70:. 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.
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208:
40:
2094:. In this model, if e < m, the steady state value of p is 1 â (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, predatorâprey 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 p
2635:, 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. 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
1159:. 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 LotkaâVolterra 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 ArditiâGinzburg model as the first approximation.
491:, 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).
1964:
901:
283:. 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
1177:, differs from predatorâprey 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 hostâpathogen models. Compartmental models that categorize host population into groups such as susceptible, infected, and recovered (SIR) are commonly used.
28:
506:
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 râ(t) = (b âa*N(t)) â (d + c*N(t)), where a and c are constants that modulate birth and death rates in a population dependent manner (e.g.
2807:(SPPs) and collectively display phase transition from ordered movement to disordered movements. Previously, it was thought that the surface-to-volume ratio was what limited the animal size in the evolutionary game. Considering the collective behaviour of the individuals, it was suggested that order is another limiting factor.
758:
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
2570:(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
2689:
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
1114:
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 âattack rateâ), c is the efficiency of conversion from prey to predator, and d is the
2876:
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
505:
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
337:
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
2658:
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
757:
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
115:
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
2483:
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 ârain of propagulesâ, where there is an abundance of new individuals entering the population at every generation. In such a
896:
species that actually or potentially compete in a local area for the same or similar resources. 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,
73:
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
2009:
Spatial analysis of ecological systems often reveals that assumptions that are valid for spatially homogenous populations â and indeed, intuitive â may no longer be valid when migratory subpopulations moving from one patch to another are considered. In a simple one-species formulation, a
1956:-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
1711:
The r coefficients give a âbaseâ 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
1906:. 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. The theory is considered one of the fundamentals of ecological theory. The application of island biogeography theory to
2607:, 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
218:
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.
2533:
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
1706:
1566:
2773:, 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. However, most models work with the Lagrangian approach, which is an
93:
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
279:, 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
2824:
firefly will synchronize their shining frequencies in a collective setting. Individually, there are no apparent patterns for the flashing. In a group setting, periodicity emerges in the shining pattern. The coexistence of the
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2467:
may be inferred by symmetry). 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
2611:, 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.
98:
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
3000:
A tentative distinction can be made between mathematical ecologists, ecologists who apply mathematics to ecological problems, and mathematicians who develop the mathematics itself that arises out of ecological problems.
1796:
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
2890:
observed in the 1970s that, though writing it only as an example, Wallace had "probably said the most powerful thing thatâd been said in the 19th
Century". Subsequently, the connection between natural selection and
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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.
731:
408:
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
2458:
2978:'s community assembly rules defending their ideas through Neutral Model Analysis. Simberloff also played a key role in the (still ongoing) debate on the utility of corridors for connecting isolated reserves.
2777:
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. Examples include
2208:
1836:, 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
814:
1805:, species are equivalent in birth rates, death rates, dispersal rates and speciation rates, when measured on a per-capita basis. This implies that biodiversity arises at random, as each species follows a
1193:, 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:
865:
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
635:
4039:
2549:
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
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experimental and descriptive study of intertidal shores, suggesting that food web complexity was key to maintaining species diversity and ecological stability. Many theoretical ecologists, including
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2010:
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
1381:
904:
LotkaâVolterra model of cheetahâbaboon interactions. Starting with 80 baboons (green) and 40 cheetahs, this graph shows how the model predicts the two species numbers will progress over time.
1885:
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.
924:, made a statistical analysis of fish catches in the Adriatic and independently developed the same equations. It is one of the earliest and most recognised ecological models, known as the
2833:
has been useful in describing this unique phenomenon. The flashings of individual fireflies could be viewed as oscillators and the global coupling models were similar to the ones used in
5684:
2081:
1940:. 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
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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.
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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.
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403:
1976:
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Benke, A. C., Chaubey, I., Ward, G. M., & Dunn, E. L. (2000). Flood Pulse
Dynamics of an Unregulated River Floodplain in the Southeastern U.S. Coastal Plain. Ecology, 2730-2741.
897:
predation is one of the most widespread population activities. Taken in its most general sense, predation comprises predatorâprey, hostâpathogen, and hostâparasitoid interactions.
2829:
and asynchronization in the flashings in the system composed of multiple fireflies could be characterized by the chimera states. Synchronization could spontaneously occur. The
1572:
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477:
5307:
Thorp, J. H., & Delong, M. D. (1994). The
Riverine Productivity Model: An Heuristic View of Carbon Sources and Organic Processing in Large River Ecosystems. Oikos, 305-308
2476:(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.
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119:
Mechanistic models: model the underlying processes directly, with functions and distributions that are based on theoretical reasoning about ecological processes of interest.
2495:
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.
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2623:
published an influential synthesis on the use of food webs, which resulted in them becoming a central concept in ecology. In 1966, interest in food webs increased after
256:, 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. In 1961,
196:), 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
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1406:
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, N
510:). 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:
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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,
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2584:, and widely used in fisheries management as a tool for modelling and visualising the complex relationships that exist in real world marine ecosystems.
323:
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.
3995:
John D. Reeve; Wiliam W. Murdoch (1986). "Biological
Control by the Parasitoid Aphytis melinus, and Population Stability of the California Red Scale".
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Deterministic models always evolve in the same way from a given starting point. They represent the average, expected behavior of a system, but lack
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A credible, simple alternative to the Lotka-Volterra predatorâprey model and their common prey dependent generalizations is the ratio dependent or
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1126:. However, the equations have subsequently been applied more generally. Other examples of these models include the Lotka-Volterra model of the
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Recently, a number of mathematical models have been discovered which explain many aspects of the emergent behaviour. Swarm algorithms follow a
1793:
1785:
1780:
1398:), 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.
185:
Models are often used to describe real ecological reproduction processes of single or multiple species. These can be modelled using stochastic
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1892:. These habitats are often a more manageable areas of study because they are more condensed than larger ecosystems on the mainland. In 1967,
1817:. The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.
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646:
6684:
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3670:
D.T.Crouse, L.B. Crowder, H.Caswell (1987). "A stage-based population model for loggerhead sea turtles and implications for conservation".
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combined theoretical and practical elements into works that extended MacArthur and Wilson's Island
Biogeography Theory - Hubbell with his
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2675:, which usually is not otherwise considered in ecosystem ecology. For the most part, systems ecology is a subfield of ecosystem ecology.
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739:
The biological significance of K becomes apparent when stabilities of the equilibria of the system are considered. The constant K is the
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5122:
Sarfati, Raphael; Joshi, Kunaal; Martin, Owen; Hayes, Julie C; Iyer-Biswas, Srividya; Peleg, Orit (2023-03-13). Giardina, Irene (ed.).
2487:
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 â
1792:
in 2001. The hypothesis aims to explain the diversity and relative abundance of species in ecological communities, although like other
920:
developed simple equations for predatorâprey interactions in his book on biomathematics. The following year, the
Italian mathematician
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1840:, especially the management of rare species. It predicts the existence of a fundamental biodiversity constant, conventionally written
1760:. In this case, each species provides a benefit to the other, such that the presence of one aids the population growth of the other.
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provide a framework within which a complex network of predatorâprey interactions can be organised. A food web model is a network of
1902:
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516:
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Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L, Gopalakrishna G, Chew SK, Tan CC, Samore MH, Fisman D, Murray M (2003).
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interactions exhibit natural oscillations in the populations of both predator and the prey. In 1925, the
American mathematician
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First introduced in MacArthur & Wilson's (1967) book of notable mention in the history and theoretical science of ecology,
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Flocks of birds can abruptly change their direction in unison, and then, just as suddenly, make a unanimous group decision
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2709:
1972:
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2974:, about whether it is preferable to protect a single large or several small reserves. This resulted in the supporters of
146:
Stochastic models allow for the direct modeling of the random perturbations that underlie real world ecological systems.
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are where individuals act based on their own decisions without overarching guidance. Studies have shown that individual
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413:
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39:
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Bonsall, Michael B.; Hassell, Michael P. (2007). "Predatorâprey interactions". In May, Robert; McLean, Angela (eds.).
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2624:
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1748:. In this case, each species detracts from the other, potentially over competition for scarce resources. When both α
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1932:
A population ecology concept is r/K selection theory, one of the first predictive models in ecology used to explain
207:
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Grenfell, Bryan; Keeling, Matthew (2007). "Dynamics of infectious disease". In May, Robert; McLean, Angela (eds.).
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1824:(such as competition and cooperation), providing all individuals obey the same rules. Asymmetric phenomena such as
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This applies to
British and American academics; landscape ecology has a distinct genesis among European academics.
2911:
argues that the annual flood pulse is the most important aspect and the most biologically productive feature of a
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2016:
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The form of the differential equations used in this simplistic modelling approach can be modified. For example:
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exhibited by animals of similar size which aggregate together, perhaps milling about the same spot or perhaps
5059:"Growth produces coordination trade-offs in Trichoplax adhaerens, an animal lacking a central nervous system"
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Topaz C, Bertozzi A (2004). "Swarming patterns in a two-dimensional kinematic model for biological groups".
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Biogeography is most keenly observed on islands, which has led to the development of the subdiscipline of
1745:
1701:{\displaystyle {\frac {dN_{2}}{dt}}={\frac {r_{2}N_{2}}{K_{2}}}\left(K_{2}-N_{2}+\alpha _{21}N_{1}\right)}
1561:{\displaystyle {\frac {dN_{1}}{dt}}={\frac {r_{1}N_{1}}{K_{1}}}\left(K_{1}-N_{1}+\alpha _{12}N_{2}\right)}
79:
268:, who in his seminal 1972 paper, âGame Theory and the Evolution of Fighting", defined the concept of the
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Carrillo, J; Fornasier, M; Toscani, G (2010). "Particle, kinetic, and hydrodynamic models of swarming".
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4608:
Ilkka Hanski (1982). "Dynamics of
Regional Distribution: The Core and Satellite Species Hypothesis".
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Volterra, V (1926). "Variazioni e fluttuazioni del numero d'individui in specie animali conviventi".
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1937:
1936:. The premise behind the r/K selection model is that natural selection pressures change according to
1911:
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839:
174:
95:
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Hubbell, S. P. (2005). "The neutral theory of biodiversity and biogeography and Stephen Jay Gould".
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Under unified neutral theory, complex ecological interactions are permitted among individuals of an
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dynamical equations. The maps were popularized in a seminal 1976 paper by the theoretical ecologist
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181:, for example, mathematically represents the discrete time change of an age structured population.
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is often used to investigate the evolution of age-structured or stage-structured populations. The
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5018:. Modeling and Simulation in Science, Engineering and Technology. Vol. 3. pp. 297â336.
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Toner J and Tu Y (1995) "Long-range order in a two-dimensional xy model: how birds fly together"
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1941:
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239:. The difference equation is intended to capture the two effects of reproduction and starvation.
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59:
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173:. These model ecological processes that can be described as occurring over discrete time steps.
111:
As in most other sciences, mathematical models form the foundation of modern ecological theory.
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in some direction. Swarm behaviour is commonly exhibited by insects, but it also occurs in the
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Volterra originally used the model to explain fluctuations in fish and shark populations after
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Topaz C, Bertozzi A, Lewis M (2006). "A nonlocal continuum model for biological aggregation".
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4351:
4287:
4171:
4100:
3977:
3760:
3638:
3609:
3599:
3550:
3500:
3438:
3413:
3390:
3367:
3344:
3323:
3274:
3244:"Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series"
3225:
3197:
3169:
2950:
2946:
2860:
2830:
2774:
2551:
2530:
1945:
1915:
1860:
887:
740:
484:
280:
186:
3853:
Goel, N.S. et al., "On the Volterra and Other Non-Linear Models of Interacting Populations",
2663:
and develops other macroscopic descriptions of complex systems. It also takes account of the
7527:
7390:
7382:
7300:
7182:
7167:
7103:
7083:
7000:
6990:
6985:
6950:
6782:
6722:
6593:
6394:
6336:
6248:
6208:
5962:
5934:
5623:
5376:
5368:
5208:
5192:
5135:
5094:
5078:
5029:
4975:
4930:
4863:
4744:
4681:
4625:
4541:
4471:
4461:
4408:
4343:
4279:
4236:
4198:
4189:
Takeuchi, Y. (1989). "Cooperative systems theory and global stability of diffusion models".
