Fig. 1

Experimental design. a Study area of 12 nest box plots (rectangular boxes) situated in Southern Germany. Colored great tit symbols represent each plot’s treatment (blue: low perceived predation level (PPL): orange: high PPL) in the first (left-hand bird) and second (right-hand bird) year of study. Scale bar is 1 km. b The among-individual variance (V_I), the residual within-individual variance (V_e), and the cross-year repeatability (\(R = \frac{{V_{\mathrm{I}}}}{{V_{\mathrm{I}} + V_{\mathrm{e}}}}\)) for timing of breeding (and other traits) were calculable for the low-PPL and high-PPL environment since six plots received the same treatment (3 low, 3 high) across years. The phenotypic cross-context correlation (\(r_{{\mathrm{P}}_{{\mathrm{L}},{\mathrm{H}}}}\)) between a female’s timing of breeding under low versus high PPL was calculated using data from six plots that changed treatment across years. This parameter represents an attenuated estimate of the among-individual cross-context correlation (\(r_{{\mathrm{I}}_{{\mathrm{L}},{\mathrm{H}}}}\)) that our unique partial crossover study design allowed estimating (for details, see Methods). c This in turn enabled us to differentiate between four distinct scenarios describing how individual reaction norms for timing of breeding (and other traits) varied as a function of PPL (detailed in main text). Those scenarios differed in whether treatment-specific among-individual variance was absent (\(V_{{\mathrm{I}}_{\mathrm{L}}} = V_{{\mathrm{I}}_{\mathrm{H}}}\)) versus present (\(V_{{\mathrm{I}}_{\mathrm{L}}} \ne V_{{\mathrm{I}}_{\mathrm{H}}}\)) and whether reaction norm crossing was absent (\(r_{{\mathrm{I}}_{{\mathrm{L}},{\mathrm{H}}}} = 1\)) versus present (\(r_{{\mathrm{I}}_{{\mathrm{L}},{\mathrm{H}}}} < 1\)). Here we illustrate possible scenarios given the assumption that mean breeding date is similar in both contexts, and the variance is either the same or higher under high-PPL