Ecosystem

From Wikipedia, the free encyclopedia

There are many different ecosystems on Earth. Left: Coral reefs are a highly productive marine ecosystem^[1], right: Temperate rainforest on the Olympic Peninsula in Washington state.

An ecosystem is a community made up of living organisms and nonliving components such as air, water, and mineral soil.^[3] Ecosystems can be studied in two different ways. They can be thought of as interdependent collections of plants and animals, or as structured systems and communities governed by general rules.^[4] The living (biotic) and non-living (abiotic) components interact through nutrient cycles and energy flows.^[5] Ecosystems include interactions among organisms, and between organisms and their environment.^[6] Ecosystems can be of any size but each ecosystem has a specific, limited space.^[7] Some scientists view the entire planet as one ecosystem.

Energy, water, nitrogen and soil minerals are essential abiotic components of an ecosystem. The energy used by ecosystems comes primarily from the sun, via photosynthesis. Photosynthesis uses energy from the sun and also captures carbon dioxide from the atmosphere. Animals also play an important role in the movement of matter and energy through ecosystems. They influence the amount of plant and microbial biomass that lives in the system. As organic matter dies, carbon is released back into the atmosphere. This process also facilitates nutrient cycling by converting nutrients stored in dead biomass back to a form that can be used again by plants and other microbes.^[9]

Ecosystems are controlled by both external and internal factors. External factors such as climate, the parent material that forms the soil, topography and time each affect ecosystems. However, these external factors are not themselves influenced by the ecosystem.^[10] Ecosystems are dynamic: they are subject to periodic disturbances and are often in the process of recovering from past disturbances and seeking balance.^[11] Internal factors are different: They not only control ecosystem processes but are also controlled by them. Another way of saying this is that internal factors are subject to feedback loops.^[10]

Humans operate within ecosystems and can influence both internal and external factors.^[10] Global warming is an example of a cumulative effect of human activities. Ecosystems provide benefits, called "ecosystem services", which people depend on for their livelihood. Ecosystem management is more efficient than trying to manage individual species.

Definition

There is no single definition of what constitutes an ecosystem.^[4] German ecologist Ernst-Detlef Schulze and coauthors defined an ecosystem as an area which is "uniform regarding the biological turnover, and contains all the fluxes above and below the ground area under consideration." They explicitly reject Gene Likens' use of entire river catchments as "too wide a demarcation" to be a single ecosystem, given the level of heterogeneity within such an area.^[12] Other authors have suggested that an ecosystem can encompass a much larger area, even the whole planet.^[8] Schulze and coauthors also rejected the idea that a single rotting log could be studied as an ecosystem because the size of the flows between the log and its surroundings are too large, relative to the proportion cycles within the log.^[12] Philosopher of science Mark Sagoff considers the failure to define "the kind of object it studies" to be an obstacle to the development of theory in ecosystem ecology.^[4]

Ecosystems can be studied in a variety of ways. Those include theoretical studies or more practical studies that monitor specific ecosystems over long periods of time or look at differences between ecosystems to better understand how they work. Some studies involve experimenting with direct manipulation of the ecosystem.^[13] Studies can be carried out at a variety of scales, ranging from whole-ecosystem studies to to studying microcosms or mesocosms (simplified representations of ecosystems).^[14] American ecologist Stephen R. Carpenter has argued that microcosm experiments can be "irrelevant and diversionary" if they are not carried out in conjunction with field studies done at the ecosystem scale. Microcosm experiments often fail to accurately predict ecosystem-level dynamics.^[15]

The Hubbard Brook Ecosystem Study started in 1963 to study the White Mountains in New Hampshire. It was the first successful attempt to study an entire watershed as an ecosystem. The study used stream chemistry as a means of monitoring ecosystem properties, and developed a detailed biogeochemical model of the ecosystem.^[16] Long-term research at the site led to the discovery of acid rain in North America in 1972. Researchers documented the depletion of soil cations (especially calcium) over the next several decades.^[17]

Related concepts

Terrestrial ecosystems (found on land) and aquatic ecosystems (found in water) are concepts related to ecosystems. Aquatic ecosystems are split into marine ecosystems and freshwater ecosystems.

Processes

Rainforest ecosystems are rich in biodiversity. This is the Gambia River in Senegal's Niokolo-Koba National Park.

Flora of Baja California Desert, Cataviña region, Mexico

Biomes of the world

External and internal factors

Ecosystems are controlled both by external and internal factors. External factors, also called state factors, control the overall structure of an ecosystem and the way things work within it, but are not themselves influenced by the ecosystem. The most important of these is climate.^[10] Climate determines the biome in which the ecosystem is embedded. Rainfall patterns and seasonal temperatures influence photosynthesis and thereby determine the amount of water and energy available to the ecosystem.^[10]

Parent material determines the nature of the soil in an ecosystem, and influences the supply of mineral nutrients. Topography also controls ecosystem processes by affecting things like microclimate, soil development and the movement of water through a system. For example, ecosystems can be quite different if situated in a small depression on the landscape, versus one present on an adjacent steep hillside.^[10]

Other external factors that play an important role in ecosystem functioning include time and potential biota. Similarly, the set of organisms that can potentially be present in an area can also significantly affect ecosystems. Ecosystems in similar environments that are located in different parts of the world can end up doing things very differently simply because they have different pools of species present.^[10] The introduction of non-native species can cause substantial shifts in ecosystem function.

Unlike external factors, internal factors in ecosystems not only control ecosystem processes but are also controlled by them. Consequently, they are often subject to feedback loops.^[10] While the resource inputs are generally controlled by external processes like climate and parent material, the availability of these resources within the ecosystem is controlled by internal factors like decomposition, root competition or shading.^[10] Other factors like disturbance, succession or the types of species present are also internal factors.

Primary production

Global oceanic and terrestrial phototroph abundance, from September 1997 to August 2000. As an estimate of autotroph biomass, it is only a rough indicator of primary production potential and not an actual estimate of it.