4161:
4153:
4062:
4012:
3967:
3959:
3918:
3752:
3687:
3542:
3492:
3266:
3219:
3077:
2942:
2735:
2600:
2559:
2510:
2504:
1893:
1844:, that appears to govern species richness on a wide variety of spatial and temporal scales.
1814:
1422:
827:
257:
136:
55:
4394:"r- and K-selection revisited: The role of population regulation in life-history evolution"
3735:
M. Fujiwara; H. Caswell (2001). "Demography of the endangered North Atlantic right whale".
7663:
7522:
7492:
7487:
7477:
7410:
7395:
7275:
7255:
7137:
7005:
6911:
6802:
6712:
6654:
6639:
6238:
6164:
6113:
6096:
6070:
6027:
6022:
5997:
5967:
3092:
2912:
2887:
2826:
2770:
2727:
2647:
2526:
1872:
1810:
1148:
1123:
917:
500:
320:
252:, which introduced the idea that frequency-dependent fitness brings a strategic aspect to
140:
3132:
3062:
5609:
5188:
5099:
5074:
5058:
4916:
4859:
4621:
4275:
4058:
4008:
3955:
3748:
3683:
3538:
3488:
3459:
3262:
2811:
were indicated to be vital for large multicellular animals in the evolutionary pathway.
7643:
7467:
7420:
7350:
7345:
7240:
7107:
6980:
6787:
6777:
6757:
6634:
6560:
6525:
6464:
6341:
6296:
6188:
5924:
5919:
5912:
5880:
5774:
5213:
5172:
4545:
4476:
4449:
3972:
3939:
2934:
2892:
2864:
2747:
2660:
2571:
2004:
2000:
488:
224:
197:
147:
5057:
Davidescu, Mircea R.; Romanczuk, Pawel; Gregor, Thomas; Couzin, Iain D. (2023-03-14).
4685:
4424:
4166:
4133:
4066:
17:
7697:
7668:
6644:
6618:
6575:
6565:
6520:
6507:
6487:
6379:
6213:
6168:
5977:
5972:
5939:
5907:
5899:
5885:
5875:
5794:
5405:
5372:
4210:
3546:
3496:
2975:
2714:
2684:
2671:
in the ecological networks. Systems ecology also considers the external influence of
2668:
2608:
2488:
1927:
1798:
1131:
1127:
921:
870:
within the population will be. This has been done for a number of species including
847:
178:
155:
67:
4995:
4942:
4756:
4248:
4157:
3707:
1724:, by competing with it, preying on it, or any number of other possibilities. When α
7653:
7638:
7295:
7265:
7210:
7093:
7058:
6935:
6434:
6118:
6012:
5987:
5929:
5807:
5802:
5010:
4871:
4498:
4299:
3772:
3286:
2971:
2722:
2473:
1989:
1882:
1852:
1837:
276:
228:
220:
100:
3906:
5718:
5546:
5033:
4466:
2366:
will be zero at steady state. However, when the rate of extinction is moderate, p
2348:{\displaystyle {\frac {dp_{2}}{dt}}=m_{2}p_{2}(1-p_{1}-p_{2})-ep_{2}-mp_{1}p_{2}}
1134:
in North America, any infectious disease modeling such as the recent outbreak of
842:
that contains the survival probability and fecundity for each class. The matrix
6945:
6674:
6492:
6454:
6429:
6419:
6384:
6331:
6311:
6045:
5766:
5012:
Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences
4867:
4782:
3796:
3583:
2954:
2938:
2883:
2632:
2612:
1963:
1806:
900:
875:
243:
5262:
5240:
4347:
3519:
7658:
7235:
7200:
6840:
6792:
6737:
6707:
6613:
6530:
6474:
6351:
6301:
5831:
5826:
4979:
4934:
4725:
Elton CS (1927) Animal Ecology. Republished 2001. University of Chicago Press.
4262:
McGill, B. J. (2003). "A test of the unified neutral theory of biodiversity".
2596:
2546:
2091:
1968:
1186:
1143:
312:
232:
128:
5204:
5149:
5090:
4420:
7563:
7517:
7245:
6689:
6659:
6459:
6414:
6389:
6326:
6316:
6291:
6283:
6228:
5949:
5263:"On the Tendency of Varieties to Depart Indefinitely From the Original Type"
5082:
3963:
3907:"Periodic fluctuations in the numbers of animals - Their causes and effects"
2856:
2604:
2518:
2484:
scenario, the steady state where the population is zero is usually unstable.
1832:
are ruled out by the terms of reference; but cooperative strategies such as
913:
893:
284:
253:
83:
51:
5354:"What do genetics and ecology tell us about the design of nature reserves?"
5222:
5196:
5157:
5108:
4987:
4485:
4355:
4291:
3981:
3764:
3504:
2793:
On cellular levels, individual organisms also demonstrated swarm behavior.
2529:
and the death of many species within the ecosystem. The abstract notion of
1736:, through some kind of mutualistic interaction between the two. When both α
5124:"Emergent periodicity in the collective synchronous flashing of fireflies"
4175:
3613:
3554:
3278:
7618:
7547:
7078:
6585:
6497:
6444:
6399:
6108:
5381:
2655:
2592:
2535:
2491:â and it is again harder to drive a population extinct under this regime.
1833:
1829:
1825:
1802:
1174:
855:
82:, evolutionary theory, epidemiology, animal behavior and group dynamics,
32:
5140:
5123:
4283:
4132:
H. M. Tsuchiya; J. F. Drake; J. L. Jost & A. G. Fredrickson (1972).
3940:"Transmission dynamics and control of severe acute respiratory syndrome"
3923:
3196:
University of Chicago Press, reprint of 1982 edition with new foreword.
2941:
are generally recognised as the founders of modern theoretical ecology.
7608:
7415:
7285:
7280:
6907:
6855:
6515:
6160:
5635:
4637:
4202:
3699:
3594:(Second ed.). Philadelphia and London: W. B. Saunders Co. p.
3168:
Princeton University Press, reprint of 1973 edition with new foreword.
2577:
2514:
1119:
309:
305:
5727:
5243:. Complexity (publisher Wiley Periodicals, Inc.) Volume 10, No 2, 2004
4970:
3793:"The Unified Neutral Theory of Biodiversity and Biogeography (MPB-32)"
3004:
Some notable theoretical ecologists can be found in these categories:
726:{\displaystyle {\frac {dN(t)}{dt}}=rN(t)\left(1-{\frac {N}{K}}\right)}
4841:"Minimal mechanisms for school formation in self-propelled particles"
3756:
3270:
2904:
2580:
is a free ecosystem modelling software suite, initially developed by
31:
Mathematical models developed in theoretical ecology predict complex
5627:
5464:
Matrix Population Models: Construction, Analysis, and Interpretation
4629:
4024:
3691:
3657:
Matrix Population Models: Construction, Analysis, and Interpretation
4748:
4096:
How Species Interact: Altering the Standard View on Trophic Ecology
3341:
Systems analysis and simulation in wildlife and fisheries sciences.
2453:{\displaystyle p_{2}^{*}={\frac {e}{m_{1}}}-{\frac {m_{1}}{m_{2}}}}
27:
5895:
5862:
5287:
4824:
2708:
1962:
899:
206:
38:
26:
4016:
1426:, as well as theoretical analysis of the behavior of the system.
1115:
exponential death rate for predators in the absence of any prey.
5412:. The 2007 edition is published by the Oxford University Press.
2581:
1135:
6880:
6133:
5731:
4672:
Post, D. M. (1993). "The long and short of food-chain length".
2203:{\displaystyle {\frac {dp_{1}}{dt}}=m_{1}p_{1}(1-p_{1})-ep_{1}}
809:{\displaystyle \mathbf {N} _{t+1}=\mathbf {L} \mathbf {N} _{t}}
4735:
Paine RT (1966). "Food web complexity and species diversity".
4527:"Metapopulation dynamics: brief history and conceptual domain"
227:, and are often cited as providing archetypal examples of how
2992:
and Rosenzweig with his Species Diversity in Space and Time.
2903:
In contrast to previous ecological theories which considered
630:{\displaystyle {\frac {dN(t)}{dt}}=((b-aN(t))-(d-cN(t)))N(t)}
2963:, a seminal work in the development of theoretical ecology.
5557:
Modelling for field biologists and other interesting people
4413:
10.1890/0012-9658(2002)083[1509:RAKSRT]2.0.CO;2
4241:
10.1666/0094-8373(2005)031[0122:TNTOBA]2.0.CO;2
3570:
Optimal harvesting theory for predatorâprey metapopulations
2566:
tools to describe the structure of ecosystems, emphasizing
892:
An ecological community is a group of trophically similar,
200:
where the dynamic relationships that are to be modeled are
4121:(3rd ed.). Oxford University Press. pp. 132â147.
3573:
University of Adelaide, Department of Applied Mathematics.
3475:
R C Lewontin (1961). "Evolution and the theory of games".
2872:
The action of this principle is exactly like that of the
3826:(3rd ed.). Oxford University Press. pp. 46â61.
1104:{\displaystyle {\frac {dP(t)}{dt}}=P(t)(c\alpha N(t)-d)}
189:. Examples are the dynamics of interacting populations (
4329:"Historical biogeography, ecology and species richness"
2990:
Unified Neutral Theory of Biodiversity and Biogeography
1012:{\displaystyle {\frac {dN(t)}{dt}}=N(t)(r-\alpha P(t))}
5548:
The Ecological Detective: Confronting Models with Data
5234:
5232:
4040:"Coupling in predatorâprey dynamics: ratio dependence"
2855:
is best known for independently proposing a theory of
4561:
Biogeography: An Ecological and Evolutionary Approach
3894:. Blackwell Scientific Publications Inc., Oxford, UK.
2929:
Theoretical ecology draws on pioneering work done by
2769:
approach. The Eulerian approach views the swarm as a
2387:
2217:
2111:
2019:
1847:
Hubbell built on earlier neutral concepts, including
1575:
1435:
1394:) describes the probability of infection (typically,
1302:
1202:
1026:
937:
767:
649:
519:
425:
347:
50:
is the scientific discipline devoted to the study of
7556:
7456:
7381:
7254:
7191:
7051:
6919:
6821:
6700:
6627:
6584:
6506:
6473:
6370:
6282:
6176:
6079:
6036:
5948:
5894:
5857:
5816:
5793:
5765:
3520:"Theory of games and evolution of animal conflicts"
1944:for rapid population growth. These early phases of
830:of the number of individuals in each class at time
260:applied game theory to evolutionary biology in his
5686:Mathematical Ecology of Populations and Ecosystems
5328:Ecological paradigms lost: routes of theory change
4705:(2nd ed.). John Wiley and Sons. p. 283.
3888:Begon, M.; Harper, J. L.; Townsend, C. R. (1988).
3587:
2452:
2347:
2202:
2075:
1700:
1560:
1375:
1287:
1103:
1011:
808:
725:
629:
471:
397:
3891:Ecology: Individuals, Populations and Communities
3817:
3815:
3813:
5483:Society for Industrial and Applied Mathematics.
5402:Theoretical Ecology: Principles and Applications
4119:Theoretical Ecology: Principles and Applications
3824:Theoretical Ecology: Principles and Applications
3435:Theoretical Ecology: Principles and Applications
1376:{\displaystyle P_{t+1}=c\ N_{t}\ f(N_{t},p_{t})}
5063:Proceedings of the National Academy of Sciences
4825:"Collective decision making in cohesive flocks"
4392:Reznick, D.; Bryant, M. J.; Bashey, F. (2002).
