## All here given defintions are taken from the MCED book and therefore,

## when using these, please quote (see Quote).

**Agent-based Modelling** Modelling concept which emerged predominantly in the

context of the social sciences to depict human interactions. It uses the same basic

concept as individual-based modelling (which emerged in ecology). Both terms can

be used synonymously.

**Alternative Stable States** Concept that describes ecological systems with

diverse stable states that depend on key drivers. The system can change from one

state to another (e.g. algae- vs. coral-dominated reef systems), when a critical

threshold is exceeded; this phenomenon is addressed as phase-shift or regime

shift ( –>hysteresis).

**Artificial Intelligence** Visionary branch of informatics that deals with the autom-

atization of intelligent behaviour, important in research and development; origi-

nally based on the idea of mimicking human-like intelligence.

**Autonomously Acting Agents **Autonomously Acting Agents in ! agent-based

modelling, system behaviour emerges on the basis of the interaction of “agents”

which change their state as a response to external influences and their internal

conditions. The concept is comparable to individual-based modelling, in which the

low-level component is referred to as individual.

**Bayesian Inference** A method of modern statistics, based on the Bayses’ Theo-

rem, which describes the relation of two reverse conditional probabilities.

Beer-Lambert Function Basic absorptiometric law that describes the absorption

of light dependent on the concentration of an absorbing component in the material

through which the light is travelling.

**Black-Box Approach** In general, this is any kind of machinery or construct in

which only input/output relations are focused on, without requiring considerations

of internal operation.

**Bootstrapping** A resampling with replacement method in statistics for drawing

conclusions from data that are subject to random variation.

Bray-Curtis Index An ecological metric that is used to describe the dissimilarity

of different sites using the species number at each site in relation to the total species

number.

**Carrying Capacity** A population size which does not allow a further increase

because of resource or environmental limitations.

**Cause-Effect Chain** The philosophical assumption that any effect has an ante-

cedent cause, allows a chain- or net-like arrangement of observed interactions that

are considered for modelling or other forms of description.

Chaotic Dynamics Special behaviour of dynamic systems with strong depen-

dency on initial conditions which can make long-term predictions impossible.

**Classical Logic** Logic is a subfield of mathematics concentrated on aspects of

reasoning. Classical logic is based on a number of axioms: law of identity (if a

statement is true, then it is true), law of the excluded middle (a statement is either

true or false), law of non-contradiction (a statement cannot be both true and false).

Classical logic is bivalent: the truth value of a statement may only be either true or

false. Statements can be connected by logical operators (and, or, if..then, …), whose

definition allows to identify the truth value of the resulting statement. There are also

types of nonclassical, multivalued logic, e.g. fuzzy logic, which rejects the laws of

excluded middle and non-contradiction, allowing a statement to be both true and false.

**Computer Scenarios** In computer experiments, different sets of conditions are

grouped into alternative cases and the reaction of the model components to the

variation of these characteristics is assessed through simulation. Scenarios are

widely used to evaluate the outcomes of possible future situations (e.g. global

climate change situation at increased temperatures) on the target variables.

**Cybernetics** This is an interdisciplinary approach of control and regulation of

complex systems, like machinery or living organisms, founded by Norbert Wiener.

A classic example is the regulation of temperature by a thermostat.

**Ecological Niche** Describes the position of a species in a formalized multi-

dimensional space of environmental variables and variables describing resource

requirements – e.g. the tolerated range of temperature, salinity, or minimum

quantities of soil nutrients.

**Ecosystem Indicators** Measurable features in management and conservation

ecology which are used to document certain ecosystem states (like ecosystem

health). An indicator has to be measurable more easily than the target that it

indicates. To be usable as an indicator, it needs to have a defined relationship to

the ecological condition that is indicated.

**Ecosystem Resilience** The ability of an ecological system to resist external

disturbances and to maintain its primary state with state variables, driving variables,

and parameters. To trigger a –>phase-shift the disturbance has to be stronger in

higher resilient systems.

