Unraveling the fluctuations of animal motor activity

Abstract

Human and animal behavior exhibits power law correlations whose origin is controversial. In this work, the spontaneous motion of laboratory rodents was recorded during several days. It is found that animal motion is scale-free and that the scaling is introduced by the inactivity pauses both by its length as well as by its specific ordering. Furthermore, the scaling is also demonstrable in the rates of event's occurrence. A comparison with related results in humans is made and candidate models are discussed to provide clues for the origin of such dynamics.

Figure 1

Three day activity plot obtained from six laboratory animals (“A”–“F”) exposed to a cycle of 12 h of light (6 a.m.–6 p.m.) and darkness (6 p.m.–6 a.m.), individually housed and continuously monitored by an infrared device scanning the field at a rate of 1 Hz. The bottom time series depicts the group average activity $⟨R⟩$ computed with a binwidth of 1 min and normalized.

Figure 2

Interevent time ${\tau }_i$ as a function of the event number i (data from animal A).

Figure 3

Normalized distributions of interevent times τ (empty symbols), duration of motion episodes (gray symbols), and duration of immobility periods (black symbols) computed from 9 days of continuous recording. Symbols joined by dotted lines correspond to the results from each one of the six animals. The solid lines correspond to a double exponential fit (with characteristic times of the order of 1 and 4 s). The dashed line, drawn for comparison, has a slope of −1.75. Inset: representation of the distribution of motion episodes in log-linear scale. Statistics computed individually for each of the six animals and plotted overimposed.

Figure 4

Distributions of duration of (a) immobility and (b) mobility episodes at day (circles) and night (triangles) for animal A. Insets: normalized distributions of the same data. A linear binning was used to emphasize the tail fluctuations.

Figure 5

Long-range correlations of interevent times. Log-log plot of the power spectra for the six series of interevent intervals (open symbols) and of their increments (filled symbols). Data were logarithmically binned. Here f is the inverse of the instantaneous period between consecutive events. Dotted lines are a guide to the eyes. Dashed lines with slopes of −0.4 and 1.6 are drawn for comparison. Notice that $\alpha =0.4$ and $\beta =1.6$ verify $\alpha =2-\beta$. Inset: separate analysis of day and night periods for animal B. Spectra were normalized for better comparison.

Figure 6

(a) Cumulative number of events as a function of time. A zoom is displayed in the inset. (b) Scaled distribution of local rates R computed over nonoverlapping time windows of lengths T indicated on the figure. Data collapse is obtained for $\nu \simeq 0.2$. and $\gamma =0.75$. Inset: time series of local rates R for time window length of 256 (black) and 1024 s (green), vertically shifted for better visualization. (c) Separate analysis of nighttime and daytime data: $\nu \simeq 0.2$, $\zeta =0.75∕\gamma$ with $\gamma \approx 0.5$ (daytime) 1.5 (nighttime). Inset: unscaled plots of the same data. Note the absence of any characteristic scale for the local rates demonstrated by the fact that the three calculated rate densities follow a truncated scale-free distribution. The dashed lines with slope $\gamma =0.75$ are drawn for comparison. All data are from animal A.

Figure 7

Long-range anticorrelations in the increments $I_n$ of activity rates $R_n$ computed over 1-min windows. Log-log plot of the power spectra for the six I time series (symbols). The dashed line with slope $\beta =1$ indicates the correlations expected for pink noise (data from six animals). Inset: the same analysis performed separately for day and nighttime data of animal F. (In all cases spectra were log binned and normalized for better comparison.)

Figure 8

Fano and Allan factors as a function of the counting time-window length T. (a) For comparison, the same analysis over the series of shuffled time intervals is also shown. Solid lines are the results of fits giving slopes $d\simeq 0.7$ and $d\simeq 0.8$, respectively. (b) Separate analysis for daytime and nighttime data (data are from animal A).

Figure 9

Relaxation toward a fluctuating threshold model. (a) Plots as a function of time of the threshold Θ (black line) that fluctuates diffusively (with coefficient D) between the levels 0 and $V_1$ (dashed lines); the dynamical variable V (thin red line) that describes the relaxation from the excited level $V_2$ (dotted line) down to the threshold and is characterized by amplitude K and exponent κ. [(b)–(d)] Results of simulations performed up to time ${10}^6$ in units that correspond to $\sim 1\text{\hspace{0.5em}s}$ of real time. Model parameters are $\left(V_1,V_2,D,K,\kappa \right)=\left(27,30,0.04,3.0,0.25\right)$. (b) Series of interevent intervals. (c) Distribution of interevent times. Dotted line indicates $\mu =1.75$. (d) Fano and Allan factors vs counting window length T. Dotted line corresponds to $d=0.7$.