2374:can stably coexist. The steady state value of p
1744:are negative, the relationship is described as
4222:
4220:
3786:
3784:
3782:
2521:can be disruptive. In some cases, it leads to
1756:are positive, the relationship becomes one of
201:
193:
190:
6892:
6145:
5743:
4839:Li YX; Lukeman R; Edelstein-Keshet L (2007).
4580:
4578:
1952:forces of natural selection, which is called
8:
5173:"Chimera states among synchronous fireflies"
5171:Sarfati, Raphaël; Peleg, Orit (2022-11-18).
4773:, University of Queensland Press, 1983, p.9.
4699:Jerry Bobrow, Ph.D.; Stephen Fisher (2009).
3720:: CS1 maint: multiple names: authors list (
3165:Stability and Complexity in Model Ecosystems
315:and how these populations interact with the
5448:An illustrated guide to theoretical ecology
5265:. The Alfred Russel Wallace Page hosted by
4834:
4832:
4450:"Beyond NeutralityâEcology Finds Its Niche"
2076:{\displaystyle {\frac {dp}{dt}}=mp(1-p)-ep}
7113:Latitudinal gradients in species diversity
6899:
6885:
6877:
6152:
6138:
6130:
5750:
5736:
5728:
4590:Princeton University Press, page 175â176.
3343:Wiley, University of Minnesota, page 223.
3312:
3310:
2877:and extinction almost sure soon to follow.
5617:
5380:
5212:
5139:
5098:
5023:
4969:
4924:
4534:Biological Journal of the Linnean Society
4475:
4465:
4165:
3971:
3922:
3461:The genetical theory of natural selection
3319:A practical guide to ecological modelling
2442:
2432:
2426:
2415:
2406:
2397:
2392:
2386:
2339:
2329:
2313:
2294:
2281:
2262:
2252:
2228:
2218:
2216:
2194:
2175:
2156:
2146:
2122:
2112:
2110:
2020:
2018:
1971:systems make them good sites for testing
1910:spurred the development of the fields of
1863:'s concepts of symmetry and null models.
1687:
1677:
1664:
1651:
1634:
1623:
1613:
1606:
1586:
1576:
1574:
1547:
1537:
1524:
1511:
1494:
1483:
1473:
1466:
1446:
1436:
1434:
1364:
1351:
1332:
1307:
1301:
1288:{\displaystyle N_{t+1}=\lambda \ N_{t}\ }
1273:
1260:
1232:
1207:
1201:
1173:The second interaction, that of host and
1027:
1025:
938:
936:
854:models, and as the Lefkovitch matrix for
800:
795:
789:
774:
769:
766:
708:
650:
648:
520:
518:
460:
424:
398:{\displaystyle {\frac {dN(t)}{dt}}=rN(t)}
348:
346:
275:Because ecological systems are typically
249:The Genetical Theory of Natural Selection
154:Species can be modelled in continuous or
54:using theoretical methods such as simple
7011:Predatorâprey (LotkaâVolterra) equations
6650:Tritrophic interactions in plant defense
5347:
5345:
4804:The Ecological Implications of Body Size
3214:
3212:
3210:
2545:If ecosystems are governed primarily by
1185:The third interaction, that of host and
43:Life on Earth-Flow of Energy and Entropy
7043:Random generalized LotkaâVolterra model
5531:Population Biology: Concepts and Models
3627:
3625:
3623:
3224:Princeton University Press, pages 6â9.
3150:
2996:Theoretical and mathematical ecologists
2966:Simberloff added statistical rigour to
2895:has become an area of active research.
211:Bifurcation diagram of the logistic map
86:, ecosystems, spatial ecology, and the
6851:Herbivore adaptations to plant defense
4327:Wiens, J. J.; Donoghue, M. J. (2004).
3713:
3631:Moss R, Watson A and Ollason J (1982)
3186:
3184:
3182:
2957:, with whom MacArthur collaborated on
1781:Unified neutral theory of biodiversity
1414:. Examples include relations between
5290:. CoEvolutionary Quarterly, June 1976
4584:Vandermeer JH and Goldberg DE (2003)
4093:Arditi, R. and Ginzburg, L.R. (2012)
3158:
3156:
3154:
2907:to be catastrophic events, the river
1769:for further extensions of this model.
1728:is positive, however, it means that N
35:can be less stable than simpler webs.
7:
7714:Mathematical and theoretical biology
6866:Predator avoidance in schooling fish
5591:"Are there general laws in ecology?"
4587:Population ecology: first principles
3363:Modeling Complex Ecological Dynamics
1767:Competitive LotkaâVolterra equations
1169:Compartmental models in epidemiology
416:can be solved to yield the solution
7316:Intermediate disturbance hypothesis
5325:Cuddington K and Beisner BE (2005)
4823:Bhattacharya K and Vicsek T (2010)
4702:CliffsNotes CSET: Multiple Subjects
4038:Arditi, R.; Ginzburg, L.R. (1989).
3437:. Blackwell Scientific Publishers.
3409:Bifurcation theory and applications
2470:Intermediate Disturbance Hypothesis
736:where r = b-d and K = (b-d)/(a+c).
7069:Ecological effects of biodiversity
5720:Ecology: The Ascendant Perspective
5511:Gotelli NJ & A Ellison (2005)
4652:Ecology, the Ascendant Perspective
4546:10.1111/j.1095-8312.1991.tb00548.x
4312:MacArthur RH and Wilson EO (1967)
2538:of the introduced element and the
2509:Introducing new elements, whether
338:of population growth is given by:
162:Continuous time is modelled using
25:
6405:Generalist and specialist species
5514:A Primer Of Ecological Statistics
4380:The Theory of Island Biogeography
4315:The theory of island biogeography
3316:Soetaert K and Herman PMJ (2009)
2960:The Theory of Island Biogeography
2650:can be seen as an application of
2358:In this case, if e is too high, p
1967:The diversity and containment of
1903:The Theory of Island Biogeography
472:{\displaystyle N(t)=N(0)\ e^{rt}}
262:Evolution and the Theory of Games
7128:Occupancyâabundance relationship
5574:Elements of Mathematical Ecology
3009:Category:Mathematical ecologists
2758:follow simple behavioral rules.
2599:. Each food chain starts with a
796:
790:
770:
308:that deals with the dynamics of
169:Discrete time is modelled using
7148:Relative abundance distribution
6861:Plant defense against herbivory
6728:Competitive exclusion principle
6440:Mesopredator release hypothesis
5545:Hilborn R & M Clark (1997)
5517:Sinauer Associates Publishers.
5431:Ecological Models and Data in R
5352:Soulé ME, Simberloff D (1986).
5241:"Wallace's Unfinished Business"
4789:. Date accessed: 9 August 2017.
4674:Trends in Ecology and Evolution
4564:John Wiley and Sons, page 146.
4336:Trends in Ecology and Evolution
4158:10.1128/JB.110.3.1147-1153.1972
4134:"PredatorâPrey Interactions of
3911:Journal of Experimental Biology
3221:Ecological models and data in R
3035:Journal of Mathematical Biology
3014:Category:Theoretical biologists
2750:of quadrupeds. It is a complex
6733:Consumerâresource interactions
5669:Mathematical Biology, Volume 2
5652:Mathematical Biology, Volume 1
5480:Mathematical Models in Biology
4848:Physica D: Nonlinear Phenomena
4047:Journal of Theoretical Biology
3527:Journal of Theoretical Biology
3477:Journal of Theoretical Biology
3464:. Oxford: The Clarendon press.
3386:New trends in ecology research
3056:Theoretical Population Biology
3042:Journal of Theoretical Biology
2300:
2268:
2181:
2162:
2061:
2049:
1370:
1344:
1282:
1279:
1253:
1241:
1098:
1089:
1083:
1071:
1068:
1062:
1042:
1036:
1006:
1003:
997:
982:
979:
973:
953:
947:
694:
688:
665:
659:
624:
618:
612:
609:
606:
600:
585:
579:
576:
570:
555:
552:
535:
529:
450:
444:
435:
429:
392:
386:
363:
357:
270:evolutionarily stable strategy
1:
7579:Biological data visualization
7406:Environmental niche modelling
7133:Population viability analysis
4686:10.1016/S0169-5347(02)02455-2
4191:Acta Applicandae Mathematicae
4067:10.1016/s0022-5193(89)80211-5
2098:, and that by the second as p
319:. It is the study of how the
7064:Density-dependent inhibition
5577:Cambridge University Press.
5560:Cambridge University Press.
5500:Sinauer Associates, 4th Ed.
5434:Princeton University Press.
5373:10.1016/0006-3207(86)90025-X
5034:10.1007/978-0-8176-4946-3_12
4807:Cambridge University Press.
4467:10.1371/journal.pbio.0040278
3838:Elements of Physical Biology
3547:10.1016/0022-5193(74)90110-6
3497:10.1016/0022-5193(61)90038-8
2970:and was a key figure in the
2933:and his students. Brothers
1809:. This can be considered a
1788:is a hypothesis proposed by
1716:is negative, it means that N
747:Structured population growth
414:linear differential equation
7533:Liebig's law of the minimum
7368:Resource selection function
6259:Metabolic theory of ecology
5703:Primer of Ecological Theory
5551:Princeton University Press.
5267:Western Kentucky University
4868:10.1016/j.physd.2007.10.009
4558:Cox CB and Moore PD (2010)
4525:Hanski I, Gilpin M (1991).
3518:John Maynard Smith (1974).
3389:Nova Publishers, page 136.
3100:â widely used to model the
2788:particle swarm optimization
2754:behaviour that occurs when
2542:of the original ecosystem.
1181:Hostâparasitoid interaction
1142:by the introduction of its
231:can arise from very simple
7730:
7433:Niche apportionment models
7153:Relative species abundance
6357:Primary nutritional groups
6254:List of feeding behaviours
5723:Columbia University Press.
5477:Edelstein-Keshet L (2005)
5288:"For God's Sake, Margaret"
4348:10.1016/j.tree.2004.09.011
3634:Animal population dynamics
3242:Sugihara G, May R (1990).
3098:Integrodifference equation
2922:
2844:
2720:
2697:
2682:
2502:
1998:
1987:
1925:
1870:
1778:
1732:has a positive effect on N
1720:has a negative effect on N
1166:
1138:and biological control of
885:
750:
640:This can be rewritten as:
498:
330:
294:
7682:
7614:Ecosystem based fisheries
7226:Interspecific competition
7118:Minimum viable population
6976:Maximum sustainable yield
6961:Intraspecific competition
6956:Effective population size
6836:Anti-predator adaptations
6347:Photosynthetic efficiency
5451:Oxford University Press.
4980:10.1007/s11538-006-9088-6
4935:10.1137/S0036139903437424
4892:75 (23)(1995), 4326â4329.
4507:Oxford University Press.
4099:Oxford University Press.
3997:Journal of Animal Ecology
3104:and growth of populations
3088:Ecological systems theory
1402:Competition and mutualism
1189:, can be analyzed by the
1163:Hostâpathogen interaction
1122:was curtailed during the
909:Predatorâprey interaction
508:intraspecific competition
198:mathematical epidemiology
194:competition and mutualism
143:models are deterministic.
123:Ecological models can be
88:effects of climate change
64:computational simulations
7604:Ecological stoichiometry
7569:Alternative stable state
4654:. Columbia Univ. Press.
