### Excerpt from Preface

A preface normally presents a brief background for a book’s content. The present outline is more extensive. Given the theoretical challenge with respect to making sense of animal space use in a realistic and coherent manner, I have chosen to enlarge this section in two directions. First, some basic memory- and scale-related concepts are described. Second, some main points from each chapter are outlined and given some introductory comments. Hopefully, these enlargements of the preface will provide a valuable theoretical preparation to the main body of the book. It should in fact be read as an introduction to the introduction.

Animal space use may be conceptualized and modelled at two levels, individual and population. At the individual level movement, ecology is a field in rapid theoretical progress (Nathan et al. 2008; Smouse et al. 2010; Viswanathan et al. 2011; Lewis et al. 2013; Humphries and Sims 2014; Méndez et al. 2014). Population ecological theory has also matured; with emphasis on spatially explicit model designs, age-structured dynamics, and multi-species interactions (Hiebeler 1997; Keeling 1999; Turchin 2003; Hanski and Gaggiotti 2004; Ranta et al. 2006). However, the main theme for the present book is not ecological inference, but rather a critical evaluation of the biophysical framework implicitly assumed when making ecological inference. "Biophysical" does in this context specify a meso-scale observational level of movement and space use.

For example, when studying individual space use, this level is reflected in a sample of GPS fixes, where behavioural modes and movement-influencing events are hidden at finer temporal and spatial resolutions than the sampled path. The temporal scale interval from the fine-resolved movement path to the sampled path (leading to a set of relocation dots on the map, rather than a continuous line) is referred to as “the hidden layer” in this book. At the population level the hidden layer is best reflected by the spatial resolution of the study. This resolution determines local population density; number of individuals per spatial unit at this resolution; and at a chosen temporal resolution (a day, week, or year, depending on context). Again, the actual biological events and interactions like individual searching, feeding, courting, resting, and a myriad of other aspects are spatially and temporally fine-grained processes being executed by the population’s constituents at micro-scale below the resolution for the study; i.e., in the hidden layer.

Whether we consider local density of GPS fixes from a given individual as accumulated over a sampling period or local population density representing a snapshot of individuals’ whereabouts, we have changed focus away from direct observation of biological processes at micro-scales. Instead we perform indirect observation of these processes at a coarser resolution; the biophysical system representation. The hidden layer, which has both temporal, a spatial, and a scale range dimension, is a core concept under the extended framework for analysis of animal space use to be presented in this book. Observe that I define scale range as an independent aspect of time and space. I define this dimension as a scale range, not a specific scale. This dimension reflects the depth of the hidden layer. In process terms the deeper the layer the clearer the difference between the fine-grained biological scales and the coarse-grained biophysical scales.

Such system coarse-graining is common in ecological research both at the individual and the population level, but the transition from a biological to a biophysical system abstraction is only rarely explicitly acknowledged. This is unfortunate, for three main reasons. First, the biophysical approach opens the door towards a huge theoretical framework, “statistical mechanics,” which few biologists are trained in or even consider relevant. Second, statistical mechanics in its present state is—in my view—unfortunately not sufficiently extensive to cover the kind of biophysics generally applicable to animal space use. Third, this discrepancy has led to implicit application in ecological theory of principles from classical statistical mechanics—as a consequence of invoking the hidden layer for system modelling—despite the intrinsic issue that the current framework is based on assumptions that are frequently violated by animal space use behaviour. This book circulates among these three aspects and in particular the third one. Hence, proposals for extensions of the traditional biophysical framework percolate the chapters, for the sake of—hopefully—stepping towards a more realistic biophysical representation of animal space use.

Scrutinizing the foundation of ecological models based on the hidden layer is not a walk in the park. It implies that movement ecology’s standard toolbox (containing model designs and statistical protocols, see Box 1 towards the end of the preface) is rattled with respect to applicability of very general assumptions (Box 2). A critical evaluation of the foundation of individual movement models by necessity percolates to the population level, where I put a corresponding set of core assumptions under scrutiny. At respective levels—individual space use behaviour and population dynamics—the specific assumptions I refer to are in fact so deeply buried under layers of historic consensus that they are rarely explicitly mentioned in ecological analyses that depend on their support (Gautestad and Mysterud 2005; Gautestad 2011, 2013b). For some, this consensus may simply reflect “case solved”; others are not so confident. Here are examples of opposing views:

It seems to me to be beyond doubt that population ecology has a mature theory.