Primary production is the production of organic matter from inorganic carbon sources. This mainly occurs through photosynthesis. The energy incorporated through this process supports life on earth, while the carbon makes up much of the organic matter in living and dead biomass, soil carbon and fossil fuels. It also drives the carbon cycle, which influences global climate via the greenhouse effect.

Through the process of photosynthesis, plants capture energy from light and use it to combine carbon dioxide and water to produce carbohydrates and oxygen. The photosynthesis carried out by all the plants in an ecosystem is called the gross primary production (GPP).^[18] About 48–60% of the GPP is consumed in plant respiration.

The remainder, that portion of GPP that is not used up by respiration, is known as the net primary production (NPP).^[19]

Energy flow

Energy and carbon enter ecosystems through photosynthesis, are incorporated into living tissue, transferred to other organisms that feed on the living and dead plant matter, and eventually released through respiration.^[19]

The carbon and energy incorporated into plant tissues (net primary production) is either consumed by animals while the plant is alive, or it remains uneaten when the plant tissue dies and becomes detritus. In terrestrial ecosystems, roughly 90% of the net primary production ends up being broken down by decomposers. The remainder is either consumed by animals while still alive and enters the plant-based trophic system, or it is consumed after it has died, and enters the detritus-based trophic system.

In aquatic systems, the proportion of plant biomass that gets consumed by herbivores is much higher.^[20] In trophic systems photosynthetic organisms are the primary producers. The organisms that consume their tissues are called primary consumers or secondary producers—herbivores. Organisms which feed on microbes (bacteria and fungi) are termed microbivores. Animals that feed on primary consumers—carnivores—are secondary consumers. Each of these constitutes a trophic level.^[20]

The sequence of consumption—from plant to herbivore, to carnivore—forms a food chain. Real systems are much more complex than this—organisms will generally feed on more than one form of food, and may feed at more than one trophic level. Carnivores may capture some prey which are part of a plant-based trophic system and others that are part of a detritus-based trophic system (a bird that feeds both on herbivorous grasshoppers and earthworms, which consume detritus). Real systems, with all these complexities, form food webs rather than food chains.^[20]

Ecosystem ecology

A hydrothermal vent is an ecosystem on the ocean floor. (The scale bar is 1 m.)

Ecosystem ecology studies "the flow of energy and materials through organisms and the physical environment". It seeks to understand the processes which govern the stocks of material and energy in ecosystems, and the flow of matter and energy through them. The study of ecosystems can cover 10 orders of magnitude, from the surface layers of rocks to the surface of the planet.^[21]

Decomposition

The carbon and nutrients in dead organic matter are broken down by a group of processes known as decomposition. This releases nutrients that can then be re-used for plant and microbial production and returns carbon dioxide to the atmosphere (or water) where it can be used for photosynthesis. In the absence of decomposition, the dead organic matter would accumulate in an ecosystem, and nutrients and atmospheric carbon dioxide would be depleted.^[22] Approximately 90% of terrestrial net primary production goes directly from plant to decomposer.^[20]

Decomposition processes can be separated into three categories—leaching, fragmentation and chemical alteration of dead material.

Leaching

As water moves through dead organic matter, it dissolves and carries with it the water-soluble components. These are then taken up by organisms in the soil, react with mineral soil, or are transported beyond the confines of the ecosystem (and are considered lost to it).^[22] Newly shed leaves and newly dead animals have high concentrations of water-soluble components and include sugars, amino acids and mineral nutrients. Leaching is more important in wet environments and much less important in dry ones.^[22]

Fragmentation

Fragmentation processes break organic material into smaller pieces, exposing new surfaces for colonization by microbes. Freshly shed leaf litter may be inaccessible due to an outer layer of cuticle or bark, and cell contents are protected by a cell wall. Newly dead animals may be covered by an exoskeleton. Fragmentation processes, which break through these protective layers, accelerate the rate of microbial decomposition.^[22] Animals fragment detritus as they hunt for food, as does passage through the gut. Freeze-thaw cycles and cycles of wetting and drying also fragment dead material.^[22]

Chemical alteration

The chemical alteration of the dead organic matter is primarily achieved through bacterial and fungal action. Fungal hyphae produce enzymes which can break through the tough outer structures surrounding dead plant material. They also produce enzymes which break down lignin, which allows them access to both cell contents and to the nitrogen in the lignin. Fungi can transfer carbon and nitrogen through their hyphal networks and thus, unlike bacteria, are not dependent solely on locally available resources.^[22]

Decomposition rates

Decomposition rates vary among ecosystems. The rate of decomposition is governed by three sets of factors—the physical environment (temperature, moisture, and soil properties), the quantity and quality of the dead material available to decomposers, and the nature of the microbial community itself.^[23] Temperature controls the rate of microbial respiration; the higher the temperature, the faster microbial decomposition occurs. It also affects soil moisture, which slows microbial growth and reduces leaching. Freeze-thaw cycles also affect decomposition—freezing temperatures kill soil microorganisms, which allows leaching to play a more important role in moving nutrients around. This can be especially important as the soil thaws in the spring, creating a pulse of nutrients which become available.^[23]

Decomposition rates are low under very wet or very dry conditions. Decomposition rates are highest in wet, moist conditions with adequate levels of oxygen. Wet soils tend to become deficient in oxygen (this is especially true in wetlands), which slows microbial growth. In dry soils, decomposition slows as well, but bacteria continue to grow (albeit at a slower rate) even after soils become too dry to support plant growth.

