#### 0409: Daisyworld

##### Niall Palfreyman

Darwinian Daisyworld model from and Watson & Lovelock (1983), Robertson & Robinson (1998) and Lenton & Lovelock (2001).

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 1 year 10 months ago

#### Blutzucker Regulierung durch Integral-Rein-Control + Setpoint-Verschiebung

##### Michael

Modell für den Kurs Dynamic Modelling zur Simulierung von Insulin-Glukagon Haushalt nach Saunders et. al.

©Michael Stühler

©Michael Stühler

Dynamic Modelling Integral-Rein-Control Insulin Glukagon Glukose HSWT Hochschule Weihenstephan-Triesdorf

- 3 years 11 months ago

#### 0408: Integral-rein control (IRC)

##### Niall Palfreyman

A simple implementation of Koeslag & Saunders' IRC model of blood-glucose regulation.

- 2 years 4 months ago

#### 0406: The simplest possible brain

##### Niall Palfreyman

This simple, generic biological integral-control component is used by E. coli to decide on an adaptive tumbling frequency.

1. If Ligand concentration stays constant, the bacterium tumbles at a low, exploratory rate of ~2 Hz.

2. If Ligand concentration rises (attractant), tumbling frequency falls to continue moving toward the source.

3. If Ligand concentration falls (repellant), tumbling frequency rises to avoid the source.

1. If Ligand concentration stays constant, the bacterium tumbles at a low, exploratory rate of ~2 Hz.

2. If Ligand concentration rises (attractant), tumbling frequency falls to continue moving toward the source.

3. If Ligand concentration falls (repellant), tumbling frequency rises to avoid the source.

- 1 year 10 months ago

#### Influence of Sympatric Speciation on Regulation

##### Adrian Marcus

We extended Daisyworld to evaluate the effects of sympatric speciation on regulation. Sympatric speciation occurs when organisms are segregated from each other by functional, rather than spatial, constraints. To emphasize the sympatric aspect of our model we halved the original value of 'q'. The dynamical model contains five potential species: gray, light gray, dark gray, black and white daisies, whose phenotypes differ only in their albedo.

Initially the model contains only gray daisies. Mutation of gray daisies leads to new daisy types. These new types can interbreed with their genetic neighbors or mutate even further. These mutations ultimately lead to black or white daisies. When two types are functionally different enough they cannot interbreed and we consider them separate species.

'gamma' is the general death rate for all daisies.

The 'Flow' defines the percentage of the actual population which mutates.

'q' defines the spatial distribution of thermal energy between the dasies.

'Base' is the optimal temperature of the general daisy.

'mu' is the probability of a mutation event.

Our model contains two possible luminosity scenarios. One relates to the increasing luminosity of the original Daisyworld. There is a second scenario implemented, which simulates different pertubations over a normally constant luminosity. To change between the scenarios simply reconnect the 'Absorbed Luminosity' variable with one of the container 'L'. Both scenarios are depicted in the diagram, so no changes are neccessary.

Initially the model contains only gray daisies. Mutation of gray daisies leads to new daisy types. These new types can interbreed with their genetic neighbors or mutate even further. These mutations ultimately lead to black or white daisies. When two types are functionally different enough they cannot interbreed and we consider them separate species.

**Instructions:**

You can change the 'Spread' of albedo between the different daisy types centered at the albedo of the gray daisies and in symmetric shades.'gamma' is the general death rate for all daisies.

The 'Flow' defines the percentage of the actual population which mutates.

'q' defines the spatial distribution of thermal energy between the dasies.

'Base' is the optimal temperature of the general daisy.

'mu' is the probability of a mutation event.

Our model contains two possible luminosity scenarios. One relates to the increasing luminosity of the original Daisyworld. There is a second scenario implemented, which simulates different pertubations over a normally constant luminosity. To change between the scenarios simply reconnect the 'Absorbed Luminosity' variable with one of the container 'L'. Both scenarios are depicted in the diagram, so no changes are neccessary.

- 1 year 11 months ago

#### 0401: Constrained growth

##### Niall Palfreyman

Two simple models of constrained growth, showing how stable structure arises through coupling positive feedback of one order with negative feedback of a higher order. This mechanism forms the basis of all stable states (and therefore of all memory) in nature.

In the first model a Protein is expressed at a constant growth rate betaP, and is degraded exponentially - that is, at a rate alphaP * Protein which is directly proportional to its current concentration. The result is the so-called 'leaky barrel' model, which grows to a stable value of betaP/alphaP.

In the second model Rabbits are born at a rate betaR * Rabbits which is proportional to the current number of Rabbits, but due to competition they die hyperexponentially (i.e. proportional to the square of the number of Rabbits). The result is the logistic model, which grows to a stable value of betaR/alphaR.