Turchin (2003), p. 392

It is time to acknowledge the need for a scathing indictment of the poor practices that have accumulated in species distribution modelling over the decades.

O’Connor (2002), p. 33

Does the book’s focus on modelling theory and accompanying assumptions make it peripheral to a general audience of animal ecologists? Definitely not! Ecology regards the branch of biology that deals with the relations of organisms to one another and to their physical surroundings. What regards animal space use and population dynamics, the basic level of ecological inference regards exploration of (a) why intensity of habitat use is stronger in some places than other places (and/or other times), (b) how this insight may produce predictions about space use intensity at other locations, and (c) what kind of statistical consistency may be expected when changing observational scale (spatial or temporal resolution; changing the depth of the hidden layer). From this broad perspective the present book drills to the core of animal ecology by proposing both revisions and enlargements of the generally applied biophysical space-use framework, which currently provides conceptual and predictive models for ecological inference.

Any ecologist with field experience will agree that animal space use is more challenging than appears in textbooks. From a trivial perspective this may be because of insufficient data or too simplistic models. Even larger samples of GPS relocations, improved GIS data, and more fine-grained population monitoring should then suffice to resolve the challenges at hand. The model might also gain from additional terms to cover the system in more detail. Such a quest for improved system details may also need to be supplemented by considering the given model foundation at a deeper theoretical level. I advocate that an explicit application of the biophysics of space use that is most relevant for the given system should determine the most realistic set of models for ecological inference.

In this book I present eight such conditions, called biophysical universality classes, for animal movement and space use. In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Unfortunately, at present only one of these classes provides the foundation for most of ecological theory, and two others are only now slowly making a broader entry. The other five classes are probably totally unfamiliar to you. In my view, the broadly applied class of movement is stretched to the extent that the model assumptions become unrealistic for many scenarios. Old challenges and even paradoxes that haunt the present arena may thus find better solutions in the extended system containing a broader range of universality classes. Hopefully you will agree after reading the following chapter that the eight classes present great opportunities for a more diversified arena for realistic model representation of animal space use both at the individual and the population level.

In a concrete example of the potential shortcoming of the dominating class (yes, I will define it in more detail shortly), consider space-use intensity. What is space-use intensity? According to the dominating system class, it may be represented by local variability of density, either the spatial dispersion of GPS relocations (individual level) or the dispersion of individuals themselves (population level). However, an individual or a population may express higher space-use intensity in some parts of available space even when the habitat characteristics seem similar to less utilized areas. There may be many reasons for this apparently paradoxical pattern, but in this book I’m focusing on some intrinsic drivers. In particular, by diversifying ...

In a concrete example of the potential shortcoming of the dominating class (yes, I will define it in more detail shortly), consider space-use intensity. What is space-use intensity? According to the dominating system class, it may be represented by local variability of density, either the spatial dispersion of GPS relocations (individual level) or the dispersion of individuals themselves (population level). However, an individual or a population may express higher space-use intensity in some parts of available space even when the habitat characteristics seem similar to less utilized areas. There may be many reasons for this apparently paradoxical pattern, but in this book I’m focusing on some intrinsic drivers. In particular, by diversifying ...

...

In

*Chapter 1*, I suggest a feasible reason—backed up by recent third party research—why the home-range ghost paradox (Gautestad and Mysterud 1995) still has not been more generally recognized among wildlife ecologists, more than twenty years since its presentation and subsequent empirical support. The most widely acknowledged method to demarcate space use from a set of relocations—the Kernel Density Estimate (KDE) (Worton 1989)—has an Achilles’ heel, as verified by relatively recent simulations and application of KDE on real data. KDE produces isopleths; contour lines representing expected equal-sized intensity of space use given the actual sample of relocations (fixes), N. If the dynamics behind the pattern do not comply with standard statistical assumptions, the demarcated area from KDE will overcompensate for the effect from change in N (Belant and Follmann 2002; Barg et al. 2005; Fieberg 2007; Fieberg and Börger 2012; Schuler et al. 2014). In other words, the home-range ghost paradox from non-asymptotic space-use demarcation with increasing N (based on a non-parametric protocol for area demarcations) may be camouflaged by violation of a specific statistical assumption under the KDE protocol. Crucially, this hypothesis is supported by applying simple, non-parametric demarcation methods described in Chapter 1.In

