Which version is correct?
...plus proven ability to collaborate with people from culturally diverse backgrounds is evidenced in his success in the US, Europe and Asia.
...plus proven ability to collaborate with people from culturally diverse backgrounds is evidenced by his success in the US, Europe and Asia.
In this instance, evidenced by.
See the second definition of by, from Oxford Dictionaries:
By
2. [OFTEN WITH VERBAL NOUN] Indicating the means of achieving something:'Malaria can be controlled by attacking the parasite'
When combined with the definition of evidenced, also from Oxford Dictionaries:
Evidenced
Be or show evidence of:'The quality of the bracelet, as evidenced by the workmanship, is exceptional'
The thing that is being achieved in your sample sentence is the evidencing of the "ability to collaborate with people from culturally diverse backgrounds", the means of achieving it is the "success in the US, Europe and Asia.".
In general however, it's not quite so simple. Indeed, the third example sentence for evidenced at OD is:
'This was evidenced in the cohesive and selfless display against Rangers.'
In is used in situations where the evidence is provided by a specific item1 or event. In the above sentence, this would be the match against Rangers. Compare with
'This was evidenced by the cohesive and selfless display.'
Similarly, taking a sample sentence from yourdictionary:
Everything he wrote was animated by the ardent spirit of piety evidenced in his life.
Where 'his life' is the event which the evidence for his ardent spirit is included within, meeting the 5th definition of in from oxford dictionaries:
In
5.'Expressing inclusion or involvement'
Just to demonstrate the difference, we can rephrase that last sentence to use by:
Everything he wrote was animated by the ardent spirit of piety evidenced by his lifestyle.
Removing reference to the specific 'event' of his life makes by again the better option.
Summary: Use in where the evidence is in a specific item/event, otherwise use by.
1. Item could include a text, for example:
Spending could be reduced by as much as 13%, as evidenced in Carter's 2004 report