In the first model a Protein is expressed at a constant growth rate betaP, and is degraded exponentially - that is, at a rate alphaP * Protein which is directly proportional to its current concentration. The result is the so-called 'leaky barrel' model, which grows to a stable value of betaP/alphaP.

In the second model Rabbits are born at a rate betaR * Rabbits which is proportional to the current number of Rabbits, but due to competition they die hyperexponentially (i.e. proportional to the square of the number of Rabbits). The result is the logistic model, which grows to a stable value of betaR/alphaR.

- 2 years 1 month ago

#### 0402: Interacting species

##### Niall Palfreyman

This is a very general model of two interacting species which describes a wide variety of different kinds of interaction, for example: cooperation, symbiosis, competition or predation.

Note that in systems biology the word 'species' can mean species of organism, species of chemical or species of cell. Similarly, 'interaction' can mean chemical interaction, genetic interaction or phenotypic interaction. We are talking here about very general kinds of system.

Note that in systems biology the word 'species' can mean species of organism, species of chemical or species of cell. Similarly, 'interaction' can mean chemical interaction, genetic interaction or phenotypic interaction. We are talking here about very general kinds of system.

- 2 years 4 months ago

#### 0411: Recombination and mutation

##### Niall Palfreyman

This is an example of how to model populations involving recombination and mutation. The Hardy-Weinberg Law gives us the effects of recombination, and mutation is represented by a flux between alleles.

Possible extensions: Build in differential fitness of the three genotypes, have them differentially interact with an external environment, or have them interact with each other. (There is already an interaction term in the three 'die' flows.)

Possible extensions: Build in differential fitness of the three genotypes, have them differentially interact with an external environment, or have them interact with each other. (There is already an interaction term in the three 'die' flows.)

- 2 years 4 months ago

#### 0403: Chaotic pendulum

##### Niall Palfreyman

A damped, driven pendulum. The combination of damping and driving provokes a minimal case of chaos. The system is not in itself biological, however its chaotic behaviour arises from competing oscillatory influences - a situation which plays a role in many biological systems.

- 2 months 3 days ago

#### 0407: Relaxation oscillator

##### Niall Palfreyman

Oscillators in biology are generally anharmonic: their differential equations are non-linear and they are not described by trig functions. This is a simple implementation of Tyson's oscillatory model of the timing of the cell cycle.

- 2 years 2 weeks ago

#### 0410: Sympatric speciation

##### Niall Palfreyman

It is easy to imagine allopatric speciation taking place as populations become confined to physically separate locations (for example Darwin's finches on separate Galapagos islands). It is less easy to imagine how sympatric speciation can occur when the nascent species are physically mixed. Golubitsky and Stewart demonstrate a mathematical model of functional segregation in precisely such completely mixed populations.

- 2 years 4 months ago

#### 0404: The Griffith switch

##### Niall Palfreyman

The Griffith switch illustrates how the nonlinear interaction between a protein and its own promoter can implement a simple biological switching network.

- 2 years 4 months ago

#### 0405: Genetic assimilation

##### Niall Palfreyman

This model implements Saunders' (1993) model of genetic assimilation and punctuated equilibrium. It illustrates how apparently phenotype-free random mutations in K can become selectively biased by raising the probability of a fitter phenocopy via fluctuations in S.

- 2 years 4 months ago

#### Daisyworld 2.0

##### HelloWorld

Darwinian Daisyworld model from and Watson & Lovelock (1983), Robertson & Robinson (1998) and Lenton & Lovelock (2001).

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 2 years 1 week ago

#### Genetic Origins of Speciation

##### Alexander

Darwinian Daisyworld model from and Watson & Lovelock (1983), Robertson & Robinson (1998), enton & Lovelock (2001) and Heinzinger, Holm and Schuler (2016)

This shown model extends the conventional Daisyworld model from Watson & Lovelock.to investigate the effects of speciation. Daisies in this model undergo random genetic mutation. This is subject to selection on its phenotypic consequences for the daisies' niche-construction. The diverse simulations were processed with different values of capacity of interbreeding theta, mutation rate mu and luminosity L.

This shown model extends the conventional Daisyworld model from Watson & Lovelock.to investigate the effects of speciation. Daisies in this model undergo random genetic mutation. This is subject to selection on its phenotypic consequences for the daisies' niche-construction. The diverse simulations were processed with different values of capacity of interbreeding theta, mutation rate mu and luminosity L.

**Advices for using our model:**- The capacity of interbreeding theta can be set from 0.5 up to 1.0
- Any of the four different luminosities can be chosen
- You can change the mutation rate mu from 0.009 up to 1 (maximum mutation rate). But with theta = 0.5, the lowest mutation rate mu is 0.01. Beneath this value, there is no growth.

