  We introduce a model of traveling agents ({\it e.g.} frugivorous animals) who
feed on randomly located vegetation patches and disperse their seeds, thus
modifying the spatial distribution of resources in the long term. It is assumed
that the survival probability of a seed increases with the distance to the
parent patch and decreases with the size of the colonized patch. In turn, the
foraging agents use a deterministic strategy with memory, that makes them visit
the largest possible patches accessible within minimal travelling distances.
The combination of these interactions produce complex spatio-temporal patterns.
If the patches have a small initial size, the vegetation total mass (biomass)
increases with time and reaches a maximum corresponding to a self-organized
critical state with power-law distributed patch sizes and L\'evy-like movement
patterns for the foragers. However, this state collapses as the biomass sharply
decreases to reach a noisy stationary regime characterized by corrections to
scaling. In systems with low plant competition, the efficiency of the foraging
rules leads to the formation of heterogeneous vegetation patterns with
$1/f^{\alpha}$ frequency spectra, and contributes, rather counter-intuitively,
to lower the biomass levels.
