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 level. 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. Ecologists can broadly define all life forms as either autotrophs or heterotrophs, based on their trophic levels, the position that they occupy in the food web. To maintain their bodies, grow, develop, and to reproduce, autotrophs produce organic matter from inorganic substances, including both minerals and gases such as carbon dioxide. These chemical reactions require energy, which mainly comes from the Sun and largely by photosynthesis, although a very small amount comes from bioelectrogenesis in wetlands, and mineral electron donors in hydrothermal vents and hot springs. These trophic levels are not binary, but form a gradient that includes complete autotrophs, which obtain their sole source of carbon from the atmosphere, mixotrophs, which are autotrophic organisms that partially obtain organic matter from sources other than the atmosphere, and complete heterotrophs that must feed to obtain organic matter.
The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey. The populations change through time according to the pair of equations:
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.
The Leslie matrix is a discrete, age-structured model of population growth that is very popular in population ecology named after Patrick H. Leslie. The Leslie matrix is one of the most well-known ways to describe the growth of populations, in which a population is closed to migration, growing in an unlimited environment, and where only one sex, usually the female, is considered.
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.
The paradox of enrichment is a term from population ecology coined by Michael Rosenzweig in 1971. He described an effect in six predator–prey models where increasing the food available to the prey caused the predator's population to destabilize. A common example is that if the food supply of a prey such as a rabbit is overabundant, its population will grow unbounded and cause the predator population to grow unsustainably large. That may result in a crash in the population of the predators and possibly lead to local eradication or even species extinction.
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.
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 stabilizing and destabilizing processes alike. Stabilizing processes allow ecosystems to adequately respond to destabilizing changes, or pertubations, 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.
