Suppose you have n broods followed up during x years. In each brood there are a varying number of sons and daughters that sum up to a varying number of offspring in each brood.

You dispose of this information at the brood- and individual-level (individual refers to offspring): parQuality, a variable resembling the quality of parents (one value for each brood); indSex, sex of offspring (one value for each offspring individual); indFitness, the fitness, i.e. the number of descendants of each individual during their entire lifetime (it refers to the individuals born in the brood); motherID, the identity (ring name) of mother (one value for each brood); fatherID, the identity of father (one value for each brood); year, you have data from about ten years. Note that pairs of parents may change over years and that mothers may have only one brood per year while sometimes fathers sire two broods within one year (they are polygamous).

You want to test the hypothesis that the fitness of sons and daughters (indFitness) is affected diversely by the quality of their parents (parQuality). How would you do it?

I would use a GLMM to control for the pseudoreplication by motherID, fatherID, and year. There are other issues related to the distribution of the response variable that I have already controlled: for instance the need of using a zero-inflation (I have lot of zeros in indFitness), a beta-binomial instead of a binomial or a negative binomial instead of a poisson. Here, I am especially interested in getting advice on how to define the response variable and how to account for the variable number of offspring in each brood. I am undecided to consider as response variable the ratio of indFitness from sons and daughters of one brood (therefore using a binomial, or a betabinomial family), or to consider as response variable indFitness (using a poisson, or a negative binomial) and, in this case, testing as predictor the interaction between parQuality and indSex. In both cases, I am unsure on how should I account on the different number of offspring at each brood.


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