Discover DaisyWorld

The aim of this site is to provide a singular source of information about DaisyWorld, a notional planet conceived to demonstrate the Gaia hypothesis and to attempt to show how planets and life may work together for joint advantage.

The various sections of this website give detailed information about DaisyWorld and what the model has achieved since its conception. There is also an opportunity to construct your own DaisyWorld simulation with a novel JavaScript implementation of the original DaisyWorld equations.

Please note references are contained in the References section at the end of the page.

Getting Around

The site is split up into smaller sections for you to navigate more easily.

You can use the navigation bar at the top to skip from section to section across the site.

You can also use the next and previous section links at the top and bottom of each section to jump to the nearby sections.

Alternatively, use your mouse's scroll wheel or arrow keys to go down the page - one section follows another.

Recommended capabilities

This site uses the latest standards in web technology. JavaScript should be enabled in whichever browser you use for the DaisyWorld simulation to work.

It is advised that the latest version of Google Chrome is used to browse this site. It available from the following website: Google Chrome. It is also available on all of the SSE lab PCs.

The minimum recommended screen resolution is 1024x768 pixels. All SSE lab PCs exceed this resolution. The optimal viewing resolution is 1680x1050 pixels.

100% open source

This site is completely open source.

View the code behind the website, how it was developed, and access the DaisyWorld javascript library by visiting the project's GitHub page.

Please note this site remains under copyright.

The first paper on DaisyWorld was published in 1983, authored by James Lovelock and Andrew Watson. DaisyWorld itself is a simple mathematical model, which aims to illustrate that the Gaia hypothesis is valid for systems such as the Earth. It does this by modelling some of the core components of the Earth's solar system and a simple biosphere.

The original DaisyWorld was a theoretical, barren planet orbiting a foreign star, whose grey soil was sown with the seeds of black and white daisies. It is an artificial life system: while it is designed to mimic some of the effects of life, it can not hope to ever encompass all of the complexity that a real-life Earth would produce.

The daisies have temperature windows and optimal temperatures at which they can grow. They only need the correct temperature to grow - the original model is simplistic in that it does not include other features such as animals, multiple species, water and so on.

Being different colours, the two types of daisies and the soil of the planet absorb and reflect light differently - this is known as their albedo.

Albedo

In the simplest terms, Albedo is how reflective an object or surface is.

The albedo of an object is technically stated as its reflection coefficient - the proportion of how much radiation the surface reflects from the radiation that it is exposed to.

As the value is a ratio, it is often expressed as a value between 0 and 1. An albedo of 1 indicates a highly reflective object (such as a white daisy). A value of 0 indicates a highly absorbant surface (such as a black daisy).

Albedo intuitively has a relationship to the temperature of the object. The more energy the surface absorbs, the warmer the body will become. You can feel this yourself if you wear a black t-shirt on a sunny day.

Hence black daisies have the effect of warming the planet's surface because they absorb more (and reflect less) radiation from the sun; white daisies have the opposite effect.

During the course of the DaisyWorld simulation, the population of black and white daisies on the planet's surface is tracked. The surface temperature of the planet is also recorded.

DaisyWorld's sun is constantly getting warmer, much like the Earth's sun. Despite this, the surface temperature of DaisyWorld is maintained almost constant for a long period of time, owing to the different populations of white and black daisies that grow.

This feedback loop regulates the temperature of the surface, despite a constantly warming solar environment. It illustrates that an entire planetary population can work together for mutual benefit, which is a core component of Gaia theory, discussed in the next section.

Since its original design, DaisyWorld has been modified numerous times to include more detail and better simulations. The model works with 10 or more differently coloured daisy species, rabbits and foxes, and its performance and temperature regulation capability improves with more species included - even remaining stable when perturbed.

The Gaia Hypothesis

The Gaia hypothesis, or Gaia theory, was established by James Lovelock, who subsequently developed DaisyWorld as a proof-of-concept mathematical experiment.

While there are different descriptions and variations of the theory, some of which are studied today and some of which are not, the original idea was that the Earth itself is self-regulating as a system involving every part of the planet.

The idea that the atmosphere, biosphere (the biological ecosystems of the planet), hydrospheres (the water systems of the Earth) and the pedosphere (the soil surface) - together called Gaia - work together to sustain life was initially generated in the 1970's.

The main purpose of DaisyWorld's development was to show that the previously outlined Gaia hypothesis is plausible.

While the simple one-species two-colour model is an over-simplification of the hugely complex Earth systems, it does demonstrate that feedback mechanisms can evolve between groups of species interested only in themselves, rather than through other processes such as natural selection.

DaisyWorld does not, and never sought to, prove any of the theories laid out in Gaia; however, when it was published, it did go some way towards convincing scientists that the Gaia hypothesis may at least be plausible. Thus, further research was carried out on Earth, which lead to disoveries that prove some components of Gaia theory to be true for the Earth.

For example, it is now generally accepted that the Earth's tropical forests play an important part in global climate regulation, and it has been confirmed that the oxygen content of the air has not varied from 21% +/- 5% for 1 million years. Both of these are strong indicators that the Gaia theory may be correct, but are not enough to prove it on their own.

The DaisyWorld simulation is run as a series of discrete computations with varying luminosity values for the output of the sun. The simulation parameters for start luminosity, final luminosity, and the step change in luminosity between each sample determines the length of the simulation.

Each of the subsequent actions are performed at each step of the simulation, and are repeated in that simulation step until the area changes for the daisies has converged. This has the effect of predicting a very long solar period, where the solar output is changing over years rather than the rate of days in which daisies grow and die out.

