The charts in your link show a steep decline in illegal immigration over the last decade.

Your Arizona study appears to be an anomaly compared to most other research. The total incarceration rate is invalid, skewed by those incarcerated for immigration violations.

A paper published by the National Bureau of Economic Research in 2007 found that immigrants had incarceration rates about one-fifth that of native-born Americans, and that the difference actually increased between 1980 and 2000.
http://www.nber.org/papers/w13229

According to analysis of the 2010 census and the American Communities Survey done by the non-profit American Immigration Council, immigrants to the United States are significantly less likely than native-born citizens to be incarcerated. The authors found that 1.6 percent of immigrant males age 18-39 are incarcerated, compared to 3.3 percent of the native-born.

http://www.americanimmigration...igration-united-states