Adaptation of a stage-projection model for species with multiple year reproductive cycles

We apply stage projection matrices to multiple age and reproductive categories, deriving the stable age - reproductive category distribution for populations with multi-year reproductive cycles and identifying conditions for the existence of a dominant latent root. Given the stable distribution of age and reproductive category and the number of female young for each reproductive category, the age specific fecundity rates can be calculated. For species with multi-year reproductive cycles, the fecundity rate associated with the stable age distribution is often not a smooth function of age, but fluctuates as a larger or smaller fraction of females becomes available to breed. We suggest that fecundity rates for species with multi-year reproductive cycles be defined in terms of litter size and probabilities of conception and successful gestation rather than average fecundity.