Detrended fluctuation analysis (DFA) of foraging sequences from a little penguin carrying a small logger (first column) and a little penguin carrying a large logger (second column). a, c Integrated dive sequences (y(t)) generated by the accumulation of a binary time series of diving (+1) vs surface time (−1) across the entire length of the single-day foraging trips performed by each little penguin. b, d Log–log plots of the average fluctuation F(n) at each scale (window size) across the dive sequences on the y axes as a function of scale (n) on the x axes. The values of α
DFA reflect the slope of the regression lines, with lower α
DFA reflecting greater complexity (stochasticity). Note that only the points in black were used to fit the regression line to avoid biases introduced at small and large scales; these ‘best scaling regions’ were calculated using methods described in the text.