Nutrient cycling

Biological nitrogen cycling

Ecosystems continually exchange energy and carbon with the wider environment. Mineral nutrients, on the other hand, are mostly cycled back and forth between plants, animals, microbes and the soil. Most nitrogen enters ecosystems through biological nitrogen fixation, is deposited through precipitation, dust, gases or is applied as fertilizer.^[24]

Nitrogen cycle

Since most terrestrial ecosystems are nitrogen-limited, nitrogen cycling is an important control on ecosystem production.^[24]

Until modern times, nitrogen fixation was the major source of nitrogen for ecosystems. Nitrogen-fixing bacteria either live symbiotically with plants or live freely in the soil. The energetic cost is high for plants which support nitrogen-fixing symbionts—as much as 25% of gross primary production when measured in controlled conditions. Many members of the legume plant family support nitrogen-fixing symbionts. Some cyanobacteria are also capable of nitrogen fixation. These are phototrophs, which carry out photosynthesis. Like other nitrogen-fixing bacteria, they can either be free-living or have symbiotic relationships with plants.^[24] Other sources of nitrogen include acid deposition produced through the combustion of fossil fuels, ammonia gas which evaporates from agricultural fields which have had fertilizers applied to them, and dust.^[24] Anthropogenic nitrogen inputs account for about 80% of all nitrogen fluxes in ecosystems.^[24]

When plant tissues are shed or are eaten, the nitrogen in those tissues becomes available to animals and microbes. Microbial decomposition releases nitrogen compounds from dead organic matter in the soil, where plants, fungi, and bacteria compete for it. Some soil bacteria use organic nitrogen-containing compounds as a source of carbon, and release ammonium ions into the soil. This process is known as nitrogen mineralization. Others convert ammonium to nitrite and nitrate ions, a process known as nitrification. Nitric oxide and nitrous oxide are also produced during nitrification.^[24] Under nitrogen-rich and oxygen-poor conditions, nitrates and nitrites are converted to nitrogen gas, a process known as denitrification.^[24]

Other nutrients

Other important nutrients include phosphorus, sulfur, calcium, potassium, magnesium and manganese.^[25] Phosphorus enters ecosystems through weathering. As ecosystems age this supply diminishes, making phosphorus-limitation more common in older landscapes (especially in the tropics).^[25] Calcium and sulfur are also produced by weathering, but acid deposition is an important source of sulfur in many ecosystems. Although magnesium and manganese are produced by weathering, exchanges between soil organic matter and living cells account for a significant portion of ecosystem fluxes. Potassium is primarily cycled between living cells and soil organic matter.^[25]

Function and biodiversity

Loch Lomond in Scotland forms a relatively isolated ecosystem. The fish community of this lake has remained stable over a long period until a number of introductions in the 1970s restructured it's food web.^[26]

Spiny forest at Ifaty, Madagascar, featuring various Adansonia (baobab) species, Alluaudia procera (Madagascar ocotillo) and other vegetation.

Biodiversity plays an important role in ecosystem functioning.^[27] The reason for this is that ecosystem processes are driven by the number of species in an ecosystem, the exact nature of each individual species, and the relative abundance organisms within these species.^[28] Ecosystem processes are broad generalizations that actually take place through the actions of individual organisms. The nature of the organisms—the species, functional groups and trophic levels to which they belong—dictates the sorts of actions these individuals are capable of carrying out and the relative efficiency with which they do so.

Ecological theory suggests that in order to coexist, species must have some level of limiting similarity—they must be different from one another in some fundamental way, otherwise one species would competitively exclude the other.^[29] Despite this, the cumulative effect of additional species in an ecosystem is not linear—additional species may enhance nitrogen retention, for example, but beyond some level of species richness, additional species may have little additive effect.^[28]

The addition (or loss) of species which are ecologically similar to those already present in an ecosystem tends to only have a small effect on ecosystem function. Ecologically distinct species, on the other hand, have a much larger effect. Similarly, dominant species have a large effect on ecosystem function, while rare species tend to have a small effect. Keystone species tend to have an effect on ecosystem function that is disproportionate to their abundance in an ecosystem.^[28] Similarly, an ecosystem engineer is any organism that creates, significantly modifies, maintains or destroys a habitat.

Dynamics

Ecosystems are dynamic entities. They are subject to periodic disturbances and are in the process of recovering from some past disturbance.^[11] When a perturbation occurs, an ecoystem responds by moving away from its initial state. The tendency of an ecosystem to remain close to its equilibrium state, despite that disturbance, is termed its resistance. On the other hand, the speed with which it returns to its initial state after disturbance is called its resilience.^[11] Time plays a role in the development of soil from bare rock and the recovery of a community from disturbance.^[10]

From one year to another, ecosystems experience variation in their biotic and abiotic environments. A drought, an especially cold winter and a pest outbreak all constitute short-term variability in environmental conditions. Animal populations vary from year to year, building up during resource-rich periods and crashing as they overshoot their food supply. These changes play out in changes in net primary production decomposition rates, and other ecosystem processes.^[11] Longer-term changes also shape ecosystem processes—the forests of eastern North America still show legacies of cultivation which ceased 200 years ago, while methane production in eastern Siberian lakes is controlled by organic matter which accumulated during the Pleistocene.^[11]

Disturbance also plays an important role in ecological processes. F. Stuart Chapin and coauthors define disturbance as "a relatively discrete event in time and space that alters the structure of populations, communities, and ecosystems and causes changes in resources availability or the physical environment".^[30] This can range from tree falls and insect outbreaks to hurricanes and wildfires to volcanic eruptions. Such disturbances can cause large changes in plant, animal and microbe populations, as well soil organic matter content.^[11] Disturbance is followed by succession, a "directional change in ecosystem structure and functioning resulting from biotically driven changes in resources supply."^[30]

The frequency and severity of disturbance determine the way it affects ecosystem function. A major disturbance like a volcanic eruption or glacial advance and retreat leave behind soils that lack plants, animals or organic matter. Ecosystems that experience such disturbances undergo primary succession. A less severe disturbance like forest fires, hurricanes or cultivation result in secondary succession and a faster recovery.^[11] More severe disturbance and more frequent disturbance result in longer recovery times.