Planetary albedo

The first step is to determine the planetary albedo, \(A_p\). This is simply a sum of the albedos of the \(N\) daisies (\(A_d\)) weighted by their current surface area (\(S_d\)) and the area of the soil (\(S_s\)) multiplied by its albedo (\(A_s\)).

$$ A_p = A_s S_s + \sum_{i=1}^N A_d S_d $$

The albedo for the whole planet is thus computed as the average of the albedos of the components that are covering the surface of the planet, weighted by the proportion of the planet that they occupy. Note that the sum of the areas of the daisies and the soil is always 1:

$$ A_s + \sum_{i=1}^N A_d = 1 $$

Planetary temperature

The temperature of the planet is governed by Stefan's law, or the Stefan-Boltzmann law. This law states that the total energy radiated by an object per unit time (\(E\)) is directly proportional to the fourth power of the object's absolute temperature \(T\):

$$ E \propto T^4 $$

The constant of proportionality in this case is Stefan's constant (or the Stefan-Boltzmann constant), \(\sigma\). The constant value is derived from Planck's constant \(h\), the Boltzmann constant \(k\), and the speed of light \(c\):

$$ \sigma = {2\pi^{5}k^{4} \over 15c^{2}h^{3}} = 5.67040\times10^{-8}Js^{-1}m^{-2}K^{-4} $$

When the object is not totally black, its emission is modulated by an emissivity. In the case of DaisyWorld surfaces (daisies and the soil), this emissivity is governed by its albedo.

Additionally, the energy reflection depends on the incident energy from the sun. For easier computations, we split this into a constant solar input, the solar flux density constant \(\xi\) and the solar luminosity \(\lambda\). It is the solar luminosity that is varied over the course of the simulation at each sample time. Thus our final equation for the temperature of the planet \(T_p\) will be:

$$ T_p = \sqrt[4]{{\lambda\xi(1-A_p)}\over{\sigma}} $$

Local temperature

The local temperature of the regions of daisies and the soil is determined by a similar use of Stefan's law. However in this case the emissivity is determined by the regions' albedo \(A_l\) compared to the planetary albedo \(A_p\), and the input energy is based on the energy from the sun as well as the energy transferred locally from nearby regions, which is expressed as an energy transfer factor \(\tau\) = 0.12. Thus the equation for the local temperature (of a daisy population or soil area) \(T_l\) is:

$$ T_l = \sqrt[4]{{{\tau\lambda\xi(A_p-A_l)}\over{\sigma}}+T_p^{4}} $$

Birth rate

From the local temperatures of the areas, we can work out the birth rate of each of the daisy species.

For each of the daisy colours, the birth rate of that colour \(B_d\) is determined by an inverted parabolic function of growth rate which peaks at the daisy's optimum growth temperature \(T_{opt}\) and reaches zero at its maximum survivable temperature \(T_{max}\), and the daisy's current temperature \(T_l\):

$$ B_d = 1 - {{(T_l-T_{opt})^2}\over{(T_{opt}-T_{max})^2}} $$

Try out the interactive feature to the right to create birth rate parabolas for various optimal and maximum temperature tolerances.

Area change

Once the birth rate of each of the daisy colours has been established, it is possible to compute the area change for the individual colour areas.

However the first piece of information required is how much barren area is left on the planet's surface, or the soil area \(S_s\). This is simply the planetary surface not taken up with current daisy populations:

$$ S_s = 1 - \sum_{i=1}^N A_d $$

Now the area change can be computed. It is based on the current surface area occupied by that daisy colour \(A_d\), the birth rate computed in the previous sub-section (\(B_d\)), the soil surface area (which is the area that the daisy can expand into) \(S_s\), and the globally configured death rate at each stage \(D\) = 0.3:

$$ \Delta A_d = A_d((B_d S_s) - D) $$

Thus the area may simply be updated to the new value \(A_d^*\) by the formula:

$$ A_d^* = A_d + \Delta A_d $$

Note how this mathematical model does not restrict the number of daisy colours that are actually present. While Lovelock originally computed the simulation with two colours - mostly as little computer aid was available at the time - it extends seamlessly to additional daisy colours. This is possible to render in the interactive section following.

Both DaisyWorld and the Gaia theory have come under criticism in the past.

DaisyWorld has been seriously criticised for omitting key components of the Earth system as it is understood, such as a difference between species- and individual-level phenomena. These concerns were addressed in a 2011 paper by Lovelock and Lenton.

It has also been criticised for requiring the planet and its inhabitants to somehow agree on the best desired outcome, and for its inconsistency with natural selection (natural selection of planets would require evidence of planets which had not successfully been regulated by a Gaia process).

Gaia theory has been criticised as unnecessarily portraying the Earth as a living organism, which some scientists claim has given laymen the wrong impression of how the Earth's systems work. The Gaia hypothesis, before it was recognised as a theory, was also called "unscientific" for having an apparent connection to the real scenario without offering any mechanism which explains how it actually works.

The mathematics for this simulation was based on that from Lovelock and Watson's original DaisyWorld paper. This is a completely novel implementation based solely on this mathematics. Their model is sufficiently generic such that more than two daisy species can be easily implemented, which is what has been done here.

There was a project to implement DaisyWorld in JavaScript last modified over a year ago which is incomplete and does not appear to work. The most complete DaisyWorld browser implementation is in Flash by Ginger Booth and is closed-source, so of little community benefit. However the mathematical descriptions provided by this project did clarify some minor details which were omitted in the original paper.

This implementation is both open source and comes with a user experience designed to maximise user engagement and learning, unlike other web-based implementations.

Note that the DaisyWorld library itself is in the js/daisyworld.js file. The UI implementation and rendering is in the js/daisymanager.js file. Both of these files are completely novel to this site.