Geom_smooth doesn't plot on ggplot2

OP. The reason your line doesn't show is due to you x axis values being discrete. In effect, ggplot2 does not know how to connect your data along the x axis, since with discrete data there is no obvious reason to connect along that axis.

There are two general solutions here. One is simple and gives you a line with hard edges, whereas the other is more involved, but you will get a line that has completely smooth edges.

Simple Solution: Not Smooth Line

To get a "not-smooth" line, all you need to do is tell ggplot2 that the points along the x axis are all connected in that dimension and that it should use the number value of the level to assign to the x axis. Without treating the scale numerically, there is no way to calculate a formula along that axis so this is necessary. Since the axis is still discrete in this case, there is no point that would make sense if it were in-between any two values along x, so the line you get is going to be angular (not-smooth). Thank @teunbrand for this solution:

ggplot(data.fam, aes(x=site, y=specnumber_f)) +
  geom_point() + geom_smooth(aes(group=-1))

Getting a Smooth Line

If you are aesthetically pleased with the simple solution, then it's the easiest so go with that. If you really wanted a smooth line, here's one way to do it. The basic idea is that we need to change your discrete axis into a continuous one. The problem is that data.fam$site is not continuous. Therefore, we need to basically map the values of data.fam$site to another column that is numeric, then use scale_x_continous() to label our axis with the correct names from data.fam$site.

First, we set the order of your axis labels aside:

lat.order.levels <- c("MS", "CU", "CA", "CF", "ST", "AB", "FN",
                      "RO", "SPSP")

Then, we make another data frame that will be used to map our continuous column (herein site_num) onto the original data frame, data.fam.

site.data <- data.frame(
  site = lat.order.levels,
  site_num = 1:length(lat.order.levels)
)

Finally, we merge the two frames, keeping all the points in data.fam. I create a new data.frame for this called df:

df <- dplyr::left_join(data.fam, site.data, by= "site")

For the plot, you assign the x aesthetic to site_num, and use lat.order.levels to label the axis via scale_x_continuous().

ggplot(df, aes(x=site_num, y=specnumber_f)) +
  geom_point() + geom_smooth() +
  scale_x_continuous(
    breaks=1:length(lat.order.levels),
    labels=lat.order.levels
  )