4136:Dictyostelium discoideum
2835:condensed matter physics
2805:self-propelled particles
2784:self-propelled particles
753:Matrix population models
96:quantitative predictions
7448:Ontogenetic niche shift
7311:Ideal free distribution
7221:Ecological facilitation
6971:Malthusian growth model
6941:Consumer-resource model
6798:Paradox of the plankton
6763:Energy systems language
6483:Chemoorganoheterotrophy
6450:Optimal foraging theory
6425:Heterotrophic nutrition
6051:Ecological anthropology
5361:Biological Conservation
5083:10.1073/pnas.2206163120
4889:Physical Revue Letters,
4737:The American Naturalist
4146:Journal of Bacteriology
4142:in Continuous Culture1"
3964:10.1126/science.1086616
3590:Fundamentals of Ecology
3406:Ma T and Wang S (2005)
3028:The American Naturalist
2809:Central nervous systems
2780:ant colony optimization
2654:to ecology. It takes a
2090:, and e is the rate of
2086:where m is the rate of
861:If parameter values in
7594:Ecological forecasting
7538:Marginal value theorem
7336:Landscape epidemiology
7271:Cross-boundary subsidy
7206:Biological interaction
6556:Microbial intelligence
6244:Green world hypothesis
6061:Ecological engineering
5197:10.1126/sciadv.add6690
4504:Metapopulation ecology
3870:Mem. Acad. Lincei Roma
3637:Springer, page 52â54.
3458:Fisher, R. A. (1930).
3083:Complex system biology
2880:
2851:The British biologist
2718:
2667:through the different
2652:general systems theory
2454:
2349:
2204:
2077:
1980:
1934:life-history evolution
1786:Unified neutral theory
1702:
1562:
1377:
1289:
1191:NicholsonâBailey model
1105:
1013:
905:
872:loggerhead sea turtles
846:is referred to as the
810:
727:
631:
483:a trajectory known as
473:
399:
264:, followed closely by
246:published his classic
212:
164:differential equations
44:
36:
18:Mathematical ecologist
7599:Ecological humanities
7498:Ecological energetics
7443:Niche differentiation
7306:Habitat fragmentation
7074:Ecological extinction
7021:Small population size
6773:Feed conversion ratio
6753:Ecological succession
6685:San Francisco Estuary
6599:Ecological efficiency
6541:Microbial cooperation
5700:Roughgarden J (1998)
4650:Robert Ulanowicz ().
2869:
2853:Alfred Russel Wallace
2795:Decentralized systems
2712:
2455:
2350:
2205:
2078:
1966:
1703:
1563:
1378:
1290:
1157:Arditi-Ginzburg model
1106:
1014:
903:
811:
728:
632:
474:
400:
210:
42:
30:
7624:Evolutionary ecology
7589:Ecological footprint
7584:Ecological economics
7508:Ecological threshold
7503:Ecological indicator
7373:Sourceâsink dynamics
7326:Land change modeling
7321:Insular biogeography
7173:Species distribution
6912:Modelling ecosystems
6571:Microbial metabolism
6410:Intraguild predation
6199:Biogeochemical cycle
6165:Modelling ecosystems
6056:Ecological economics
5983:Evolutionary ecology
5950:Ecological phenomena
5780:Quantitative ecology
5400:The classic text is
3842:Williams and Wilkins
3791:Hubbell, SP (2001).
3655:Hal Caswell (2001).
3567:Supriatna AK (1998)
3366:Springer, page 122.
3128:Quantitative ecology
3113:Mathematical biology
3063:Ecological Modelling
2968:experimental ecology
2931:G. Evelyn Hutchinson
2874:centrifugal governor
2847:Evolutionary ecology
2841:Evolutionary ecology
2800:Trichoplax adhaerens
2732:collective behaviour
2673:ecological economics
2385:
2215:
2109:
2017:
1922:r/K-selection theory
1912:conservation biology
1822:ecological community
1573:
1433:
1396:Poisson distribution
1300:
1200:
1140:California red scale
1024:
935:
926:Lotka-Volterra model
765:
647:
517:
423:
345:
171:difference equations
107:Modelling approaches
7709:Ecological theories
7704:Theoretical ecology
7674:Theoretical ecology
7649:Natural environment
7513:Ecosystem diversity
7483:Ecological collapse
7473:Bateman's principle
7428:Limiting similarity
7341:Landscape limnology
7163:Species homogeneity
7001:Population modeling
6996:Population dynamics
6813:Trophic state index
6102:Restoration ecology
6092:Glossary of ecology
6038:Interdisciplinarity
5785:Theoretical ecology
5759:Branches of ecology
5717:Ulanowicz R (1997)
5610:1999Oikos..84..177L
5497:A Primer of Ecology
5466:, Sinauer, 2nd Ed.
5189:2022SciA....8D6690S
5141:10.7554/eLife.78908
5075:2023PNAS..12006163D
5069:(11): e2206163120.
4917:2004APS..MAR.t9004T
4860:2008PhyD..237..699L
4622:1982Oikos..38..210H
4284:10.1038/nature01583
4276:2003Natur.422..881M
4059:1989JThBi.139..311A
4009:1986JAnEc..55.1069R
3956:2003Sci...300.1966L
3924:10.1242/jeb.2.1.119
3905:C.S. Elton (1924).
3855:Academic Press Inc.
3749:2001Natur.414..537F
3684:1987Ecol...68.1412C
3539:1974JThBi..47..209M
3489:1961JThBi...1..382L
3263:1990Natur.344..734S
3138:Theoretical biology
3123:Population modeling
3118:Population dynamics
3108:Limiting similarity
3049:Theoretical Ecology
2953:was the student of
2909:flood pulse concept
2886:and anthropologist
2556:species composition
2523:ecological collapse
2402:
1950:density-independent
1890:island biogeography
1857:island biogeography
225:polynomial mappings
187:branching processes
148:Markov chain models
60:mathematical models
48:Theoretical ecology
7685:Outline of ecology
7634:Industrial ecology
7629:Functional ecology
7493:Ecological deficit
7438:Niche construction
7401:Ecosystem engineer
7178:Speciesâarea curve
7099:Introduced species
6914:: Other components
6846:Deimatic behaviour
6748:Ecological network
6680:North Pacific Gyre
6665:hydrothermal vents
6604:Ecological pyramid
6551:Microbial food web
6362:Primary production
6307:Foundation species
6087:History of ecology
5993:Functional ecology
5958:Behavioral ecology
5837:Population ecology
5672:Springer, 3rd Ed.
5655:Springer, 3rd Ed.
5589:Lawton JH (1999).
5528:Hastings A (1996)
5494:Gotelli NJ (2008)
5239:Smith, Charles H.
4203:10.1007/BF00046673
3412:World Scientific.
2986:Michael Rosenzweig
2982:Stephen P. Hubbell
2945:brought theory to
2925:History of ecology
2821:Photinus carolinus
2719:
2700:Behavioral ecology
2694:Behavioral ecology
2568:mutual information
2564:information theory
2450:
2388:
2345:
2200:
2073:
1981:
1938:population density
1790:Stephen P. Hubbell
1698:
1558:
1373:
1285:
1101:
1009:
906:
806:
723:
627:
469:
395:
333:Exponential growth
327:Exponential growth
304:is a sub-field of
302:Population ecology
297:Population ecology
291:Population ecology
281:agent-based models
266:John Maynard Smith
216:Bifurcation theory
213:
52:ecological systems
45:
37:
7691:
7690:
7574:Balance of nature
7331:Landscape ecology
7216:Community ecology
7158:Species diversity
7094:Indicator species
7089:Gradient analysis
6966:Logistic function
6874:
6873:
6831:Animal coloration
6808:Trophic mutualism
6546:Microbial ecology
6337:Photoheterotrophs
6322:Myco-heterotrophy
6234:Ecosystem ecology
6219:Carrying capacity
6184:Abiotic component
6127:
6126:
6066:Political ecology
6008:Molecular ecology
6003:Landscape ecology
5871:Microbial ecology
5847:Ecosystem ecology
5842:Community ecology
5712:978-0-13-442062-2
5695:978-1-4051-8811-1
5689:Wiley-Blackwell.
5678:978-0-387-95228-4
5666:Murray JD (2003)
5661:978-0-387-95223-9
5649:Murray JD (2002)
5583:978-0-521-00150-2
5566:978-0-521-83132-1
5540:978-0-387-94853-9
5523:978-0-87893-269-6
5506:978-0-87893-318-1
5489:978-0-89871-554-5
5472:978-0-87893-096-8
5462:Caswell H (2000)
5457:978-0-19-508512-9
5440:978-0-691-12522-0
5428:Bolker BM (2008)
5418:978-0-19-920998-9
5337:978-0-12-088459-9
5261:Wallace, Alfred.
5043:978-0-8176-4945-6
4712:978-0-470-45546-3
4596:978-0-691-11441-5
4570:978-0-470-63794-4
4513:978-0-19-854065-6
4270:(6934): 881â885.
3950:(5627): 1966â70.
3743:(6863): 537â541.
3643:978-0-412-22240-5
3444:978-0-632-00768-4
3418:978-981-256-287-6
3395:978-1-59454-379-1
3372:978-3-642-05028-2
3349:978-0-471-89236-6
3328:978-1-4020-8623-6
3230:978-0-691-12522-0
3218:Bolker BM (2008)
3202:978-0-226-66832-1
3174:978-0-691-08861-7
2951:Daniel Simberloff
2947:community ecology
2913:river's ecosystem
2861:natural selection
2831:agent-based model
2775:agent-based model
2756:individual agents
2552:balance of nature
2531:ecological health
2499:Ecosystem ecology
2448:
2421:
2243:
2137:
2038:
1946:population growth
1916:landscape ecology
1908:habitat fragments
1640:
1601:
1500:
1461:
1340:
1327:
1240:
1227:
1054:
965:
888:Community ecology
882:Community ecology
741:carrying capacity
716:
677:
547:
485:Malthusian growth
455:
375:
229:chaotic behaviour
56:conceptual models
16:(Redirected from
7721:
7391:Ecological niche
7363:selection theory
7183:Umbrella species
7168:Species richness
7104:Invasive species
7084:Flagship species
6991:Population cycle
6986:Overexploitation
6951:Ecological yield
6901:
6894:
6887:
6878:
6783:Mesotrophic soil
6723:Climax community
6655:Marine food webs
6594:Biomagnification
6395:Chemoorganotroph
6249:Keystone species
6209:Biotic component
6154:
6147:
6140:
6131:
5963:Chemical ecology
5935:Tropical ecology
5752:
5745:
5738:
5729:
5683:Pastor J (2008)
5646:
5644:
5638:. Archived from
5621:
5595:
5387:
5386:
5384:
5358:
5349:
5340:
5331:Academic Press.
5323:
5317:
5314:
5308:
5305:
5299:
5298:
5296:
5295:
5286:Brand, Stewart.
5283:
5277:
5276:
5274:
5273:
5258:
5252:
5251:
5249:
5248:
5236:
5227:
5226:
5216:
5183:(46): eadd6690.
5177:Science Advances
5168:
5162:
5161:
5143:
5119:
5113:
5112:
5102:
5054:
5048:
5047:
5027:
5017:
5006:
5000:
4999:
4973:
4964:(7): 1601â1623.
4953:
4947:
4946:
4928:
4905:SIAM J Appl Math
4900:
4894:
4885:
4879:
4878:
4876:
4870:. Archived from
4845:
4836:
4827:
4821:
4815:
4796:
4790:
4780:
4774:
4767:
4761:
4760:
4732:
4726:
4723:
4717:
4716:
4696:
4690:
4689:
4669:
4663:
4648:
4642:
4641:
4605:
4599:
4582:
4573:
4556:
4550:
4549:
4531:
4522:
4516:
4496:
4490:
4489:
4479:
4469:
4460:(8): 1306â1310.
4448:Gewin V (2006).
4445:
4439:
4438:
4436:
4435:
4429:
4423:. Archived from
4407:(6): 1509â1520.
4398:
4389:
4383:
4375:
4369:
4366:
4360:
4359:
4333:
4324:
4318:
4310:
4304:
4303:
4259:
4253:
4252:
4224:
4215:
4214:
4186:
4180:
4179:
4169:
4140:Escherichia coli
4129:
4123:
4122:
4114:
4108:
4091:
4085:
4084:
4082:
4081:
4075:
4069:. Archived from
4044:
4035:
4029:
4028:
4003:(3): 1069â1082.