A freshwater ecosystem in Gran Canaria, an island of the

Canary Islands

Classification methods

Classifying ecosystems into ecologically homogeneous units is an important step towards effective ecosystem management.^[31] There is no single, agreed-upon way to do this. A variety of systems exist, based on vegetation cover, remote sensing, and bioclimatic classification systems.^[31]

Ecological land classification is a cartographical delineation or regionalisation of distinct ecological areas, identified by their geology, topography, soils, vegetation, climate conditions, living species, habitats, water resources, and sometimes also anthropic factors.^[32]

Human activities

Human activities are important in almost all ecosystems. Although humans exist and operate within ecosystems, their cumulative effects are large enough to influence external factors like climate.^[10]

Ecosystem goods and services

The High Peaks Wilderness Area in the 6,000,000-acre (2,400,000 ha) Adirondack Park is an example of a diverse ecosystem.

Ecosystems provide a variety of goods and services upon which people depend.^[33] Ecosystem goods include the "tangible, material products" of ecosystem processes such as food, construction material, medicinal plants.^[34] They also include less tangible items like tourism and recreation, and genes from wild plants and animals that can be used to improve domestic species.^[33]

Ecosystem services, on the other hand, are generally "improvements in the condition or location of things of value".^[34] These include things like the maintenance of hydrological cycles, cleaning air and water, the maintenance of oxygen in the atmosphere, crop pollination and even things like beauty, inspiration and opportunities for research.^[33] While ecosystem goods have traditionally been recognized as being the basis for things of economic value, ecosystem services tend to be taken for granted.^[34]

Ecosystem management

When natural resource management is applied to whole ecosystems, rather than single species, it is termed ecosystem management.^[35] Although definitions of ecosystem management abound, there is a common set of principles which underlie these definitions.^[36] A fundamental principle is the long-term sustainability of the production of goods and services by the ecosystem;^[36] "intergenerational sustainability [is] a precondition for management, not an afterthought".^[33]

While ecosystem management can be used as part of a plan for wilderness conservation, it can also be used in intensively managed ecosystems^[33] (see, for example, agroecosystem and close to nature forestry).

Threats caused by humans

As human populations and per capita consumption grow, so do the resource demands imposed on ecosystems and the effects of the human ecological footprint. Natural resources are vulnerable and limited. The environmental impacts of anthropogenic actions are becoming more apparent. Problems for all ecosystems include: environmental pollution, climate change and biodiversity loss. For terrestrial ecosystems further threats include air pollution, soil degradation, and deforestation. For aquatic ecosystems threats include also unsustainable exploitation of marine resources (for example overfishing of certain species), marine pollution, microplastics pollution, water pollution, and building on coastal areas.^[37]

Society is increasingly becoming aware that ecosystem services are not only limited but also that they are threatened by human activities. The need to better consider long-term ecosystem health and its role in enabling human habitation and economic activity is urgent. To help inform decision-makers, many ecosystem services are being assigned economic values, often based on the cost of replacement with anthropogenic alternatives. The ongoing challenge of prescribing economic value to nature, for example through biodiversity banking, is prompting transdisciplinary shifts in how we recognize and manage the environment, social responsibility, business opportunities, and our future as a species.

History

The term "ecosystem" was first used in 1935 in a publication by British ecologist Arthur Tansley.^{[fn 1][38]} Tansley devised the concept to draw attention to the importance of transfers of materials between organisms and their environment.^[39] He later refined the term, describing it as "The whole system, ... including not only the organism-complex, but also the whole complex of physical factors forming what we call the environment".^[40] Tansley regarded ecosystems not simply as natural units, but as "mental isolates".^[40] Tansley later defined the spatial extent of ecosystems using the term ecotope.^[41]

G. Evelyn Hutchinson, a limnologist who was a contemporary of Tansley's, combined Charles Elton's ideas about trophic ecology with those of Russian geochemist Vladimir Vernadsky. As a result, he suggested that mineral nutrient availability in a lake limited algal production. This would, in turn, limit the abundance of animals that feed on algae. Raymond Lindeman took these ideas further to suggest that the flow of energy through a lake was the primary driver of the ecosystem. Hutchinson's students, brothers Howard T. Odum and Eugene P. Odum, further developed a "systems approach" to the study of ecosystems. This allowed them to study the flow of energy and material through ecological systems.

Theoretical ecology

From Wikipedia, the free encyclopedia

Mathematical models developed in theoretical ecology predict complex food webs are less stable than simple webs.^{[1]:75–77[2]:64}

Life on Earth-Flow of Energy and Entropy

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.

The field is broad and includes foundations in applied mathematics, computer science, biology, statistical physics, genetics, chemistry, evolution, and conservation biology. Theoretical ecology aims to explain a diverse range of phenomena in the life sciences, such as population growth and dynamics, fisheries, competition, evolutionary theory, epidemiology, animal behavior and group dynamics, food webs, ecosystems, spatial ecology, and the effects of climate change.

Theoretical ecology has further benefited from the advent of fast computing power, allowing the analysis and visualization of large-scale computational simulations of ecological phenomena. Importantly, these modern tools provide quantitative predictions about the effects of human induced environmental change on a diverse variety of ecological phenomena, such as: species invasions, climate change, the effect of fishing and hunting on food network stability, and the global carbon cycle.

Modelling approaches

As in most other sciences, mathematical models form the foundation of modern ecological theory.

• Phenomenological models: distill the functional and distributional shapes from observed patterns in the data, or researchers decide on functions and distribution that are flexible enough to match the patterns they or others (field or experimental ecologists) have found in the field or through experimentation.^[3]
• Mechanistic models: model the underlying processes directly, with functions and distributions that are based on theoretical reasoning about ecological processes of interest.^[3]

Ecological models can be deterministic or stochastic.^[3]

• Deterministic models always evolve in the same way from a given starting point.^[4] They represent the average, expected behavior of a system, but lack random variation. Many system dynamics models are deterministic.
• Stochastic models allow for the direct modeling of the random perturbations that underlie real world ecological systems. Markov chain models are stochastic.

