Ascendency or ascendancy is a quantitative attribute of an

ecosystem An ecosystem (or ecological system) consists of all the organisms and the physical environment with which they interact. These biotic and abiotic components are linked together through nutrient cycles and energy flows. Energy enters the syst ...

, defined as a function of the ecosystem's

trophic network A food web is the natural interconnection of food chains and a graphical representation of what-eats-what in an ecological community. Another name for food web is consumer-resource system. Ecologists can broadly lump all life forms into one ...

. Ascendency is derived using mathematical tools from

information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...

. It is intended to capture in a single index the ability of an ecosystem to prevail against

disturbance Disturbance and its variants may refer to: Math and science * Disturbance (ecology), a temporary change in average environmental conditions that causes a pronounced change in an ecosystem * Disturbance (geology), linear zone of faults and folds ...

by virtue of its combined organization and size. One way of depicting ascendency is to regard it as "organized power", because the index represents the magnitude of the power that is flowing within the system towards particular ends, as distinct from power that is dissipated naturally. Almost half a century earlier,

Alfred J. Lotka Alfred James Lotka (March 2, 1880 – December 5, 1949) was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics. An American biophysicist, Lotka is best known for his proposa ...

(1922) had suggested that a system's capacity to prevail in evolution was related to its ability to capture useful power. Ascendency can thus be regarded as a refinement of Lotka's supposition that also takes into account how power is actually being channeled within a system. In mathematical terms, ascendency is the product of the aggregate amount of material or energy being transferred in an ecosystem times the coherency with which the outputs from the members of the system relate to the set of inputs to the same components ( Ulanowicz 1986). Coherence is gauged by the

average mutual information In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the " amount of information" (in units such a ...

shared between inputs and outputs (Rutledge et al. 1976). Originally, it was thought that ecosystems increase uniformly in ascendency as they developed, but subsequent empirical observation has suggested that all sustainable ecosystems are confined to a narrow "window of vitality" (Ulanowicz 2002). Systems with relative values of ascendency plotting below the window tend to fall apart due to lack of significant internal constraints, whereas systems above the window tend to be so "brittle" that they become vulnerable to external perturbations. Sensitivity analysis on the components of the ascendency reveals the controlling transfers within the system in the sense of

Liebig Justus Freiherr von Liebig (12 May 1803 – 20 April 1873) was a German scientist who made major contributions to agricultural and biological chemistry, and is considered one of the principal founders of organic chemistry. As a professor at t ...

(Ulanowicz and Baird 1999). That is, ascendency can be used to identify which resource is limiting the functioning of each component of the ecosystem. It is thought that autocatalytic feedback is the primary route by which systems increase and maintain their ascendencies (Ulanowicz 1997.)

References

* * * Ulanowicz, R.E. 1986. Growth & Development: Ecosystems Phenomenology. Springer-Verlag, NY. 203 p. * Ulanowicz, R.E. 1997. Ecology, the Ascendent Perspective. Columbia University Press, NY. 201p. * * {{modelling ecosystems Information theory Entropy and information Trophic ecology