Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy (ESS) have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in molecular biology, economics, politics and social sciences. However, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this paper, we briefly introduce the concept of stochastic evolutionary stability (SES) that we recently proposed. The stochastic evolutionary stability not only extends the classic concept of the evolutionarily stably strategy but also provides a fundamental theoretical framework for understanding the evolutionary dynamics of animal behavior in a stochastic environment.

Plant-microbe mutualism, a special form of cooperation, has been crucial throughout the evolutionary history of life and terrestrial ecosystems. With human activities changing the condition of Earth’s surface at an unprecedented rate and scale, we expect this ancient bond between plants and microbes to continue to play a key role. Yet, despite its importance, there has been a historical bias towards cooperation/mutualism in biology, and a general underrepresentation in mathematical biology/theoretical ecology. Moreover, even though theoretical representation of mutualism has come a long way, there exists multiple disparate perspectives with diverse associated scientific communities, among which interaction has been limited. This review focuses on two seemingly opposite schools of perspectives: microbiologists’ perspective that zooms in for the microscale mechanisms vs. ecosystem ecologists’ perspective that zooms out for the macroscale consequences. Macroscale models often start with a simple set of naive assumptions. But over time microscale mechanisms (once understood well) will eventually be incorporated into newer-generation process-based large models, greatly enhancing our ability to quantitatively predict our future. I hope this review can facilitate this process, a process that will only become more important against the backdrop of rapid global change. Lastly, but perhaps more broadly, I hope this review will attract more attention to the important role of cooperation/mutualism, a concept that we can maybe leverage to solve a range of other broader problems in ecology and our society.

Fig and fig-pollinating wasps constitute one of the most well-known systems of mutualistic interactions between species. However, interspecific competition and antagonism is increasingly observed in this obligate mutualism system, including competition over common resources, pollination cheating and host sanction, and an evolutionary arms race between the host tree and its pollinators. In the competitive and antagonistic interactions between fig and fig-pollinating wasps, three main asymmetric relationships have been identified: (1) asymmetric payoffs, i.e., asymmetric power between figs (host) and their pollinators (symbionts); (2) asymmetric rates of evolution; and (3) asymmetric information between figs and their pollinators. The asymmetric relationships may affect population dynamics and the mutual adaptation and evolutionary strategies of each species, which helps explain why both cooperation and conflict are simultaneously observed within a specific mutualism, and why diversified strategies and species coexistence are found in nearly all mutualism systems.

It is well known that interactions between organisms are the key to species coexistence and biodiversity maintenance. Traditional studies focused overwhelmingly on direct interactions between species pairs, ignoring the more complex indirect interactions. In this review, we first distinguished two types of indirect interactions, i.e. interaction chains and higher-order interactions (HOIs). Then we reviewed the definition of higher-order interactions including the hard-HOIs and soft-HOIs, and the studies of HOIs among multiple trophic levels and within a single trophic level. In the food-web literature (among multiple trophic levels), ecologists widely studied the properties, mechanisms, pathways and experimental evidence of HOIs. Recently, there is an increasing interest in HOIs within a single trophic level. Therefore, we further introduced the significance and quantification of individual-level HOIs within a single trophic level. Not only can individual-level HOIs reconcile the hard-HOIs and soft-HOIs, but also allow us to consider variatons between individuals (e.g. individual size and spatial distribution). Finally, we proposed some promising research directions of HOIs including but not limited to: testing the prevalence and relative importance of HOIs in natural communities, exploring the mechanisms of HOIs and integrating HOIs to existing theories of community ecology. Inclusion of HOIs will help us understand the mechanisms of species coexistence and biodiversity maintenance profoundly and comprehensively, enrich and refine the theoretical framework of community ecology, and lay the foundation for biodiversity conservation and management of ecosystems in the Anthropocene.

Ecological networks—how species interactions are organized within ecological communities—are highly structured, which has motivated generations of ecologists to elucidate how these structures affect species coexistence. Unfortunately, we still do not have a clear and consistent answer about the link between network structure and species coexistence. A possible explanation is that most of the studies do not take into account that the environment affects both network structure and species coexistence due to the multidimensional and changing nature of environmental factors. In this context, the structural stability approach provides a theoretical framework grounded on biological realism to quantitatively link network structure, species coexistence, and environmental factors. I begin by an overview of the heated debates in the study of ecological networks. Then I introduce the theoretical framework and computational tools of the structural stability approach in a nutshell. Then I show the empirical applications in different ecological questions across a broad range of ecological systems. Overall, the structural stability approach provides a new perspective to understand the maintenance of biodiversity in ecological communities.

