Fig. 1

Conceptual framework of the two interrelated measures of carry-over effects between events in the annual cycle. The framework assumes the population mean represents the overall optimal timing, while throughout the range of timings different advantages and disadvantages can be attributed. A Here an example delay (\({d}_{1}\)) relative to the population mean timing (\({\overline{x}}_{{t}_{1}}\)) of event 1 affects the timing of a subsequent event \({t}_{2}\) relative to the population mean \({\overline{x}}_{{t}_{2}}\) to different degrees. The resulting degree of advancement or delay in event (\({t}_{2}\)) is the net of carry-over effects and is described by its strength as partial, complete, or amplified carry-over effect, or a complete compensation. The strength of the carry-over effect can be quantified as the slope between \({t}_{1}\) and \({t}_{2}\) (B), or, between \({t}_{1}\) and the duration of the period between \({t}_{1}\) and \({t}_{2}\) (C)