Modelling and Simulation - Important steps - An overwiew

1 Modelling

An ecosystem model is an abstract, usually mathematical, representation of an ecological (sub)system that is studied to better understand the real system. Ecological systems consist of an enormous number of biotic and abiotic factors that interact in often unknows ways or are so complex that they cannot be fully integrated into a computable model.
The process of modelling consists of 2 steps:
  1. Abstraction/Simplification:
    Because of this complexity, ecosystem models are typically simplifications consisting of a limited number of components that are well understood and considered relevant to the problem. The number of system components that enter the model is reduced by grouping similar processes and entities into functional groups that are then treated as a single entity.
  2. Translation into the language of mathematics (not programming language!)
    The process of Abstraction/Simplification often leads to smaller number of state variables. The underlying physical, chemical or biological processes and the relationships between them are then described with mathematical equations.
Therefore, for the task of modeling an apriory knowledge is needed of how the physical, chemical, and biological processes which determine the behavior of an ecosystem can be described with mathematical equations.


Population ecology/dynamics
$\frac{dN}{dt} = (b - m) * N = r * N$

$\frac{dN}{dt} = a * N ( 1 - \frac{N}{K})$

Model description languages

Modeling Tools

Bond Graph

2 Verification

The verification of a model includes:

3 Simulation

math. Classes and Concepts

Ordinary differential equations
Partial differential equations
discrete event modelling
agent based modelling and celluar automata
Stochastic processes
Simulation Modeling Methodolgy and Guides:

Simulation software

General Purpose Software
Free or open-source:
Finite Element Method
Finite Volume Method
Computational Fluid Dynamics
Individual/Agent based Simulation
Numerical libraries:
Documents about simulation and simulation software
List of products (general):
Cellular automata:
Neural Networks:
Qualitative and semi-quantitative modelling:

4 Validation

Model validation is the process by which model outputs are (systematically) compared to independent real-world observations to judge the quantitative and qualitative correspondence with reality.

5 Sensitivity Analysis



6 Inverse Modelling, (nonlinear) Parameter Estimation

Mathematical models are developed to improve the understanding of a system and to make predictions regarding system behavior. Typically, these models often depend on poorly defined or not measurable parameters/boundary conditions to which a value must be assigned. Fitting a model to the observed data, called Inverse modeling, is often the only way to find reasonable values for these parameters.
Under certain conditions, inverse problems can be viewed as an optimization problems in which model parameters are modified so that predictions from forward models can match measurements as closely as possible. Moreover, prior knowledge can be used to optimize the objective function and obtain the maximum a posteriori estimate of the model parameters.
The objective function is usually the (weighted) sum of squared residuals.
With the optimization algorithm (minimization) the minimum of the objective function is searched. Common algorithms are the Rosenbrock method, the Levenberg-Marquardt method, Nelder Mead's simplex method or the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm.
A major difference between these methods is the computation/approximation of the Jacobian and Hessian matrices. Convergence of these methods are not guaranteed, and it converges only to a local optimum that depends on the starting parameters. Therefore, random-based (evolution) strategies are also often used. A new approach based on Theory-guided Neural Network (TgNN) is described in Wang et al. (2021).
But the task of inverse modeling is not completed with the parameter estimation, a further essential aspect of inverse modeling is the assessment of the goodness of the estimated parameters. In this context are in the center of focus.




Curve fitting:

Societies & Organizations

Related to ecology, environmental sciences, and/or mathematical modeling & simulation.

Research Centers



Scientific search engines:
Extensive Lists of Links:

We wish you success in your ecological modelling efforts. T. Legovic' and J. Benz.