Should we use mole traps or not ?

Mole control is one of the most complicated problems that can face a gardening enthusiast.

It is not from lack of information. Plenty of information is available. University research and white papers, government brochures, and plenty of expert opinions.

It is not from a lack of products either. At any time there are 10 or more different varieties of mole trap on sale, plus various poisons and repellants.

The experts, university professors and even the government, when they express an opinion, even come close to a consensus. Mole traps are probably the most effective method of mole control, if set correctly, checked on a regular basis etc.

Most reports however take a very simplistic view:-

A single plot of land

No regard to whether neighbouring plots are residential, farmland or wooded. No recommendations on how to co-ordinate efforts with neighbours. If one neighbour has a huge infestation of moles, but
refuses to take action, can they be force to do so? If you used fumigation in such a case, could they hold you liable for killing their moles?

Rules apply to specific locality

There are states in the US where the use of mole traps are restricted. There are areas of Canada where both the Eastern Mole and the Townsend mole are a protected species. The bordering states in the US have no restrictions, yet species conservation is meant to be a global concern.

Lethal methods of mole control can only be used in Germany where the moles are a confirmed hazard.
The use of traps in many US States currently falls under hunting regulations which can require a license, and specific measures to be taken. This is often not enforced.