The plant in the labyrinth: Adaptive growth and branching in heterogeneous environments

•We present a percolation model of a growing plant.•Some parts of the organism stop by rooting, while others move on by horizontal growth and branching.•We describe a new kind of threshold, pt, that is higher than the classical percolation threshold.•Below pt, the plant cannot track along the pathways of suitable habitat.•The demonstrated “labyrinth effect” is a considerable factor in the self-organization of plant communities.

The "ant in the labyrinth" problem describes spatial constraints upon a moving agent in a disordered medium. In contrast with an animal-like agent (an "ant"), a clonal plant can stay in a place and move at the same time: some parts develop roots, while others continue moving by horizontal growth and branching. Hereby we present a spatially explicit, dynamic model for the study of percolation by plant growth rules in lattices that consist of open and closed sites. Growth always starts from a single seed in an open percolation cluster (patch). By increasing the proportion of open sites (p), we describe a new kind of threshold (the “tracking threshold”, approximately pt=0.73), which is higher than the site percolation threshold (pc=0.5 in this lattice). At pc