number of proteins encoded, RNA viruses and other subviral pathogens are often considered as being genetically too simple. However, this structural simplicity also creates the necessity for viral RNA sequences to encode for more than one protein and for proteins to carry out multiple functions, all together resulting in complex patterns of genetic interactions. In this work we will first review the experimental studies revealing that the architecture of viral genomes is dominated by antagonistic interactions among loci. Second, we will also review mathematical models and provide a description of computational tools for the study of RNA virus dynamics and evolution. As an application of these tools, we will finish this review article by analyzing a stochastic bit-string model of in silico virus replication. This model analyzes the interplay between epistasis and the mode of replication on determining the population load of deleterious mutations. The model suggests that, for a given mutation rate, the deleterious mutational load is always larger when epistasis is predominantly antagonistic than when synergism is the rule. However, the magnitude of this effect is larger if replication occurs geometrically than if it proceeds linearly

Simple genomes, complex interactions: epistasis in RNA virus

Owed to their reduced size and low number of proteins encoded, RNA viruses and other subviral pathogens are often considered as being genetically too simple. However, this structural simplicity also creates the necessity for viral RNA sequences to encode for more than one protein and for proteins to carry out multiple functions, all together resulting in complex patterns of genetic interactions. In this work we will first review the experimental studies revealing that the architecture of viral genomes is dominated by antagonistic interactions among loci. Second, we will also review mathematical models and provide a description of computational tools for the study of RNA virus dynamics and evolution. As an application of these tools, we will finish this review article by analyzing a stochastic bit-string model of in silico virus replication. This model analyzes the interplay between epistasis and the mode of replication on determining the population load of deleterious mutations. The model suggests that, for a given mutation rate, the deleterious mutational load is always larger when epistasis is predominantly antagonistic than when synergism is the rule. However, the magnitude of this effect is larger if replication occurs geometrically than if it proceeds linearly

Dynamical mechanism behind ghosts unveiled in a map complexification

Complex systems such as ecosystems, electronic circuits, lasers or chemical reactions can be modelled by dynamical systems which typically experience bifurcations. Transients typically suffer extremely long delays at the vicinity of bifurcations and it is also known that these transients follow scaling laws as the bifurcation parameter gets closer the bifurcation value in deterministic systems. The mechanisms involved in local bifurca- tions are well-known. However, for saddle-node bifurcations, the relevant dynamics after the bifurcation occur in the complex phase space. Hence, the mechanism responsible for the delays and the associated inverse-square root scaling law for this bifurcation can be better understood by looking at the dynamics in the complex space. We follow this approach and complexify a simple ecological system undergoing a saddle-node bifurcation. The discrete model describes a biological system with facilitation (cooperation) under habitat destruction for species with non-overlapping generations. We study the complex (as opposed to real) dynamics once the bifurcation has occurred. We identify the fundamental mechanism causing these long delays (called ghosts), given by two repellers in the complex space. Such repellers appear to be extremely close to the real line, thus forming a nar- row channel close to the two new fixed points and responsible for the slow passage of the orbits, which remains tangible in the real numbers phase space. We analytically provide the relation between the inverse square-root scaling law and the multipliers of these repellers. We finally prove that the same phenomenon occurs for more general i.e., non-necessarily polynomial, models

Dynamics in a time-discrete food-chain model with strong pressure on preys

Discrete-time dynamics, mainly arising in boreal and temperate ecosystems for species with non-overlapping generations, have been largely studied to understand the dynamical outcomes due to changes in relevant ecological parameters. The local and global dynamical behaviour of many of these models is difficult to investigate analytically in the parameter space and, typically, numerical approaches are employed when the dimension of the phase space is large. In this article we provide topological and dynamical results for a map modelling a discrete-time, three-species food chain with two predator species interacting on the same prey. The domain where dynamics live is characterised, as well as the so-called escaping regions, which involve species extinctions. We also provide a full description of the local stability of equilibria within a volume of the parameter space given by the prey’s growth rate and the predation rates. We have found that the increase of the pressure of predators on the prey results in chaos via a supercritical Neimark-Sacker bifurcation. Then, period-doubling bifurcations of invariant curves take place. Interestingly, an increasing predation directly on preys can shift the extinction of top predators to their survival, allowing an unstable persistence of the three species by means of periodic and chaotic attractors

Variability in mutational fitness effects prevents full lethal transitions in large quasispecies populations

The distribution of mutational fitness effects (DMFE) is crucial to the evolutionary fate of quasispecies. In this article we analyze the effect of the DMFE on the dynamics of a large quasispecies by means of a phenotypic version of the classic Eigen's model that incorporates beneficial, neutral, deleterious, and lethal mutations. By parameterizing the model with available experimental data on the DMFE of Vesicular stomatitis virus (VSV) and Tobacco etch virus (TEV), we found that increasing mutation does not totally push the entire viral quasispecies towards deleterious or lethal regions of the phenotypic sequence space. The probability of finding regions in the parameter space of the general model that results in a quasispecies only composed by lethal phenotypes is extremely small at equilibrium and in transient times. The implications of our findings can be extended to other scenarios, such as lethal mutagenesis or genomically unstable cancer, where increased mutagenesis has been suggested as a potential therapy.This work was partially funded by the Botín Foundation (JS, RVS), by the Spanish Secretaria de Estado de Investigación, Desarrollo e Innovación grants MTM2010-16425 (CS, RM) and BFU2012-30805 (SFE), by grant 2009-SGR-67 from the Catalan government (CS, RM), by grant NSF PHY05-51164 (JS, SFE), and by the Santa Fe Institute (RVS, SFE)

Computational implementation of a tunable multicellular memory circuit for engineered eukaryotic consortia

Cells are complex machines capable of processing information by means of an entangled network of molecular interactions. A crucial component of these decision-making systems is the presence of memory and this is also a specially relevant target of engineered synthetic systems. A classic example of memory devices is a 1-bit memory element known as the flip-flop. Such system can be in principle designed using a single-cell implementation, but a direct mapping between standard circuit design and a living circuit can be cumbersome. Here we present a novel computational implementation of a 1-bit memory device using a reliable multicellular design able to behave as a set-reset flip-flop that could be implemented in yeast cells. The dynamics of the proposed synthetic circuit is investigated with a mathematical model using biologically-meaningful parameters. The circuit is shown to behave as a flip-flop in a wide range of parameter values. The repression strength for the NOT logics is shown to be crucial to obtain a good flip-flop signal. Our model also shows that the circuit can be externally tuned to achieve different memory states and dynamics, such as persistent and transient memory. We have characterized the parameter domains for robust memory storage and retrieval as well as the corresponding time response dynamics.This work was partially funded by the European Research Council Grant ERC SYNCOM 294294 (JM, RS, AB, NC), by grants of the Botin Foundation, by Banco Santander through its Santander Universities Global Division (RS, JS), and the Santa Fe Institute (RS)

Synthetic criticality in cellular brains

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 an 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.This work was supported by the Spanish Ministry of Economy and Competitiveness, Grant PID2019-111680GB-I00, an MICIN Grant PID2019-111680GB-I00 and an AGAUR FI 2018 Grant. JS has been partially funded by the CERCA Programme of the 'Generalitat de Catalunya', by 'Agencia Estatal de Investigación' Grant RTI2018-098322-B-I00 and by the 'Ramón y Cajal' contract RYC-2017-22243. AG has been funded by the AGAUR Grant 2017-SGR-1049 and by the MINECO-FEDER-UE Grants PGC-2018-098676-B-100 and RTI2018-093860-B-C21. JP was funded by FPI 202