In ecology, an ecosystem is said to possess ecological stability (or equilibrium) if it is capable of returning to its equilibrium state after a perturbation (a capacity known as resilience) or does not experience unexpected large changes in its characteristics across time. [1] Although the terms community stability and ecological stability are sometimes used interchangeably, [2] community stability refers only to the characteristics of communities. It is possible for an ecosystem or a community to be stable in some of their properties and unstable in others. For example, a vegetation community in response to a drought might conserve biomass but lose biodiversity. [3]
Stable ecological systems abound in nature, and the scientific literature has documented them to a great extent. Scientific studies mainly describe grassland plant communities and microbial communities. [4] Nevertheless, it is important to mention that not every community or ecosystem in nature is stable (for example, wolves and moose on Isle Royale). Also, noise plays an important role on biological systems and, in some scenarios, it can fully determine their temporal dynamics.
The concept of ecological stability emerged in the first half of the 20th century. With the advancement of theoretical ecology in the 1970s, the usage of the term has expanded to a wide variety of scenarios. This overuse of the term has led to controversy over its definition and implementation. [3]
In 1997, Grimm and Wissel made an inventory of 167 definitions used in the literature and found 70 different stability concepts. [5] One of the strategies that these two authors proposed to clarify the subject is to replace ecological stability with more specific terms, such as constancy, resilience and persistence. In order to fully describe and put meaning to a specific kind of stability, it must be looked at more carefully. Otherwise the statements made about stability will have little to no reliability because they would not have information to back up the claim. [6] Following this strategy, an ecosystem which oscillates cyclically around a fixed point, such as the one delineated by the predator-prey equations, would be described as persistent and resilient, but not as constant. Some authors, however, see good reason for the abundance of definitions, because they reflect the extensive variety of real and mathematical systems. [3]
When the species abundances of an ecological system are treated with a set of differential equations, it is possible to test for stability by linearizing the system at the equilibrium point. [7] Robert May used this stability analysis in the 1970s which uses the Jacobian matrix or community matrix to investigate the relation between the diversity and stability of an ecosystem. [8]
To analyze the stability of large ecosystems, May drew on ideas from statistical mechanics, including Eugene Wigner's work successfully predicting the properties of Uranium by assuming that its Hamiltonian could be approximated as a random matrix, leading to properties that were independent of the system's exact interactions. [8] [9] [10] May considered an ecosystem with species with abundances whose dynamics are governed by the couples system of ordinary differential equations,Assuming the system had a fixed point, , May linearized dynamics as,The fixed point will be linearly stable if all the eigenvalues of the Jacobian, , are positive. The matrix is also known as the community matrix. May supposed that the Jacobian was a random matrix whose off-diagonal entries are all all drawn as random variates from a probability distribution and whose diagonal elements are all -1 so that each species inhibits its own growth and stability is guaranteed in the absence of inter-species interactions. According to Girko's circular law, when , the eigenvalues of are distributed in the complex plane uniformly in a circle whose radius is and whose center is , where is the standard deviation of the distribution for the off-diagonal elements of the Jacobian. Using this result, the eigenvalue with the largest real part contained in the support of the spectrum of is . Therefore, the system will lose stability when,This result is known as the May stability criterion. It implies that dynamical stability is limited by diversity, and the strictness of this tradeoff is related to the magnitude of fluctuations in interactions.
Recent work has extended the approaches of May to construct phase diagrams for ecological models, like the generalized Lotka–Volterra model or consumer-resource models, with large complex communities with disordered interactions. [11] [12] [9] This work has relied on uses and extensions of random matrix theory, the cavity method, the replica formalism, and other methods inspired by spin-glass physics.
Although the characteristics of any ecological system are susceptible to changes, during a defined period of time, some remain constant, oscillate, reach a fixed point or present other type of behavior that can be described as stable. [13] This multitude of trends can be labeled by different types of ecological stability.
Dynamical stability refers to stability across time.
A stable point is such that a small perturbation of the system will be diminished and the system will come back to the original point. On the other hand, if a small perturbation is magnified, the stationary point is considered unstable.
