What could be the reason for this link with vegetarian diets and depression?
One factor could be the lack of EPA and DHA, these are two compounds that are found only in fish and algae. When we eat fish or fish oils, we get an abundance of these products which are essential for brain structure and function. Low levels of which have been linked with depression.
The vegetarian, vegan diet is often low in EPA and DHA as it is difficult to get EPA and DHA from plant foods. Yes, you can get ALA (alpha linolenic acid) from plant foods such as hemp oil, but this has to be converted to EPA and DHA by the body and often our bodies are not very good at making this conversion. Possibly due to lack of certain nutrients needed for the enzymes.
I always recommend that non fish eaters take an vegetarian EPA / DHA oil supplements (it is derived from algae) to ensure that they are getting enough of these important brain nutrients.