Related papers: A general model for vegetation patterns including …
Evolutionary dynamics is often viewed as a subtle process of change accumulation that causes a divergence among organisms and their genomes. However, this interpretation is an inheritance of a gradualistic view that has been challenged at…
The process of desertification in the semi-arid climatic zone is considered by many as a catastrophic regime shift, since the positive feedback of vegetation density on growth rates yields a system that admits alternative steady states.…
From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely…
A fundamental task in developmental biology is to identify the mechanisms which drive morphogenesis. In many cases, pattern formation is driven by the positional information determined by both the gradient of maternal factors and hard-wired…
This chapter is about Complexity and Spatial Dynamics in Urban Systems. Strong inequalities in the size of cities and the apparent difficulty of limiting their growth raise practical issues for spatial planning. At a time when new…
Urban streets patterns form planar networks whose empirical properties cannot be accounted for by simple models such as regular grids or Voronoi tesselations. Striking statistical regularities across different cities have been recently…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
The capability of cells to form surface extensions to non-locally probe the surrounding environment plays a key role in cell migration. The existing mathematical models for migration of cell populations driven by this non-local form of…
Understanding biological phenomena requires a systemic approach that incorporates different mechanisms acting on different spatial and temporal scales, since in organisms the workings of all components, such as organelles, cells, and organs…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
The characterisation of the spatial and temporal distribution of the root system in a cultivated field depends on the soil volume occupied by the root systems (the scatter), and the local intensity of the root colonisation in the field (the…
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
In large clonal populations, several clones generally compete which results in complex evolutionary and ecological dynamics: experiments show successive selective sweeps of favorable mutations as well as long-term coexistence of multiple…
We study the influence of the bulk dynamics of a growing cluster of particles on the properties of its interface. First, we define a {\it general bulk growth model} by means of a continuum Master equation for the evolution of the bulk…
Quantifying the spatial organization of human settlements is fundamental to understanding the complexity of urban systems. However, the quantitative patterns of the distribution of villages, towns, and cities that lie between random and…
Seagrass meadows are among the most important coastal ecosystems, in terms of both spatial extent and ecosystem services, but they are also declining worldwide. Understanding the drivers of seagrass meadow dynamics is essential for…
Different classes of phenomenological universalities of environment dependent growths have been proposed. The logistic as well as environment dependent West-type allometry based biological growth can be explained in this proposed framework…
We study optimal two-sector (vegetative and reproductive) allocation models of annual plants in temporally variable environments, that incorporate effects of density dependent lifetime variability and juvenile mortality in a fitness…
Shape is one of the important characteristics for the structures observed in living organisms. Whereas biologists have proposed models where the shape is controlled on a molecular level [1], physicists, following Turing [2] and d'Arcy…
Comprehensive models of stochastic, clonally reproducing populations are defined in terms of general branching processes, allowing birth during maternal life, as for higher organisms, or by splitting, as in cell division. The populations…