Coding interaction between 2 covars when one is non-linear

[Summer Burdick]

I am working on an occupancy analysis for juvenile suckers (fish). I obtained my capture histories with spatial replicates set over a six week period between late-June and early-August. Sites were selected randomly and were not visited multiple times (single season design). Because of this sample design, aspects of habitat that vary with time are site covariates. For example dissolved oxygen (DO) concentrations vary with time and with site but do not vary among sampling occasions at a site.

I hypothesize that juvenile sucker habitat use is greatest at water depths intermediate within the range of water depths we sampled. That is, I think juvenile suckers are most likely to use depths in the range of 3-6 m and we sampled depths between 0.4 and 15 m. To model this effect I can include a second order polynomial for depth (beta0+beta1*depth+beta2*depth^2). In mid-July DO concentrations decline, especially at depths of 3 m or more. When this happens I hypothesize that juvenile suckers vacate the deeper water for shallower water. This means that the most used habitats will be at depths of 1-2 m instead of 3-6 m.

I realize that the best way to model this would have been to set up a multi-season study design, but I didn’t do that for several reasons. One reason being it is difficult to predict when DO concentrations will decline. Given the data structure I have, how would I code a model with an interaction between depth and DO concentrations in either MARK or PRESENCE?