All of them use the nutrients in the decomposed parts of the others (and those they themselves have discarded.
They do not prey upon each other, unless you count parasitic plants (see http://en.wikipedia.org/wiki/Parasitic_p…
They do compete for light, with many grasses unable to grow under dense shade, while other plants do not thrive or reproduce in deep shade, but there are shade-loving plants that will only grow under trees that give dense shade.
In periods of drought, they may compete for water.
Some plants, such as sunflowers and walnut trees, emit compounds that are toxic to other plants.
VCE Master Gardener
they are competing only for light