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With the "five sites mutation" mode for opsin gene evolution, the probability of speciation increased with increasing mutation rate (Fig. 2f).
Thus, over roughly two billion years of eukaryotic evolution, the probability of a given intron in a given lineage having undergone a boundary change would be on the order of 0.008 to 0.08.
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Modeling the system behavior in a stochastic manner means the examination of not only the evolution of the average system state that represents a possible trajectory, but examination of the evolution of the probability distribution over all possible system states.
Two ways how to solve the evolution of the probability distribution are presented.
This model equation governs the evolution for the probability density function that describes anomalously diffusing particles.
To illustrate this method, the effect of a sudden temporary increase in temperature on the evolution of the probability distribution of Lactobacillus plantarum population size is presented.
The scheme is derived from the master equations for the evolution of the probability density of a sum of discrete time random walks.
In this paper a numerical solution procedure is presented to compute the evolution of the probability density in the state space for a single degree of freedom system excited by white noise.
One of the features of this model is that the governing equations for the evolution of the probability density function, in the diffusion limit, can generally be simplified using fractional calculus.
The internal dislocation structure and the surface relief at room and at elevated temperature were studied and correlated with the cyclic stress strain response and the evolution of the probability density function of the internal critical stresses.
Further, examination of the evolution of the probability density function (PDF) of the AE energy (counts) reveals two scaling zones wherein the transition from the low energy (count) to high energy (count) regime is identified.
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