Using zero-inflated models to quantify stochastic and deterministic variation in fecundity

Abstract.  Fecundity is a primary component in evolutionary and ecological theory and applications, yet requires long-term study to quantify the range of stochastic variation and deterministic responses to ecosystem dynamics needed to develop strategies to insure population sustainability.  Fecundity data often include a large proportion of zeros because many individuals fail to produce young during a breeding season, but surprisingly few fecundity studies use zero-inflated Poisson models.  We conducted colorbanding and monthly censuses of Florida scrub-jays (Aphelocoma coerulescens) from 31 years, 15 populations, and 761 territories with much replication across years along central Florida’s Atlantic coast. Our study quantified how fecundity (juveniles/pair/year) was influenced by habitat quality states, presence/absence of nonbreeders, population density, breeder experience, and rainfall considering both success versus failure and count submodels for zero-inflated data with random effects.  Habitat quality and the presence of nonbreeders were important deterministic factors having more influence on the success than the count submodel. The results identified the importance of increasing optimal habitat, which was a mid-successional state related to fire frequency and extent, because optimal habitat in territories, and the proportion of optimal territories in the overall population, influenced fecundity of breeding pairs.  Populations subject to supplementary feeding also had greater fecundity, but random effects among populations still remained important.  Random annual variation was great, but residuals associated with annual variation were not correlated between the success and count submodels.  Increased territory size suggested increased success and juvenile counts, but the posterior distributions overlapped zero.  Population density, breeder experience, and rainfall surprisingly had no or small effects.  The increased fecundity for pairs with nonbreeders, compared to pairs without, identified future empirical research needed to understand how the proportion of marginal habitat influences population recovery and sustainability, because dispersal into marginal habitat can drain nonbreeders from optimal habitat and decrease overall fecundity.