*Chapter 2*, Basics of movement physics: the standard models, I turn more explicitly towards the biophysics of animal movement. This is important background for what follows. Starting with very basic principles and illustrations (and a few simple equations), I describe the current paradigm for movement dynamics and the transitions between (a) deterministic-mechanistic models, (b) stochastic-mechanistic models, and (c) a mixture of the two as representation of animal space use. In particular, I describe how the common denominator—the mechanistic approach—depends on a shared assumption with respect to the dynamics: Markov compliance. In statistical-mechanical terms a Markovian process reflects a system close to local equilibrium. An animal makes a move based on a superposition of local movement-influencing factors at that point in time. These factors embed both environmental influence (for example, attraction and repellence) and internal state (for example, hungry or frightened). At successive moments previous factors are already reflected in the animal’s current location, and new influences are leading to new moves. In absence of further change in these conditions the animal is expected either to stay put or to unidirectionally continue to move forward with a constant speed.

In simple systems, as a bouncing billiard ball, a deterministic-mechanistic model reflects the actual process well; principles from differential and integral calculus may be applied to describe it realistically. In other systems like a moving individual where motion is influenced by a myriad of factors from one point in time to the next, the deterministic-mechanistic approach is typically replaced by a stochastic-mechanistic model. Creating a large equation with many terms for the respective influences (in order to keep the model deterministic-mechanistic) will in this case be counterproductive. The archetypical stochastic-mechanistic function is a Brownian motion model. Movement satisfying a Brownian motion process leads to classical (so-called Fickian) diffusion at the population level and, consequently, provides the necessary support for application of classical calculus to model the dynamics of both individual space use and population dispersion. Again—as for the deterministic system description—a stochastic-mechanistic model may provide realism and thus high predictive power, given that the Markov premise is satisfied.

Markov compliance is a very convenient assumption both from a modeller’s perspective and with respect to statistical analysis of empirical data. Accepting the Markov premise a priori allows for application of a mature and broad toolbox of classical and contemporary mathematics and statistical methods. This approach rests on the theory of standard statistical mechanics. Fine-grained Markov-based theory, represented by mechanistic models and “standard” statistics, provides the backbone of movement ecology in particular and idealization of animal space use in general both at the individual and the population level.

What if Markov is not satisfied? The answer seems simple, but difficult to digest: remove differential and integral calculus from population dynamical theory, and little remains. Remove Brownian motion (and variants like correlated random walk with or without environmental bias) from movement ecology and little is left there as well. These broad theoretical foundations rest on the Markov assumption as satisfied for the underlying process. Consequently, the core question raised in this book is this: may a Markovian biophysical framework be extended to account for spatial memory and multi-scaled dynamics in a realistic manner? There are currently many theoreticians in the Yes camp, where sophisticated mechanistic models are now flourishing. This book—on the other hand—represents the (non-crowded) No camp, where a conditional “No” is raised as a testable working hypothesis by scrutinizing the statistical-mechanical premises on which the Yes camp depend. The No answer is conditional, since I advocate that a distinction between mechanistic and non-mechanistic dynamics is needed. There are obviously a large number of systems and a range of observational scales where the Markovian framework not only suffices but is the correct choice. However, in my view there are also a large number of systems for which the Markovian framework should be considered unrealistic. Thus, the answer Yes should not be accepted a priori, but should be verified empirically as a realistic premise for the system in question.

Alternatives to the Markovian methods in general terms are the theme of

*Chapter 3*, Approaching memory, and

*Chapter 4*, Movement physics beyond Markov compliance. Here the Markov assumption in the classical biophysics of animal movement is scrutinized theoretically. As already mentioned, the rapid growth of the field of movement ecology has been sparked by two main directions of research; on one hand a recognition of scale-free movement and on the other hand a more sophisticated modelling of spatial memory influence. Designing dynamic models where memory-influenced space use (site fidelity) is explicitly considered are now popping up and growing in sophistication (Gautestad and Mysterud 2010b; Song et al. 2010; Boyer et al. 2012; Gautestad and Mysterud 2013; Nabe-Nielsen et al. 2013).