In the sense of perturbation amplitude, local stability indicates that a system is stable over small short-lived disturbances, while global stability indicates a system highly resistant to change in species composition and/or food web dynamics.
In the sense of spatial extension, local instability indicates stability in a limited region of the ecosystem, while global (or regional) stability involves the whole ecosystem (or a large part of it). [14]
Stability can be studied at the species or at the community level, with links between these levels. [14]
Observational studies of ecosystems use constancy to describe living systems that can remain unchanged.
Resistance and inertia deal with a system's inherent response to some perturbation.
A perturbation is any externally imposed change in conditions, usually happening in a short time period. Resistance is a measure of how little the variable of interest changes in response to external pressures. Inertia (or persistence) implies that the living system is able to resist external fluctuations. In the context of changing ecosystems in post-glacial North America, E.C. Pielou remarked at the outset of her overview,
"It obviously takes considerable time for mature vegetation to become established on newly exposed ice scoured rocks or glacial till...it also takes considerable time for whole ecosystems to change, with their numerous interdependent plant species, the habitats these create, and the animals that live in the habitats. Therefore, climatically caused fluctuations in ecological communities are a damped, smoothed-out version of the climatic fluctuations that cause them." [15]
Resilience is the tendency of a system to retain its functional and organizational structure and the ability to recover after a perturbation or disturbance. [16] Resilience also expresses the need for persistence although from a management approach it is expressed to have a broad range of choices and events are to be looked at as uniformly distributed. [17] Elasticity and amplitude are measures of resilience. Elasticity is the speed with which a system returns to its original / previous state. Amplitude is a measure of how far a system can be moved from the previous state and still return. Ecology borrows the idea of neighborhood stability and a domain of attraction from dynamical systems theory.
Researchers applying mathematical models from system dynamics usually use Lyapunov stability. [18] [19]
Focusing on the biotic components of an ecosystem, a population or a community possesses numerical stability if the number of individuals is constant or resilient. [20]
It is possible to determine if a system is stable just by looking at the signs in the interaction matrix.
The relationship between diversity and stability has been widely studied. [4] [21] Diversity can enhance the stability of ecosystem functions at various ecological scales. [22] For example, genetic diversity can enhance resistance to environmental perturbations. [23] At the community level, the structure of food webs can affect stability. The effect of diversity on stability in food-web models can be either positive or negative, depending on the trophic coherence of the network. [24] At the level of landscapes, environmental heterogeneity across locations has been shown to increase the stability of ecosystem functions. [25] A stability diversity tradeoff has also been recently observed in microbial communities from human and sponge host environments. [26] In the context of large and heterogeneous ecological networks, stability can be modeled using dynamic Jacobian ensembles. [27] These show that scale and heterogeneity can stabilize specific states of the system in the face of environmental perturbations.
The term 'oekology' was coined by Ernst Haeckel in 1866. Ecology as a science was developed further during the late 19th and the early 20th century, and increasing attention was directed toward the connection between diversity and stability. [28] Frederic Clements and Henry Gleason contributed knowledge of community structure; among other things, these two scientists introduced the opposing ideas that a community can either reach a stable climax or that it is largely coincidental and variable. Charles Elton argued in 1958 that complex, diverse communities tended to be more stable. Robert MacArthur proposed a mathematical description of stability in the number of individuals in a food web in 1955. [29] After much progress made with experimental studies in the 60's, Robert May advanced the field of theoretical ecology and refuted the idea that diversity begets stability. [8] Many definitions of ecological stability have emerged in the last decades while the concept continues to gain attention.
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: CS1 maint: multiple names: authors list (link)Ecology is the natural science of the relationships among living organisms, including humans, and their physical environment. Ecology considers organisms at the individual, population, community, ecosystem, and biosphere levels. Ecology overlaps with the closely related sciences of biogeography, evolutionary biology, genetics, ethology, and natural history.
Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world.
A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Position in the food web, or trophic level, is used in ecology to broadly classify organisms as autotrophs or heterotrophs. This is a non-binary classification; some organisms occupy the role of mixotrophs, or autotrophs that additionally obtain organic matter from non-atmospheric sources.
