Statistical analyses
Generalized Linear Models were chosen assuming binomial family and logit link function to investigate how the probability of nesting (1, presence of nest vs 0, absence of nest) is influenced by water depth, vegetation height, distance to the water edge, grazing intensity, and their pair-wise interactions. Tests for potential non-linear relationships with each of the predictor variables by introducing their quadratic terms in the models and comparing their Akaike’s Information Criterion (AICc corrected for small sample sizes; Burnham & Anderson, 2002) were carried out. Test for multi-collinearity (using the Variance Inflation Factor, VIF) and over dispersion in all models, as well as log-transformation of all predictor variables, were carried out to normalize their residuals.
The importance of different predictor variables for nest-site selection was investigated using multi-model inference methods (Burnham & Anderson, 2002). First, the set of best candidate models were computed (i.e. those with ΔAICc<2) using an automatic model selection algorithm, and then derived the importance of each predictor variable by summing the AIC weights of the models where this variable is included (Burnham & Anderson, 2002). The average predictions were computed over the set of candidate models to analyse the relationship of nesting probability with each of the most important predictor variables. All of the above analyses were conducted in R v3.5.3 (Barton, 2019; R Core Team, 2019). The density of breeding pairs was computed as several breeding pairs per unit area (km2) of marshes where Google Earth Pro “Add Polygon” tool was used to approximate the marshes area.