4 simultaneous non-independent measures – should nested ANOVA work?

Hi all, this is my first time posting here, but I’m very stuck. I have to analyze data from an animal behavior experiment. I have 3 strains, with 20 trials each. In each trial, a group of animals is given a choice of 4 pieces of food: 2 high-nutrient and 2-low nutrient. Within each food type, the animals tend to aggregate their choices to one piece of food (call it “more”) than the other (“less”).

I’m interested in possible strain effects on preference for the high-nutrient versus low-nutrient food types, but aggregation could potentially explain any observed clustering of choice so it must also be included in the analysis somehow. The data I’m working with is the number of times each piece of food was chosen per trial, and the proportion of the total choices made per trial.

Using a nested ANOVA has been proposed to me, with the following nesting: strain > trial > food type (high vs low) > aggregation (more vs less). Trying this analysis in JMP doesn’t work as long as “trial” is included, and I’m not sure if this way of including trial makes sense anyway, but I’m not sure how else to include in the analysis that measures from the same trial are not independent of each other (when an animal is making a choice, it’s not choosing any of the other three pieces of food).

Should a nested ANOVA work here, and is it appropriate? Do I not need to group by trial? Any input would be greatly appreciated. I can clarify or provide some additional details if necessary. Thanks!