**Eigenvector** See –>eigenvalue.

**Eigenvalue** It is a number l satisfying the equation Av = lv, the non-zero

vector v being the eigenvector of the ! square matrix A. In general, a matrix

acts on a vector by changing both its magnitude and its direction. A matrix acts on

an eigenvector by multiplying its magnitude by a factor, which is positive if its

direction is unchanged and negative if its direction is reversed. This factor is the

eigenvalue associated with that eigenvector. They both give important information

about the matrix, and can be used e.g. in matrix factorization.

**Emergent Properties** On the basis of interactions between lower-level compo-

nents, new qualities can appear on higher hierarchical integration levels which

represent more than the sum of the constituting elements.

**Exergy** A thermodynamical concept, that indicates the sum of the energy in a

system that can realize work, when the system is brought into a thermodynamic

equilibrium.

**Feedback Process** It describes the mechanism in a –> cause-effect chain, in

which the output signal loops back and influences the input conditions.

**Fractal** A geometric term to describe objects which show self-similarity on

different levels of magnification. Any part of the object thus has the same type of

basic pattern/structure as the whole. The geometry of many natural phenomena like

coastlines, snowflakes, clouds, dispersal pathways, can be described using fractal

geometry. Plotting the measured quantities versus scale on a log-log graph gives a

straight line with the slope indicating the fractal dimension.

**Functional Groups** Collection of organisms that respond to environmental stimuli

in a similar way or have similar properties with respect to the investigated questions.

**Gaussian Distribution** A very common continuous probability distribution,

based on the central limit theorem stating that a collection of independent random

variables with n ! 1, is normally distributed around a single mean value (normal

distribution).

**General Systems Theory** An interdisciplinary approach for explaining complex

phenomena by their system’s character, founded by the biologist Ludwig von

Bertalanffy, closely related to –> Cybernetics.

**Generic Model** A model that describes general properties of an ecological

system and can be easily adapted to different specific situations.

**Goal Functions** In the ecological context adapted principles from thermodynamics

to describe systems being far from equilibrium and which have the tendency to

develop towards a particular state.

**Hierarchy Theory** This was derived from –> general systems theory to deal with

complexities in a system that is spanned over a range of hierarchical interacting

levels in space and time. For ecology, these principles were successfully adapted

since the works of Allen and Starr during the 1980s.

**Hysteresis** For systems with a memory effect, the strong correlation between

input signal and output reaction can be impaired. Then, multiple systems’ states can

shift rapidly from one state to another. As a consequence, predictions for future

time intervals might be impossible.

**Inference** This (in logic) is the transition from premises to conclusion, in such

a way that they are logically connected. The typical form of the logical connection

for inference is the so-called modus ponens: “if p then q”: premises are taken and

a conclusion is returned. If the premises are true, they guarantee the truth of the

conclusion. An inference system is composed by a set of “if…then” rules, and it

provides the support for mapping from a given input to an output.

**Information Criteria Measure** of the goodness of fit of a statistical model which

formally describes the relation between model complexity and accuracy. Some

examples are the Akaike’s information criteria (AIC), the area under the curve

(AUC), the coefficient of determination (R2), or the Nash-Sutcliffe model effi-

ciency coefficient.

**Intermediate Disturbance Hypothesis** Concept that hypothesizes that local

species diversity is highest for intermediate levels of disturbance; because very

low disturbance levels favour competitively superior species, whereas exception-

ally high disturbance levels increase the risk of extinction for most of the species.

**Lacunarity Analysis** Statistical analysis to describe the scale-dependent distri-

bution of gap sizes.

**Landscape Fragmentation** A major threat to local biodiversity relates to the

fragmentation of former coherent habitats as population size may fall below a

critical threshold and dispersal and exchange between populations may be reduced

or prevented.

**Landscape Metrics** General term that is used for the available collection of

metrics for analyzing and interpreting landscape composition and configuration.