Interesting models have begun also to invoke non-Markovian mathematics in this respect: continuous time random walk (CTRW) to mimic scale-free movement and biased random walk to mimic scale-specific but memory-influenced movement (van Moorter et al. 2009; Bartumeus et al. 2010; Giuggioli and Bartumeus 2011; Spencer 2012; Nabe-Nielsen et al. 2013). Implementation of temporal (but not spatially explicit) memory effects on movement by applying the CTRW approach (Giuggioli et al. 2006; Bartumeus et al. 2010) may seem to contradict my claim above that a mechanistic model by necessity has to be Markov compliant. However, I argue in Chapters 3 and 4 that the respective model classes are—in a statistical-mechanical frame of reference—in fact Markov compliant. The apparent contradiction is resolved by considering that the mathematics of scale-free movement may be non-Markov (current behaviour is influenced by the past in a slowly decaying manner), while the statistical-mechanical application of this class of mathematics implies a Markovian interpretation. This aspect will also be elaborated on later in the book.

Similarly, mechanistic models describing spatially explicit memory-influenced movement—resulting in site fidelity under some parameter range—also describe a slowly decaying influence from past experiences on present movement behaviour, in the form of a potential drift towards locations that were visited in the past (Börger et al. 2008; Dalziel et al. 2008; van Moorter et al. 2009; Song et al. 2010; Spencer 2012; Fronhofer et al. 2013; Nabe-Nielsen et al. 2013; Boyer and Solis-Salas 2014). While this may sound non-Markovian, it is not. Biophysically, the memory influence is implemented as a “field” force. This field regards the directional bias towards historically visited locations, owing to utilization of spatial memory. At every point along a movement path, the direction, directional persistence, and movement speed are determined by a resultant vector where the influence from the memory field represents one of many components of movement. The memory-invoked vector field implies that the next displacement is recalculated on a moment-to-moment basis.

In summary, I advocate the need to make a distinction between models where (a) the memory influence is processed in a sequential and immediate manner and thus leading to micro-scale local/temporal equilibrium in statistical-mechanical terms at the model's time resolution (increments), and (b) memory influence where such micro-scale equilibrium cannot be expected. The first variant regards mechanistic and thus Markov-compliant modelling while the latter regards the extended toolbox proposal; non-Markovian and non-mechanistic system dynamics represented by parallel processing.

In

*Chapter 5*, Parallel processing: the concept, I confront the third direction of contemporary space-use models at the individual level: integration of scale-free movement (direction 1) and spatial memory-influenced movement (direction 2). Applying a statistical-mechanical approach, the concept of parallel processing—as opposed to Markov-compliant processing—is outlined. Parallel processing regards system dynamics, but in a non-mechanistic sense. I suggest that a statistical-mechanical representation is not only an option but a necessity to model this kind of process. This direction of memory implementation is—according to the parallel-processing postulate—incompatible with mechanistic principles in biophysical terms. In a stepwise manner the concept of parallel processing has matured from a loosely defined graphical illustration in our publications in the 1990s to more mathematically and biophysically formulated models over the last ten years or so. In the present description additional elements of the parallel-processing framework are introduced.

I show how the application of the parallel-processing postulate has resulted in theory and space-use simulations that seem to resolve specific paradoxes. Under this conjecture the actual system properties appear paradoxical only from the perspective of classical premises. Crucially, statistical expectations from parallel processing are now in the onset of being supported by larger and better empirical datasets, where the falsified null hypothesis is based on Markovian statistics (Gautestad et al. 2013; Gautestad and Mysterud 2013).

*Chapter 6*, Modelling parallel processing, transforms for the first time the concept of non-mechanistic space-use dynamics at the individual level to the framework of statistical mechanics at the population level. Several new aspects and specifications are introduced. For example, the principle of ergodicity and inter-level system coherence between individual movement and population dynamics is here outlined in more detail. I propose in a biophysical (statistical-mechanical) context how kinetic energy of scale-free space use should be expected to be distributed in a self-organized manner over a scale range. Also for the first time, I describe a population-level simulation model of parallel processing, the “zoomer model”. The model allows for “fine-tuning” of the dynamics along the continuum from a scale-specific and Markovian-compliant (mechanistic) kind of population kinetics to a non-mechanistic and parallel processing-compliant kind of process. By this approach the alternative framework not only connects individual and population dynamics in a coherent manner; it also presents a transition between apparently disparate system classes by connecting non-mechanistic dynamics to its mechanistic counterpart.

