Scaling in organismal behaviour, where behaviour comprises a series of actions such as the consecutive distances moved between turns (step lengths) during searching, or inter-event times (time spent waiting between periods of activity), has been studied in detail only relatively recently. Thus, identifying behavioural scaling laws across diverse species may help to understand how apparently complex behaviours evolved. Results show that behavioural sequences in diverse organisms spanning insects to humans can show spatial and temporal scaling, patterns that may embody such general rules. To explore spatial and temporal patterning in behaviour, some recent investigations have used a statistical modelling approach centred on identifying simple features or rules operating in complex biological systems, which draws on concepts and techniques used in statistical physics to describe stochastic dynamical physical systems. The temporal structuring of behaviour may be strongly influenced by natural selection, and so it seems probable that general ‘rules’ of behaviour operate in stochastic biological systems and have naturally evolved to be optimal in specific situations or environments. In a foraging context, for example, how long an ambush predator waits in a particular location in the absence of prey encounters before energy is expended in moving to a new location will have an important impact on positive energy balance and hence growth rate. The timing of different activities chosen by an individual animal, such as when to search for resources, to rest or to avoid threats, has a central influence on the success of behaviours that can affect survival and lifetime reproductive output. Results indicate temporal power-law scaling is a behavioural ‘rule of thumb’ that is tuned to species’ ecological traits, implying a common pattern may have naturally evolved that optimizes move–wait decisions in less predictable natural environments. A stochastic–deterministic decision model reproduced the empirical waiting time scaling and species-specific exponents, indicating that apparently complex scaling can emerge from simple decisions. Scaling exponents quantifying ratios of frequent short to rare very long waits are species-specific, being determined by traits such as foraging mode (active versus ambush predation), body size and prey preference. Here, we demonstrate from tracking the activities of 15 sympatric predator species (cephalopods, sharks, skates and teleosts) under natural and controlled conditions that bursty waiting times are an intrinsic spontaneous behaviour well approximated by heavy-tailed (power-law) models over data ranges up to four orders of magnitude. However, a general theory linking this phenomenon across the animal kingdom currently lacks an ecological basis. ![]() Remarkably, for diverse animal species, including humans, spontaneous patterns of waiting times show random ‘burstiness’ that appears scale-invariant across a broad set of scales. The decisions animals make about how long to wait between activities can determine the success of diverse behaviours such as foraging, group formation or risk avoidance.
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