How this present participle is formed

Solution 1:

In a comment, BillJ wrote:

There's no 'reduction'. The gerund-participial clause has been preposed to a position before the subject. The basic version would be: We have expert Sonia Tarrington from the University of California's Nutrition Research Centre [joining us here in the studio to start things off]. Semantically, it's the equivalent of the relative clause "who joins us".

Solution 2:

In a comment, John Lawler wrote:

In BillJ's theory there is no reduction; in other theories there is. It's not a fact, it's an analytic tool. The relation between the sentences with preposed and final participial phrases is independent from the relation between the participial phrase and the relative clause in any event.