Tail‐dependent spatial synchrony arises from nonlinear driver–response relationships

Abstract

Spatial synchrony may be tail‐dependent, that is, stronger when populations are abundant than scarce, or vice‐versa. Here, ‘tail‐dependent’ follows from distributions having a lower tail consisting of relatively low values and an upper tail of relatively high values. We present a general theory of how the distribution and correlation structure of an environmental driver translates into tail‐dependent spatial synchrony through a non‐linear response, and examine empirical evidence for theoretical predictions in giant kelp along the California coastline. In sheltered areas, kelp declines synchronously (lower‐tail dependence) when waves are relatively intense, because waves below a certain height do little damage to kelp. Conversely, in exposed areas, kelp is synchronised primarily by periods of calmness that cause shared recovery (upper‐tail dependence). We find evidence for geographies of tail dependence in synchrony, which helps structure regional population resilience: areas where population declines are asynchronous may be more resilient to disturbance because remnant populations facilitate reestablishment.

Disturbance and nutrients synchronise kelp forests across scales through interacting Moran effects

“…(3) The influence of Moran drivers and their interactions differ strongly across timescales and geographical regions, reinforcing the importance of studying synchrony using timescale‐ and geography‐specific approaches (e.g. Defriez et al, 2016; Sheppard et al, 2016; Walter et al, 2017, 2022). These findings represent an important advance because, to our knowledge, interactions among Moran drivers of synchrony have been identified only once previously (Sheppard et al, 2019).…”

“…periods of fluctuations, such as annual or decadal) or during specific, transient periods (Keitt, 2008;Vasseur et al, 2014;Walter et al, 2020;Walter, Hallett, et al, 2021), but traditional approaches often ignore or misidentify such temporal complexity (Anderson et al, 2019(Anderson et al, , 2021Defriez et al, 2016;Desharnais et al, 2018;Sheppard et al, 2016Sheppard et al, , 2019. ( 2) Synchrony can differ regionally, but most investigations overlook geographical patterns in synchrony and their underlying drivers (Anderson et al, 2019;Koenig et al, 2017;Walter et al, 2017Walter et al, , 2022.…”

How to measure response diversity

“…Though threshold responses may be rare and/or difficult to detect in experiments (Hillebrand et al 2020), nonlinear responses to many variables are common, such as Type II or III functional responses to prey availability (Holling 1966;Daugaard et al 2019), or light or temperature response curves (e.g., Peek et al 2002;Payne et al 2016). Nonlinear responses to the environment may result in environment-dependencies in species asynchrony (Shoemaker et al 2022)-recently described using tail association methods (Ghosh et al 2020a(Ghosh et al , 2020bWalter et al 2022)-in turn, producing environment-dependencies in ecosystem multifunctionality and stability (Morin et al 2014;Sasaki et al 2019). Environment-dependent response diversity may therefore explain inconsistencies in the reported effects of biodiversity on ecological stability across studies (Jacquet et al 2016;Pennekamp et al 2018).…”

“…2022)—recently described using tail association methods (Ghosh et al . 2020a, 2020b; Walter et al . 2022).…”

“…2022)—recently described using tail association methods (Ghosh et al . 2020a, 2020b; Walter et al . 2022)—in turn, producing environment-dependencies in ecosystem multifunctionality and stability (Morin et al .…”