For Switzerland, there are currently no figures with respect to the incidence of food allergies, also not to peanuts or tree nuts. There is an anaphylaxis register, fed by a number of hospitals from Germany, Switzerland and Austria, but by far not all cases of anaphylactic reactions are fed into the register (since not all hospitals and/or doctors report to this register).
We know that over the course of the last ten years, the number of kids with food allergies with potential anaphylactic reaction has increased massively. We know this also as an organisation which is contacted more and more by families affected by this severe form of allergies.
A study from the UK showed already 2007 an increase in the number of cases of anaphylaxis reported to the emergency room of 700% since 1990 (Gupta R, Sheikh A, Strachan DP, Anderson HR. Time trends in allergic disorders in the UK.Thorax 2007;62(1):91-6).
The incidence of food allergy in children in the US is between 6 and 8%. Allergists in Switzerland assume that the incidence is about the same for Switzerland. In the US, every three minutes, a food allergy reaction sends someone to the emergency room. Every six minutes, it's an anaphylactic reaction. Details on facts and statistics for the US can be found at the website of Food Allergy Research & Education FARE, one of the big patient organisations in the US.
To which allergen a child is allergic depends on the frequency and amount of exposure and varies therefore regionally. Thus, eg. fish allergy is common in Japan, milk allergy in Europe, and peanut allergy in the U.S.