When creating a project inside the RStudio IDE, your project files are actively monitored for changes. This allows RStudio to index functions and files to enable code completion and navigation. If you are simultaneously using the Dropbox application to remotely sync your work, Dropbox will also actively monitor your files.
To prevent conflicts, you should tell Dropbox to ignore the .Rproj.user directory inside your RStudio Project. For example:
.../Dropbox/RStudioProject/.Rproj.userNote this is a hidden directory
To ignore a file in Dropbox, you will need to use Dropbox's Selective Sync feature. First make sure to quit RStudio. Then go to Dropbox Preferences | Advanced and select Selective Sync This will open a file browser in which you can navigate to your RStudio Project, and unselect the .Rproj.user directory.