Partitioning variance in population growth for models with environmental and demographic stochasticity.

How demographic factors lead to variation or change in growth rates can be investigated using life table response experiments (LTRE) based on structured population models. Traditionally, LTREs focused on decomposing the asymptotic growth rate, but more recently decompositions of annual 'realized' growth rates using 'transient' LTREs have gained in popularity. Transient LTREs have been used particularly to understand how variation in vital rates translate into variation in growth for populations under long-term study. For these, complete population models may be constructed to investigate how temporal variation in environmental drivers affect vital rates. Such investigations have usually come down to estimating covariate coefficients for the effects of environmental variables on vital rates, but formal ways of assessing how they lead to variation in growth rates have been lacking. We extend transient LTREs to further partition the contributions from vital rates into contributions from temporally varying factors that affect them. The decomposition allows one to compare the resultant effect on the growth rate of different environmental factors, as well as density dependence, which may each act via multiple vital rates. We also show how realized growth rates can be decomposed into separate components from environmental and demographic stochasticity. The latter is typically omitted in LTRE analyses. We illustrate these extensions with an integrated population model (IPM) for data from a 26 years study on northern wheatears (Oenanthe oenanthe), a migratory passerine bird breeding in an agricultural landscape. For this population, consisting of around 50-120 breeding pairs per year, we partition variation in realized growth rates into environmental contributions from temperature, rainfall, population density and unexplained random variation via multiple vital rates, and from demographic stochasticity. The case study suggests that variation in first year survival via the unexplained random component, and adult survival via temperature are two main factors behind environmental variation in growth rates. More than half of the variation in growth rates is suggested to come from demographic stochasticity, demonstrating the importance of this factor for populations of moderate size.