Species can be modelled in continuous or discrete time.^[5]

• Continuous time is modelled using differential equations.
• Discrete time is modelled using difference equations. These model ecological processes that can be described as occurring over discrete time steps. Matrix algebra is often used to investigate the evolution of age-structured or stage-structured populations. The Leslie matrix, for example, mathematically represents the discrete time change of an age structured population.^[6][7][8]

Models are often used to describe real ecological reproduction processes of single or multiple species. These can be modelled using stochastic branching processes. Examples are the dynamics of interacting populations (predation competition and mutualism), which, depending on the species of interest, may best be modeled over either continuous or discrete time. Other examples of such models may be found in the field of mathematical epidemiology where the dynamic relationships that are to be modeled are host–pathogen interactions.^[5]

Bifurcation diagram of the logistic map

Bifurcation theory is used to illustrate how small changes in parameter values can give rise to dramatically different long run outcomes, a mathematical fact that may be used to explain drastic ecological differences that come about in qualitatively very similar systems.^[9] Logistic maps are polynomial mappings, and are often cited as providing archetypal examples of how chaotic behaviour can arise from very simple non-linear dynamical equations. The maps were popularized in a seminal 1976 paper by the theoretical ecologist Robert May.^[10] The difference equation is intended to capture the two effects of reproduction and starvation.

In 1930, R.A. Fisher published his classic The Genetical Theory of Natural Selection, which introduced the idea that frequency-dependent fitness brings a strategic aspect to evolution, where the payoffs to a particular organism, arising from the interplay of all of the relevant organisms, are the number of this organism' s viable offspring.^[11] In 1961, Richard Lewontin applied game theory to evolutionary biology in his Evolution and the Theory of Games,^[12] followed closely by John Maynard Smith, who in his seminal 1972 paper, “Game Theory and the Evolution of Fighting",^[13] defined the concept of the evolutionarily stable strategy.

Because ecological systems are typically nonlinear, they often cannot be solved analytically and in order to obtain sensible results, nonlinear, stochastic and computational techniques must be used. One class of computational models that is becoming increasingly popular are the agent-based models. These models can simulate the actions and interactions of multiple, heterogeneous, organisms where more traditional, analytical techniques are inadequate. Applied theoretical ecology yields results which are used in the real world. For example, optimal harvesting theory draws on optimization techniques developed in economics, computer science and operations research, and is widely used in fisheries.^[14]

Population ecology

Population ecology is a sub-field of ecology that deals with the dynamics of species populations and how these populations interact with the environment.^[15] It is the study of how the population sizes of species living together in groups change over time and space, and was one of the first aspects of ecology to be studied and modelled mathematically.

Exponential growth

The most basic way of modeling population dynamics is to assume that the rate of growth of a population depends only upon the population size at that time and the per capita growth rate of the organism. In other words, if the number of individuals in a population at a time t, is N(t), then the rate of population growth is given by:

${\displaystyle {\frac {dN(t)}{dt}}=rN(t)}$

where r is the per capita growth rate, or the intrinsic growth rate of the organism. It can also be described as r = b-d, where b and d are the per capita time-invariant birth and death rates, respectively. This first order linear differential equation can be solved to yield the solution

${\displaystyle N(t)=N(0)\ e^{rt}}$,

a trajectory known as Malthusian growth, after Thomas Malthus, who first described its dynamics in 1798. A population experiencing Malthusian growth follows an exponential curve, where N(0) is the initial population size. The population grows when r > 0, and declines when r < 0. The model is most applicable in cases where a few organisms have begun a colony and are rapidly growing without any limitations or restrictions impeding their growth (e.g. bacteria inoculated in rich media).

Logistic growth

The exponential growth model makes a number of assumptions, many of which often do not hold. For example, many factors affect the intrinsic growth rate and is often not time-invariant. A simple modification of the exponential growth is to assume that the intrinsic growth rate varies with population size. This is reasonable: the larger the population size, the fewer resources available, which can result in a lower birth rate and higher death rate. Hence, we can replace the time-invariant r with r’(t) = (b –a*N(t)) – (d + c*N(t)), where a and c are constants that modulate birth and death rates in a population dependent manner (e.g. intraspecific competition). Both a and c will depend on other environmental factors which, we can for now, assume to be constant in this approximated model. The differential equation is now:^[16]

${\displaystyle {\frac {dN(t)}{dt}}=((b-aN(t))-(d-cN(t)))N(t)}$

This can be rewritten as:^[16]

${\displaystyle {\frac {dN(t)}{dt}}=rN(t)\left(1-{\frac {N}{K}}\right)}$

where r = b-d and K = (b-d)/(a+c).

The biological significance of K becomes apparent when stabilities of the equilibria of the system are considered. The constant K is the carrying capacity of the population. The equilibria of the system are N = 0 and N = K. If the system is linearized, it can be seen that N = 0 is an unstable equilibrium while K is a stable equilibrium.^[16]

Structured population growth

Another assumption of the exponential growth model is that all individuals within a population are identical and have the same probabilities of surviving and of reproducing. This is not a valid assumption for species with complex life histories. The exponential growth model can be modified to account for this, by tracking the number of individuals in different age classes (e.g. one-, two-, and three-year-olds) or different stage classes (juveniles, sub-adults, and adults) separately, and allowing individuals in each group to have their own survival and reproduction rates. The general form of this model is

${\displaystyle \mathbf {N} _{t+1}=\mathbf {L} \mathbf {N} _{t}}$

where N_t is a vector of the number of individuals in each class at time t and L is a matrix that contains the survival probability and fecundity for each class. The matrix L is referred to as the Leslie matrix for age-structured models, and as the Lefkovitch matrix for stage-structured models.

