# Theoretical ecology

Theoretical ecology is the scientific discipline devoted to the study of ecological systems using theoretical methods such as simple conceptual models, mathematical models, computational simulations, and advanced data analysis. Effective models improve understanding of the natural world by revealing how the dynamics of species populations are often based on fundamental biological conditions and processes. Further, the field aims to unify a diverse range of empirical observations by assuming that common, mechanistic processes generate observable phenomena across species and ecological environments. Based on biologically realistic assumptions, theoretical ecologists are able to uncover novel, non-intuitive insights about natural processes. Theoretical results are often verified by empirical and observational studies, revealing the power of theoretical methods in both predicting and understanding the noisy, diverse biological world.

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

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

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

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

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