Theoretical ecology

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.

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.

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.

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.

This first order linear differential equation can be solved to yield the solution a trajectory known as Malthusian growth, after Thomas Malthus, who first described its dynamics in 1798.

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).

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).

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.

[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.

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.

The hypothesis has sparked controversy, and some authors consider it a more complex version of other null models that fit the data better.

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.

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.

[37] The application of island biogeography theory to habitat fragments spurred the development of the fields of conservation biology and landscape ecology.

As the population becomes more crowded, it approaches the island's carrying capacity, thus forcing individuals to compete more heavily for fewer available resources.

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.

For example: 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.

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.

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.

[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.

[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.

Like other fields in theoretical ecology, it uses and extends concepts from thermodynamics and develops other macroscopic descriptions of complex systems.

[62] The coexistence of the synchronization and asynchronization in the flashings in the system composed of multiple fireflies could be characterized by the chimera states.

The flashings of individual fireflies could be viewed as oscillators and the global coupling models were similar to the ones used in condensed matter physics.

In his famous 1858 paper, Wallace proposed natural selection as a kind of feedback mechanism which keeps species and varieties adapted to their environment.

[64] 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.

[65]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".

[69] 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.

[70] This resulted in the supporters of Jared Diamond's community assembly rules defending their ideas through Neutral Model Analysis.

Stephen P. 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.