Contrasting Global Patterns of Spatially Periodic Fairy Circles and Regular Insect Nests in Drylands

Abstract

Numerical analysis of spatial pattern is widely used in ecology to describe the characteristics of floral and faunal distributions. These methods allow attribution of pattern to causal mechanisms by uncovering the specific signatures of patterns and causal agents. For example, grassland-gap patterns called fairy circles (FCs) in Namibia and Australia are characterized by highly regular and homogenous distributions across landscapes that show spatially periodic ordering. These FCs have been suggested to be caused by both social insects and competitive plant interactions. We compared eight Namibian and Australian FC patterns and also modeled FCs to 16 patterns of social insect nests in Africa, Australia, and America that include the most regular termite mound patterns known. For pattern-process inference, we used spatial statistics based on both nearest-neighbor analysis and neighborhood-density functions. None of the analyzed insect-nest distributions attain the spatially periodic ordering that is typical of FCs. The inherently more variable patterns of termite and ant nests are commonly attributable to well documented aspects of the faunal life-history. Our quantitative evidence from drylands shows that the more variable insect-nest distributions in water-limited environments cannot explain the characteristic spatial signature of FCs. The analysis demonstrates the interpretation of scale-dependent neighborhood-density functions and that it is the identification of unique spatial signatures in regular patterns that need to be linked to process. While our results cannot verify a specific hypothesis, they support the hypothesis that FCs in these drylands are more likely an emergent vegetation pattern caused by strong plant competition for water.

Growth, death, and resource competition in sessile organisms

“…13 ), this measure changes weakly with competitive strength, suggesting that statistical approaches to measuring competition are limited. Instead, an integrated framework considering deviations from predicted scaling in demographics as well as spatial patterning may better specify the range of competitive forces acting across environments ( 4 , 18 , 60 , 82 , 83 ).…”

Bridging ecology and physics: Australian fairy circles regenerate following model assumptions on ecohydrological feedbacks

“…The FCs are distributed in a spatially periodic pattern and, as predicted by pattern‐formation theory, form a grid‐like hexagonal array (Getzin, Yizhaq, Cramer, et al, 2019). Our empirical results thus support the theoretical model assumptions based on the reaction‐diffusion principle and scale‐dependent feedbacks where the hardened FC gaps function as an important additional source of water for the surrounding vegetation matrix (Getzin et al., 2016; Meron, 2018).…”

“…This signature is characterized by each fairy circle having on average six nearest neighbours that are located at approximately the same distance from the focal circle, leading to a hexagonal grid. The fairy circles are thus spatially periodic and constitute probably the most regularly distributed vegetation gaps that are currently known from arid environments (Getzin, Yizhaq, Cramer, & Tschinkel, 2019; Getzin, Yizhaq, Munoz‐Rojas, Wiegand, & Erickson, 2019). It is obvious that such exceptionally ordered patterns can only result from strong interactive processes, because in the absence of interaction, the probability of creating order in a noisy environment is very unlikely (Saha & Galic, 2018).…”

“…Fairy circles (FCs) are subject to an ongoing controversy about their origin (Sahagian, 2017). More recent theories have focused on vegetation self‐organization and argued that FCs are an emergent vegetation phenomenon that reflects a population‐level response to aridity stress where ecohydrological biomass‐water feedbacks lead to strictly geometric patterns (Cramer & Barger, 2013; Cramer, Barger, & Tschinkel, 2017; Getzin et al., 2015a,b; 2016; Getzin, Yizhaq, Cramer, et al, 2019; Ravi, Wang, Kaseke, Buynevich, & Marais, 2017; Zelnik, Meron, & Bel, 2015). The periodically ordered pattern is thus an expression that there is not enough water to sustain uniform vegetation coverage at the landscape scale and the distinct, so‐called ‘wavelength’ of the gap pattern reflects the spatial scale at which water is most limiting to the plants (Meron, 2016).…”

“…This successful matching, however, is not a verification that the modelled processes and mechanisms of plant self‐organization are indeed right and happening in the real world to cause the observed patterns (Borgogno et al., 2009). Within a framework of pattern‐process inference, these coarse‐graining methods are mainly useful to identify unlikely processes for the cause of the pattern and to narrow down the most plausible working hypotheses (Getzin, Yizhaq, Cramer, et al, 2019; McIntire & Fajardo, 2009; Schurr, Bossdorf, Milton, & Schumacher, 2004). Consequently, if the extensive achievements of the mathematical process‐based models are to find greater acceptance in ecology, then it is necessary not only to reconstruct the higher‐level structures but also to demonstrate true evidence of the validity of the modelled lower‐level processes assumed a priori.…”