Interesting statistical properties of population dispersion emerge from the simulations of the zoomer model, which brings up what may appear to be a potential solution to an old and still unsolved controversy in ecology: Taylor’s power law (Taylor 1961, 1986). This empirically derived law has over the years been subject to a large number of attempts to explain it, but a consensus has still not been obtained (Kendal and Jørgensen 2011). Taylor’s power law is one of the most widely tested empirical patterns in ecology and is the subject of an estimated thousand papers (Eisler et al. 2008)! It describes how variance (V) of population abundance (M) in a time series or over a spatial transect tends to comply empirically with V(M)=aM

^{b}, with b>>1 (often close to 2). However, one aspect of this law has by and large been ignored: the V(M) pattern unexpectedly emerges also when abundance is measured at different spatial resolutions within a given extent (Taylor 1986). Larger spatial units (grain size) give larger M on average, and the scaling law with b≈2 even in spatially non-auto-correlated data appears even more paradoxical in the context of this property. I call this the Z-paradox, and propose (with support from simulations) that a parallel-processing kind of population kinetics may contribute to solve it. Will it succeed under closer scrutiny and when confronted with real data? Time will show, but in a later chapter I provide a pilot test.

In

*Chapter 7*, Parallel processing at the individual level, I show that individual-level statistics for V(M) when generated from the parallel processing- compliant MRW model is coherent with population-level statistics for the same aspect in output from the zoomer model. The MRW model is also specified in more detail than in previous publications, with weight on clarifying some aspects that have led to common misinterpretations. Chapter 7 also summarizes various methods—called protocols—to test for compliance with MRW, using respective standard models in respective fields as null hypotheses. The methods now span many statistical aspects of space use, like the distribution of step lengths of a path that is sampled at regular intervals (the Lagrangian aspect), the extent of space use as a function of sample size of fixes (the Eulerian aspect, also containing home-range ghost paradox), the fractal dimension of fix dispersion, and so on. In all respects, MRW is now a testable hypothesis, and I summarize already published empirical support for the model.

*Chapter 8*, Movement classes at the statistical-mechanical level, focuses on one main topic: a conceptual model I call the scaling cube, which is presented here for the first time. In a statistical-mechanical frame of reference, I show how a three-dimensional system (the cube) may diversify between Markov-compliant types of movement (represented by the x- and y-dimension) and parallel processing-compliant space-use dynamics (the z-dimension). The x-axis regards degree of spatial memory utilization, the y-axis regards degree of compliance with scale-free movement in the time dimension, and the z-axis represents hierarchical scaling. The latter expresses the degree of parallel-processing compliance by linking past experiences to execution of future goals. In contrast, a Markovian-based memory model only implements past experience as a term in the model for current movement decision in a stepwise manner (the memory field vector, as explained above). It does not allow embedment of parallel execution of future goals at different temporal resolutions. For example, an animal may decide to move towards a given target even if the direction deviates from a parallel goal to reach another target in a different direction within a wider time frame, and thus higher in the temporal hierarchy of parallel goals. Under the Markov premise only one goal may be executed at any point in time, but this goal may contain influence from past experiences. This goal is embedded in the resultant vector for the directional bias under Markovian memory execution; see above. Consequently, in the scaling cube spatial memory is represented by two qualitatively different processes: with and without hierarchical execution of goals. This aspect thus requires an independent axis, orthogonal on the Markov floor of degree of scaling and degree of memory implementation. A cube has eight corners tentatively representing eight universality classes of movement. In Chapter 8, various methods to distinguish individual space use under the respective eight movement classes that are embedded in the scaling cube are summarized.

*Chapter 9*, Is parallel processing applicable to invertebrates?, returns focus to the population level. In 1990, I sampled a local population of sycamore aphids,

