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Evolvix Output Plots

Evolvix models produce time series when simulated, which are best understood when plotted.

Here are a few output plots that were automatically produced by the Evolvix System from what we call an Evolvix Quest. Such a Quest describes our model in plain text, what we want to know about it and how to simulate it. Here is what the Evolvix System does behind the scenes:

  1. Read the Evolvix Quest file and interpret it.
  2. Transform the model into a representation ready for simulation.
  3. Simulate and while doing so record only the results requested.
  4. Write raw simulation output to file and document the work done.
  5. Automatically move output data into a visualization solution and plot it; here we used R.

 

Example: Below we show time series of amounts observed in a predator-prey system that oscillates. Oscillating system are frequent in biology, from the molecules that build circadian clocks (waking us up in the morning) to host-parasite oscillations (which can make us sick). Analyses like those below show how the amounts of different parts in the system change over time. This often helps to think through how such systems work. In the time series of the two species toy-example below, rabbits are shown in red, and foxes in black.

 

 

Oscillating systems are frequent in biology, from molecular circadian clocks to predator-prey systems. This time series is computed as if the system was deterministic, ignoring all possible sources of variability.

This time series overview is computed as if the system was deterministic, ignoring all possible sources of variability. It shows all requested parts in one overview plot together to make it easy to check for some general features.

 

 

 

Oscillations in stochastic systems can deviate substantially from what would be expected in an equivalent deterministic system

The same time series as above, only now they were simulated stochastically. The sole source of variation in this picture is the variation caused by the inevitable sampling that results from respecting the fact that individuals do not exist in fractions. To switch from deterministic to stochastic simulations for these types of models (CTMCs) requires changing only 1 word in Evolvix.

 

 

 

Phase diagram of a deterministic oscillating system

 Here is a phase diagram that illustrates how predator and prey numbers relate to each other at each point in time in a deterministic simulation.

 

 

 

Phase diagrams are important tools for analyzing the stability of a system. This one shows simple predator prey dynamics that result in a so-called limit cycle. 

 The same phase diagram as above in a stochastic simulation shows that the oscillations in a real system of this type would be much more noisy.