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Jellyfish behavior: LFF or MRW?

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Scale-free distribution of displacement lengths is often found in animal data, both vertebrates and invertebrates. In marine species this pattern has often been interpreted in the context of the Lévy flight foraging hypothesis (LFF), where optimal search is predicting a scale-free power law compliant movement when prey patches are scarce and unpredictably distributed and a more classic and scale-specific Brownian motion-like motion when such patches are encountered (Viswanathan et al. 1999). In a study on the jellyfish Rhizostoma octopus such an apparent toggling between two foraging modes were found, but critical questions were also raised by the authors (Hays et al. 2012). Here I come the authors “to the rescue” by suggesting that an alternative model – the Multi-scaled Random Walk (MRW) – could be included when testing statistical classes of foraging behaviour.

I cite from their Discussion:

In some periods (when integrated vertical movement was low), vertical excursions were follo…

Accepting Spatial Memory: Some Alternative Ecological Methods

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In this post I present a guideline that summarizes how a memory-based model with an increasing pile of empirical verification covering many species – the Multi-scaled Random Walk model (MRW) – may be applied in ecological research. The methods are in part based on published papers and in part based on some of the novel methods which you find scattered throughout this blog.

In the following, let us assume for a given data set that we have verified MRW compliance (using the standard memory-less models or alternative memory-implementing models as null hypotheses) by performing the various tests that have already been proposed in my papers, blog posts and book. Typically, a standard procedure should be to verify (a) site fidelity; i.e., presence of a home range, (b) scale-free space use by studying the step length distribution from high frequency sampling, and (c) the fractal dimension D≈1 of the spatial scatter of relocations in the resolution range between the dilution effect (very sm…

Temporally Constrained Space Use, Part III: Critique of Common Models

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There is no doubt among field ecologists that animals from a broad range of taxa and over wide range of ecological conditions utilize their environment in a spatial memory-influenced manner. Spatial map utilization have now been verified also well beyond vertebrates, like dragonflies and some solitary wasps. To me at least it is thus a mystery why theoretical models that are void of influence from a memory map; for example ARS, Lévy walk and CTRW (see Part I, II), are still dominating ecological research with mostly no critical questions asked about their feasibility.

It is a fact that the memory-less mainstream models all have a premise that the data should not be influenced by map-dependent site fidelity. In other words, applying ARS, Lévy walk and CTRW models as stochastic representation of space use also implies accepting that the animal’s path is self-crossing by chance only, and not influenced by targeted returns. Such returns can be expected to seriously disrupt results on – f…

Temporally Constrained Space Use, Part II: Approaching the Memory Challenge

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In Part I three models for temporally constrained space use were summarized. Here in Part II I put them more explicitly into the context of ecology with focus on some key assumptions for the respective models. Area restricted search (ARS), Lévy walk (LW) and Continuous time random walk (CTRW) are statistical representations of disparate classes of temporally constrained space use without explicit consideration of spatial memory effects. Hence, below I reflect on a fourth model, Multi-scaled Random Walk (MRW), where site fidelity gets a different definition relative to its spatially memory-less counterparts.

Picture: A cattle egret Bubulcus ibis is foraging within a wide perimeter surrounding its breeding site. Spatial memory is utilized not only to be able to return to the nest but also to revisit favored foraging locations during a bout, based on a memory map of past experience. Photo AOG.

First, ARS is typically formulated as a composite random walk-like behaviour in statistical t…