*Drepanosiphum platanoides*, at the campus of University of Oslo. The purpose was to test compliance with the parallel-processing concept, and how it might cast new light on Taylor’s power law and scale-free (fractal-compliant) population kinetics. Owing to the challenge of the home-range ghost paradox that received the focus over the following years, the aphid material had to be put on the shelf for a later day. This day has hereby finally arrived twenty-five years later. Chapter 9 provides a synthesis of novel theoretical aspects—as outlined in the previous chapters—and what appear to be matching empirical patterns in the spatial dispersion of the aphid population. In particular, the analysis shows coherence between how the home-range ghost paradox was resolved at the individual level and how the Z-paradox gets its proposed solution at the population level. Thus, the Z-paradox may represent the population-level analogue to the individual-level home-range ghost! Both concepts turn up as respective levels’ expressions of parallel processing, and the aphid data apparently support compliance with this memory-extended kind of statistical mechanics. This is obviously a speculative and controversial statement, since it implies a quite advanced memory capacity of these tiny insects with respect to spatial reorientation and non-random path crossing. I’m looking forward to learning whether others may find less contrarian (read: Markov-compliant and mechanistic) biophysical explanations for the results. With respect to the variance-mean relationship, the aphid population shows scaling compliance with Taylor’s power law, and the empirical pattern is thus encouragingly similar also to the simulated data from the zoomer model.

In

*Chapter 10*, Intrinsic complexity: 1/f noise and the scaling paradox, I turn towards yet another nagging issue of statistical mechanics, 1/f noise (also called flicker noise, fractal noise, and pink noise). An alternative way of demonstrating the increase of V over spatial or temporal scales in a series is to decompose population variability into cycles using techniques like Fast Fourier Transforms (FFT) and then study how the power (squared magnitude of amplitudes) of those cycles varies with their frequency. The frequency equals the inverse of cycle length, and the power spectrum is an expression for cycle-specific variance. A larger frequency means a smaller cycle length. Cycle length is proportional with the lag in the series, which is the time interval or space distance between successive measurements we use for calculating the power. In the spectra this analysis produces, the longer cycles typically have the greatest power (larger squared amplitude).

The theoretical issue in this respect regards systems which show power increasing inversely proportional with frequency; P ≈ 1/f

^{η}with η≈1. This statistical pattern is problematic when trying to explain the underlying process, since it apparently does not comply with classical Markovian-compliant statistical mechanics (η≈2 for Brownian motion and η≈0 for white noise; the latter satisfies increments of Brownian motion). On one hand I show in Chapter 10 how simulated space use from the population-level—the zoomer model—seem to confirm a 1/f noise pattern. On the other hand I verify 1/f noise also empirically. Both the sycamore aphid population and a multi-year time series of leaf miners, Leucoptera meyricki (Bigger and Tapley 1969), apparently comply with 1/f fluctuations. Again the parallel-processing extended kind of statistical mechanics allows for a potential solution of a paradox, in this case the issue of 1/f noise. Again I hope for the emergence of presentations and discussions of alternative model proposals that may show similar statistical coherence between simulation output and real data, both with respect to variability at a specific scale (a time series or a spatial transect) and with respect to variability over a range of scales.

In Chapter 10, I show how the Z-paradox in V(M) and the 1/f paradox are inter-related. Thus, apparently for the first time, Taylor’s power law is studied in the context of 1/f noise. The coherence between inter-scale V(M) analysis and output from power spectrograms at the population level and a similarly coherent V(M) and power pattern at the individual level (from population and MRW simulations, respectively) indicates an interesting path forward for the parallel processing concept, which represents a key postulate for the present theory for scaling/memory implementation. The fact that parallel processing is a postulate rather than being verified from first principles at this stage is not necessarily a critical weakness. As I mention in Chapter 10, Boltzmann’s famous definition of entropy under condition of system equilibrium in classical statistical mechanics was also based on a specific postulate. In fact, it is still just a postulate, which has proven tremendously successful since its formulation in 1875.

In summary, this book’s chapters zigzag between various properties of complex systems, with emphasis on individual space use and population kinetics. I hope that the reader is not too overwhelmed by all the new concepts, model formulations, and occasionally provocative hypotheses. Provocations may spark creative thinking and constructive proposals, bringing some elements of the proposed framework perhaps closer to general consensus and other aspects perhaps closer to their termination from lack of empirical support. Again, time will show.

