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Almost all viruses, regardless of their genomic material, produce defective viral genomes (DVG) as an unavoidable byproduct of their error-prone replication. Defective interfering (DI) elements are a subgroup of DVGs that have been shown to interfere with the replication of the wild-type (WT) virus. Along with DIs, other genetic elements known as satellite RNAs (satRNAs), that show no genetic relatedness with the WT virus, can co-infect cells with WT helper viruses and take advantage of viral proteins for their own benefit. These satRNAs have effects that range from reduced symptom severity to enhanced virulence. The interference dynamics of DIs over WT viruses has been thoroughly modeled at within-cell, within-host, and population levels. However, nothing is known about the dynamics resulting from the nonlinear interactions between WT viruses and DIs in the presence of satellites, a process that is frequently seen in plant RNA viruses and in biomedically relevant pathosystems like hepatitis B virus and its satellite. Here, we look into a simple phenomenological mathematical model that describes how a WT virus replicates and produces DIs in presence of a satRNA. The WT virus is subject to mechanisms of complementation, competition, and various levels of interference from DIs and the satRNA. Examining the dynamics analytically and numerically reveals three possible regimes: (i) full extinction, (ii) satellite extinction and virus-DIs coexistence and (iii) full coexistence. Assuming DIs replicate faster than the satRNA owed to their smaller size drives to scenario (ii), which implies that DIs could wipe out the satRNA. In addition, a small region of the parameter space exists wherein the system is bistable (either scenarios (ii) or (iii) are concurrently stable). We have identified transcritical bifurcations in the transitions between scenarios (i) to (iii) and saddle–node bifurcations behind the change from bistability to monostability. Despite the model simplicity, Peer Reviewed, Postprint (author's final draft)

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle’s unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population., Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This work has been supported by the Spanish State Research Agency (AEI) through Grants PGC2018- 100928-B-I00 (DP), PGC2018-100699-B-I00 (MCIU/AEI/FEDER, UE) (MJC), and by Catalan Government Grant 2017 SGR 1374 (MJC). JS has been supported by the Ramón y Cajal Grant RYC-2017-22243 funded by MCIN/AEI/10.13039/501100011033 “FSE invests in your future”, and by the 2020-2021 Biodiversa+ and Water JPI joint call under the BiodivRestore ERA-NET Cofund (GA No 101003777) pro- ject MPA4Sustainability with funding organizations: Innovation Fund Denmark (IFD), Agence Nationale de la Recherche (ANR), Fundação para a Ciência e a Tecnologia (FCT), Swedish Environmental Protec- tion Agency (SEPA), and grant PCI2022-132926 funded by MCIN/ AEI/10.13039/501100011033 and by the European Union NextGen- erationEU/PRTR. This work has been also funded through the Severo Ochoa and María de Maeztu Program for Centres and Units of Excel- lence in R &D (CEX2020-001084-M). We thank CERCA Programme/ Generalitat de Catalunya for institutional support. DP has been sup- ported by the Research Program 2021–2023 of Universidad Internac- ional de la Rioja. RO thanks to the Faculty for the Future program of the Schlumberger Foundation for the scholarship., Peer Reviewed, Postprint (published version)

Slowing down occurs in dynamical systems close to bifurcations or phase transitions. The time length (t) of ghost transients close to a saddle-node bifurcation in deterministic systems follows t~|¿-¿c|-1/2, ¿ being the bifurcation parameter and ¿c its critical value. Recently, we numerically investigated how intrinsic noise affected the deterministic picture, finding a more complicated scaling law. We here provide a theoretical basis for this new law with two models of cooperation using a Wentzel–Kramers–Brillouin asymptotic approximation of the Master Equation. A study of the phase space of the Hamiltonian derived from the Hamilton–Jacobi equation shows that the statistically significant orbits (paths) reproduce the scaling function observed in the stochastic simulations. The flight times tied to these orbits underpin the scaling law of the stochastic system, and the same properties should extend in a universal way to all stochasticsystems whose associated Hamiltonian exhibits the same behaviour. Our approach allows to make useful theoretical predictions of transient times in stochastic systems close to a bifurcation., Peer Reviewed, Postprint (published version)

Peer Reviewed, Postprint (published version)

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, 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, Peer Reviewed, Postprint (published version)