A short review of cellular automata models in ecology is given. Introduction of a spatial dimension into a discrete-time Markov chain leads to a class of cellular automata called spatio-temporal Markov chains (STMC). The behaviour of the model is determined by its temporal and spatial orders. It is proved that STMC models have ergodic distributions in certain cases for spatial order 0. Simulations suggest that STMC models of higher spatial order also have ergodic distributions. The model of Dytham (1995) is demonstrated to be an STMC. Modelling population dynamics of three plant species on a lawn, two STMC models of different order are compared. The model validation shows a good agreement for Glechoma hederacea, but large deviations for Lolium perenne and Trifolium repens. The species-dependent performance of the models can be explained by selective grazing. Modifications of the transition matrices are used to examine possible causes of the deviations.
Understanding the partitioning of genetic variance in peripheral and central populations may shed more light on the effects of genetic drift and gene flow on population genetic structure and, thereby, improve attempts to conserve genetic diversity. We analysed genetic structure of peripheral and central populations of three insect-pollinated violets (Viola elatior, Viola pumila, Viola stagnina) to evaluate to what extent these patterns can be explained by gene flow and genetic drift. Amplified fragment length polymorphism was used to analyse 930 individuals of 50 populations. Consistent with theoretical predictions, peripheral populations were smaller and more isolated, differentiation was stronger, and genetic diversity and gene flow lower in peripheral populations of V. pumila and V. stagnina. In V. elatior, probably historic fragmentation effects linked to its specific habitat type were superimposed on the plant geographic (peripheral-central) patterns, resulting in lower relative importance of gene flow in central populations. Genetic variation between regions (3-6%), among (30-37%) and within populations (60-64%) was significant. Peripheral populations lacked markers that were rare and localized in central populations. Loss of widespread markers in peripheral V. stagnina populations indicated genetic erosion. Autocorrelation within populations was statistically significant up to a distance of 10-20 m. Higher average genetic similarity in peripheral populations than in central ones indicated higher local gene flow, probably owing to management practices. Peripheral populations contributed significantly to genetic variation and contained unique markers, which made them valuable for the conservation of genetic diversity.
The successfully tested interaction potential of H2 -H 2 obtained from quantum chemical calculations (M 80) has been used again as input in the attempt of determining a fit interaction potential of the H 2 -H2 system. It does not only give quantitative agreement with measurements as obtained previously, but also reproduces the second virial coefficients at low temperatures, calculated via quantum mechanical pair correlation functions, as measured in several independent experiments. Since the unique determination of this fit is not possible in principle, we have chosen a final version by means of plausible estimates of the limitations of previous ab initio calculations. The new potential is included in this paper in a table. Our isotropic rigid rotor potential term will be discussed in comparisons with experimentally determined potential fits. More tests of our fit potential have already been completed and can be used for a final judgement.
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