3992:
3986:
3985:
3975:
3935:
3929:
3928:
3926:
3902:
3896:
3895:
3885:
3879:
3878:
3864:
3858:
3851:
3845:
3834:
3828:
3827:
3819:
3808:
3807:
3805:
3804:
3795:. Archived from
3788:
3777:
3776:
3757:10.1038/35107054
3732:
3726:
3725:
3719:
3711:
3678:(5): 1412â1423.
3667:
3661:
3660:
3652:
3646:
3629:
3618:
3617:
3593:
3580:
3574:
3565:
3559:
3558:
3524:
3515:
3509:
3508:
3472:
3466:
3465:
3455:
3449:
3448:
3427:
3421:
3404:
3398:
3381:
3375:
3358:
3352:
3339:Grant WE (1986)
3337:
3331:
3314:
3305:
3304:
3302:
3301:
3295:
3289:. Archived from
3271:10.1038/344734a0
3257:(6268): 734â41.
3248:
3239:
3233:
3216:
3205:
3188:
3177:
3160:
3078:Butterfly effect
2943:Robert MacArthur
2746:of fish and the
2601:primary producer
2560:Robert Ulanowicz
2527:trophic cascades
2505:Ecosystem models
2459:
2457:
2456:
2451:
2449:
2447:
2446:
2437:
2436:
2427:
2422:
2420:
2419:
2407:
2401:
2396:
2354:
2352:
2351:
2346:
2344:
2343:
2334:
2333:
2318:
2317:
2299:
2298:
2286:
2285:
2267:
2266:
2257:
2256:
2244:
2242:
2234:
2233:
2232:
2219:
2209:
2207:
2206:
2201:
2199:
2198:
2180:
2179:
2161:
2160:
2151:
2150:
2138:
2136:
2128:
2127:
2126:
2113:
2082:
2080:
2079:
2074:
2039:
2037:
2029:
2021:
1977:neutral theories
1894:Robert MacArthur
1794:neutral theories
1707:
1705:
1704:
1699:
1697:
1693:
1692:
1691:
1682:
1681:
1669:
1668:
1656:
1655:
1641:
1639:
1638:
1629:
1628:
1627:
1618:
1617:
1607:
1602:
1600:
1592:
1591:
1590:
1577:
1567:
1565:
1564:
1559:
1557:
1553:
1552:
1551:
1542:
1541:
1529:
1528:
1516:
1515:
1501:
1499:
1498:
1489:
1488:
1487:
1478:
1477:
1467:
1462:
1460:
1452:
1451:
1450:
1437:
1382:
1380:
1379:
1374:
1369:
1368:
1356:
1355:
1338:
1337:
1336:
1325:
1318:
1317:
1294:
1292:
1291:
1286:
1278:
1277:
1265:
1264:
1238:
1237:
1236:
1225:
1218:
1217:
1110:
1108:
1107:
1102:
1055:
1053:
1045:
1028:
1018:
1016:
1015:
1010:
966:
964:
956:
939:
868:age distribution
856:stage-structured
815:
813:
812:
807:
805:
804:
799:
793:
785:
784:
773:
732:
730:
729:
724:
722:
718:
717:
709:
678:
676:
668:
651:
636:
634:
633:
628:
548:
546:
538:
521:
478:
476:
475:
470:
468:
467:
453:
404:
402:
401:
396:
376:
374:
366:
349:
321:population sizes
258:Richard Lewontin
137:random variation
116:experimentation.
21:
7729:
7728:
7724:
7723:
7722:
7720:
7719:
7718:
7694:
7693:
7692:
7687:
7678:
7664:Systems ecology
7552:
7523:Extinction debt
7488:Ecological debt
7478:Bioluminescence
7459:
7452:
7421:marine habitats
7396:Ecological trap
7377:
7257:
7250:
7193:
7187:
7143:Rapoport's rule
7138:Priority effect
7079:Endemic species
7047:
7006:Population size
6922:
6915:
6905:
6875:
6870:
6823:
6817:
6803:Trophic cascade
6713:Bioaccumulation
6696:
6623:
6580:
6502:
6469:
6366:
6278:
6239:Ecosystem model
6172:
6158:
6128:
6123:
6114:Natural history
6097:Applied ecology
6075:
6071:Systems ecology
6032:
6028:Thermal ecology
6023:Spatial ecology
5998:Genetic ecology
5968:Disease ecology
5944:
5900:biogeographical
5890:
5853:
5812:
5789:
5761:
5756:
5726:
5706:Prentice Hall.
5642:
5628:10.2307/3546712
5619:10.1.1.331.1173
5593:
5588:
5554:Kokko H (2007)
5445:Case TJ (2000)
5424:
5423:
5396:
5394:Further reading
5391:
5390:
5356:
5351:
5350:
5343:
5324:
5320:
5315:
5311:
5306:
5302:
5293:
5291:
5285:
5284:
5280:
5271:
5269:
5260:
5259:
5255:
5246:
5244:
5238:
5237:
5230:
5170:
5169:
5165:
5121:
5120:
5116:
5056:
5055:
5051:
5044:
5025:10.1.1.193.5047
5015:
5008:
5007:
5003:
4955:
4954:
4950:
4902:
4901:
4897:
4886:
4882:
4874:
4843:
4838:
4837:
4830:
4822:
4818:
4797:
4793:
4781:
4777:
4771:Systems ecology
4769:R.L. Kitching,
4768:
4764:
4734:
4733:
4729:
4724:
4720:
4713:
4698:
4697:
4693:
4671:
4670:
4666:
4649:
4645:
4630:10.2307/3544021
4607:
4606:
4602:
4583:
4576:
4557:
4553:
4529:
4524:
4523:
4519:
4497:
4493:
4447:
4446:
4442:
4433:
4431:
4427:
4396:
4391:
4390:
4386:
4376:
4372:
4367:
4363:
4342:(12): 639â644.
4331:
4326:
4325:
4321:
4311:
4307:
4261:
4260:
4256:
4226:
4225:
4218:
4188:
4187:
4183:
4131:
4130:
4126:
4116:
4115:
4111:
4092:
4088:
4079:
4077:
4073:
4042:
4037:
4036:
4032:
3994:
3993:
3989:
3937:
3936:
3932:
3904:
3903:
3899:
3887:
3886:
3882:
3866:
3865:
3861:
3852:
3848:
3835:
3831:
3821:
3820:
3811:
3802:
3800:
3790:
3789:
3780:
3734:
3733:
3729:
3712:
3692:10.2307/1939225
3669:
3668:
3664:
3654:
3653:
3649:
3630:
3621:
3606:
3584:Odum, Eugene P.
3582:
3581:
3577:
3566:
3562:
3522:
3517:
3516:
3512:
3474:
3473:
3469:
3457:
3456:
3452:
3445:
3429:
3428:
3424:
3405:
3401:
3383:Burk AR (2005)
3382:
3378:
3359:
3355:
3338:
3334:
3315:
3308:
3299:
3297:
3293:
3246:
3241:
3240:
3236:
3217:
3208:
3190:Pimm SL (2002)
3189:
3180:
3161:
3152:
3147:
3142:
3093:Ecosystem model
3073:
3068:
3022:
2998:
2927:
2921:
2901:
2888:Gregory Bateson
2849:
2843:
2827:synchronization
2817:
2815:Synchronization
2765:approach or an
2728:Swarm behaviour
2725:
2707:
2705:Swarm behaviour
2702:
2696:
2687:
2681:
2648:Systems ecology
2645:
2643:Systems ecology
2639:of a food web.
2590:
2507:
2501:
2466:
2438:
2428:
2411:
2383:
2382:
2377:
2373:
2369:
2365:
2361:
2335:
2325:
2309:
2290:
2277:
2258:
2248:
2235:
2224:
2220:
2213:
2212:
2190:
2171:
2152:
2142:
2129:
2118:
2114:
2107:
2106:
2101:
2097:
2030:
2022:
2015:
2014:
2007:
1997:
1995:Metapopulations
1992:
1986:
1930:
1924:
1880:
1875:
1873:Spatial ecology
1869:
1867:Spatial ecology
1811:null hypothesis
1783:
1777:
1755:
1751:
1743:
1739:
1735:
1731:
1727:
1723:
1719:
1715:
1683:
1673:
1660:
1647:
1646:
1642:
1630:
1619:
1609:
1608:
1593:
1582:
1578:
1571:
1570:
1543:
1533:
1520:
1507:
1506:
1502:
1490:
1479:
1469:
1468:
1453:
1442:
1438:
1431:
1430:
1413:
1409:
1404:
1393:
1389:
1360:
1347:
1328:
1303:
1298:
1297:
1269:
1256:
1228:
1203:
1198:
1197:
1183:
1171:
1165:
1149:Aphytis melinus
1124:First World War
1046:
1029:
1022:
1021:
957:
940:
933:
932:
918:Alfred J. Lotka
911:
890:
884:
824:
794:
768:
763:
762:
755:
749:
701:
697:
669:
652:
645:
644:
539:
522:
515:
514:
503:
501:Logistic growth
497:
495:Logistic growth
456:
421:
420:
367:
350:
343:
342:
335:
329:
299:
293:
150:are stochastic.
