Fractal analysis provides new insights into the complexity of marine mammal behavior: A review, two methods, their application to diving and surfacing patterns, and their relevance to marine mammal welfare assessment

Abstract

Fractals have been applied to describe the complexity of behavioral displays in a range of organisms. Recent work suggests that they may represent a promising tool in the quantification of subtle behavioral responses in marine mammals under chronic exposure to disturbance. This paper aims at introducing the still seldom used fractals to the broader community of marine mammal scientists. We first briefly rehearse some of the fundamental principles behind fractal theory and review the previous uses of fractals in marine mammal science. We subsequently introduce two methods that may be used to assess the complexity of marine mammal diving patterns, and we apply them to the temporal dynamics of the diving patterns of killer whales in the presence and absence of sea kayaks, the sequential behavior of harbor and gray seals in environments with distinct levels of anthropogenic influence, and southern right whales with and without calves. We discuss the ecological relevance of identifying fractal properties in marine mammal behavior, and the potential strength of the fractal behavioral parameters in comparison to more standard behavioral metrics. We finally briefly address the relevance fractal methods may have for the design and implementation of management and conservation strategies.

Computational animal welfare: towards cognitive architecture models of animal sentience, emotion and wellbeing

“…However, in a situation of high need (high arousal), top-down attention control would significantly block all the stimuli not associated with the current GOS, leading to reduced behavioural complexity. Similar patterns have been documented, with stress reducing the diversity of behaviour in mammals [234][235][236].…”

Effects of temperature on the behaviour and metabolism of an intertidal foraminifera and consequences for benthic ecosystem functioning

“…The complexity of the trajectory of each individual was assessed using fractal dimension analysis. Because the principles behind fractal theory, fractal analysis techniques and their applications to behavioural data, including foraminifera behaviour 48 , have all been described in detail elsewhere 61 – 63 , we only briefly describe hereafter the basic principles of the box-counting method, which is likely among the most widely applied and intuitive methods available to date to characterize the geometric complexity of movement paths. This method superimposes a regular grid of squares of length l on a path and counts the number of occupied squares, N ( l ).…”

Welfare Challenges Influence the Complexity of Movement: Fractal Analysis of Behaviour in Zebrafish

“…Medicine in particular has benefited from using this approach, extracting 'hidden information' from physiological time series data, identifying for example, changing complexities in heart rate as a response to age and disease in humans where standard analysis revealed little detail [42]. Fractal analysis has also been applied in animal welfare studies to demonstrate a reduction in behavioural complexity linked to parasitic infection and pregnancy in Spanish ibex (Capra pyrenaica) [44], impaired health, ageing and low dominance status in Japanese macaques (Macaca fuscata yakui) [45], sickness in chimpanzees (Pan troglodytes schweinfurthii) [46,47], exposure to toxicants in fish and shrimps [48][49][50], welfare of marine diving mammals [51] and stress in dolphins (Tursiops aduncus) [52]. Surprisingly in most of these studies, standard behavioural approaches revealed little difference between treatments.…”