(1) Load your Google Plus App
(2) Press on the cogwheel Settings button
(3) Press 'Circles' and the list of categories of people in your Google Plus Circles which includes: Friends, Family, Acquaintances, Following, Public appears. Select one or all of the 'Circles' that you do not want to have Push Notifications/Alerts sent from your Google Plus to your Google Gmail.
For example, if you no longer want Push Notifications from your 'Acquaintances' Google Plus 'Circle', press on 'Acquaintances' then slide 'Notifications' to OFF.