**Metapopulation** An ecological concept describing the overall dynamics of a

number of sub-populations in space and time. It assumes partially independent

dynamics of the sub-populations, a risk of local extinction and recolonization

events. Thus the overall population may survive under conditions where the sub-

populations would go extinct. In nature conservation this concept has also been

discussed in the context of increasing –> landscape fragmentation.

**Michaelis-Menten Equation** Mathematical model for enzyme kinetics which

quantitatively relates the reaction speed of the enzyme-substrate complex to the

substrate concentration.

**Monod Kinetics** Mathematical model that describes enzymatically mediated

chemical reactions depending on the concentration of the substrates. See also –>

Michaelis-Menten kinetics.

**Monte Carlo Approach** Stochastic procedure, based on the law of large num-

bers; uses repeated random sampling techniques to solve complex problems

numerically.

**Nonlinear Systems** This do not react proportionally to input signals in every case

and usually cannot be solved by first order equations. Many ecological relationships

are nonlinear, e.g. predator-prey population interactions tend to be proportional to

the product of the population sizes.

**Numerical Approximation** When no explicit analytical solution exists for a

mathematical problem or the solution cannot be obtained without reasonable

costs, numerical computing can be introduced for calculating close estimates.

**Percolation Theory Percolation** describes the movement of entities or fluids in

porous materials. In landscape ecology it has been used to describe the movement

of organisms in fragmented landscapes and to detect critical levels of connectivity

between habitat patches.

**Phase Shifts ** See –> alternative stable states and hysteresis.

**Phenotypic Plasticity** The ability of an organism to change its phenotype (physi-

cal shape) in response to changes in the environmental conditions.

**Poisson Distribution** A discrete probability distribution that can be obtained by

performing repeated random experiments (e.g. Bernoulli experiments) where

occurrence is independent of the former events.

**Population Viability Analysis** A mathematical tool often applied in conserva-

tion biology, which calculates the probability that a population becomes extinct

under a set of environmental conditions within a given time span.

**Random Walk** Mathematical description of a trajectory which is constructed

from successive random elements. In ecology it is often used to describe the

movement of organisms.

**Self-Organization** A process in which an overall systems state emerges from

parallel and distributed interaction of its constituent elements without any central

steering instance. Usually, nonlinear and nonequilibrium processes are involved.

Many ecosystem states can be described as a result of self-organized processes.

Social-Ecological Systems A combined system of social and ecological compo-

nents and drivers which interact and give rise to results which could not be

understood on the basis of sociological or ecological considerations alone.

**Soft Computing** An emerging computer science area, inspired by biological

systems and human mind, used to model complex systems arising in management

science, medicine, biology and ecology. It consists of a variety of techniques,

including fuzzy logic, neural networks, genetic algorithms, Bayesian networks.

They all differ from conventional (hard) computing since they tolerate uncertainty,

partial truth, approximation, lack of categoricity, and imprecision to achieve trac-

tability, robustness and low solution cost. Soft computing approaches emulate

characteristics of human reasoning such as the learning, training, and other types

of high-order cognitive power.

**Square Matrix **This is a matrix which has the same number of rows and columns.

An nÂn-matrix is a square matrix of order n. The Identity Matrix In is a square

matrix of order n in which all elements on the main diagonal are equal to 1 and

all other elements are equal to 0. The inverse A–1 of a square matrix is defined as:

A Â A–1 = In. If an inverse exists, A is called invertible or non-singular.

**State Variable** In dynamical systems, it is understood that the state of the system

is completely characterized by the states of the variables within the system.

**Trophic Efficiency** The ratio of production which relates one trophic level in

terms of energy and biomass with the adjacent level.

**Trophic Level** The hierarchical position which an organism occupies in the

trophic web structure.

**Weibull Distribution** A continuous probability distribution in statistics that is

used to describe, e.g. lifespans and failure rates of compound aggregates in analytical

quality assurance procedures.