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In this article we extend the study performed in our previous article on the collapse of primordial objects. We here analyze the behavior of the physical parameters for clouds ranging from $10^7M_\odot$ to $10^{15}M_\odot$. We studied the…
Calhoun's Rat Utopia experiments demonstrated a puzzling population trajectory: initial growth, plateau, and eventually a total collapse of the rat population despite abundant resources. This paper proposes a hypothesis that the enclosure's…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
Experimental studies have shown the ubiquity of altruistic behavior in human societies. The social structure is a fundamental ingredient to understand the degree of altruism displayed by the members of a society, in contrast to…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
The distribution of waiting times until the occurrence of a critical event is a crucial statistical problem across several disciplines in Science. In this work we present a statistical model in which a relevant quantity X accumulates until…
We introduce the logistic model of consumption growth, which captures a negative feedback loop preventing an unlimited growth of consumption due to finite biophysical resources of our planet. This simple dynamic model allows for derivation…
Dynamics of a social population is analyzed taking into account some physical constraints on individual behavior and decision making abilities. The model, based on Evolutionary Game Theory, predicts that a population has to pass through a…
Current techniques for predicting climate change are mainly based on "massive" deterministic numerical modeling. However, the ocean-atmosphere system is a so-called "complex system", made up of a large number of interacting elements. We…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Collectives form non-equilibrium social structures characterised by a volatile dynamics. Individuals join or leave. Social relations change quickly. Therefore, differently from engineered or ecological systems, a resilient reference state…
Species extinction occurs regularly and unavoidably in ecological systems. The time scales for extinction can broadly vary and inform on the ecosystem's stability. We study the spatio-temporal extinction dynamics of a paradigmatic…
In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph…
We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a…
The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they…
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data…
Take a continuous-time Galton-Watson tree. If the system survives until a large time $T$, then choose $k$ particles uniformly from those alive. What does the ancestral tree drawn out by these $k$ particles look like? Some special cases are…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
This paper will introduce a theory of emergent animal social complexity using various results from computational models and empirical results. These results will be organized into a vertical model of social complexity. This will support the…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…