Choice of model and re-nesting probability function influences behaviour of avian seasonal productivity models and their demographic predictions

Measuring seasonal productivity is difficult in multi-brooded species without labour-intensive ringing studies. Individual-based (IB) models have been used to estimate seasonal productivity with no direct knowledge of number of nesting attempts, but they are often based on simplified re-nesting probability (f(R)) step-functions instead of observed or more biologically plausible ones. We present a new, open-source IB seasonal productivity model parameterized from studies of Black Redstart Phoenicurus ochruros and Yellowhammer Emberiza citrinella. We examined how the f(R) function shape (empirical versus simplified) influenced (1) model performance, (2) re-nesting compensation and (3) population-level predictions of a simulated management intervention. Population-level predictions were made only for Yellowhammer as we had more detailed demographic data, such as survival rates, available. Pattern-oriented modelling revealed that IB models produced realistic within-population distributions of breeding parameters, and those specified with an observed or empirically derived f(R) function generally outperformed those specified with simpler step functions. Strength of re-nesting compensation differed depending on the f(R) function used. For Yellowhammers, type of f(R) function in IB models marginally influenced population-level predictions of a simulated management intervention (potential population growth rate increased between 23% and 29% relative to no management intervention). In contrast, a simple deterministic productivity model, which did not simulate re-nesting compensation, predicted a 41% increase in potential population growth. At a population level, choice of f(R) function may have less influence on IB model predictions, but choice of model itself (IB versus deterministic) may have substantial impact. We discuss how more biologically plausible f(R) functions might either be observed directly, derived from nest data, or estimated from proxy information such as moult or brood patch changes.