Wrong projection of raster using R

Question

I have a raster layer with the following structure:
ncols 4320
nrows 2160
xllcorner -180.0
yllcorner -90.0
cellsize 0.0833333
NODATA_value -9999.0
-9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0 -9999.0

If I then try to read it and project, it does not appear:
library(raster)
library(tmap)

r <- raster("baseline/baseline/zip/1870AD_pop/popc_1870AD.asc")
crs(r) <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"

tmap_mode("view")
tm_shape(r)+tm_raster("red")

For some reason, I'm unable to display it properly, even with the added crs.
plot(r) does give me an expected output:

However, when trying to plot it on another map, it fails to do it correctly.
summary(r) gives the following output:
> summary(r)
         popc_1870AD
Min.    0.000000e+00
1st Qu. 0.000000e+00
Median  7.089942e+00
3rd Qu. 1.621315e+02
Max.    1.331152e+05
NA's    7.092085e+06
Warnmeldung:
In .local(object, ...) :
  summary is an estimate based on a sample of 1e+05 cells (1.07% of all cells)

The file can be downloaded here:
http://www.filedropper.com/popc1870ad

Spacedman · Accepted Answer

Your data goes up/down to 90N/S. On a Mercator projection, like on most web mapping software, this goes to +Infinity/-Infinity.
tmap seems to have even tighter limits on what it can display. If I crop to +/-50 I can see your data within that latitude band:
> rc50 = crop(r,extent(c(-180,180,-50,50)))
> tm_shape(rc50) + tm_raster()

but if I change it to -51 and 51, I see nothing!
If you reproject the data to the web mercator projection, then you can display more, but you still have to crop it first because otherwise you go off to infinity:
> rc = crop(r,extent(c(-180,180,-80,85)))
> rp = projectRaster(rc, crs="+init=epsg:3857")

It doesn't matter if you set the CRS like you do or not, since you are using the default CRS anyway (but its a Good Thing to set it anyway).

Wrong projection of raster using R

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