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Over the last few decades, ecologists have come to appreciate that keyecological patterns, which describe ecological communities at relatively largespatial scales, are not only scale dependent, but also intimately intertwined.The relative abundance of species, which informs us about the commonness andrarity of species, changes its shape from small to large spatial scales. Theaverage number of species as a function of area has a steep initial increase,followed by decreasing slopes at large scales. Finally, if we find a species ina given location, it is more likely we find an individual of the same speciesclose-by, rather than farther apart. Such spatial turnover depends on thegeographical distribution of species, which often are spatially aggregated.This reverberates on the abundances as well as the richness of species within aregion, but so far it has been difficult to quantify such relationships. Withina neutral framework, which considers all individuals competitively equivalent,we introduce a spatial stochastic model, which phenomenologically accounts forbirth, death, immigration and local dispersal of individuals. We calculate thepair correlation function, which encapsulates spatial turnover, and theconditional probability to find a species with a certain population within agiven circular area. Also, we calculate the macro-ecological patterns, which wehave referred to above, and compare the analytical formul{\ae} with thenumerical integration of the model. Finally, we contrast the model predictionswith the empirical data for two lowland tropical forest inventories, showingalways a good agreement.

A phenomenological spatial model for macro-ecological patterns in species-rich ecosystems