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Stochastic Communities presents a theory of biodiversity by analyzing the distribution of abundances among species in the context of a community. The basis of this theory is a distribution called the "J distribution." This distribution is a pure hyperbola and mathematically implied by the "stochastic species hypothesis" assigning equal probabilities of birth and death within the population of each species over varying periods of time. The J distribution in natural communities has strong empirical support resulting from a meta-study and strong theoretical support from a theorem that is mathematically implied by the stochastic species hypothesis.
Stochastic Communities presents a theory of biodiversity by analyzing the distribution of abundances among species in the context of a community. The basis of this theory is a distribution called the "J distribution." This distribution is a pure hyperbola and mathematically implied by the "stochastic species hypothesis" assigning equal probabilities of birth and death within the population of each species over varying periods of time. The J distribution in natural communities has strong empirical support resulting from a meta-study and strong theoretical support from a theorem that is mathematically implied by the stochastic species hypothesis.
1. Demographic and environmental stochasticity -- 2. Extinction dynamics -- 3. Age structure -- 4. Spatial structure -- 5. Population viability analysis -- 6. Sustainable harvesting -- 7. Species diversity -- 8. Community dynamics.
Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Stochastic models of epidemics" which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo). The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.
This self-contained, compact monograph is an invaluable introduction to the field of Community Detection for researchers and students working in Machine Learning, Data Science and Information Theory.
The vast majority of random processes in the real world have no memory - the next step in their development depends purely on their current state. Stochastic realizations are therefore defined purely in terms of successive event-time pairs, and such systems are easy to simulate irrespective of their degree of complexity. However, whilst the associated probability equations are straightforward to write down, their solution usually requires the use of approximation and perturbation
The book focuses on stochastic modeling of population processes. The book presents new symbolic mathematical software to develop practical methodological tools for stochastic population modeling. The book assumes calculus and some knowledge of mathematical modeling, including the use of differential equations and matrix algebra.
This volume provides an overview of two of the most important examples of interacting particle systems, the contact process, and the voter model, as well as their many variants introduced in the past 50 years. These stochastic processes are organized by domains of application (epidemiology, population dynamics, ecology, genetics, sociology, econophysics, game theory) along with a flavor of the mathematical techniques developed for their analysis.