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A Model of Large-Scale Evolution of Complex Food Webs

C. Guill (2010)

Mathematical Modelling of Natural Phenomena

A simple model of biological evolution of community food webs is introduced. This model is based on the niche model, which is known to generate model food webs that are very similar to empirical food webs. The networks evolve by speciation and extinction. Co-extinctions due to the loss of all prey species are found to play a major role in determining the longterm shape of the food webs. The central aim is to design the model such that the characteristic...

An approximate necessary condition for the optimal bandwidth selector in kernel density estimation

L. Gajek, A. Lenic (1993)

Applicationes Mathematicae

An approximate necessary condition for the optimal bandwidth choice is derived. This condition is used to construct an iterative bandwidth selector. The algorithm is based on resampling and step-wise fitting the bandwidth to the density estimator from the previous iteration. Examples show fast convergence of the algorithm to the bandwidth value which is surprisingly close to the optimal one no matter what is the initial knowledge on the unknown density.

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