I would like to plot the make-up of a population over time as it changes its composition. For this, I'd like to make a simplex plot, a classic method in some fields - such as this example from a paper in Biology Letters (Sasaki & Uchida, 2014):
My population consists of three types of entity, so a simplex plot would be a very natural way to visualise it. I have a set of coordinates for the population over time, which it would be easy to plot in an x-by-y graph (if the population consisted of only two types of entity), but I am having some difficulty working out how to plot these on a simplex. I wonder if anyone could advise as to best method? (Perhaps there is even a Mathematica function that I am unaware of.)
Each point in my data consists of three pieces of information: the proportion of each of the three types of entity at that time.
The data looks like this (here's the first few lines):
A B C 0.7065 0.2492 0.0443 0.7380 0.2342 0.0278 0.7429 0.2065 0.0506 0.7357 0.1712 0.0931 0.7652 0.1740 0.0608 0.7466 0.1452 0.1082 0.6907 0.1193 0.1900 0.6008 0.0870 0.3122 0.4817 0.0584 0.4599 0.5989 0.0701 0.3310 0.6907 0.0806 0.2287 0.5904 0.0592 0.3504
I would like to plot these points in the simplex and connect them with lines.
Many thanks if you can help.
Cited: Sasaki, T. & Uchida, S. 2014. Biol. Lett., 10: 20130903