141:system dynamics
109:
66:, and advanced
23:
22:
15:
12:
11:
5:
7727:
7725:
7717:
7716:
7711:
7706:
7696:
7695:
7689:
7688:
7683:
7680:
7679:
7677:
7676:
7671:
7666:
7661:
7656:
7651:
7646:
7644:Microecosystem
7641:
7636:
7631:
7626:
7621:
7616:
7611:
7606:
7601:
7596:
7591:
7586:
7581:
7576:
7571:
7566:
7560:
7558:
7554:
7553:
7551:
7550:
7545:
7543:Thorson's rule
7540:
7535:
7530:
7525:
7520:
7515:
7510:
7505:
7500:
7495:
7490:
7485:
7480:
7475:
7470:
7468:Assembly rules
7464:
7462:
7454:
7453:
7451:
7450:
7445:
7440:
7435:
7430:
7425:
7424:
7423:
7413:
7408:
7403:
7398:
7393:
7387:
7385:
7379:
7378:
7376:
7375:
7370:
7365:
7353:
7351:Patch dynamics
7348:
7346:Metapopulation
7343:
7338:
7333:
7328:
7323:
7318:
7313:
7308:
7303:
7298:
7293:
7288:
7283:
7278:
7273:
7268:
7262:
7260:
7252:
7251:
7249:
7248:
7243:
7241:Storage effect
7238:
7233:
7228:
7223:
7218:
7213:
7208:
7203:
7197:
7195:
7189:
7188:
7186:
7185:
7180:
7175:
7170:
7165:
7160:
7155:
7150:
7145:
7140:
7135:
7130:
7125:
7123:Neutral theory
7120:
7115:
7110:
7108:Native species
7101:
7096:
7091:
7086:
7081:
7076:
7071:
7066:
7061:
7055:
7053:
7049:
7048:
7046:
7045:
7040:
7039:
7038:
7033:
7023:
7018:
7013:
7008:
7003:
6998:
6993:
6988:
6983:
6981:Overpopulation
6978:
6973:
6968:
6963:
6958:
6953:
6948:
6943:
6938:
6933:
6927:
6925:
6917:
6916:
6906:
6904:
6903:
6896:
6889:
6881:
6872:
6871:
6869:
6868:
6863:
6858:
6853:
6848:
6843:
6838:
6833:
6827:
6825:
6819:
6818:
6816:
6815:
6810:
6805:
6800:
6795:
6790:
6788:Nutrient cycle
6785:
6780:
6778:Feeding frenzy
6775:
6770:
6765:
6760:
6758:Energy quality
6755:
6750:
6745:
6740:
6735:
6730:
6725:
6720:
6718:Cascade effect
6715:
6710:
6704:
6702:
6698:
6697:
6695:
6694:
6693:
6692:
6687:
6682:
6677:
6672:
6667:
6662:
6652:
6647:
6642:
6637:
6631:
6629:
6625:
6624:
6622:
6621:
6616:
6611:
6606:
6601:
6596:
6590:
6588:
6582:
6581:
6579:
6578:
6573:
6568:
6563:
6561:Microbial loop
6558:
6553:
6548:
6543:
6538:
6533:
6528:
6526:Lithoautotroph
6523:
6518:
6512:
6510:
6508:Microorganisms
6504:
6503:
6501:
6500:
6495:
6490:
6485:
6479:
6477:
6471:
6470:
6468:
6467:
6465:Prey switching
6462:
6457:
6452:
6447:
6442:
6437:
6432:
6427:
6422:
6417:
6412:
6407:
6402:
6397:
6392:
6387:
6382:
6376:
6374:
6368:
6367:
6365:
6364:
6359:
6354:
6349:
6344:
6342:Photosynthesis
6339:
6334:
6329:
6324:
6319:
6314:
6309:
6304:
6299:
6297:Chemosynthesis
6294:
6288:
6286:
6280:
6279:
6277:
6276:
6271:
6266:
6261:
6256:
6251:
6246:
6241:
6236:
6231:
6226:
6221:
6216:
6211:
6206:
6201:
6196:
6191:
6189:Abiotic stress
6186:
6180:
6178:
6174:
6173:
6159:
6157:
6156:
6149:
6142:
6134:
6125:
6124:
6122:
6121:
6116:
6111:
6106:
6105:
6104:
6094:
6089:
6083:
6081:
6077:
6076:
6074:
6073:
6068:
6063:
6058:
6053:
6048:
6042:
6040:
6034:
6033:
6031:
6030:
6025:
6020:
6018:Social ecology
6015:
6010:
6005:
6000:
5995:
5990:
5985:
5980:
5975:
5970:
5965:
5960:
5954:
5952:
5946:
5945:
5943:
5942:
5937:
5932:
5927:
5925:Forest ecology
5922:
5920:Desert ecology
5917:
5916:
5915:
5913:Arctic ecology
5904:
5902:
5892:
5891:
5889:
5888:
5883:
5881:Insect ecology
5878:
5873:
5867:
5865:
5855:
5854:
5852:
5851:
5850:
5849:
5844:
5839:
5829:
5823:
5821:
5814:
5813:
5811:
5810:
5805:
5799:
5797:
5791:
5790:
5788:
5787:
5782:
5777:
5771:
5769:
5763:
5762:
5757:
5755:
5754:
5747:
5740:
5732:
5725:
5724:
5715:
5698:
5681:
5664:
5647:
5645:on 2010-06-11.
5604:(2): 177â192.
5586:
5569:
5552:
5543:
5526:
5509:
5492:
5475:
5460:
5443:
5425:
5422:
5421:
5397:
5395:
5392:
5389:
5388:
5341:
5318:
5309:
5300:
5278:
5253:
5228:
5163:
5114:
5049:
5042:
5001:
4958:Bull Math Biol
4948:
4926:10.1.1.88.3071
4911:(1): 152â174.
4895:
4880:
4877:on 2011-10-01.
4854:(5): 699â720.
4828:
4816:
4791:
4775:
4762:
4749:10.1086/282400
4743:(910): 65â75.
4727:
4718:
4711:
4691:
4680:(6): 269â277.
4664:
4643:
4616:(2): 210â221.
4600:
4574:
4551:
4517:
4491:
4440:
4384:
4370:
4361:
4319:
4305:
4254:
4216:
4197:(1â2): 49â57.
4181:
4152:(3): 1147â53.
4124:
4109:
4086:
4053:(3): 311â326.
4030:
3987:
3930:
3917:(1): 119â163.
3897:
3880:
3859:
3846:
3836:Lotka, A.J.,
3829:
3809:
3778:
3727:
3662:
3647:
3619:
3604:
3575:
3560:
3510:
3483:(3): 382â403.
3467:
3450:
3443:
3422:
3399:
3376:
3360:Jopp F (2011)
3353:
3332:
3306:
3234:
3206:
3178:
3162:May RM (2001)
3149:
3148:
3146:
3143:
3141:
3140:
3135:
3130:
3125:
3120:
3115:
3110:
3105:
3095:
3090:
3085:
3080:
3074:
3072:
3069:
3067:
3066:
3059:
3052:
3045:
3038:
3031:
3023:
3021:
3018:
3017:
3016:
3011:
2997:
2994:
2920:
2917:
2900:
2899:Other theories
2897:
2893:systems theory
2865:Charles Darwin
2863:that prompted
2845:Main article:
2842:
2839:
2816:
2813:
2748:herd behaviour
2742:of birds, the
2706:
2703:
2698:Main article:
2695:
2692:
2683:Main article:
2680:
2677:
2669:trophic levels
2661:thermodynamics
2644:
2641:
2629:Sir Robert May
2625:Robert Paine's
2609:trophic levels
2589:
2586:
2572:eutrophication
2500:
2497:
2493:
2492:
2485:
2464:
2461:
2460:
2445:
2441:
2435:
2431:
2425:
2418:
2414:
2410:
2405:
2400:
2395:
2391:
2375:
2371:
2367:
2363:
2359:
2356:
2355:
2342:
2338:
2332:
2328:
2324:
2321:
2316:
2312:
2308:
2305:
2302:
2297:
2293:
2289:
2284:
2280:
2276:
2273:
2270:
2265:
2261:
2255:
2251:
2247:
2241:
2238:
2231:
2227:
2223:
2210:
2197:
2193:
2189:
2186:
2183:
2178:
2174:
2170:
2167:
2164:
2159:
2155:
2149:
2145:
2141:
2135:
2132:
2125:
2121:
2117:
2099:
2095:
2084:
2083:
2072:
2069:
2066:
2063:
2060:
2057:
2054:
2051:
2048:
2045:
2042:
2036:
2033:
2028:
2025:
2005:Patch dynamics
2001:Metapopulation
1996:
1993:
1988:Main article:
1985:
1982:
1926:Main article:
1923:
1920:
1879:
1876:
1871:Main article:
1868:
1865:
1779:Main article:
1776:
1775:Neutral theory
1773:
1772:
1771:
1753:
1749:
1741:
1737:
1733:
1729:
1725:
1721:
1717:
1713:
1709:
1708:
1696:
1690:
1686:
1680:
1676:
1672:
1667:
1663:
1659:
1654:
1650:
1645:
1637:
1633:
1626:
1622:
1616:
1612:
1605:
1599:
1596:
1589:
1585:
1581:
1568:
1556:
1550:
1546:
1540:
1536:
1532:
1527:
1523:
1519:
1514:
1510:
1505:
1497:
1493:
1486:
1482:
1476:
1472:
1465:
1459:
1456:
1449:
1445:
1441:
1417:D. discoiderum
1411:
1407:
1403:
1400:
1391:
1387:
1384:
1383:
1372:
1367:
1363:
1359:
1354:
1350:
1346:
1343:
1335:
1331:
1324:
1321:
1316:
1313:
1310:
1306:
1295:
1284:
1281:
1276:
1272:
1268:
1263:
1259:
1255:
1252:
1249:
1246:
1243:
1235:
1231:
1224:
1221:
1216:
1213:
1210:
1206:
1182:
1179:
1164:
1161:
1112:
1111:
1100:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1052:
1049:
1044:
1041:
1038:
1035:
1032:
1019:
1008:
1005:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
972:
969:
963:
960:
955:
952:
949:
946:
943:
910:
907:
886:Main article:
883:
880:
852:age-structured
822:
817:
816:
803:
798:
792:
788:
783:
780:
777:
772:
748:
745:
734:
733:
721:
715:
712:
707:
704:
700:
696:
693:
690:
687:
684:
681:
675:
672:
667:
664:
661:
658:
655:
638:
637:
626:
623:
620:
617:
614:
611:
608:
605:
602:
599:
596:
593:
590:
587:
584:
581:
578:
575:
572:
569:
566:
563:
560:
557:
554:
551:
545:
542:
537:
534:
531:
528:
525:
499:Main article:
496:
493:
489:Thomas Malthus
481:
480:
466:
463:
459:
452:
449:
446:
443:
440:
437:
434:
431:
428:
406:
405:
394:
391:
388:
385:
382:
379:
373:
370:
365:
362:
359:
356:
353:
331:Main article:
328:
325:
295:Main article:
292:
289:
204:interactions.
