Question

First question from me, hope it’s phrased correctly. I couldn’t find anything on this so I’ll bite the bullet.

I’d like to create a geom_tile plot in which for each combination of x and y, I have 5 variables for the z that all sum to one. I’d like the colour of the square for each x-y combination to reflect which z number is largest. For example, imagine I have 5 z variables a, b, c, d and e. If a=1 and b=c=d=e=0, the square would be blue, if b=1 and a=c=d=e=0 it would be red, etc. If a=b=0.5 and the others are zero, it would be an interpolated colour (i.e. purple). Perhaps even better, a crosshatch of red and blue, but I don’t know if that is possible in ggplot.

I am not sure how best to go ahead. I thought about plotting 5 geom_tile plots on top of each other, where each one is a different colour and the alpha is scaled by e.g. the value of a (so the cell is transparent when a = 0 and strongly coloured when a = 1). There might also be a way to do it using colour ramps, but I drew a blank there too.

If anyone can see how to do this off the top of their head, I’d be much obliged. Here’s a dataset of random numbers in the same format as my actual data.

rand <- matrix(runif(50*50*5), ncol=5, nrow=50*50)
rand <- rand / apply(rand, 1, sum) # Make sure the numbers sum to one in each row
d <- data.frame(a = rand[,1],
                b = rand[,2],
                c = rand[,3],
                d = rand[,4],
                e = rand[,5],
                expand.grid(x = 1:50, y = 1:50))

Update: By using the first answer from sebastian-c and my own dataset, I was able to make this figure. I obtained the colours using the function brewer.pal(5,”Spectral”) in the package RColorBrewer. Needs a custom legend, but otherwise I am pretty happy with it. The solid colours show pure “Evolutionarily stable strategies” (ESS; i.e. strategies that cannot be beaten by a mutant strategy). Areas of overlapping colours show mixed ESS, in which the equilibrium is a stable balance of two or more strategies.

Answer 1

I took the liberty of simplifying your example a bit down to 3 columns. Honestly, I don’t think this works well with any more than 2, but here’s how I’ve gone about it. I’ve also abused alpha channels so if you lay down the tiles in a different order, the colours change. This should hopefully work as a starting point for someone else. First, we’ll generate data:

set.seed(100)

rand <- matrix(runif(100*3), ncol=3, nrow=100)
rand <- rand / apply(rand, 1, sum) # Make sure the numbers sum to one in each row
d <- data.frame(a = rand[,1],
                b = rand[,2],
                c = rand[,3],
                expand.grid(x=1:10, y=1:10))

Now for the plot:

ggplot(d, aes(x=x, y=y))+
  theme_bw() + #For a clearer background
  geom_tile(alpha=d$a, fill="red")+
  geom_tile(alpha=d$b, fill="blue")+
  geom_tile(alpha=d$c, fill="green")+
  theme(panel.grid.major=element_blank())

I was thinking about, for 3 columns, using amounts of red, green and blue, but this doesn’t work for anything greater than 3 columns.

EDIT: A specific solution for up to 3 columns (I mixed the blue and green up):

d2 <- data.frame(col=rgb(rand), expand.grid(x=1:10, y=1:10))

ggplot(d2, aes(x=x, y=y)) +
  theme_bw()+
  geom_tile(aes(fill=col))+
  scale_fill_identity()

You could do this with 2 colours if you set one of red, green or blue to 0.