What would be the independent variable in the following hypothesis?
if sea turtle sickness is related to red tide, then an increase in red tide will result in an increase in sea turtle sickness.

The independent variable in the hypothesis of an observed increased in sea turtle sickness once an increase in red tide can be seen would be the increase of red tide. 

The reason for this is that red tide increases or decreases will happen independently of the amount of sea turtle sickness - therefore increasing sea turtle sickness will be dependent on the first variable. (independent one).