If parameter values in L are estimated from demographic data on a specific population, a structured model can then be used to predict whether this population is expected to grow or decline in the long-term, and what the expected age distribution within the population will be. This has been done for a number of species including loggerhead sea turtles and right whales.^[18][19]

Community ecology

An ecological community is a group of trophically similar, sympatric species that actually or potentially compete in a local area for the same or similar resources.^[20] Interactions between these species form the first steps in analyzing more complex dynamics of ecosystems. These interactions shape the distribution and dynamics of species. Of these interactions, predation is one of the most widespread population activities.^[21] Taken in its most general sense, predation comprises predator–prey, host–pathogen, and host–parasitoid interactions.

Lotka–Volterra model of cheetah–baboon interactions. Starting with 80 baboons (green) and 40 cheetahs, this graph shows how the model predicts the two species numbers will progress over time.

Predator–prey interaction

Predator–prey interactions exhibit natural oscillations in the populations of both predator and the prey.^[21] In 1925, the American mathematician Alfred J. Lotka developed simple equations for predator–prey interactions in his book on biomathematics.^[22] The following year, the Italian mathematician Vito Volterra, made a statistical analysis of fish catches in the Adriatic^[23] and independently developed the same equations.^[24] It is one of the earliest and most recognised ecological models, known as the Lotka-Volterra model:

${\displaystyle {\frac {dN(t)}{dt}}=N(t)(r-\alpha P(t))}$

${\displaystyle {\frac {dP(t)}{dt}}=P(t)(c\alpha N(t)-d)}$

where N is the prey and P is the predator population sizes, r is the rate for prey growth, taken to be exponential in the absence of any predators, α is the prey mortality rate for per-capita predation (also called ‘attack rate’), c is the efficiency of conversion from prey to predator, and d is the exponential death rate for predators in the absence of any prey.

Volterra originally used the model to explain fluctuations in fish and shark populations after fishing was curtailed during the First World War. However, the equations have subsequently been applied more generally.^[25] Other examples of these models include the Lotka-Volterra model of the snowshoe hare and Canadian lynx in North America,^[26] any infectious disease modeling such as the recent outbreak of SARS ^[27] and biological control of California red scale by the introduction of its parasitoid, Aphytis melinus .^[28]

A credible, simple alternative to the Lotka-Volterra predator–prey model and their common prey dependent generalizations is the ratio dependent or Arditi-Ginzburg model.^[29] The two are the extremes of the spectrum of predator interference models. According to the authors of the alternative view, the data show that true interactions in nature are so far from the Lotka–Volterra extreme on the interference spectrum that the model can simply be discounted as wrong. They are much closer to the ratio-dependent extreme, so if a simple model is needed one can use the Arditi–Ginzburg model as the first approximation.^[30]

Host–pathogen interaction

The second interaction, that of host and pathogen, differs from predator–prey interactions in that pathogens are much smaller, have much faster generation times, and require a host to reproduce. Therefore, only the host population is tracked in host–pathogen models. Compartmental models that categorize host population into groups such as susceptible, infected, and recovered (SIR) are commonly used.^[31]

Host–parasitoid interaction

The third interaction, that of host and parasitoid, can be analyzed by the Nicholson-Bailey model, which differs from Lotka-Volterra and SIR models in that it is discrete in time. This model, like that of Lotka-Volterra, tracks both populations explicitly. Typically, in its general form, it states:

${\displaystyle N_{t+1}=\lambda \ N_{t}\ [1-f(N_{t},P_{t})]}$

${\displaystyle P_{t+1}=c\ N_{t}\ f(N_{t},p_{t})}$

where f(N_t, P_t) describes the probability of infection (typically, Poisson distribution), λ is the per-capita growth rate of hosts in the absence of parasitoids, and c is the conversion efficiency, as in the Lotka-Volterra model.^[21]

Competition and mutualism

In studies of the populations of two species, the Lotka-Volterra system of equations has been extensively used to describe dynamics of behavior between two species, N₁ and N₂. Examples include relations between D. discoiderum and E. coli,^[32] as well as theoretical analysis of the behavior of the system.^[33]

${\displaystyle {\frac {dN_{1}}{dt}}={\frac {r_{1}N_{1}}{K_{1}}}\left(K_{1}-N_{1}+\alpha _{12}N_{2}\right)}$

${\displaystyle {\frac {dN_{2}}{dt}}={\frac {r_{2}N_{2}}{K_{2}}}\left(K_{2}-N_{2}+\alpha _{21}N_{1}\right)}$

The r coefficients give a “base” growth rate to each species, while K coefficients correspond to the carrying capacity. What can really change the dynamics of a system, however are the α terms. These describe the nature of the relationship between the two species. When α₁₂ is negative, it means that N₂ has a negative effect on N₁, by competing with it, preying on it, or any number of other possibilities. When α₁₂ is positive, however, it means that N₂ has a positive effect on N₁, through some kind of mutualistic interaction between the two. When both α₁₂ and α₂₁ are negative, the relationship is described as competitive. In this case, each species detracts from the other, potentially over competition for scarce resources. When both α₁₂ and α₂₁ are positive, the relationship becomes one of mutualism. In this case, each species provides a benefit to the other, such that the presence of one aids the population growth of the other.

Neutral theory

Unified neutral theory is a hypothesis proposed by Stephen Hubbell in 2001.^[20] The hypothesis aims to explain the diversity and relative abundance of species in ecological communities, although like other neutral theories in ecology, Hubbell's hypothesis assumes that the differences between members of an ecological community of trophically similar species are "neutral," or irrelevant to their success. Neutrality means that at a given trophic level in a food web, species are equivalent in birth rates, death rates, dispersal rates and speciation rates, when measured on a per-capita basis.^[34] This implies that biodiversity arises at random, as each species follows a random walk.^[35] This can be considered a null hypothesis to niche theory. The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.