- 1 year 11 months ago

#### 0415: Rayleigh's violin-string model

##### Niall Palfreyman

In 1877 Rayleigh constructed this model of the vibrations in a violin string:

x is the disturbance of the string,

v is the rate of change of x.

x is the disturbance of the string,

v is the rate of change of x.

- 2 years 2 weeks ago

#### Daisyworld 2.0

##### Alexander

Darwinian Daisyworld model from and Watson & Lovelock (1983), Robertson & Robinson (1998) and Lenton & Lovelock (2001).

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 2 years 2 weeks ago

#### Daisyworld BW ohne Temp

##### Alexander

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 2 years 1 week ago

#### 0414: Two-species niche-construction IRC

##### Niall Palfreyman

This model displays the basic structure of a closed system IR controller, which uses two competing species to regulate a Resource up or down.

Consumers lower the quantity of Resource, and have a higher optimum requirement for the Resource; Producers raise the quantity of Resource, and have a lower optimum requirement. Between them, they maintain the Resource at an intermediate level.

Consumers lower the quantity of Resource, and have a higher optimum requirement for the Resource; Producers raise the quantity of Resource, and have a lower optimum requirement. Between them, they maintain the Resource at an intermediate level.

- 2 years 1 month ago

#### The Best Daisyworld 3.0

##### HelloWorld

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 2 years 1 week ago

#### 0413: Single-species niche-construction IRC

##### Niall Palfreyman

This is the simplest possible niche-construction IR controller. It assumes that a population P metabolises Food into Poo when it is above a threshold value Theta, but metabolises Poo into Food (!) when P falls below this threshold. Food and Poo therefore integrate over time P's divergence from Theta, and this information is used to combat that divergence.

Notice that the 'rein' contribution to this controller arises from the fact that P can metabolise Poo into Food, thus also correcting for values of P below Theta. From thermodynamic considerations this is only possible if the system is open to energy input from an external source. Indeed, this model is precisely the structure of the chemotaxis tumbling circuit in E. coli, which relies on an external supply of energy in the form of ATP.

On the other hand, a closed system can only achieve IR control if it has at least two competing species to pull the 'reins' in the two different directions. That is the subject of the next model.

Notice that the 'rein' contribution to this controller arises from the fact that P can metabolise Poo into Food, thus also correcting for values of P below Theta. From thermodynamic considerations this is only possible if the system is open to energy input from an external source. Indeed, this model is precisely the structure of the chemotaxis tumbling circuit in E. coli, which relies on an external supply of energy in the form of ATP.

On the other hand, a closed system can only achieve IR control if it has at least two competing species to pull the 'reins' in the two different directions. That is the subject of the next model.

- 2 years 1 month ago

#### Daisyworld final 23_06_16

##### Charlotte Weinschenk

Darwinian Daisyworld model from and Watson & Lovelock (1983), Robertson & Robinson (1998) and Lenton & Lovelock (2001).

extended by Anna Blümel, Tobias Meier, Charlotte Weinschenk(2016)

The Research deals with a stress test of Watson and Lovelock’s Daisyworld model. The authors tested the stability of the model by applying modified growth curves for the Daisies. These modified curves were tested in several modes of the grouping constant q.

- to see different growth curves for the Daisies, pull a flow from desired fertilityB/fertilityW to birthB/birthW

Consider: Only one fertilityB/fertilityW should be connected to birthB/birthW.

-to see different modes of the homeostasis, change grouping constant q to different values.

The authors reccomend following values:

q= 3; 6; 15; 20; 25; 30; 35; 40; 50

extended by Anna Blümel, Tobias Meier, Charlotte Weinschenk(2016)

The Research deals with a stress test of Watson and Lovelock’s Daisyworld model. The authors tested the stability of the model by applying modified growth curves for the Daisies. These modified curves were tested in several modes of the grouping constant q.

**For testing the different modes of the project:**- to see different growth curves for the Daisies, pull a flow from desired fertilityB/fertilityW to birthB/birthW

Consider: Only one fertilityB/fertilityW should be connected to birthB/birthW.

-to see different modes of the homeostasis, change grouping constant q to different values.

The authors reccomend following values:

q= 3; 6; 15; 20; 25; 30; 35; 40; 50

- 1 year 12 months ago

#### Better Daisyworld 3.0

##### Alexander

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 2 years 1 week ago

#### Hübsches Daisyworld 2.0

##### Alexander

Units of time are 40 Myr, giving R&R's span of 10 Gyr.

This model offers many opportunities for modification. Maybe the Black and White populations can mutate into each other? The role of q as a measure of segregation of the B and W populations is interesting, and while this model uses purely stigmergic communication between species, direct interaction would also be possible.

- 2 years 2 weeks ago