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This chapter presents a detailed explanation on the common misconceptions that occur when ecologists discuss the characteristics of multiple stable states in the natural ecosystem. These four have been repeatedly stated in many literatures that study multiple stable states, but they are considered false. The misconceptions are: thresholds are always part of systems with multiple stable states; multiple stable states are central to the state-and-transition concept; in the cup and ball model, the landscape is defined by parameters and the position of the ball by state variables; and characteristics of species and the environment predispose ecosystems to have multiple states. This chapter aims to shed light on these issues by clarifying the incongruity of these misconceptions to the multiple stable states.

This chapter examines the differential equations used for the modeling of ecological process of multiple stable states. The equations quickly reveal what experimentalists can test; thus, the discussion of theory in this chapter is limited to one-, two-, and three-species models of differential equations. Furthermore, the Allee or dispensation effects and multiple stable states for a single species is discuss to support the theory. In conclusion, this chapter argues that the complexity of the basins of attraction increases with the number of multiple stable states. In systems with two alternative states, the boundaries between two basins are smooth. However, as the number of stable states increase, the majority of the basins will have fractal boundaries.

This chapter examines other modeling approaches developed by ecologists to test the multiple stable states. Most of these approaches tend to fall into one of the two categories: the conceptual approach and the functional approach. Conceptual approach relies on verbal reasoning and visual representations while functional approach involves specification of a functional relationship between state variables and parameters. This chapter explains the conceptual approach by citing the state-and-transition models and other conceptual approaches. It also describes the weakly dissipative systems and the Coupled systems to give further details about the functional approach.

This chapter addresses the problems and issues that arise from trying to infer the existence of multiple stable states from observations of patterns in time and space. Patterns in nature are often used by ecologists to infer processes and causality, however, the temporal and spatial scales of ecological processes are too long and too broad to undertake informative experiments. This chapter explains the method of inferring causality from patterns, and its connection to catastrophe flags. Moreover, it discusses biases derived from assessing and selecting the evidence of multiple stable states. Examples of evidence from spatial patterns, and temporal patterns are also given.

This introductory chapter explains how natural ecosystems can appear to be so persistent and susceptible to catastrophic change, such as the replacement of coral reefs with seaweeds; and the replacement of semi-arid grasslands with shrub forests. Ecologists are interested in these sudden changes since these characteristics are often seen as indicators of an ecosystem with multiple stable states. Moreover, the unpredictable nature of those changes and the inability to reverse it can cause serious management problems. This chapter also defines the persistence and the susceptibility of ecosystem by addressing the questions: how do we know if a sudden shift in species composition is an evidence for multiple stable states? And how do we define terms such as ‘sudden,’ ‘abrupt,’ ‘persistent,’ and ‘irreversible,’ which are so often used to discuss multiple stable states in natural communities?

This chapter reviews the different experiments that support the evidence of multiple stable states. Among the thirty-five experiments published between 1980 and 2004 as proof of the multiple stable states, Schröder et al concluded that only nine were good enough or appropriate to be considered field tests. A study of these nine cases and several others suggests that very few experiments contain adequate controls and are well-replicated without pseudoreplication. The chapter also discusses Morley's comments on live weights of ewes, and explains how Jonathan Chase's experiment supports the multiple stable states. A case of multiple stable states on the Gulf of Maine is presented.

This chapter explains the reason why experimental tests and modeling cannot provide accurate answers to the issues surrounding multiple stable states. It remains an open question if multiple stable states are common in nature, but their existence implies that previous events could have a vital role in shaping present-day accumulations. The chapter also discusses the results of Before-After-Impact-Control (BACI) in testing the multiple stable states. It concludes that there are two things that could be done to improve the quality and quantity of experimental results — to improve access to primary data and negative results, and to have greater transparency about causality in order to make bolder conjectures.

This chapter focuses on the Catastrophe Theory, particularly its standpoint in the well-known conventional views of multiple stable states. It discusses why the theory has been widely used by mathematicians, chemists, and physicists, but disregarded by most ecologists. The most infamous proponent of catastrophe theory is René Thom, who developed the topology of catastrophes. Thom showed that for systems with one or two state variables and four or fewer parameters, there are seven elementary catastrophes or basic models that contain discontinuous jumps. The chapter also presents different ecological examples supporting the theory.

Fisheries Sustainability. Sustainability is defined as the ability of a socio-ecological system to continue to produce benefits to humans, and it has three distinct elements: biological, social, and economic. The key to biological sustainability is keeping fishing pressure at or below the level that will provide maximum long-term yield. This requires a scientific program to determine that level and a management system that can effectively regulate fishing pressure. Social and economic sustainability depend not only on biological sustainability, but also on other aspects such as who gets to fish and how the catch is allocated among different users.