Does physical aerobic exercise ameliorate depression? Studies seem to find correlation, but has the causal link been established?
There are different theories about the causes of depression. Three of them assume a cause that could be affected by aerobic exercise.

Neurochemical theory of depression:

It seems that depression might be caused by low serotonin and/or noradrenalin levels. Physical activity releases both neurotransmitters, thus alleviating depressive symptoms.

Cognitive theory of depression:

It seems that negative cognitive schemata cause depression. Sports improves self-efficacy and other schemata.

Diathesis–stress model of depression:

Depression is the result of a predispositional vulnerability combined with stress from adverse life experiences. Aerobic exercise relaxes the sympathetic nervous system thus alleviating stress and, as a consequence, depression.

Maybe someone else will come up with studies showing a causal connection. These (and other) theories might explain the connection.