Related papers: Measurement scale in maximum entropy models of spe…
We show that the natural scaling of measurement for a particular problem defines the most likely probability distribution of observations taken from that measurement scale. Our approach extends the method of maximum entropy to use…
This is a preliminary article stating and proving a new maximum entropy theorem. The entropies that we consider can be used as measures of biodiversity. In that context, the question is: for a given collection of species, which frequency…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Measures of biodiversity change such as the Living Planet Index describe proportional change in the abundance of a typical species, which can be thought of as change in the size of a community. Here, I discuss the orthogonal concept of…
The abundance of different species in a community often follows the log series distribution. Other ecological patterns also have simple forms. Why does the complexity and variability of ecological systems reduce to such simplicity? Common…
We derive a linear recursion relation for the species abundance distribution in a statistical model of ecology and demonstrate the existence of a scaling solution.
In this paper entropy based methods are compared and used to measure structural diversity of an ensemble of 21 classifiers. This measure is mostly applied in ecology, whereby species counts are used as a measure of diversity. The measures…
Studies on distribution, abundance and diversity of species revealed fascinating universalities in macroecology. Many of these patterns, like the species-area and range-abundance relationship or the year-to-year fluctuations in population…
Entropy measures of probability distributions are widely used measures in ecology, biology, genetics, and in other fields, to quantify species diversity of a community. Unfortunately, entropy-based diversity indices, or diversity indices…
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,…
One of the first successes of neutral ecology was to predict realistically-broad distributions of rare and abundant species. However, it has remained an outstanding theoretical challenge to describe how this distribution of abundances…
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…
Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify…
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…
Quantitative methods for studying biodiversity have been traditionally rooted in the classical theory of finite frequency tables analysis. However, with the help of modern experimental tools, like high throughput sequencing, we now begin to…
By creating networks of biochemical pathways, communities of micro-organisms are able to modulate the properties of their environment and even the metabolic processes within their hosts. Next-generation high-throughput sequencing has led to…
The paper makes the observation that all orders of information entropy are equal in signals composed of repeating units of distinct symbols where the units can be classified as a member of a symmetry group. This leads to an improved metric…
Observational entropy -- a quantity that unifies Boltzmann's entropy, Gibbs' entropy, von Neumann's macroscopic entropy, and the diagonal entropy -- has recently been argued to play a key role in a modern formulation of statistical…
Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the R\'enyi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation…
Entropy, under a variety of names, has long been used as a measure of diversity in ecology, as well as in genetics, economics and other fields. There is a spectrum of viewpoints on diversity, indexed by a real parameter q giving greater or…