183:
182:
175:Matrix algebra
167:
152:
151:
144:
121:
120:
117:
108:
105:
24:
14:
13:
10:
9:
6:
4:
3:
2:
7726:
7715:
7712:
7710:
7707:
7705:
7702:
7701:
7699:
7686:
7681:
7675:
7672:
7670:
7669:Urban ecology
7667:
7665:
7662:
7660:
7657:
7655:
7652:
7650:
7647:
7645:
7642:
7640:
7637:
7635:
7632:
7630:
7627:
7625:
7622:
7620:
7617:
7615:
7612:
7610:
7607:
7605:
7602:
7600:
7597:
7595:
7592:
7590:
7587:
7585:
7582:
7580:
7577:
7575:
7572:
7570:
7567:
7565:
7562:
7561:
7559:
7555:
7549:
7546:
7544:
7541:
7539:
7536:
7534:
7531:
7529:
7528:Kleiber's law
7526:
7524:
7521:
7519:
7516:
7514:
7511:
7509:
7506:
7504:
7501:
7499:
7496:
7494:
7491:
7489:
7486:
7484:
7481:
7479:
7476:
7474:
7471:
7469:
7466:
7465:
7463:
7461:
7455:
7449:
7446:
7444:
7441:
7439:
7436:
7434:
7431:
7429:
7426:
7422:
7419:
7418:
7417:
7414:
7412:
7409:
7407:
7404:
7402:
7399:
7397:
7394:
7392:
7389:
7388:
7386:
7384:
7380:
7374:
7371:
7369:
7366:
7364:
7362:
7358:
7354:
7352:
7349:
7347:
7344:
7342:
7339:
7337:
7334:
7332:
7329:
7327:
7324:
7322:
7319:
7317:
7314:
7312:
7309:
7307:
7304:
7302:
7301:Foster's rule
7299:
7297:
7294:
7292:
7289:
7287:
7284:
7282:
7279:
7277:
7274:
7272:
7269:
7267:
7264:
7263:
7261:
7259:
7253:
7247:
7244:
7242:
7239:
7237:
7234:
7232:
7229:
7227:
7224:
7222:
7219:
7217:
7214:
7212:
7209:
7207:
7204:
7202:
7199:
7198:
7196:
7190:
7184:
7181:
7179:
7176:
7174:
7171:
7169:
7166:
7164:
7161:
7159:
7156:
7154:
7151:
7149:
7146:
7144:
7141:
7139:
7136:
7134:
7131:
7129:
7126:
7124:
7121:
7119:
7116:
7114:
7111:
7109:
7105:
7102:
7100:
7097:
7095:
7092:
7090:
7087:
7085:
7082:
7080:
7077:
7075:
7072:
7070:
7067:
7065:
7062:
7060:
7057:
7056:
7054:
7050:
7044:
7041:
7037:
7034:
7032:
7029:
7028:
7027:
7024:
7022:
7019:
7017:
7014:
7012:
7009:
7007:
7004:
7002:
6999:
6997:
6994:
6992:
6989:
6987:
6984:
6982:
6979:
6977:
6974:
6972:
6969:
6967:
6964:
6962:
6959:
6957:
6954:
6952:
6949:
6947:
6944:
6942:
6939:
6937:
6934:
6932:
6929:
6928:
6926:
6924:
6918:
6913:
6909:
6902:
6897:
6895:
6890:
6888:
6883:
6882:
6879:
6867:
6864:
6862:
6859:
6857:
6854:
6852:
6849:
6847:
6844:
6842:
6839:
6837:
6834:
6832:
6829:
6828:
6826:
6820:
6814:
6811:
6809:
6806:
6804:
6801:
6799:
6796:
6794:
6791:
6789:
6786:
6784:
6781:
6779:
6776:
6774:
6771:
6769:
6766:
6764:
6761:
6759:
6756:
6754:
6751:
6749:
6746:
6744:
6741:
6739:
6736:
6734:
6731:
6729:
6726:
6724:
6721:
6719:
6716:
6714:
6711:
6709:
6706:
6705:
6703:
6699:
6691:
6688:
6686:
6683:
6681:
6678:
6676:
6673:
6671:
6668:
6666:
6663:
6661:
6658:
6657:
6656:
6653:
6651:
6648:
6646:
6643:
6641:
6638:
6636:
6633:
6632:
6630:
6626:
6620:
6619:Trophic level
6617:
6615:
6612:
6610:
6607:
6605:
6602:
6600:
6597:
6595:
6592:
6591:
6589:
6587:
6583:
6577:
6576:Phage ecology
6574:
6572:
6569:
6567:
6566:Microbial mat
6564:
6562:
6559:
6557:
6554:
6552:
6549:
6547:
6544:
6542:
6539:
6537:
6534:
6532:
6529:
6527:
6524:
6522:
6521:Bacteriophage
6519:
6517:
6514:
6513:
6511:
6509:
6505:
6499:
6496:
6494:
6491:
6489:
6488:Decomposition
6486:
6484:
6481:
6480:
6478:
6476:
6472:
6466:
6463:
6461:
6458:
6456:
6453:
6451:
6448:
6446:
6443:
6441:
6438:
6436:
6435:Mesopredators
6433:
6431:
6428:
6426:
6423:
6421:
6418:
6416:
6413:
6411:
6408:
6406:
6403:
6401:
6398:
6396:
6393:
6391:
6388:
6386:
6383:
6381:
6380:Apex predator
6378:
6377:
6375:
6373:
6369:
6363:
6360:
6358:
6355:
6353:
6350:
6348:
6345:
6343:
6340:
6338:
6335:
6333:
6330:
6328:
6325:
6323:
6320:
6318:
6315:
6313:
6310:
6308:
6305:
6303:
6300:
6298:
6295:
6293:
6290:
6289:
6287:
6285:
6281:
6275:
6272:
6270:
6267:
6265:
6262:
6260:
6257:
6255:
6252:
6250:
6247:
6245:
6242:
6240:
6237:
6235:
6232:
6230:
6227:
6225:
6222:
6220:
6217:
6215:
6214:Biotic stress
6212:
6210:
6207:
6205:
6202:
6200:
6197:
6195:
6192:
6190:
6187:
6185:
6182:
6181:
6179:
6175:
6170:
6166:
6162:
6155:
6150:
6148:
6143:
6141:
6136:
6135:
6132:
6120:
6117:
6115:
6112:
6110:
6107:
6103:
6100:
6099:
6098:
6095:
6093:
6090:
6088:
6085:
6084:
6082:
6078:
6072:
6069:
6067:
6064:
6062:
6059:
6057:
6054:
6052:
6049:
6047:
6044:
6043:
6041:
6039:
6035:
6029:
6026:
6024:
6021:
6019:
6016:
6014:
6011:
6009:
6006:
6004:
6001:
5999:
5996:
5994:
5991:
5989:
5986:
5984:
5981:
5979:
5978:Ecotoxicology
5976:
5974:
5973:Ecophysiology
5971:
5969:
5966:
5964:
5961:
5959:
5956:
5955:
5953:
5951:
5947:
5941:
5940:Urban ecology
5938:
5936:
5933:
5931:
5928:
5926:
5923:
5921:
5918:
5914:
5911:
5910:
5909:
5908:Polar ecology
5906:
5905:
5903:
5901:
5897:
5893:
5887:
5886:Human ecology
5884:
5882:
5879:
5877:
5876:Plant ecology
5874:
5872:
5869:
5868:
5866:
5864:
5860:
5856:
5848:
5845:
5843:
5840:
5838:
5835:
5834:
5833:
5830:
5828:
5825:
5824:
5822:
5819:
5815:
5809:
5806:
5804:
5801:
5800:
5798:
5796:
5795:Spatial scale
5792:
5786:
5783:
5781:
5778:
5776:
5775:Field ecology
5773:
5772:
5770:
5768:
5764:
5760:
5753:
5748:
5746:
5741:
5739:
5734:
5733:
5730:
5722:
5721:
5716:
5713:
5709:
5705:
5704:
5699:
5696:
5692:
5688:
5687:
5682:
5679:
5675:
5671:
5670:
5665:
5662:
5658:
5654:
5653:
5648:
5641:
5637:
5633:
5629:
5625:
5620:
5615:
5611:
5607:
5603:
5599:
5592:
5587:
5584:
5580:
5576:
5575:
5571:Kot M (2001)
5570:
5567:
5563:
5559:
5558:
5553:
5550:
5549:
5544:
5541:
5537:
5533:
5532:
5527:
5524:
5520:
5516:
5515:
5510:
5507:
5503:
5499:
5498:
5493:
5490:
5486:
5482:
5481:
5476:
5473:
5469:
5465:
5461:
5458:
5454:
5450:
5449:
5444:
5441:
5437:
5433:
5432:
5427:
5426:
5419:
5415:
5411:
5407:
5406:Angela McLean
5403:
5399:
5398:
5393:
5383:
5382:2027.42/26318
5378:
5374:
5370:
5366:
5362:
5355:
5348:
5346:
5342:
5338:
5334:
5330:
5329:
5322:
5319:
5313:
5310:
5304:
5301:
5289:
5282:
5279:
5268:
5264:
5257:
5254:
5242:
5235:
5233:
5229:
5224:
5220:
5215:
5210:
5206:
5202:
5198:
5194:
5190:
5186:
5182:
5178:
5174:
5167:
5164:
5159:
5155:
5151:
5147:
5142:
5137:
5133:
5129:
5125:
5118:
5115:
5110:
5106:
5101:
5096:
5092:
5088:
5084:
5080:
5076:
5072:
5068:
5064:
5060:
5053:
5050:
5045:
5039:
5035:
5031:
5026:
5021:
5014:
5013:
5005:
5002:
4997:
4993:
4989:
4985:
4981:
4977:
4972:
4971:q-bio/0504001
4967:
4963:
4959:
4952:
4949:
4944:
4940:
4936:
4932:
4927:
4922:
4918:
4914:
4910:
4906:
4899:
4896:
4893:
4890:
4884:
4881:
4873:
4869:
4865:
4861:
4857:
4853:
4849:
4842:
4835:
4833:
4829:
4826:
4820:
4817:
4814:
4813:9780521288866
4810:
4806:
4805:
4800:
4799:Peters, R. H.
4795:
4792:
4788:
4784:
4783:Ecophysiology
4779:
4776:
4772:
4766:
4763:
4758:
4754:
4750:
4746:
4742:
4738:
4731:
4728:
4722:
4719:
4714:
4708:
4704:
4703:
4695:
4692:
4687:
4683:
4679:
4675:
4668:
4665:
4661:
4660:0-231-10828-1
4657:
4653:
4647:
4644:
4639:
4635:
4631:
4627:
4623:
4619:
4615:
4611:
4604:
4601:
4597:
4593:
4589:
4588:
4581:
4579:
4575:
4571:
4567:
4563:
4562:
4555:
4552:
4547:
4543:
4540:(1â2): 3â16.
4539:
4535:
4528:
4521:
4518:
4514:
4510:
4506:
4505:
4500:
4495:
4492:
4487:
4483:
4478:
4473:
4468:
4463:
4459:
4455:
4451:
4444:
4441:
4430:on 2010-12-30
4426:
4422:
4418:
4414:
4410:
4406:
4402:
4395:
4388:
4385:
4382:
4381:
4374:
4371:
4365:
4362:
4357:
4353:
4349:
4345:
4341:
4337:
4330:
4323:
4320:
4317:
4316:
4309:
4306:
4301:
4297:
4293:
4289:
4285:
4281:
4277:
4273:
4269:
4265:
4258:
4255:
4250:
4246:
4242:
4238:
4234:
4230:
4223:
4221:
4217:
4212:
4208:
4204:
4200:
4196:
4192:
4185:
4182:
4177:
4173:
4168:
4163:
4159:
4155:
4151:
4147:
4143:
4141:
4137:
4128:
4125:
4120:
4113:
4110:
4106:
4105:9780199913831
4102:
4098:
4097:
4090:
4087:
4076:on 2016-03-04
4072:
4068:
4064:
4060:
4056:
4052:
4048:
4041:
4034:
4031:
4026:
4022:
4018:
4014:
4010:
4006:
4002:
3998:
3991:
3988:
3983:
3979:
3974:
3969:
3965:
3961:
3957:
3953:
3949:
3945:
3941:
3934:
3931:
3925:
3920:
3916:
3912:
3908:
3901:
3898:
3893:
3892:
3884:
3881:
3876:
3872:
3871:
3863:
3860:
3856:
3850:
3847:
3843:
3839:
3833:
3830:
3825:
3818:
3816:
3814:
3810:
3799:on 2011-07-18
3798:
3794:
3787:
3785:
3783:
3779:
3774:
3770:
3766:
3762:
3758:
3754:
3750:
3746:
3742:
3738:
3731:
3728:
3723:
3717:
3709:
3705:
3701:
3697:
3693:
3689:
3685:
3681:
3677:
3673:
3666:
3663:
3658:
3651:
3648:
3644:
3640:
3636:
3635:
3628:
3626:
3624:
3620:
3615:
3611:
3607:
3605:9780721669410
3601:
3597:
3592:
3591:
3585:
3579:
3576:
3572:
3571:
3564:
3561:
3556:
3552:
3548:
3544:
3540:
3536:
3533:(1): 209â21.
