PHYSICAL REVIEW E 99, 032216 (2019) Dynamic environment-induced multistability and critical transition in a metacommunity ecosystem Ramesh Arumugam, 1, 2 Sukanta Sarkar, 1 Tanmoy Banerjee, 3 Sudipta Sinha, 4 and Partha Sharathi Dutta 1 1 Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India 2 Department of Biology, McGill University, Montreal, Quebec, Canada H3A 1B1 3 Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India 4 Department of Chemistry, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India (Received 31 January 2019; published 20 March 2019) We study a metacommunity model of consumer-resource populations coupled via dispersal under an environment-dependent framework, and we explore the occurrence of multistability and critical transition. By emphasizing two magnitudes acting on a dynamic environment at temporal and spatial scales, the coupled system with simple diffusive coupling and the nonlinear environmental coupling enables various interesting complex dynamics such as bistability, multistability, and critical transitions. Using the basin stability measure, we find the probability of attaining each alternative state in a multistable region. In addition, critical transitions (one from a high to a low species density and the other from a low to a high species density) are identified at different magnitudes in the presence of stochastic fluctuations. We also explore the robustness of critical slowing-down indicators, e.g., lag-1 autocorrelation and variance, to forewarn the critical transition in the metacommunity model. Further, a network structure also identifies synchronization and multiclustering for a different choice of initial conditions. In contrast with the earlier studies on dynamic environmental coupling, our results based on the defined magnitudes provide important insights into environmental heterogeneity, which determines the set of environmental conditions to predict metacommunity stability and persistence. DOI: 10.1103/PhysRevE.99.032216 I. INTRODUCTION Systems of coupled oscillators construct an efficient frame- work to study interacting oscillatory processes relevant to different fields such as physics, chemistry, biology, ecol- ogy, engineering, and many other disciplines of science and technology [1,2]. The impact of such studies becomes more advantageous due to the fact that natural systems are rarely isolated and hence their dynamics can be explored using potential models of interacting oscillators. Extensive research on network of coupled oscillators explored a diver- sity of cooperative phenomena, such as synchronization [3,4], phase-locking [5,6], oscillation quenching [7], and chimera states [8–10]. In the context of coupled oscillators, coupling plays a crucial role in determining their dynamics [11]. In natural systems, units interact with each other directly through dif- fusion and also indirectly, e.g., via a common environment. Particularly, this type of coupling is very much relevant in ecology where species interact with common resources as well as shared resources [12]. However, existing studies with generic oscillators considered the shared resource as a linear one [11], which deviates from reality. In the context of ecology diffusion (or dispersion) is generally considered as a linear process, however, other forms of coupling are typically nonlinear. For example, the interaction between resources and consumers can be nonlinear in nature, e.g., via the type-II functional response [13]. Functional response determines how consumption rate varies with resource den- sity. The type-II functional response is a saturating non- linear function such that the consumption rate increases up to a level and then saturates with increasing resource density. In complex spatial ecosystems, habitats where species re- side are highly dynamic in nature [14]. Furthermore, multiple tropic interactions [15,16] and its distribution with underlying spatial heterogeneity [17,18], and the magnitude of environ- mental conditions affect the metacommunity dynamics [19]. Investigations on numerous coupled nonlinear systems and stochastic oscillators describe the theoretical understanding of various biological mechanisms arising in metacommunity ecosystems [20,21]. Particularly, different types of network topologies emphasize the structure of habitat connectivity, dispersal, and spatial distributions on ecosystem function- ing [10,22,23]. Therefore, to model and study spatial ecosys- tems by incorporating proper forms of coupling that encap- sulates local as well as shared interactions are challenging tasks. In this paper, we take into account two types of species interaction in the coupling, namely diffusive coupling and nonlinear environmental coupling, to incorporate various complexities of metacommunity systems [24]. In fact, these couplings characterize the consumer-resource interactions in three fundamental ways: (i) the interaction within the patch (interaction with a local resource), (ii) the interaction be- tween the patches (species migration), and (iii) the interaction through a common dynamic environment (interaction with a shared resource). Due to the spatial pattern of landscape structure, the magnitude of species interactions acting on the dynamic environment over time has a profound impact on the species persistence. Here, we aim to address the following questions: How do the magnitudes of spatially distributed 2470-0045/2019/99(3)/032216(12) 032216-1 ©2019 American Physical Society