Chapter 3 - Simple feedback explains complex channel patterns in coastal wetlands Version 30

Spatial patterns are omnipresent in nature (Rodriguez-Iturbe and Rinaldo, 1997; Kondo, 2002; Meinhardt, 2003; Rietkerk and van de Koppel, 2008; Petit and Anfodillo, 2009) and directly affect the functioning and resilience of the (eco)systems in which they manifest themselves (Rietkerk et al., 2004; van de Koppel et al., 2005; Weerman et al., 2010; Liu et al., 2014b). Scale-dependent feedback, which typically is positive nearby and negative further away, provides a widely accepted explanation for the formation of simple, single-scale patterns (Meinhardt, 2003; Rietkerk and van de Koppel, 2008; Petit and Anfodillo, 2009). However, it is unclear whether the more complex, multi-scale patterns that characterize many natural systems can be explained by equally generic mechanisms. As a model system, we here study the tidal channels that characterize coastal wetlands (Hughes, 2012), as these channels constitute patterns that vary greatly in geometry, ranging from simple parallel channels (Temmerman et al., 2007; Weerman et al., 2010; van de Vijsel et al., 2020) to complexly branching networks (Rodriguez-Iturbe and Rinaldo, 1997; Rinaldo et al., 1999), with direct consequences for the functioning and resilience of valuable wetland ecosystems. We reveal that the broad spectrum of geometries typical for tidal channel patterns can be explained by one scale-dependent feedback. This is a biogeomorphic feedback that roughly follows Turing's activator-inhibitor principle (Rietkerk and van de Koppel, 2008) and results from flow deflection and channel incision around biotically (biofilms, algae, plants) stabilized sediment (Temmerman et al., 2007; Weerman et al., 2010; van de Vijsel et al., 2020). Using a mathematical model, we now show that as the biogeomorphic feedback gets stronger, complex multi-scale patterns emerge due to self-induced recursion of the scale-dependent feedback, which results in nesting of regular channel patterns at successively finer scales. This recursive mechanism provides an explanation for poorly understood geometric properties of real-world tidal networks (Rinaldo et al., 1999). We further find that increased network complexity directly translates to enhanced drainage efficiency, sediment accretion rates and ecosystem productivity. These results highlight the vital importance of network complexity for the functioning of coastal wetlands, ultimately determining their resilience to sea level rise (Kirwan and Megonigal, 2013) and storm surge buffering capacity (Temmerman et al., 2013), and with that their potential to mitigate the effects of global change that threaten densely populated coastal lowlands worldwide.