A question can derive from theoretical considerations, intuition (e.g. after the
personal observation of a phenomenon). tasks coming from outside science (e.g.
the demand for a conservation concept) or from the results of former quantitative
studies. Also a question's origin, its "quantitative level", plays a role in choosing
the adequate mathematical methods to answer it. In the following, conceptual
research, which is often situated between answers and new questions, is excluded
from the considerations, because it does not require mathematical methods.
To find an answer which is based on scientific reasoning (i.e. objectively
found), the question must be in a form that allows quantitative research, i.e. it must
be operationalized. The advantage will be that other scientists can follow the argument leading to a certain answer. The disadvantage is that only measurable
phenomena can be treated.
A research programme must be planned in such a way that the measurements
allow the question to be answered (at least come closer to be answered), logical
conclusions must be possible and alternative answers must be excluded. To that
extent, quantitative work enforces a sufficiently precise formulation of questions.
This includes that the planning of the experimental design can only be started
when it is clear in which way the collected data are to be analysed, i.e. in which
way they can be used to find an answer. Thus, the choice of a mathematical
method is closely connected to the formulation of the question (in its most precise
form).
The method of ecological modelling, as used in theoretical ecology, is described
by Wissel (1989) as "the pursuit of reasoning in the language of formal logic". Its
special aim is to gain understanding of an ecological system. Models are taken as a
first step towards a general theory. achieved for example by reproducing mechanisms of a system in the model and studying their plausibility. In the circular
course of research from questions over answers to new questions, ecological modelling comes directly after the question. For modelling nothing else is required than
a precise question and some primary information about the system. This also allows the inclusion of qualitative knowledge, experiences or suppositions, rules and
mechanisms. Answers are often of the form "if ... , then ... ". Ecological models
show the conclusions that are to be drawn if certain assumptions are made about
the system.
Mathematical modelling refers to the abstract description of a system in relation
to a certain question (Murthy et al. 1990). This requires a formulation of the system and the question in such a precise form that a translation into the "language of
mathematics" becomes possible. In this context models are representations of a
system by symbols and formulas whose meaning and rules are defined by mathematics. These models can be deterministic and/or stochastic.
The term simulation model describes a mapping of an ecological or mathematical model into a computer programme. The use of a simulation model is indispensable, if the system cannot be determined analytically, i.e. by mathematical rules
only (Example: the model ahout Lanice conchilega in Chap.SA). A simulation
model can also be used to demonstrate the spatial and temporal behaviour of a
system, e.g. by graphical representation on the screen (Example: Baumer 1994).
In contrast to the approaches mentioned so far, models in applied statistics serve
primarily for data analysis and are not restricted to a specific system. Here, models
are assumptions about the (mathematical) properties of the data and/or form a
personal observation of a phenomenon). tasks coming from outside science (e.g.
the demand for a conservation concept) or from the results of former quantitative
studies. Also a question's origin, its "quantitative level", plays a role in choosing
the adequate mathematical methods to answer it. In the following, conceptual
research, which is often situated between answers and new questions, is excluded
from the considerations, because it does not require mathematical methods.
To find an answer which is based on scientific reasoning (i.e. objectively
found), the question must be in a form that allows quantitative research, i.e. it must
be operationalized. The advantage will be that other scientists can follow the argument leading to a certain answer. The disadvantage is that only measurable
phenomena can be treated.
A research programme must be planned in such a way that the measurements
allow the question to be answered (at least come closer to be answered), logical
conclusions must be possible and alternative answers must be excluded. To that
extent, quantitative work enforces a sufficiently precise formulation of questions.
This includes that the planning of the experimental design can only be started
when it is clear in which way the collected data are to be analysed, i.e. in which
way they can be used to find an answer. Thus, the choice of a mathematical
method is closely connected to the formulation of the question (in its most precise
form).
The method of ecological modelling, as used in theoretical ecology, is described
by Wissel (1989) as "the pursuit of reasoning in the language of formal logic". Its
special aim is to gain understanding of an ecological system. Models are taken as a
first step towards a general theory. achieved for example by reproducing mechanisms of a system in the model and studying their plausibility. In the circular
course of research from questions over answers to new questions, ecological modelling comes directly after the question. For modelling nothing else is required than
a precise question and some primary information about the system. This also allows the inclusion of qualitative knowledge, experiences or suppositions, rules and
mechanisms. Answers are often of the form "if ... , then ... ". Ecological models
show the conclusions that are to be drawn if certain assumptions are made about
the system.
Mathematical modelling refers to the abstract description of a system in relation
to a certain question (Murthy et al. 1990). This requires a formulation of the system and the question in such a precise form that a translation into the "language of
mathematics" becomes possible. In this context models are representations of a
system by symbols and formulas whose meaning and rules are defined by mathematics. These models can be deterministic and/or stochastic.
The term simulation model describes a mapping of an ecological or mathematical model into a computer programme. The use of a simulation model is indispensable, if the system cannot be determined analytically, i.e. by mathematical rules
only (Example: the model ahout Lanice conchilega in Chap.SA). A simulation
model can also be used to demonstrate the spatial and temporal behaviour of a
system, e.g. by graphical representation on the screen (Example: Baumer 1994).
In contrast to the approaches mentioned so far, models in applied statistics serve
primarily for data analysis and are not restricted to a specific system. Here, models
are assumptions about the (mathematical) properties of the data and/or form a