Alternative stable states, tipping points, and early warning signals of ecological transitions

Ecological systems are prone to dramatic shifts between alternative stable states. In reality, these shifts are often caused by slow forces external to the system that eventually push it over a tipping point. Theory predicts that when ecological systems are brought close to a tipping point, the dynamical feedback intrinsic to the system interact with intrinsic noise and extrinsic perturbations in characteristic ways. The resulting phenomena thus serve as “early warning signals” for shifts such as population collapse. In this chapter, we review the basic (qualitative) theory of such systems. We then illustrate the main ideas with a series of models that both represent fundamental ecological ideas (e.g. density-dependence) and are amenable to mathematical analysis. These analyses provide theoretical predictions about the nature of measurable fluctuations in the vicinity of a tipping point. We conclude with a review of empirical evidence from laboratory microcosms, field manipulations, and observational studies.

Non-equilibrium dynamics and stochastic processes

Most standard theoretical approaches emphasize the role of deterministic density dependence in creating and maintaining equilibrium dynamics. At the same time, it is widely recognized that ecological processes are inherently stochastic, and that disturbances and variation in the environment and in the fates of individuals prevent many ecological systems from resting at their theoretical equilibrium. A developing body of stochastic ecological theory aims to bridge the gap between the deterministic tools of classical theory and the stochastic, non-equilibrial questions that real systems present to us. This chapter provides an overview of this developing theory, with an emphasis on approaches that confront the complex interplay between deterministic density dependence, and perturbations. Although intuition may suggest that stochasticity and transient phenomena should obscure ecological understanding, they can actually strengthen it when viewed through the appropriate lens, as illustrated in this chapter.

The impact of temperature on population and community dynamics

Of the myriad of environmental variables that are currently in flux due to anthropogenic climate change, temperature is one of the most ubiquitous and well-studied. Temperature directly influences the vital rates and ecological thresholds that determine how quickly populations grow or decline and many studies have sought to determine how these influences culminate at the population and community level. This chapter surveys the theoretical work in this area and details how our growing understanding of the relationships between temperature and vital rates and thresholds has led to new insights and challenges. The latter sections of the chapter reveal a key principle to guide the ongoing debate about the temperature-dependence of a key parameter underlying nearly all population and community models: the carrying capacity. From this, a simple model is used to demonstrate how linkages between the thermal sensitivity of population growth and carrying capacity determine dynamics and the propensity for extinction in warming environments.

Ecological networks: From structure to dynamics

Ecological systems are undeniably complex, including many species interacting in different ways with each other (e.g., predation, competition, facilitation, parasitism). One way of visualizing, describing, and studying this complexity is to represent them as networks, where nodes are typically species and links are interactions between these species. The study of these networks allows understanding of the rules governing the topology of their links, and assessing how network structure drives ecological dynamics. Studies on different types of ecological networks have suggested that they exhibit structural regularities, which in turn affect network dynamics and resilience to perturbations. Although the use of networks to represent ecological communities dates back to the early stages of the discipline, the last two decades have seen rapid progresses in our understanding of ecological networks, as data are collected at a faster rate and better resolution, as metrics are continuously developed to better characterize network structure and as numerical simulations of mathematical models have allowed investigating how network structure and dynamics are related in more comprehensive and realistic ecological networks. This chapter describes some of the recent developments and challenges related to the study of ecological networks. After defining networks in general, and ecological networks more specifically, recent results regarding the structure of different types of ecological networks, and what is known about their dynamics and resilience, are presented.

Trait-based models of complex ecological networks

Over many decades, modelling natural communities of higher diversity and complexity has been hampered by the necessity to provide reasonable parameters for all processes at the level of populations and interactions. Trait-based approaches such as allometric scaling allow to use general species traits such as their average individual body mass to estimate the parameters of populations (e.g., metabolic rates) and interactions (e.g., attack rates). This chapter describes this trait-based network approach and illustrates its potential for understanding the structure and dynamics of complex networks using the examples of i) intrinsic community stability and ii) consequences of global change (e.g., warming). Finally, new research frontiers are illustrated that include spatial processes in meta-networks, the constraints of ecological network structure on ecosystem functioning, and non-trophic interactions.

Species coexistence

In most places on Earth, many similar species are found coexisting. This key observation is often explained in terms of ecological differences in how species interact with their shared environment, that is, in terms of their niche differences. Niche differences can to lead to stable coexistence in contrast to the ecological drift predicted by the neutral theory of community ecology. Coexistence becomes stabilized as density feedback within species is strengthened relative to density feedback between species. Coexistence is reflective of two distinct niche comparisons, niche overlap, and species relative average fitness. In general, low niche overlap (dissimilarity in use of the environment) and similar average fitnesses (similar average performance) favor coexistence. For a unified theory of species coexistence, it is shown how the Lotka–Volterra competition model can reflect and quantify several types of niche comparison, including comparisons of resource use, susceptibility to natural enemies, and temporal variation in activity.

