A L\xe9vy expansion strategy optimizes early dune building by beach grasses

Valérie C Reijers,Koen Siteur,Jim Van Belzen,Johan Van De Koppel,Laura L Govers,Tjisse Van Der Heide,Leon P M Lamers,Annieke C W Borst,Jannes H T Heusinkveld,Tjeerd J Bouma,Selwyn Hoeks

doi:10.1038/s41467-019-10699-8

Abstract

Lifeforms ranging from bacteria to humans employ specialized random movement patterns. Although effective as optimization strategies in many scientific fields, random walk application in biology has remained focused on search optimization by mobile organisms. Here, we report on the discovery that heavy-tailed random walks underlie the ability of clonally expanding plants to self-organize and dictate the formation of biogeomorphic landscapes. Using cross-Atlantic surveys, we show that congeneric beach grasses adopt distinct heavy-tailed clonal expansion strategies. Next, we demonstrate with a spatially explicit model and a field experiment that the Lévy-type strategy of the species building the highest dunes worldwide generates a clonal network with a patchy shoot organization that optimizes sand trapping efficiency. Our findings demonstrate Lévy-like movement in plants, and emphasize the role of species-specific expansion strategies in landscape formation. This mechanistic understanding paves the way for tailor-made planting designs to successfully construct and restore biogeomorphic landscapes and their services.

Highlights

Lifeforms ranging from bacteria to humans employ specialized random movement patterns
We first investigated what type of clonal expansion strategy was employed by A. arenaria along the Dutch North Sea coast and by A. breviligulata along the eastern US coast, respectively
Since point patterns generated by Lévy movement generally lack a specific scale (Lévy dust)[27,28], this provided a first indication that beach grasses seem to diverge from simple Brownian movement processes and follow more complex Lévylike expansion strategies[29]

Summary

Introduction

Lifeforms ranging from bacteria to humans employ specialized random movement patterns. They conclude that (i) higher shoot densities promote sand capture with A. arenaria typically generating more shoots per square metre than A. breviligulata in existing dune fields, and (ii) the shooting rate of A. arenaria is stronger stimulated by sand capture compared with A. breviligulata It remains to be elucidated whether dune-building grasses control biophysical engineering strength via the spatial arrangement of their shoots in the beach colonization phase when initiating dune formation is vital for escaping physical stress from flooding. Our study shows that dune-building grasses have adopted different clonal expansion strategies to optimize their engineering strength during the early phase of beach colonization These findings expand the application of heavy-tailed random walk models in biology and call for adaptive restoration schemes that take the spatial organization of landscape-forming plants into account

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