The unified neutral theory of biodiversity and biogeography is a theory and the title of a monograph by ecologist Stephen P. Hubbell. It aims to explain the diversity and relative abundance of species in ecological communities. Like other neutral theories of ecology, Hubbell assumes that the differences between members of an ecological community of trophically similar species are "neutral", or irrelevant to their success. This implies that niche differences do not influence abundance and the abundance of each species follows a random walk. The theory has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.
The diversity of species and genes in ecological communities affects the functioning of these communities. These ecological effects of biodiversity in turn are affected by both climate change through enhanced greenhouse gases, aerosols and loss of land cover, and biological diversity, causing a rapid loss of biodiversity and extinctions of species and local populations. The current rate of extinction is sometimes considered a mass extinction, with current species extinction rates on the order of 100 to 1000 times as high as in the past.
Regime shifts are large, abrupt, persistent changes in the structure and function of ecosystems, the climate, financial systems or other complex systems. A regime is a characteristic behaviour of a system which is maintained by mutually reinforced processes or feedbacks. Regimes are considered persistent relative to the time period over which the shift occurs. The change of regimes, or the shift, usually occurs when a smooth change in an internal process (feedback) or a single disturbance triggers a completely different system behavior. Although such non-linear changes have been widely studied in different disciplines ranging from atoms to climate dynamics, regime shifts have gained importance in ecology because they can substantially affect the flow of ecosystem services that societies rely upon, such as provision of food, clean water or climate regulation. Moreover, regime shift occurrence is expected to increase as human influence on the planet increases – the Anthropocene – including current trends on human induced climate change and biodiversity loss. When regime shifts are associated with a critical or bifurcation point, they may also be referred to as critical transitions.
A Boolean network consists of a discrete set of Boolean variables each of which has a Boolean function assigned to it which takes inputs from a subset of those variables and output that determines the state of the variable it is assigned to. This set of functions in effect determines a topology (connectivity) on the set of variables, which then become nodes in a network. Usually, the dynamics of the system is taken as a discrete time series where the state of the entire network at time t+1 is determined by evaluating each variable's function on the state of the network at time t. This may be done synchronously or asynchronously.
In ecology, resilience is the capacity of an ecosystem to respond to a perturbation or disturbance by resisting damage and subsequently recovering. Such perturbations and disturbances can include stochastic events such as fires, flooding, windstorms, insect population explosions, and human activities such as deforestation, fracking of the ground for oil extraction, pesticide sprayed in soil, and the introduction of exotic plant or animal species. Disturbances of sufficient magnitude or duration can profoundly affect an ecosystem and may force an ecosystem to reach a threshold beyond which a different regime of processes and structures predominates. When such thresholds are associated with a critical or bifurcation point, these regime shifts may also be referred to as critical transitions.
In ecology, the theory of alternative stable states predicts that ecosystems can exist under multiple "states". These alternative states are non-transitory and therefore considered stable over ecologically-relevant timescales. Ecosystems may transition from one stable state to another, in what is known as a state shift, when perturbed. Due to ecological feedbacks, ecosystems display resistance to state shifts and therefore tend to remain in one state unless perturbations are large enough. Multiple states may persist under equal environmental conditions, a phenomenon known as hysteresis. Alternative stable state theory suggests that discrete states are separated by ecological thresholds, in contrast to ecosystems which change smoothly and continuously along an environmental gradient.
The generalized Lotka–Volterra equations are a set of equations which are more general than either the competitive or predator–prey examples of Lotka–Volterra types. They can be used to model direct competition and trophic relationships between an arbitrary number of species. Their dynamics can be analysed analytically to some extent. This makes them useful as a theoretical tool for modeling food webs. However, they lack features of other ecological models such as predator preference and nonlinear functional responses, and they cannot be used to model mutualism without allowing indefinite population growth.
In the context of ecological stability, resistance is the property of communities or populations to remain "essentially unchanged" when subject to disturbance. The inverse of resistance is sensitivity.