3532:
3528:
3521:
3514:
3511:
3506:
3502:
3498:
3494:
3490:
3486:
3482:
3478:
3471:
3468:
3463:
3462:
3454:
3451:
3446:
3440:
3436:
3432:
3426:
3423:
3419:
3415:
3411:
3410:
3403:
3400:
3396:
3392:
3388:
3387:
3380:
3377:
3373:
3369:
3365:
3364:
3357:
3354:
3350:
3346:
3342:
3336:
3333:
3329:
3325:
3321:
3320:
3313:
3311:
3307:
3296:on 2011-08-14
3292:
3288:
3284:
3280:
3276:
3272:
3268:
3264:
3260:
3256:
3252:
3245:
3238:
3235:
3231:
3227:
3223:
3222:
3215:
3213:
3211:
3207:
3203:
3199:
3195:
3194:
3187:
3185:
3183:
3179:
3175:
3171:
3167:
3166:
3159:
3157:
3155:
3151:
3144:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3103:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3075:
3070:
3065:
3064:
3060:
3058:
3057:
3053:
3051:
3050:
3046:
3044:
3043:
3039:
3037:
3036:
3032:
3030:
3029:
3025:
3024:
3019:
3015:
3012:
3010:
3007:
3006:
3005:
3002:
2995:
2993:
2991:
2987:
2983:
2979:
2977:
2976:Jared Diamond
2973:
2969:
2964:
2962:
2961:
2956:
2952:
2948:
2944:
2940:
2936:
2932:
2926:
2918:
2916:
2914:
2910:
2906:
2898:
2896:
2894:
2889:
2885:
2884:cybernetician
2879:
2878:
2875:
2868:
2866:
2862:
2858:
2854:
2848:
2840:
2838:
2836:
2832:
2828:
2823:
2822:
2814:
2812:
2810:
2806:
2802:
2801:
2796:
2791:
2789:
2785:
2781:
2776:
2772:
2768:
2764:
2759:
2757:
2753:
2749:
2745:
2741:
2737:
2733:
2729:
2724:
2716:
2711:
2704:
2701:
2693:
2691:
2686:
2685:Ecophysiology
2679:Ecophysiology
2678:
2676:
2674:
2670:
2666:
2662:
2657:
2653:
2649:
2642:
2640:
2638:
2634:
2630:
2626:
2622:
2621:Charles Elton
2617:
2614:
2610:
2606:
2602:
2598:
2594:
2587:
2585:
2583:
2579:
2575:
2573:
2569:
2565:
2561:
2557:
2553:
2548:
2543:
2541:
2537:
2532:
2528:
2524:
2520:
2516:
2512:
2506:
2498:
2496:
2490:
2489:rescue effect
2486:
2482:
2481:
2480:
2477:
2475:
2471:
2443:
2439:
2433:
2429:
2423:
2416:
2412:
2408:
2403:
2398:
2393:
2389:
2381:
2380:
2379:
2340:
2336:
2330:
2326:
2322:
2319:
2314:
2310:
2306:
2303:
2295:
2291:
2287:
2282:
2278:
2274:
2271:
2263:
2259:
2253:
2249:
2245:
2239:
2236:
2229:
2225:
2221:
2211:
2195:
2191:
2187:
2184:
2176:
2172:
2168:
2165:
2157:
2153:
2147:
2143:
2139:
2133:
2130:
2123:
2119:
2115:
2105:
2104:
2103:
2093:
2089:
2070:
2067:
2064:
2058:
2055:
2052:
2046:
2043:
2040:
2034:
2031:
2026:
2023:
2013:
2012:
2011:
2006:
2002:
1994:
1991:
1983:
1978:
1974:
1970:
1965:
1961:
1959:
1955:
1951:
1947:
1943:
1939:
1935:
1929:
1928:r/K selection
1921:
1919:
1917:
1913:
1909:
1905:
1904:
1899:
1895:
1891:
1886:
1884:
1877:
1874:
1866:
1864:
1862:
1858:
1855:'s theory of
1854:
1850:
1845:
1843:
1839:
1835:
1831:
1827:
1823:
1818:
1816:
1812:
1808:
1804:
1800:
1799:trophic level
1795:
1791:
1787:
1782:
1774:
1770:
1768:
1763:
1762:
1761:
1759:
1747:
1694:
1688:
1684:
1678:
1674:
1670:
1665:
1661:
1657:
1652:
1648:
1643:
1635:
1631:
1624:
1620:
1614:
1610:
1603:
1597:
1594:
1587:
1583:
1579:
1569:
1554:
1548:
1544:
1538:
1534:
1530:
1525:
1521:
1517:
1512:
1508:
1503:
1495:
1491:
1484:
1480:
1474:
1470:
1463:
1457:
1454:
1447:
1443:
1439:
1429:
1428:
1427:
1425:
1424:
1419:
1418:
1401:
1399:
1397:
1365:
1361:
1357:
1352:
1348:
1341:
1333:
1329:
1322:
1319:
1314:
1311:
1308:
1304:
1296:
1274:
1270:
1266:
1261:
1257:
1250:
1247:
1244:
1233:
1229:
1222:
1219:
1214:
1211:
1208:
1204:
1196:
1195:
1194:
1192:
1188:
1180:
1178:
1176:
1170:
1162:
1160:
1158:
1153:
1151:
1150:
1145:
1141:
1137:
1133:
1132:Canadian lynx
1129:
1128:snowshoe hare
1125:
1121:
1116:
1095:
1092:
1086:
1080:
1077:
1074:
1065:
1059:
1056:
1050:
1047:
1039:
1033:
1030:
1020:
1000:
994:
991:
988:
985:
976:
970:
967:
961:
958:
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7639:Macroecology
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7266:Biogeography
7211:Commensalism
7059:Biodiversity
6936:Allee effect
6675:kelp forests
6628:Example webs
6493:Detritivores
6332:Organotrophs
6312:Kinetotrophs
6264:Productivity
6119:Biogeography
6013:Paleoecology
5988:Fire ecology
5930:Soil ecology
5818:Organisation
5808:Macroecology
5803:Microecology
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3133:Taylor's law
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2803:behave like
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2723:Swarm models
2688:
2665:energy flows
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2474:biodiversity
2472:, where the
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2088:colonization
2085:
2008:
1990:Niche models
1984:Niche theory
1960:-selection.
1957:
1953:
1949:
1931:
1901:
1887:
1883:Biogeography
1881:
1878:Biogeography
1846:
1841:
1838:biodiversity
1819:
1815:niche theory
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876:right whales
862:
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110:
101:carbon cycle
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7291:Disturbance
7194:interaction
7016:Recruitment
6946:Depensation
6738:Copiotrophs
6609:Energy flow
6531:Lithotrophy
6475:Decomposers
6455:Planktivore
6430:Insectivore
6420:Heterotroph
6385:Bacterivore
6352:Phototrophs
6302:Chemotrophs
6274:Restoration
6224:Competition
6046:Agroecology
5767:Methodology
4235:: 122â123.
3431:May, Robert
2955:E.O. Wilson
2633:Stuart Pimm
2613:Food energy
2597:food chains
1948:experience
1898:E.O. Wilson
1807:random walk
1746:competitive
411:first order
317:environment
313:populations
244:R.A. Fisher
80:competition
7698:Categories
7659:Sexecology
7236:Parasitism
7201:Antibiosis
7036:Resistance
7031:Resilience
6921:Population
6841:Camouflage
6793:Oligotroph
6708:Ascendency
6670:intertidal
6660:cold seeps
6614:Food chain
6415:Herbivores
6390:Carnivores
6317:Mixotrophs
6292:Autotrophs
6171:components
5832:Synecology
5827:Autecology
5534:Springer.
5410:Robert May
5294:2007-04-04
5272:2007-04-22
5247:2007-05-11
5134:: e78908.
4434:2015-01-05
4080:2013-06-26
3803:2010-12-16
3659:. Sinauer.
3322:Springer.
3300:2011-05-13
3145:References
2923:See also:
2763:Lagrangian
2721:See also:
2547:stochastic
2540:resiliency
2519:ecosystems
2503:See also:
2092:extinction
1999:See also:
1969:coral reef
1900:published
1826:parasitism
1187:parasitoid
1167:See also:
1144:parasitoid
751:See also:
237:Robert May
233:non-linear
129:stochastic
7564:Allometry
7518:Emergence
7246:Symbiosis
7231:Mutualism
7026:Stability
6931:Abundance
6743:Dominance
6701:Processes
6690:tide pool
6586:Food webs
6460:Predation
6445:Omnivores
6372:Consumers
6327:Mycotroph
6284:Producers
6229:Ecosystem
6194:Behaviour
5614:CiteSeerX
5205:2375-2548
5150:2050-084X
5091:0027-8424
5020:CiteSeerX
4921:CiteSeerX
4454:PLOS Biol
4421:0012-9658
4211:189902519
3877:: 31â113.
3857:, (1971)
3193:Food Webs
3102:dispersal
2939:E.P. Odum
2935:H.T. Odum
2857:evolution
2744:schooling
2736:migrating
2637:stability
2619:In 1927,
2605:autotroph
2593:Food webs
2588:Food webs
2424:−
2399:∗
2320:−
2304:−
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2275:−
2185:−
2169:−
2065:−
2056:−
1942:resources
1849:MacArthur
1830:predation
1758:mutualism
1675:α
1658:−
1535:α
1518:−
1386:where f(N
1248:−
1223:λ
1093:−
1078:α
992:α
989:−
894:sympatric
706:−
592:−
583:−
562:−
285:fisheries
277:nonlinear
254:evolution
242:In 1930,
191:predation
84:food webs
33:food webs
7619:Endolith
7548:Xerosere
7460:networks
7276:Ecocline
6822:Defense,
6498:Detritus
6400:Foraging
6269:Resource
6109:Ecosophy
5859:Taxonomy
5820:or scope
5223:36383660
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5109:36897970
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3844:, (1925)
3765:11734852
3708:16608658
3586:(1959).
3505:13761767
3433:(1976).
3071:See also
3020:Journals
2767:Eulerian
2752:emergent
2740:flocking
2656:holistic
2536:toxicity
2102:. Then,
1834:swarming
1803:food web
1175:pathogen
858:models.
487:, after
76:dynamics
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7416:Habitat
7286:Ecotype
7281:Ecotone
7258:ecology
7256:Spatial
7192:Species
7052:Species
6923:ecology
6908:Ecology
6856:Mimicry
6824:counter
6768:f-ratio
6516:Archaea
6204:Biomass
6177:General
6169:Trophic
6161:Ecology
5636:3546712
5606:Bibcode
5214:9668303
5185:Bibcode
5071:Bibcode
4913:Bibcode
4856:Bibcode
4801:(1986)
4638:3544021
4618:Bibcode
4501:(1999)
4477:1543692
4401:Ecology
4300:1627734
4272:Bibcode
4176:4555407
4055:Bibcode
4005:Bibcode
3973:2760158
3952:Bibcode
3944:Science
3773:4407832
3745:Bibcode
3700:1939225
3680:Bibcode
3672:Ecology
3555:4459582
3535:Bibcode
3485:Bibcode
3287:4370167
3279:2330029
3259:Bibcode
2919:History
2859:due to
2715:to land
2690:size".
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5632:JSTOR
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5357:(PDF)
5128:eLife
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2071:p
2068:e
2062:)
2059:p
2053:1
2050:(
2047:p
2044:m
2041:=
2035:t
2032:d
2027:p
2024:d
1979:.
1958:K
1954:r
1842:Ξ
1734:1
1730:2
1722:1
1718:2
1712:α
1695:)
1689:1
1685:N
1671:+
1666:2
1662:N
1653:2
1649:K
1644:(
1636:2
1632:K
1625:2
1621:N
1615:2
1611:r
1604:=
1598:t
1595:d
1588:2
1584:N
1580:d
1555:)
1549:2
1545:N
1531:+
1526:1
1522:N
1513:1
1509:K
1504:(
1496:1
1492:K
1485:1
1481:N
1475:1
1471:r
1464:=
1458:t
1455:d
1448:1
1444:N
1440:d
1412:2
1408:1
1392:t
1388:t
1371:)
1366:t
1362:p
1358:,
1353:t
1349:N
1345:(
1342:f
1334:t
1330:N
1323:c
1320:=
1315:1
1312:+
1309:t
1305:P
1283:]
1280:)
1275:t
1271:P
1267:,
1262:t
1258:N
1254:(
1251:f
1245:1
1242:[
1234:t
1230:N
1220:=
1215:1
1212:+
1209:t
1205:N
1099:)
1096:d
1090:)
1087:t
1084:(
1081:N
1075:c
1072:(
1069:)
1066:t
1063:(
1060:P
1057:=
1051:t
1048:d
1043:)
1040:t
1037:(
1034:P
1031:d
1007:)
1004:)
1001:t
998:(
995:P
986:r
983:(
980:)
977:t
974:(
971:N
968:=
962:t
959:d
954:)
951:t
948:(
945:N
942:d
863:L
844:L
836:L
832:t
823:t
821:N
802:t
797:N
791:L
787:=
782:1
779:+
776:t
771:N
720:)
714:K
711:N
703:1
699:(
695:)
692:t
689:(
686:N
683:r
680:=
674:t
671:d
666:)
663:t
660:(
657:N
654:d
625:)
622:t
619:(
616:N
613:)
610:)
607:)
604:t
601:(
598:N
595:c
589:d
586:(
580:)
577:)
574:t
571:(
568:N
565:a
559:b
556:(
553:(
550:=
544:t
541:d
536:)
533:t
530:(
527:N
524:d
479:,
465:t
462:r
458:e
451:)
448:0
445:(
442:N
439:=
436:)
433:t
430:(
427:N
393:)
390:t
387:(
384:N
381:r
378:=
372:t
369:d
364:)
361:t
358:(
355:N
352:d
166:.
20:)
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