Virtual Ecosystem Simulation More explanation about this Webapp, its working, mathematical backend, and...
Modeling is a powerful tool for bioscientists to understand complex systems. This introduction explains the core concepts and shows how simple rules can create complex, life-like emergent behaviors.
Virtual Ecosystem Simulation More explanation about this Webapp, its working, mathematical backend, and...
An ecosystem, a cell, a population - they aren't just collections of things; they are intricate networks of interactions, feedback loops, and processes that change over time. How do you begin to understand a system where everything seems to affect everything else?
While lab experiments and field studies are the cornerstones of biology, there's another powerful tool that can help you untangle this complexity: modeling.
If you think modeling is just for mathematicians or computer scientists, think again. It's a fundamental approach to scientific inquiry that allows you to formalize your understanding, test hypotheses that are impossible to test in the real world, and discover surprising behaviors that emerge from simple rules.
Before we dive into a complex example, let's break down the basics, using the core ideas from systems analysis.
A model is simply a simplified or abstracted representation of a system. And a system is any limited part of reality that contains interrelated elements. A leaf, a human body, a lake - these are all systems. The first step in modeling is always to define your system and its boundaries. The research questions you ask determine where those boundaries lie. For example, if you're studying nutrient cycling in a pond, your system might be the pond itself, with the surrounding land and atmosphere being the "environment" that influences it.
There are many types of models, but we can start by categorizing them in two key ways:
To build an explanatory dynamic model, we start with two fundamental assumptions:
This leads to a powerful framework using three main components. Let's use a simple, non-biological example: filling a bathtub.
State Variables: A state variable represents a quantity that defines the condition of the system at any instant. It must be something additive - a quantity you can meaningfully add or subtract.
Rate Variables: A rate variable indicates how fast a state variable is changing. These are the engines of the model, representing flows and processes.
Driving Variables (or Parameters): These are external factors or settings that influence the rates but are not, in turn, influenced by the system itself. They are the "rules" we impose on our model.
This is one of my favorit parts and the reason, why I programmed the simulator you can find here. With these three building blocks, we can describe almost any dynamic system. But here is where the magic happens: Even when the rules for each component are simple, the interactions between them can lead to incredibly complex, surprising, and life-like behavior. This is a concept called emergence.
The classic predator-prey population cycle is a perfect example. The "rules" are simple:
When you let these simple, interconnected rules run over time, you don't get a straight line. You get a dynamic, oscillating pattern of boom and bust that looks remarkably like what we observe in nature. The complexity isn't programmed in; it emerges from the interactions. This is the core power of modeling: it allows us to see how the local, simple rules we understand can give rise to the complex, large-scale patterns we observe.
Now, let's see this in action!
Here (and also above and below) is a link to a Virtual Ecosystem Simulator I have programmed. It’s a web application that models a basic ecosystem containing three types of organisms:
Go ahead and play with it. Click "Start Sim." What you are seeing is a dynamic, explanatory model at work. Can you identify the building blocks?
Initial Plants
, Plant Growth Rate
, Herbivore Speed
- these are the rules you, the modeler, are setting for this virtual world.The logic of the simulation translates our conceptual understanding into quantitative rules. While the overall behavior is complex, the underlying formulas for each interaction are straightforward. Here is a concise mathematical overview of the simulation’s main formulas and its step-by-step update process.
Distance Between Two Entities d(e1, e2) = sqrt((x1 - x2)^2 + (y1 - y2)^2) This is used to check whether a herbivore or predator is close enough to eat its target.
Movement and Energy Cost
moveCost
* speed
every step. For a herbivore with energy Eh: Eh <- Eh - (herbivoreMoveCost * herbivoreSpeed)Eating and Energy Gain
Reproduction Threshold
Plant Growth
plantGrowthRate
, a new plant is added to a random location, as long as the total number of plants is below the maxPlants
limit.So how do we get from the rules above to the moving dots and dynamic charts (or more broadly, to a simulation over time i.e., a dynamic simulation)? For many complex systems, especially those with many interacting agents or feedback loops, it's impossible to write a single equation that solves for the entire system's behavior over time. We can't just "plug in" a future time and get the answer. This is where numerical simulation comes in. Instead of solving for the whole timeline at once, we chop time into tiny, discrete steps. At each step, we calculate the changes for every component based on our simple rules and update its state. By stringing together thousands of these simple updates, we approximate the continuous, dynamic behavior of the entire system.
The Virtual Ecosystem Simulator uses numerical integration as well. In simple terms it work as follows:
stepCounter
by 1.plantGrowthRate
.This all leads back to one crucial point: modeling is a powerful method of scientific inquiry.
Modeling is not about replacing lab work; it's about extending the reach of our minds, just as a microscope extends the reach of our eyes. It’s a tool for thinking.
So, go back to the Virtual Ecosystem Simulator. But this time, look at it like a modeler.
The journey into modeling is a journey of discovery. It's a way to ask 'what if,' to test the boundaries of your understanding, and to watch the elegant dance of complexity emerge from the simplest of rules.
Modeling is a powerful tool for bioscientists to understand complex systems. This introduction...
Virtual Ecosystem Simulation More explanation about this Webapp, its working, mathematical backend, and...
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