In ecology, a priority effect refers to the impact that a particular species can have on community development as a result of its prior arrival at a site. There are two basic types of priority effects: inhibitory and facilitative. An inhibitory priority effect occurs when a species that arrives first at a site negatively affects a species that arrives later by reducing the availability of space or resources. In contrast, a facilitative priority effect occurs when a species that arrives first at a site alters abiotic or biotic conditions in ways that positively affect a species that arrives later. Inhibitory priority effects have been documented more frequently than facilitative priority effects. Studies indicate that both abiotic and biotic factors can affect the strength of priority effects.. Priority effects are a central and pervasive element of ecological community development that have significant implications for natural systems and ecological restoration efforts.
This is a bibliography of ecology.
James Ivor Prosser is a British microbiologist who is a Professor in Environmental Microbiology in the Institute of Biological and Environmental Sciences at the University of Aberdeen.
An ecosystem, short for ecological system, is defined as a collection of interacting organisms within a biophysical environment. Ecosystems are never static, and are continually subject to both stabilizing and destabilizing processes. Stabilizing processes allow ecosystems to adequately respond to destabilizing changes, or perturbations, in ecological conditions, or to recover from degradation induced by them: yet, if destabilizing processes become strong enough or fast enough to cross a critical threshold within that ecosystem, often described as an ecological 'tipping point', then an ecosystem collapse. occurs.
Critical transitions are abrupt shifts in the state of ecosystems, the climate, financial systems or other complex dynamical systems that may occur when changing conditions pass a critical or bifurcation point. As such, they are a particular type of regime shift. Recovery from such shifts may require more than a simple return to the conditions at which a transition occurred, a phenomenon called hysteresis. In addition to natural systems, critical transitions are also studied in psychology, medicine, economics, sociology, military, and several other disciplines.
Heteroclinic channels are ensembles of trajectories that can connect saddle equilibrium points in phase space. Dynamical systems and their associated phase spaces can be used to describe natural phenomena in mathematical terms; heteroclinic channels, and the cycles that they produce, are features in phase space that can be designed to occupy specific locations in that space. Heteroclinic channels move trajectories from one equilibrium point to another. More formally, a heteroclinic channel is a region in phase space in which nearby trajectories are drawn closer and closer to one unique limiting trajectory, the heteroclinic orbit. Equilibria connected by heteroclinic trajectories form heteroclinic cycles and cycles can be connected to form heteroclinic networks. Heteroclinic cycles and networks naturally appear in a number of applications, such as fluid dynamics, population dynamics, and neural dynamics. In addition, dynamical systems are often used as methods for robotic control. In particular, for robotic control, the equilibrium points can correspond to robotic states, and the heteroclinic channels can provide smooth methods for switching from state to state.
In mathematical modeling, resilience refers to the ability of a dynamical system to recover from perturbations and return to its original stable steady state. It is a measure of the stability and robustness of a system in the face of changes or disturbances. If a system is not resilient enough, it is more susceptible to perturbations and can more easily undergo a critical transition. A common analogy used to explain the concept of resilience of an equilibrium is one of a ball in a valley. A resilient steady state corresponds to a ball in a deep valley, so any push or perturbation will very quickly lead the ball to return to the resting point where it started. On the other hand, a less resilient steady state corresponds to a ball in a shallow valley, so the ball will take a much longer time to return to the equilibrium after a perturbation.
In theoretical ecology and nonlinear dynamics, consumer-resource models (CRMs) are a class of ecological models in which a community of consumer species compete for a common pool of resources. Instead of species interacting directly, all species-species interactions are mediated through resource dynamics. Consumer-resource models have served as fundamental tools in the quantitative development of theories of niche construction, coexistence, and biological diversity. These models can be interpreted as a quantitative description of a single trophic level.
The random generalized Lotka–Volterra model (rGLV) is an ecological model and random set of coupled ordinary differential equations where the parameters of the generalized Lotka–Volterra equation are sampled from a probability distribution, analogously to quenched disorder. The rGLV models dynamics of a community of species in which each species' abundance grows towards a carrying capacity but is depleted due to competition from the presence of other species. It is often analyzed in the many-species limit using tools from statistical physics, in particular from spin glass theory.