Lecture 4 - Models and Modelling I

Theory

A systematic statement of principles; a formulatio nof apparently underlying principles of phenomena that have been verfied to some extend. Theories are based on facts and laws, but are open for more improvements, modification, and new information.

Hypothesis

An uproven theory or supposition, tentatively accepted to explain certain facts, or as a basis for further research through tesitng & experiments. A scientific hypothesis would be a statement about the way a system may work.

Model

A stylised representation of abstraction used to analyse or explain something; a tool for the evaluation of hypotheses. They allow for a (usually) quantitative statement of a scientific hypothesis. But, can also be seen as actors due to their power to influence and change.

Model State

A value describing a system at a given point in time. They are the discrete variabels at a specific time.

Model Process

The processes that causes a model state to change over time and or space. ANything that has the pwoer to influence model states.

Constants

Fixed values no matter the situation or scenario, will always be the same. For example, the speed of light, the value of pi, and so on.

Parameters

Have constant values within that specific situation or secnario, but can change between situations/scenarios. So, they’d stay the same regardless of anything within that situation. These would be things such as carrying capacity, rate of growth, and so on.

Variables

Are (generally) constantly changing within a specific situation/scenario and isn’t constant. For example, the number of individuals.

Linear Models

A linear change in y proportional to change in x that are best at representing simplistic relationships.

Other relationships are non-linear (exponential, piecewise, logistic, and so on) and are better at the complex relationships and processes within environmental systems

Four Types of Models

• Conceptual

• Process-based

• Physical

• Data driven

Conceptual Models

Visual/narrative summarises that describe the components of a structure, their interactions, or just some process within a system. They can be argued to encompass all other models because they tend to be how other models start out as.

It gives a mental image of the situation and allows us to better visualise what’s going on and what could be influencing the processes and individual parts. It is a mix of science for the data and information and art for the visualisation and simplistic communication to support understanding.

• When made, they shouldn’t be so simple that it just departs from the real-world entirely or loses it’s meaning while also not being too complicated where it’s hard to understand

They show empirical variables and their interactions, allowing us the identify the outputs (responses), inputs (experimental factors, processes, etc), and any assumptions & simplifications.

Process-Based Models

“Quantitative” models that often rely on parameterisations to understand, quantify, and predict systems. They’re attractive because communicating quantitative information tends to be easier and more convincing

With these models, we have to be careful with parameters because, as we know, parameters do differ between situations. How a system is represented in a process-based model may not reveal how other similar systems may behave due to the dependency on parameters.

There are two types of process-based models:

• Mathematical

• Simulation

They’re btoh based on theoretical understand and are broken down further into finer subgroups (computer, analytical, mechanistic, CA, agent-based, and so on)

Process-Based Models: Mathematical

Describe the system using formalisms of mathematics and can either by analytical or computational. The models tend to be easier to test and transport because of its reliance on mathematics.

However, analytical solutions tend to be impossible because numerical solutions are often difficult. They tend to be abstractions of the real world and made in a way where assumptions are made to make the processes & system simpler and easier to test and model.

They’ve been made to represent ecological systems for a long time to quantify relationships and processes. However, we need to remember that environmental processes tend to be very non-linear & random, meaning we also have to include stochastic elements within these models.

Process-Based Models: Simulation

Models that imitate a real-world process or system and attempt to recreate it in a virtual world system to better understand the processes, relationships, and interactions. All models can be seen as simulations because they represent real-world systems and interactions.

However, some systems are mathematically tractable (controllable), so we use simulations to predict or make general rules of thumbs (heuristic). They often require a lot of resources to run (time, money, data, and so on).

Pros of Process-Based Models

• Being able to have controlled experiments within a virtual world with controlled variables (time, boundaries, space)

• Equation-based, giving us quantifiable results and data

• Allows us to include all our knowledge to test the systems and ourselves

• Allow us to study the sensitivities (what can influence it) and processes of systems

Cons of Process-Based Models

• Tend to have too much stability (abstractions can make it lose stochastic elements) or overcomplicate things

• The boundaries set in the virtual world may not reflect boundaries in the real-world because those real-world boundaries tend to be more blurry

• The source of data used for the model needs to be good for the model to run well

• Simplficiations may make the model miss some processes (processes that others may argue are necessary to the output)

• It requires a lot of commitment (costs & time) and investments to calibrate and parameterise the model