Best way to set an interaction in a regression between two factors when some interactions are impossible? I'm interested in determining how territory size (a continuous variable) changes as a function of species (a factor with 3 levels for the 3 species) and region (a factor with 2 levels, north and south).
The issue is all 3 species are found in the south but only 1 is in the north. If I run an additive model everything works ok but I'm missing that potentially important interaction.
glm(territory ~ species + region, family = Gamma(link = log)) 

But if I run the model with an interaction I get NAs
glm(territory ~ species * region, family = Gamma(link = log)) 

Which suggests a problem.
(Intercept)           11.15706    0.24018  46.452  < 2e-16 ***
speciesrv              0.81842    0.30268   2.704 0.007518 ** 
specieswb             -0.07331    0.18897  -0.388 0.698521    
regionsouth            0.17296    0.17341   0.997 0.319925    
speciesrv:regionsouth       NA         NA      NA       NA    
specieswb:regionsouth       NA         NA      NA       NA

Would it make more sense to recode my species variable into 4 levels with a unique identifier for the northern population of one of the species?
 A: You can't really evaluate an "interaction" except for the 1 species (your reference level for species) that has values for both Regions. If you do recode your data in the way that you suggest (4 levels, with separate coding of North vs South for that species) you will get results logically equivalent to the 4 coefficients returned by your interaction model, as implied in a comment.
The interaction model would have been a bit easier to think about if you had used South instead of North as the reference level. As it stands, the Intercept in that model is for the reference species in the North, and the coefficients for the other species are the differences of those species from that reference if they had been in the North. So you have to add back the coefficient for regionSouth to get the estimates for those species' only possible locations in the South.
Except for that numerical difference based on the choice of reference level for Region, your 4-level model should produce the same results. I'd recommend using the reference species in the South as the reference level of the 4-level predictor, for the reasons just noted. Then the coefficients for the other species are their differences from the reference species in the South where they actually are found, and the coefficient for the reference species in the North is the one North-South difference you actually can estimate.
