Fractal Long‐Range Correlations in Behavioural Sequences of Wild Chimpanzees: a Non‐Invasive Analytical Tool for the Evaluation of Health

Abstract

Quantitative evaluation of health impairments in wild chimpanzees was explored using fractal long‐range correlations of behavioural sequences. The health status of 13 chimpanzees in the Mahale Mountains National Park, Tanzania was evaluated non‐invasively using standard behavioural observation and parasitological analysis of stool samples. Based on these data, individuals were classified as being either healthy or sick. Behavioural sequences were analysed and shown to exhibit long‐range power law correlations. The behavioural sequences of individuals in healthy and sick states were quantitatively evaluated using detrended fluctuation analysis of social and non‐social behaviours within behavioural sequences. These values were compared and significant differences in long‐range correlations were found between health states. Sex differences were also noted, with female social behaviour displaying a larger fractal dimension than male social behaviour. The fractal dimension of females declined significantly in sick individuals. This analysis of behaviour provides a new and effective non‐invasive method to record and evaluate the general state of health and related stress of animals in the wild. Possible applications of this method in captive situations include the monitoring and evaluating of stress levels over time.

Estimating long-range dependence: finite sample properties and confidence intervals

“…More recently, "long memory" or "1/f noise" (as it is often called) has been observed in DNA sequences [5,6], cardiac dynamics [7,8], internet traffic [9], meteorology [10,11], geology [12] and even ethology [13].…”

Dynamical analysis reveals individuality of locomotion in goldfish

“…Indeed, studies have shown that the examination of behavioural data that appeared to be random can reveal highly non-random components when analysed with sequencesensitive nonlinear measures. For example, a number of behaviours have been described as fractal, from spontaneous locomotion (Dicke and Burrough, 1988;Coughlin et al, 1992;Motohashi et al, 1993;Cole, 1995) and foraging (Alados and Weber, 1999) in diverse species to social behaviour in chimpanzees (Alados and Huffman, 2000) and feeding-related activities in goats (Alados et al, 1996). Related tools have also been used to successfully analyse the pattern of transitions between periods of active swimming and inactivity (Faure et al, 2003).…”

“…Spatial and temporal complexity of foraging trajectories, for example, can be correlated to the pattern of occurrence of food sources (Cole, 1995;Viswanathan et al, 1996). Similarly, some bird species exhibit nonlinearities in vigilance behaviour (Ruxton and Roberts, 1999), and correlations have been drawn between fractal complexity and the ability to cope with the environment, such as in the presence of toxins or stress (Alados et al, 1996;Alados and Weber, 1999;Alados and Huffman, 2000). One can thus speculate that fish exposed to an environment more heterogeneous than that used in the present study would generate swimming trajectories with higher values of CFD and DR, indicative of a more fractal nature.…”

“…Some of these patterns are complex and cannot be characterized with the tools of classical kinematics, as they may exhibit nonlinear properties, such as persistence (the tendency to repeat a given sequence), redundancy (the relationship between the uncertainty of a signal and its length) and scale invariance (a tendency for a signal to have the same structure when observed on different temporal or spatial scales) (Faure et al, 2003). Indeed, nonlinear measures have been used to characterize locomotion and the behavioural repertoires in various species, including invertebrates (Dicke and Burrough, 1988;Cole, 1995), fish (Coughlin et al, 1992;Alados and Weber, 1999;Brewer et al, 2001), birds (Viswanathan et al, 1996;Ferriere et al, 1999) and mammals (Paulus et al, 1990;Marghitu et al, 1996;Alados et al, 1996;Alados and Huffman, 2000).…”

Magnitude and sign correlations in conductance fluctuations of horizontal oil water two-phase flow

“…They concluded that the long-range correlations of magnitude series indicate nonlinear behavior and the sign time series mainly relate to linear properties of the original series. The time series analysis methods based on long-range correlation has been successfully applied to diverse fields such as DNA sequences [10][11], long-time weather records [14], geology [15], ethnology [16], physiological dynamics [17] and economics time series [18].…”