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

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<p<pt the habitat contains a giant component, but the plant cannot spread successfully, because the pathways are too narrow compared to the scale of growth. We demonstrate this by varying the grain of the habitat pattern relative to the distance between two branching points. We conclude that fine-grained habitats can act as "labyrinths" for the plant within a broad range of p values. Within this range, the plant individual is likely to utilize only a small fraction of the available resources, leaving gaps open for colonization by other individuals. Therefore, the "labyrinth effect" is a considerable factor in the self-organization of plant communities.