Markov evolutions and hierarchical equations in the continuum I. One-component systems

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.Comment: 47 page

Organic matter dynamics control plant species coexistence in a tropical peat swamp forest

We studied the relationship between the coexistence of tree species and the dynamics of organic matter in forests. A tropical peat swamp forest was selected as a model ecosystem, where abiotic factors, such as geological topography or parent rock types, are homogeneous and only biological processes create habitat heterogeneity. The temporal or spatial variation of the ground elevation of peat soils is mainly caused by changes in the balance between organic matter inputs to soils and decomposition, which is affected by the growth and death of influential trees. To clarify the processes of elevation dynamics, we measured the microtopography around some tree groups, estimated organic matter (in the form of litter and roots) in soils under three kinds of microtopographic conditions, measured decomposition rates and detected dominant species' shifting distribution patterns in different stages of growth in relation to the locations of tree groups creating specific microtopographic conditions. We found that growth or death of buttressed trees has the greatest effects on the rising or sinking of ground surfaces through changes in litter supply and root production. We discuss here the possibility of extending our model to other forest types

Avoiding misinterpretation of biotic interactions with the intertype K12-function : population independence vs. random labelling hypotheses

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