How does 'Nesting' during operation cause erratic spring rates?

'Nesting' or 'Stacking' occurs when the waves of adjacent turns in a multi-turn spring do not remain aligned peak-to-peak and instead slip into each other's valleys. This effectively turns a Crest-to-Crest spring into a parallel-stack spring, doubling the spring rate $k$ and potentially causing the spring to reach 'solid' height prematurely. This is often caused by a lack of internal or external guidance (piloting) or by excessive vibration that 'rattles' the turns out of alignment. The solution is to use 'Shim Ends' to stabilize the ends or to increase the diametrical clearance to allow the spring to 'breathe' without catching.