Extended patchy ecosystems may increase their total biomass through self-replication

Patches of vegetation consist of dense clusters of shrubs, grass, or trees, often found to be circular characteristic size, defined by the properties of the vegetation and terrain. Therefore, vegetation patches can be interpreted as localized structures. Previous findings have shown that such localized structures can self-replicate in a binary fashion, where a single vegetation patch elongates and divides into two new patches. Here, we extend these previous results by considering the more general case, where the plants interact non-locally, this extension adds an extra level of complexity and shrinks the gap between the model and real ecosystems, where it is known that the plant-to-plant competition through roots and above-ground facilitating interactions have non-local effects, i.e. they extend further away than the nearest neighbor distance. Through numerical simulations, we show that for a moderate level of aridity, a transition from a single patch to periodic pattern occurs. Moreover, for large values of the hydric stress, we predict an opposing route to the formation of periodic patterns, where a homogeneous cover of vegetation may decay to spot-like patterns. The evolution of the biomass of vegetation patches can be used as an indicator of the state of an ecosystem, this allows to distinguish if a system is in a self-replicating or decaying dynamics. In an attempt to relate the theoretical predictions to real ecosystems, we analyze landscapes in Zambia and Mozambique, where vegetation forms patches of tens of meters in diameter. We show that the properties of the patches together with their spatial distributions are consistent with the self-organization hypothesis. We argue that the characteristics of the observed landscapes may be a consequence of patch self-replication, however, detailed field and temporal data is fundamental to assess the real state of the ecosystems.Comment: 38 pages, 12 figures, 1 tabl

Volume explored by a branching random walk on general graphs.

Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding-the branching random walk (BRW)-is required. Despite its wide range of applications, the properties of the volume explored by the BRW so far remained elusive, with exact results limited to one dimension. Here we present analytical results, supported by numerical simulations, on the scaling of the volume explored by a BRW in the critical regime, the onset of epidemics, in general environments. Our results characterise the spreading dynamics on regular lattices and general graphs, such as fractals, random trees and scale-free networks, revealing the direct relation between the graphs' dimensionality and the rate of propagation of the viral process. Furthermore, we use the BRW to determine the spectral properties of real social and metabolic networks, where we observe that a lack of information of the network structure can lead to differences in the observed behaviour of the spreading process. Our results provide observables of broad interest for the characterisation of real world lattices, tissues, and networks

Topics in statistical physics of active and living systems

In this thesis, I describe a range of scenarios, from viral propagation to stem cell dynamics, where techniques and ideas from statistical physics provide a route to describe and quantify the observed dynamics. All the systems considered here lie in the realm of out-of-equilibrium physics, where injection and dissipation of energy, matter and/or momentum drive their spatio-temporal evolution. This thesis is organised such that the topics are presented from mainly theoretical to mainly experimental. In Chapter 2, I make use of field-theoretic methods to study a branching random walk. This is a paradigmatic process in the study of viral propagation, however analytic results are very limited. Here I show how a field-theoretic approach provides an a route to obtain exact results for the scaling of the volume explored by such a process. In Chapter 3, I show how branching or self-replication can emerge in large scale ecological systems. I show, numerically, how a spatial instability of the vegetation patches gives rise to their self-replication, and discuss the implications for real ecosystems. In Chapter 4, I dive into the realm of cellular biology, where I performed experimental, analytical and numerical work in order to understand the rich dynamics of the spatio-temporal interactions of mouse embryonic stem cells and localized sources of protein signals, and discuss the implications for multicellular organisation. In Chapter 5, I discuss my work on human Keratinocytes, where I studied the interplay between the pulsatile activity of a specific pathway and differentiation. I introduce a method that allows the construction of a phase diagram from the stem cell state. Combined with numerical simulations, this method allowed the visualisation of the temporal relation between the signals to show how transitions between stem cell states occur. Finally, in Chapter 6, I discuss the main findings of this thesis. I present the general and specific conclusions and point out some key open problems on each sub-field studied.Open Acces

Rodlike localized structure in isotropic pattern-forming systems

Artículo de publicación ISIStationary two-dimensional localized structures have been observed in a wide variety of dissipative systems. The existence, stability properties, dynamical evolution, and bifurcation diagram of an azimuthal symmetry breaking, rodlike localized structure in the isotropic prototype model of pattern formation, the Swift-Hohenberg model, is studied. These rodlike structures persist under the presence of nongradient perturbations. Interaction properties of the rodlike structures are studied. This allows us to envisage the possibility of different crystal-like configurations

Inflationary theory of branching morphogenesis in the mouse salivary gland.

The mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands

Inflationary theory of branching morphogenesis in the mouse salivary gland

AbstractThe mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands.Wellcome Trust Royal Society EPSR

Inflationary theory of branching morphogenesis in the mouse salivary gland

Abstract The mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands

Inflationary theory of branching morphogenesis in the mouse salivary gland.

Acknowledgements: We are grateful for illuminating discussions with Edouard Hannezo and members of the Simons lab, especially Yanbo Yin for his help with the live-imaging. This study was supported by grants to B.D.S. (EPSRC, EP/P034616/1, Wellcome Trust, 098357/Z/12/Z and 219478/Z/19/Z, and Royal Society EP Abraham Research Professorship, RP/R1/180165), L.C. (Herchel Smith Postdoctoral Fellowship Fund) and I.B. (FONDECYT, 11230941, VID, UI-015/22). The research team also acknowledges core support from the Wellcome Trust (092096) and CRUK (C6946/A14492). We also acknowledge staff at the Gurdon Institute Imaging Facility for microscopy and image analysis support. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising from this submission.Funder: Royal Society EP Abraham Research Professorship, RP/R1/180165.Funder: VID (Universidad de Chile) Grant No UI-015/22Funder: Herchel Smith Postdoctoral Fellowship FundThe mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands.Wellcome Trust Royal Society EPSR

Volume explored by a branching random walk on general graphs.

Branching processes are used to model diverse social and physical scenarios, from extinction of family names to nuclear fission. However, for a better description of natural phenomena, such as viral epidemics in cellular tissues, animal populations and social networks, a spatial embedding-the branching random walk (BRW)-is required. Despite its wide range of applications, the properties of the volume explored by the BRW so far remained elusive, with exact results limited to one dimension. Here we present analytical results, supported by numerical simulations, on the scaling of the volume explored by a BRW in the critical regime, the onset of epidemics, in general environments. Our results characterise the spreading dynamics on regular lattices and general graphs, such as fractals, random trees and scale-free networks, revealing the direct relation between the graphs' dimensionality and the rate of propagation of the viral process. Furthermore, we use the BRW to determine the spectral properties of real social and metabolic networks, where we observe that a lack of information of the network structure can lead to differences in the observed behaviour of the spreading process. Our results provide observables of broad interest for the characterisation of real world lattices, tissues, and networks