As referred to above, in Chapter 1 and elsewhere throughout the book, the road towards the present theoretical synthesis has been both steep and long-lasting. One of the largest theoretical challenges has been the continuous struggle to cognitively depress the bias from standard system principles while trying out new directions for the sake of better compliance between theory and empirical results. All researchers working on complexity theory—whether related to biophysics or other fields—are continuously experiencing similar frustrations (www.santafe.edu is a good entry point to meet contemporary complexity theory). To some extent, cognitive “un-learning” of long-lasting imprinting of model principles and concepts in classical textbooks on animal space use and population dynamics has been necessary. In particular, this regards the concepts of parallel processing and non-mechanistic dynamics from a statistical-mechanical perspective. In this exploration I do not argue that Markov-based models should be generally abandoned! I argue that they should be supplemented to allow for a broadened scope of models for a potentially more realistic description and analysis of systems where long-term memory and scaling aspects of the dynamics are verified. For the moment the non-mechanistic toolbox extensions are in their infancy, but they do already seem to offer many potentially interesting research opportunities in the time to come. Hopefully, all the rattling of the wasp nest over the following pages may contribute to spark further clarifications in this active field of research.

The theoretical development that has culminated with this book has been driven forward by a mixture of inspirational events, personal stubbornness, and dialogue with peers. However, by and large it has been a lonely journey. Part of the reason for this fate percolates Chapter 1, A large mystery in a little detail, which illuminates the self-invoked problem of choosing confrontation over conformity. I have repeatedly locked myself out from various collaboration projects by stirring up the group harmony. I recall one occasion in particular where I was invited to discuss a spatially explicit population model. The starting point was a proposal based on a coupled map lattice equation. However, I wouldn’t continue until the hidden system assumptions for using this approach were scrutinized and accepted by the group. I argued that the constituent parts of the actual population—the individuals—did not comply with the behaviour that was assumed when transforming this kind of dynamic to the population level. At that point I unfortunately only had the critical arguments ready, not the model substitutes. The group preferred to move on rather than getting stuck in such assumptions that “everybody” seemed to accept anyway. Thus, the collaboration led nowhere. My stubbornness made me continue circling around the critical assumptions more or less on my own.

From a personality perspective one may consider such a confronting attitude from my side a weakness or strength, depending on perspective. Anyway, instead of leaving the home-range ghost and other paradoxical system behaviours alone and moving on, I decided from the onset—with never-ending acclamation from Ivar Mysterud (see 1. A large mystery in a little detail), who has a similar personality in this respect—that the home-range ghost was theoretically exciting and thus needed deeper exploration. In retrospect not such a wise choice on my part, from the perspective of career and network-building. However, given the rapid sequence of theoretical breakthroughs and more deep-drilling empirical tests of the present ideas in particular over the last five years or so, I’m finally confident that I made the right choice back then. However, the first ten to fifteen years of development (1990–2005) were challenging, albeit sufficiently rewarding to keep the ball rolling despite lack of much paper production.

Theory needs to show coherence with real data. The statistical-mechanical approach to study animal space use has been tested not only on Ivar’s and his students’ database on summer season sheep movement, but also on extensive data on black bear and red deer movement, provided by Mike Pelton and his group (University of Tennessee) and Atle Mysterud and his group (University of Oslo), respectively. I thank Ivar, Mike and Atle for their open-minded attitude with respect to allowing for projects that involve scrutinizing their data from an unconventional angle. As the years go by, some events stand out with particularly strong influence on the following path. In my case one such period was the truly inspirational two-month stay at University of Tennessee in 1994, and I thank—in particular—Mike Pelton and Stuart L. Pimm for their support and energetic impact on my research during that period (see also Chapter 6.5.2 South state hospitality). At present I have status as guest researcher at the Centre for Ecological and Evolutionary Synthesis University of Oslo, courtesy of Nils Chr. Stenseth. Nils and Atle offered affiliation as researcher during 2012–2013, and Ivar supported me with a doctoral fellowship at the Department of Biology 1993–1997 in addition to enabling some additional funding for research and travel during that period.

This book has not been subject to traditional peer reviewing. Instead the manuscript has been distributed to a selection of outstanding scientists in the field of movement ecology. Most of them I know by reputation but not personally, and I invited them to make a critical evaluation of my project. The response was encouraging, and an online forum was created for chapter-specific discussions. Thus, I want to thank members of this forum for their attendance in this rather unconventional “crowd-reviewing” process. I particularly want to thank Don DeAngelis (University of Miami) and Daniel Campos Moreno (Universitat Autònoma de Barcelona) for important contributions on the forum. A presentation of the project can be seen at www.thescalingcube.com, and there may appear project updates on this site and on my personal site www.gautestad.com as time goes by.

Oslo / Ulsteinvik / Benalmadena,

June 2015

Arild O. Gautestad