different size facets proportional of x axis on ggplot 2 r

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If I understand you correctly, space = "free_x" does what you want in facet_grid. As far as I know, facet_wrap has never supported a space argument, but many facet_wrap commands can be cast as facet_grid commands.

library(ggplot2)

ggplot(mydf, aes(X, Y)) + geom_point()+ 
facet_grid (.~ groups, scales = "free_x", space = "free_x")

enter image description here

And if you want the same style of labelling on the x axes:

ggplot(mydf, aes(X, Y)) + geom_point()+ 
 scale_x_continuous(breaks = seq(0,20,2)) +
 facet_grid (.~ groups, scales = "free_x", space = "free_x")

enter image description here

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