The bureaucratic back-and-forth between two powerful brothers — who were known to have a competitive relationship — reveals a peculiar pattern.

Records show the president rejected his younger brother’s requests at a greater rate than the national average; there is no way to know if it was a fluke of the weather or further evidence of a well-known sibling rivalry. But other governors had more luck winning federal aid than Jeb Bush.

That snapshot of the Bush brothers’ relationship is one of several contained in documents held at the George W. Bush Library here, documenting communication between them when one was president and the other was governor of the country’s fourth-largest state.

President Bush denied six of Governor Bush’s 20 major disaster or emergency requests during the time they overlapped in office, according to Federal Emergency Management Data compiled by Richard Sylves, a professor at the University of Delaware. That represents an approval rate of 70 percent, compared with an average of about 85 percent for the rest of the country.

Jeb Bush enjoyed a much better batting average during the two years he served while Bill Clinton occupied the Oval Office.