Under unified neutral theory, complex ecological interactions are permitted among individuals of an ecological community (such as competition and cooperation), providing all individuals obey the same rules. Asymmetric phenomena such as parasitism and predation are ruled out by the terms of reference; but cooperative strategies such as swarming, and negative interaction such as competing for limited food or light are allowed, so long as all individuals behave the same way. The theory makes predictions that have implications for the management of biodiversity, especially the management of rare species. It predicts the existence of a fundamental biodiversity constant, conventionally written θ, that appears to govern species richness on a wide variety of spatial and temporal scales.

Hubbell built on earlier neutral concepts, including MacArthur & Wilson's theory of island biogeography^[20] and Gould's concepts of symmetry and null models.^[34]

Spatial ecology

Biogeography

Biogeography is the study of the distribution of species in space and time. It aims to reveal where organisms live, at what abundance, and why they are (or are not) found in a certain geographical area.
Biogeography is most keenly observed on islands, which has led to the development of the subdiscipline of island biogeography. These habitats are often a more manageable areas of study because they are more condensed than larger ecosystems on the mainland. In 1967, Robert MacArthur and E.O. Wilson published The Theory of Island Biogeography. This showed that the species richness in an area could be predicted in terms of factors such as habitat area, immigration rate and extinction rate.^[36] The theory is considered one of the fundamentals of ecological theory.^[37] The application of island biogeography theory to habitat fragments spurred the development of the fields of conservation biology and landscape ecology.^[38]

r/K-selection theory

A population ecology concept is r/K selection theory, one of the first predictive models in ecology used to explain life-history evolution. The premise behind the r/K selection model is that natural selection pressures change according to population density. For example, when an island is first colonized, density of individuals is low. The initial increase in population size is not limited by competition, leaving an abundance of available resources for rapid population growth. These early phases of population growth experience density-independent forces of natural selection, which is called r-selection. As the population becomes more crowded, it approaches the island's carrying capacity, thus forcing individuals to compete more heavily for fewer available resources. Under crowded conditions, the population experiences density-dependent forces of natural selection, called K-selection.^[39][40]
 

The diversity and containment of coral reef systems make them good sites for testing niche and neutral theories.^[41]

Metapopulations

Spatial analysis of ecological systems often reveals that assumptions that are valid for spatially homogenous populations – and indeed, intuitive – may no longer be valid when migratory subpopulations moving from one patch to another are considered.^[42] In a simple one-species formulation, a subpopulation may occupy a patch, move from one patch to another empty patch, or die out leaving an empty patch behind. In such a case, the proportion of occupied patches may be represented as

${\displaystyle {\frac {dp}{dt}}=mp(1-p)-ep}$

where m is the rate of colonization, and e is the rate of extinction.^[43] In this model, if e < m, the steady state value of p is 1 – (e/m) while in the other case, all the patches will eventually be left empty. This model may be made more complex by addition of another species in several different ways, including but not limited to game theoretic approaches, predator–prey interactions, etc. We will consider here an extension of the previous one-species system for simplicity. Let us denote the proportion of patches occupied by the first population as p₁, and that by the second as p₂. Then,

${\displaystyle {\frac {dp_{1}}{dt}}=m_{1}p_{1}(1-p_{1})-ep_{1}}$

${\displaystyle {\frac {dp_{2}}{dt}}=m_{2}p_{2}(1-p_{1}-p_{2})-ep_{2}-mp_{1}p_{2}}$

In this case, if e is too high, p₁ and p₂ will be zero at steady state. However, when the rate of extinction is moderate, p₁ and p₂ can stably coexist. The steady state value of p₂ is given by

${\displaystyle p_{2}^{*}={\frac {e}{m_{1}}}-{\frac {m_{1}}{m_{2}}}}$

(p*₁ may be inferred by symmetry). It is interesting to note that if e is zero, the dynamics of the system favor the species that is better at colonizing (i.e. has the higher m value). This leads to a very important result in theoretical ecology known as the Intermediate Disturbance Hypothesis, where the biodiversity (the number of species that coexist in the population) is maximized when the disturbance (of which e is a proxy here) is not too high or too low, but at intermediate levels.^[44]

The form of the differential equations used in this simplistic modelling approach can be modified. For example:

1. Colonization may be dependent on p linearly (m*(1-p)) as opposed to the non-linear m*p*(1-p) regime described above. This mode of replication of a species is called the “rain of propagules”, where there is an abundance of new individuals entering the population at every generation. In such a scenario, the steady state where the population is zero is usually unstable.^[45]
2. Extinction may depend non-linearly on p (e*p*(1-p)) as opposed to the linear (e*p) regime described above. This is referred to as the “rescue effect” and it is again harder to drive a population extinct under this regime.^[45]

The model can also be extended to combinations of the four possible linear or non-linear dependencies of colonization and extinction on p are described in more detail in.^[46]

Ecosystem ecology

Introducing new elements, whether biotic or abiotic, into ecosystems can be disruptive. In some cases, it leads to ecological collapse, trophic cascades and the death of many species within the ecosystem. The abstract notion of ecological health attempts to measure the robustness and recovery capacity for an ecosystem; i.e. how far the ecosystem is away from its steady state. Often, however, ecosystems rebound from a disruptive agent. The difference between collapse or rebound depends on the toxicity of the introduced element and the resiliency of the original ecosystem.

If ecosystems are governed primarily by stochastic processes, through which its subsequent state would be determined by both predictable and random actions, they may be more resilient to sudden change than each species individually. In the absence of a balance of nature, the species composition of ecosystems would undergo shifts that would depend on the nature of the change, but entire ecological collapse would probably be infrequent events. In 1997, Robert Ulanowicz used information theory tools to describe the structure of ecosystems, emphasizing mutual information (correlations) in studied systems. Drawing on this methodology and prior observations of complex ecosystems, Ulanowicz depicts approaches to determining the stress levels on ecosystems and predicting system reactions to defined types of alteration in their settings (such as increased or reduced energy flow, and eutrophication.^[47]

Ecopath is a free ecosystem modelling software suite, initially developed by NOAA, and widely used in fisheries management as a tool for modelling and visualising the complex relationships that exist in real world marine ecosystems.

