Fractal analysis of the ambulation pattern of Japanese quail

Figures & data

Figure 1. Example of a power spectrum analyses of the original time series data. All data time series showed similar patterns.

Figure 2. Example of trend elimination capability of DFA in time series using linear (DFA1), quadratic (DFA2), cubic (DFA3), fourth order (DFA4) and fifth order (DFA5) DFA. For DFA1 and DFA2 a crossover is observed (change in slope) that is not present with DFA3, DFA4 and DFA5. DFA3 (▪) was selected for group comparisons, given that third order polynomials eliminated trends in data. In order to improve visualisation, the functions were shifted vertically by multiples of 0·3.

Figure 3. (a) Example of two cumulative walking time series. (b) Detrended Fluctuation Analyses for the same series presented in (a). The series corresponded to the examples of the Unstimulated and Stimulated groups and are characterized by the equations, y = 0·77x – 2·95 (R ² = 0·99) and y = 0·67x −3·49 (R ² = 0·99), respectively.

Figure 4. (a) Example of successive non-walking periods (events) and their time duration (s). Many large events are visible. (b) Example of log–log plot of the frequency distribution of non-walking events of a given duration, original and randomized time series are presented. Notice that the original time series shows a power law distribution (straight line) while the randomized time series has an exponential distribution (dotted line). (c) Examples of logã–log plots of the frequency of the duration of non-walking events in the Unstimulated and Stimulated groups. Reg. Stim. and Reg. Unstim. represent the regression line for Stimulated and Unstimulated birds, respectively.

Table 1. Behavioural analysis of the female Japanese quail walking activity

	SW	SNW	Time spent walking (%)	Average duration of W events	Average duration of NW events
Unstimulated	− 2·28 ± 0·17	− 0·66 ± 0·05	13·70 ± 2·55	2·72 ± 0·13	17·03 ± 2·07
Stimulated	− 2·71 ± 0·14	− 0·91 ± 0·06∗	18·54 ± 2·30	2·51 ± 0·06	10·65 ± 1·11∗
The values represent the mean ± SE. ∗P < 0·05 when the Stimulated group is compared to the Unstimulated group (one-way ANOVA). SW and SNW are scaling exponents calculated as the slope of the log–log plot of frequency vs. duration of the walking event or non-walking event, respectively.

Table 2. Analysis of the transition between behavioural states, walking/not walking, in behavioural time series of Japanese quails in two experimental situations

	Transitions W–W (%)	Transitions NW–W (%)	Transitions NW–NW (%)
Unstimulated	6·0 ± 1·8	7·7 ± 0·9	78·6 ± 3·4
Stimulated	6·6 ± 1·5	11·9 ± 1·2∗	69·6 ± 3·3∗∗
Transitions W–W (%): the bird that is walking at time t, will continue walking at t + 1. Transitions NW–W (%): the bird that is walking at time t, will change to a not walking state at t + 1. Transitions NW–NW (%): the bird that is not walking at time t, will continue not walking at t + 1 (t = 1 s). Transition W–NW is not shown because it has similar values to transitions NW–W. The values represent the mean ± SE. ∗P < 0·05 and ∗∗P = 0·08 when compared to control (one-way ANOVA).