I would like to ask a recommendation of a statistical test to answer a question related to an unusual data structure.

I am testing if birds change nest parental care behavior depending on offspring health status. I video recorded nests in the field, and calculated the proportion of time that parents of each nest spent on different behaviors types (eg. Brooding, Feeding or Absent). In this situation, if a parental spends more time on “Brooding”, the proportion of time on “Absent” will decline. In other word, the frequency of each behavior is not independent (and the sum will be always 1).

Furthermore, my data have several structures. Nest can have 1,2 or 3 nestlings. Parental care could be influenced by nestling age. Offspring could be not infected in a first record but become infected in the next one. Video records have different lengths (it depends of battery duration of each record, but is usually from 50-70 min).