Ascendency
Encyclopedia
Ascendency is a quantitative attribute of an ecosystem
, defined as a function of the ecosystem's trophic network. Ascendency is derived using mathematical tools from information theory
. It is intended to capture in a single index the ability of an ecosystem to prevail against disturbance
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 willy-nilly. Almost half a century earlier, Alfred J. Lotka
(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 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
(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.)
Ecosystem
An ecosystem is a biological environment consisting of all the organisms living in a particular area, as well as all the nonliving , physical components of the environment with which the organisms interact, such as air, soil, water and sunlight....
, defined as a function of the ecosystem's trophic network. Ascendency is derived using mathematical tools from information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...
. It is intended to capture in a single index the ability of an ecosystem to prevail against disturbance
Disturbance
In ecology, a disturbance is a temporary change in average environmental conditions that causes a pronounced change in an ecosystem. Outside disturbance forces often act quickly and with great effect, sometimes resulting in the removal of large amounts of biomass...
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 willy-nilly. Almost half a century earlier, Alfred J. Lotka
Alfred J. Lotka
Alfred James Lotka was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics. An American biophysicist best known for his proposal of the predator-prey model, developed simultaneously but independently of Vito Volterra...
(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
Robert Ulanowicz
Robert Edward Ulanowicz is an American theoretical ecologist and philosopher who is best known for his search for a unified theory of ecology. He was born September 17, 1943 in Baltimore, Maryland....
1986). Coherence is gauged by the average mutual information 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 von Liebig
Justus von Liebig was a German chemist who made major contributions to agricultural and biological chemistry, and worked on the organization of organic chemistry. As a professor, he devised the modern laboratory-oriented teaching method, and for such innovations, he is regarded as one of the...
(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.)