I don't believe elevated polyunsatured fatty acid consumption falls under the tendencies of the western diet, and may be more reminiscent of the Mediterranean diet, so hopefully this answers your question. This study took mice with elevated blood and tissue omega-3 levels, and were used to identify if high levels of omega-3's could prevent the deleterious effects of excessive antibiotic use on gut microbiota. Regarding microbiota diversity, antibiotics are known to create an imbalance between bacteroidetes (decreased) and firmucutes (increased) - this study evidenced that the omega-3 mice were able to rapidly recover their bacteroidetes composition and reduce the amount of firmucutes present in comparison to the control, which in short is good news, as this also prevented later-life obesity in the omega-3 mice in contrast to the obese controls.
For skeptics of microbiota-influenced weight loss (and I know there's many), there is quite a bit of literature out there describing the relationship between gut microbiota diversity and energy expenditure. The short description is that elevated bacteroidetes (in proportion to firmucutes) is associated with lean phenotypes, that diet is very much capable of modulating gut microbiota over short periods of time, and transplanting microbiota compositions into obese individuals has definitively shown an effect on metabolism. The only problem to a gung ho microbiota therapy is, no one knows the gold standard for microbiota composition.