Food webs

Food webs provide a framework within which a complex network of predator–prey interactions can be organised. A food web model is a network of food chains. Each food chain starts with a primary producer or autotroph, an organism, such as a plant, which is able to manufacture its own food. Next in the chain is an organism that feeds on the primary producer, and the chain continues in this way as a string of successive predators. The organisms in each chain are grouped into trophic levels, based on how many links they are removed from the primary producers. The length of the chain, or trophic level, is a measure of the number of species encountered as energy or nutrients move from plants to top predators.^[48] Food energy flows from one organism to the next and to the next and so on, with some energy being lost at each level. At a given trophic level there may be one species or a group of species with the same predators and prey.^[49]

In 1927, Charles Elton published an influential synthesis on the use of food webs, which resulted in them becoming a central concept in ecology.^[50] In 1966, interest in food webs increased after Robert Paine's experimental and descriptive study of intertidal shores, suggesting that food web complexity was key to maintaining species diversity and ecological stability.^[51] Many theoretical ecologists, including Sir Robert May and Stuart Pimm, were prompted by this discovery and others to examine the mathematical properties of food webs. According to their analyses, complex food webs should be less stable than simple food webs.^{[1]:75–77[2]:64} The apparent paradox between the complexity of food webs observed in nature and the mathematical fragility of food web models is currently an area of intensive study and debate. The paradox may be due partially to conceptual differences between persistence of a food web and equilibrial stability of a food web.^[1][2]

Systems ecology

Systems ecology can be seen as an application of general systems theory to ecology. It takes a holistic and interdisciplinary approach to the study of ecological systems, and particularly ecosystems. Systems ecology is especially concerned with the way the functioning of ecosystems can be influenced by human interventions. Like other fields in theoretical ecology, it uses and extends concepts from thermodynamics and develops other macroscopic descriptions of complex systems. It also takes account of the energy flows through the different trophic levels in the ecological networks. In systems ecology the principles of ecosystem energy flows are considered formally analogous to the principles of energetics. Systems ecology also considers the external influence of ecological economics, which usually is not otherwise considered in ecosystem ecology.^[52] For the most part, systems ecology is a subfield of ecosystem ecology.

Ecophysiology

This is the study of how "the environment, both physical and biological, interacts with the physiology of an organism. It includes the effects of climate and nutrients on physiological processes in both plants and animals, and has a particular focus on how physiological processes scale with organism size".^[53][54]

Behavioral ecology

Swarm behaviour

Flocks of birds can abruptly change their direction in unison, and then, just as suddenly, make a unanimous group decision to land.^[55]

Swarm behaviour is a collective behaviour exhibited by animals of similar size which aggregate together, perhaps milling about the same spot or perhaps migrating in some direction. Swarm behaviour is commonly exhibited by insects, but it also occurs in the flocking of birds, the schooling of fish and the herd behaviour of quadrupeds. It is a complex emergent behaviour that occurs when individual agents follow simple behavioral rules.

Recently, a number of mathematical models have been discovered which explain many aspects of the emergent behaviour. Swarm algorithms follow a Lagrangian approach or an Eulerian approach.^[56] The Eulerian approach views the swarm as a field, working with the density of the swarm and deriving mean field properties. It is a hydrodynamic approach, and can be useful for modelling the overall dynamics of large swarms.^[57][58][59] However, most models work with the Lagrangian approach, which is an agent-based model following the individual agents (points or particles) that make up the swarm. Individual particle models can follow information on heading and spacing that is lost in the Eulerian approach.^[56][60] Examples include ant colony optimization, self-propelled particles and particle swarm optimization

Evolutionary ecology

The British biologist Alfred Russel Wallace is best known for independently proposing a theory of evolution due to natural selection that prompted Charles Darwin to publish his own theory. In his famous 1858 paper, Wallace proposed natural selection as a kind of feedback mechanism which keeps species and varieties adapted to their environment.^[61]

The action of this principle is exactly like that of the centrifugal governor of the steam engine, which checks and corrects any irregularities almost before they become evident; and in like manner no unbalanced deficiency in the animal kingdom can ever reach any conspicuous magnitude, because it would make itself felt at the very first step, by rendering existence difficult and extinction almost sure soon to follow.^[62]

The cybernetician and anthropologist Gregory Bateson observed in the 1970s that, though writing it only as an example, Wallace had "probably said the most powerful thing that’d been said in the 19th Century".^[63] Subsequently, the connection between natural selection and systems theory has become an area of active research.^[61]

Other theories

In contrast to previous ecological theories which considered floods to be catastrophic events, the river flood pulse concept argues that the annual flood pulse is the most important aspect and the most biologically productive feature of a river's ecosystem.^[64][65]

History

Theoretical ecology draws on pioneering work done by G. Evelyn Hutchinson and his students. Brothers H.T. Odum and E.P. Odum are generally recognised as the founders of modern theoretical ecology. Robert MacArthur brought theory to community ecology. Daniel Simberloff was the student of E.O. Wilson, with whom MacArthur collaborated on The Theory of Island Biogeography, a seminal work in the development of theoretical ecology.^[66]

Simberloff added statistical rigour to experimental ecology and was a key figure in the SLOSS debate, about whether it is preferable to protect a single large or several small reserves.^[67] This resulted in the supporters of Jared Diamond's community assembly rules defending their ideas through Neutral Model Analysis.^[67] Simberloff also played a key role in the (still ongoing) debate on the utility of corridors for connecting isolated reserves.

Stephen Hubbell and Michael Rosenzweig combined theoretical and practical elements into works that extended MacArthur and Wilson's Island Biogeography Theory - Hubbell with his Unified Neutral Theory of Biodiversity and Biogeography and Rosenzweig with his Species Diversity in Space and Time.