Introduction

This book continues the authoritative and established edited series of theoretical ecology books initiated by Robert May which helped pave the way for ecology to become a more robust theoretical science, encouraging the modern biologist to better understand the mathematics behind their theories. This latest instalment in the Theoretical Ecology series builds on the legacy of its predecessors with a completely new set of contributions. Rather than placing emphasis on historical ideas in theoretical ecology, the editors have encouraged each contribution to: i) synthesize historical theoretical ideas within modern frameworks that have emerged in the last ten to twenty years (e.g., bridging population interactions to whole food webs); ii) describe novel theory that has emerged in the last twenty years from historical empirical areas (e.g., macro-ecology); and iii) cover the booming area of theoretical ecological applications (e.g., disease theory and global change theory). The result is a forward-looking synthesis that will help guide the field through a further decade of development and discovery. Early chapters are collectively more about the building blocks for understanding dynamics of interacting species in time and space, including coexistence, consumer-resource and biological lags, stochasticity, and stage structure. Later, chapters are representative of the study of networks, a large growth area. These include matrix theory, mutualistic networks, community structure, body size and system structure, and network ecology. Novel concepts such as trait-based models and meta-population ecology are then presented. Applied theoretical ecology is then covered by chapters on disease ecology, climate change dynamics, and stable states.

Theories of diversity in disease ecology

Early theoretical developments in disease ecology overwhelmingly focused on interactions between a single pathogen and a single host. Today, it is well understood that numerous pathogens circulate among multiple host species, that some pathogens are comprised of many distinct strains, and that community ecology offers important perspectives for gaining insight into the inner workings of these complex ecological systems. Here, we focus on two topics that have received intense focus in theoretical investigations of multi-host and multi-pathogen systems, respectively. First, we review developments in a rather contentious debate around relationships between host diversity and disease. The current state of theory suggests that divergent views can be reconciled by considering where along a continuum of host diversity a given system lies, which is thought to affect how community assembly processes shape host species composition and overall abundance. Second, we review developments surrounding coexistence and other outcomes in communities of interacting pathogens. Ultimately, coexistence in pathogen communities can be explained by the same mechanisms that explain coexistence in any community, yet certain ways in which pathogens interact make the tailoring of theory specific to this context well justified. Despite a rich literature on host and pathogen diversity, there has been remarkably little theoretical work at their interface. To stimulate fresh developments to theories of diversity in disease ecology, we highlight aspects of ecological theory that may have been underutilized in theoretical work on host and pathogen diversity to date.

The impact of population structure on population and community dynamics

Ecological theory about dynamics of interacting species constitutes the basis for our understanding of the functioning of ecological communities and ecosystems and their responses to changing environmental conditions, natural disturbances, and human impacts. The mathematical foundation of this theory emphasizes changes in species abundances only, ignoring those aspects that make biological organisms unique, in particular within-population variation due to individual development during life history and individual energetics. In contrast, structured population models do take these aspects into account and hence explicitly link individual life history to population dynamics. In this chapter, I review the different types of structured population models and which purposes they are especially suited for. I will subsequently focus on physiologically structured population models (PSPMs), which are especially suited to model the interactions within and between populations. I will review the key ecological insights that have been derived using PSPMs and show how and why predictions by PSPMs often contrast with the basic rules-of-thumb that make up classical theory based on unstructured models. Finally, I will discuss the experimental and empirical evidence for the counter-intuitive predictions by PSPMs, emphasizing that PSPMs allow for testing at both the individual and population level and hence for a tight link between theory and data.

Toward a general theory of metacommunity ecology

Investigation of how spatial processes affect the maintenance of biodiversity and its geographic distribution has led to landmark contributions in community ecology. Theory has followed a logical complexification of the objects of study, with specific models at each step, from populations connected by dispersal to ecosystems connected by flows of energy and material. This large body of theory is not only diverse in the questions it addresses, and the scales and organization levels it encompasses, but also in the types of models used to represent spatial dynamics. Unfortunately, this makes it hard to establish clear, standard, quantitative predictions stemming from a coherent mathematical formalism. Here our objectives are : i) to propose a general metacommunity model that allows the investigation of spatial ecology from populations to entire food webs ; ii) use the model to review a set of principles driving coexistence in all types of metacommunities; iii) reveal how these principles constrain the spatial distribution of diversity, with a particular emphasis on species co-distribution. The model is based on the well-established representation of spatial dynamics through colonization and extinction processes. We generalize Levins’ metapopulation model to all types of ecological interactions, using a formalism akin to Lotka–Volterra equations for local community dynamics. Doing so, we revisit coexistence mechanisms proposed for competitive metacommunities, along with the assembly dynamics for spatial food webs and mutualistic interactions.