Abstract
Natural and anthropogenic sources of contamination such as plankton toxins and hydrocarbons are nearly ubiquitous in the marine environment. Specifically, they are a pernicious threat especially at low concentration as nonlethal effects on the plankton propagate through the food chain and accumulate in the tissues of top predators, ultimately putting human health at risk. In this contribution, I first describe how the complexity observed in the spatial and temporal patterns of copepod swimming behaviour can be objectively quantified using a series of ‘behavioural stress indexes’ based on fractal and multifractal analyses of copepod swimming behaviour and swimming sequences. These indexes are suggested as a potential tool to critically assess behavioural responses to natural and anthropogenic forcing in the marine environment.
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- 1.
Note that it is readily seen from Eqs. (1) and (2) that D b = D d, whilst more convoluted developments show that D b = D m; hence D b = D d = D m; see (Seuront 2010a) for details. Statistically inferring the absence of significant differences between fractal dimensions returned by different methods of analysis hence constitutes an additional guarantee of the trustworthiness of the fractal dimension estimates.
- 2.
Brownian motion (i.e. normal diffusion) is characterised by β = 2. Anti-persistent and persistent fractional Brownian motions are characterised by β < 2 and β > 2, respectively. Specifically, a motion is persistent in the sense that an organism moving in some direction at time t will tend to move in the same direction at the next time step.
- 3.
For instance, the velocity components of Clausocalanus furcatus were both characterised by β ≈ 0 (Uttieri et al. 2008), indicative of a random process without internal serial correlation. In contrast, β ranged from 0.30 to 0.75 in Temora longicornis (Moison et al. 2012) and 1.4 to 1.5 in Pseudodiaptomus annandalei (Dur et al. 2010).
- 4.
Note the one-to-one correspondence between the function ζ(q) and the spectral exponent β for q = 2, i.e. β = 1 + ζ(2) (Seuront 2010a).
- 5.
It is worth noting that the increase in the complexity of Daphnia magna trajectories in contaminated waters must be treated with caution as some of the fractal dimensions reported fall outside the theoretical range 1 ≤ D ≤ 2, i.e. D > 2 (Shimizu et al. 2002).
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Seuront, L. (2015). When Complexity Rimes with Sanity: Loss of Fractal and Multifractal Behavioural Complexity as an Indicator of Sublethal Contaminations in Zooplankton. In: Ceccaldi, HJ., Hénocque, Y., Koike, Y., Komatsu, T., Stora, G., Tusseau-Vuillemin, MH. (eds) Marine Productivity: Perturbations and Resilience of Socio-ecosystems. Springer, Cham. https://doi.org/10.1007/978-3-319-13878-7_14
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