In the 60-year development of invasion ecology, many hypotheses have been proposed to explain the mechanisms behind biological invasion. However, it remains difficult to integrate these hypotheses into a unified framework. In particular, whether exotics ecologically differ from natives, and how ecological differences between exotic and native species could determine invasion outcome, have been hotly debated. By categorizing exotic-native ecological differences into niche differences and fitness differences, modern coexistence theory provides a framework to place different invasion hypotheses and mechanisms into a common context. This framework emphasizes that invasion success depends on either a niche difference between exotics and natives, or that exotics have fitness advantage over natives. By reviewing the leading invasion hypotheses, we found that most invasion hypotheses can be incorporated into this framework, as they considered different aspects of exotic-native niche and fitness differences. This framework can well explain why exotic-native phylogenetic distance and trait difference have complex influences on invasion, and therefore may help to reconcile the long-standing Darwin’s naturalization conundrum and the debate regarding the value of native versus exotic trait comparisons. Together, this framework provides a new opportunity to better understand the mechanisms of ecological invasion.

Current unprecedented declines in biodiversity have galvanized efforts to understand how changes in biodiversity affect disease risk. Empirical evidence is mixed in understanding the relationship between loss in biodiversity and disease. While some empirical research supports a dilution effect (i.e., disease risk decreases with increasing host biodiversity), many studies support an amplification effect, and in some cases no effect. In this review, we first summarize the research progresses in this area, and introduce key research topics that include: the shape of the biodiversity-disease relationship, spatial- and context dependence of dilution effect, and the phylogenetic dilution effect. Following our summary, we discuss the disputes and criticisms in this field of research. These controversies include: whether the dilution effect is prevalent, publication bias in experimental studies, and an excessive focus by some disease ecologists on the numeric relationship between biodiversity and disease. Finally, we highlight some open questions for future research looking at dilution effect that include: the relationship between dilution effect and species coexistence, the effects of global climate change on dilution effect, the relationship between dilution effect and evolution, and the implications this research can have on policy decisions.

The relationship between food web structure and functioning can have important implications for predicting the responses of ecosystems to global changes. Previous studies have mainly explored food web structure and functioning separately or in simple food web models (e.g. food chains), but recent studies made significant progress in understanding the structure and functioning of complex food webs. This paper reviews the theoretical approaches and recent advances of complex food webs. In particular, I summarize the multiple metrics for quantifying the structure, biodiversity, and functioning of complex food webs, explain the theoretical framework for modeling complex food webs, and review the recent progress in understanding the relationships between food web structure, biodiversity, and functioning, and how they respond to global changes. I end with discussion on potential future directions by integrating food web theory with functional trait, ecological stoichiometry, other types of ecological networks, metacommunity theory, and evolutionary models.

The dynamic equilibrium of mass and energy movement in ecosystems is an important basis for the Earth system to nurture and maintain biodiversity. Since the Industrial Revolution, human activities have caused the carbon exchange between terrestrial ecosystems and the atmosphere to be at dynamic disequilibrium. This paper examines a dynamic disequilibrium hypothesis for the carbon cycle of terrestrial ecosystems. The hypothesis suggests that the dynamic disequilibrium is caused by interactions of four basic properties of internal processes of the terrestrial carbon cycle with five types of external drivers. Based on these internal properties and external drivers, this paper summarizes the expression phenomena of the dynamic disequilibrium of terrestrial carbon cycle at different time and space scales, and discusses its detection methods from the perspective of observations, experiments and models. The dynamic disequilibrium hypothesis for terrestrial carbon cycle not only helps us understand the complex terrestrial carbon-cycle phenomenon, but also provides a new theoretical framework for predicting the future terrestrial carbon sink dynamics.

Many ecosystems may experience abrupt shifts at certain tipping points subject to gradual environmental changes or small perturbations. The theory of alternative stable states has been applied to explain a wide range of observed ecosystem tipping points. In recent years, alternative ecosystem states and tipping points have received increasing attention among both researchers and the public. Here, we reviewed the theoretical basis of alternative stable states, the approaches for detecting the existence of alternative stable states, and a set of “generic early warning indicators” for anticipating the transitions between alternative stable states. We also reviewed typical cases to demonstrate how the alternative stable states theory is linked to real-world ecosystems. and discuss the potential misuse and controversy with respect to the concept and applications of this theory. We expect to provide useful references to Chinese audiences in the fields of nonlinear ecosystem dynamics, ecosystem management and biodiversity conservation in a changing world.

Over the past 30 years, the self-organization theory has effectively explained the regular spatial patterning of ecosystems and has led to a proliferation of studies investigating spatial patterns in ecology and biology. Indeed, the emergent properties generated by this self-organization process are now recognized as critical to ecosystem functioning. Here, we review this important theoretical framework by assessing the definition and development of the concept of self-organization and by evaluating two fundamental theoretical principles of self-organization theory, the Turing principle and the phase separation principle. We further describe the mathematical models of each principle in the context of different, unique ecosystems, and explain the emergent properties of the Turing principle on ecosystem functioning and the phase separation principle on cell functions, respectively. Finally, we propose three promising future developments for ecological self-organization theory: multi-scale self-organization patterns, transient patterns, and individual behavioral self-organization. Our review provides an assessment of this fundamental ecological theory and offers exciting new research directions and applications.