In deterministic approaches to modeling, two species are generally regarded as capable of coexistence if the model has a stable equilibrium with both species in positive numbers. Temporal environmental variability is assumed to reduce the likelihood of coexistence by keeping species abundances away from equilibrium. Here we present a contrasting view based on a model of competition for space among coral reef fishes, or any similarly territorial animals. The model has no stable equilibrium point with both species in positive abundance, yet both species persist in the system provided environmental variability in birth rates is sufficiently high. In general the higher the environmental variability the more likely it is that coexistence will occur. This conclusion is not affected by one species having a mean advantage over the other. Not all kinds of environmental variability necessarily lead to coexistence, however, for when the death rates of the two species are highly variable and negatively correlated, th...

Probability and stochastic processes : with a view toward applications

Environmental Variability Promotes Coexistence in Lottery Competitive Systems

A new method for calculating average molecular weights is presented for nonlinear polymers. In contrast to the previous methods of Flory and Stockmayer which first calculate the distribution of all species and then use the distributions to calculate average properties, the new method calculates these properties directly. In contrast to the method of Gordon, probability generating functions are not required. Starting with elementary probability and utilizing the recursive nature of network polymers property relations can be developed more simply. We illustrate the method for calculations of Mw Mz, and the gel point for a wide variety of polyfunctional polymerizations.

A new derivation of average molecular weights of nonlinear polymers.

This paper contributes a Markov chain Monte Carlo (MCMC) method for the direct generation of synthetic time series of wind power output. It is shown that obtaining a stochastic model directly in the wind power domain leads to reduced number of states and to lower order of the Markov chain at equal power data resolution. The estimation quality of the stochastic model is positively influenced since in the power domain, a lower number of independent parameters is estimated from a given amount of recorded data. The simulation results prove that this method offers excellent fit for both the probability density function and the autocorrelation function of the generated wind power time series. The method is a first step toward simple stochastic black-box models for wind generation.

/pdf/mcmc-for-wind-power-simulation-19s5cvje4j.pdf

MCMC for Wind Power Simulation

Failure times of a software reliability growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto logarithmic, and power law models are all special cases of exponential order statistic models, but there are many additional examples as well. Various characterizations, properties, and examples of this class of models are developed and presented.

background

/pdf/exponential-order-statistic-models-of-software-reliability-3rd2yxplqq.pdf

Probability and stochastic processes : with a view toward applications

Citations

Environmental Variability Promotes Coexistence in Lottery Competitive Systems

A new derivation of average molecular weights of nonlinear polymers.

MCMC for Wind Power Simulation

Exponential order statistic models of software reliability growth

Markov switching negative binomial models: An application to vehicle accident frequencies

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