West Marin ranchers are anxiously watching a pitched battle unfold over the county line, where animal rights activists are pushing a first-in-the-nation ballot measure aimed at limiting the size of Sonoma dairies, ranches and poultry farms.

Supporters of Measure J gathered more than 37,000 signatures in March to get the measure on the ballot, but every local government in the county has since passed a resolution opposing it. It’s hard to drive along a Sonoma…