We performed a controlled experiment where the experimental units are aquariums with either no treatment or application of a treatment with several replicates of each. Within the aquariums, there were multiple species of which I am interested in whether they are located in a different location in the controls vs. the treatment aquariums. I have data of counts of species from 6 locations in aquariums. I used the counts to approximate their location in two dimensions by looking at the proportion near the surface or bottom, and proportion near the side or center.
How do I test if there is an effect of treatment on the position of a species in this 2D space, specifically did it move in response to treatment? How would I test that Species A moved in a different direction than Species B in response to treatment?
One suggestion I was given was to treat the counts at each depth as a contingency table and then use a log linear model to fit the data. I am not familiar with this approach and am wondering how I would apply it.
On the plot: when Y = 0, the animals are located on the bottom, not the surface; when X = 0, the animals are on the side, not the center. On the plot, the small open circles are the Control replicates and the small closed circles are the Treatment replicates. The large circles are the group averages. The colors represent two different species. The arrows are just there to highlight the movement I am interested in.