Related papers: A Simple Explanation for Taxon Abundance Patterns
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and…
The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade)…
A large number of models of the species abundance distribution (SAD) have been proposed, many of which are generically similar to the log-normal distribution, from which they are often indistinguishable when describing a given data set.…
Fluctuations in diversity and extinction sizes are discussed and compared for two different, individual-based models of biological coevolution. Both models display power-law distributions for various quantities of evolutionary interest,…
Complex systems theory pays much attention to simple mechanisms producing nontrivial patterns, especially power laws. However, power laws with exponent close to one also result from complex mixtures of mechanisms that, in isolation, would…
Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the ``rich get…
We investigate the distribution of flavonoids, a major category of plant secondary metabolites, across species. Flavonoids are known to show high species specificity, and were once considered as chemical markers for understanding adaptive…
Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a…
A branching process in random environment $(Z_n, n \in \N)$ is a generalization of Galton Watson processes where at each generation the reproduction law is picked randomly. In this paper we give several results which belong to the class of…
A new model ecosystem consisting of many interacting species is introduced. The species are connected through a random matrix with a given connectivity. It is shown that the system is organized close to a boundary of marginal stability in…
Many natural patterns, such as the distributions of blood particles in a blood sample, proteins on cell surfaces, biological populations in their habitat, galaxies in the universe, the sequence of human genes, and the fitness in…
Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment…
We present a simple model of adaptive radiations in evolution based on species competition. Competition is found to promote species divergence and branching, and to dampen the net species production. In the model simulations, high taxonomic…
Current-day genomes bear the mark of the evolutionary processes. One of the strongest indications is the sequence homology among families of proteins that perform similar biological functions in different species. The number of proteins in…
Raw moments are used as a way to estimate species abundance distribution. The almost linear pattern of the log transformation of raw moments across scales allow us to extrapolate species abundance distribution for larger areas. However,…
The power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…
Heavy-tailed or power-law distributions are becoming increasingly common in biological literature. A wide range of biological data has been fitted to distributions with heavy tails. Many of these studies use simple fitting methods to find…