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Parallel Processing: Towards a Broadened Biophysics of Space Use, Part III

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In this post I will again hammer wake-up calls into my own camp, researchers in the field of wildlife ecology, including the theory of habitat selection and and animal space use. For example, I have previously claimed that the Burt legacy has hampered progress in individual home range modelling, as has standard calculus done for population dynamics of open systems (including spatially extended versions). The two classical toolboxes for space use models; based on specific postulates from statistics and standard mathematics, are hampering progress towards improved model realism. As long as there still is a strong reluctance to replace these postulates by extending the theory head-on in the direction of biophysics of memory-influenced processes it is my personal conviction that the quagmire will prevail. However, there are now rapid and promising progress from research originating outside the traditional community of ecologists.

These directions are pointing towards spatial models from …

Parallel Processing: Towards a Broadened Biophysics of Space Use, Part II

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When I returned to the University of Oslo in 1990 to explore alternative pathways towards complex dispersion of populations it was natural to start out by orbiting around the Department of biology’s division that focused on population dynamical modelling. However, what became increasingly obvious was a tension that grew up between my choice of off-piste approaches, the introduction of rather unorthodox concepts and on the other side meeting a culture that stubbornly focused on the classical mathematical and statistical toolbox. I simply could not find satisfactory local support for working on scale-free dispersal processes under these terms, despite what I observed as thoroughly and broadly documented instances of such paradigm-breaking behaviour in the hundreds of papers surrounding confirmation of – for example – Taylor’s power law and fractal-patterned population dispersion. The theoretical culture was shying away from exploring a series of paradoxes that in my view were crying for…

Parallel Processing: Towards a Broadened Biophysics of Space Use, Part I

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This series of posts is an attempt to briefly summarize historically the conceptual development of the Parallel processing idea (PP) as a modelling framework to better understand the complex space use by animals. The endeavor started by a couple of enlightening Eureka moments, and swiftly split into two lines of approach. The challenge was to get the grips of the deeper process behind scale-free dispersion. This fascinating behaviour would in my view have to be coherently modelled along two lines of exploration, first from the perspective of spatio-temporal population dynamics and then from individual space use. PP was born during those early periods of confusion and frustration, and it has focused (some will say haunted) my research for more than 30 years.

Picture: Spaced-out gregariousness in sycamore aphids Drepanosiphum platanoides under tree leaves in Oslo, Norway. Photo: AOG.

At the population side it all started out with a couple of frustrating years exploring mathematical mo…

Non-Mechanistic Dynamics: a Simple Illustration

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In my previous post I summarized my critique of mechanistic modelling when applied on animal movement. Simply stated, the Markovian design on which mechanistic models depend is in my view incompatible with a realistic representation of memory-influenced and scale-free space use. Below I illustrate the alternative approach, non-mechanistic dynamics, by a simple Figure. As conceptually described by the Scaling cube, an extra system dimension based on relative scale (“hierarchical scaling” of the dynamics), resolves the apparent paradox of non-mechanistic dynamics.

I cite from my first post on the Scaling cube (December 25, 2015):

The scaling cube brings these directions of research together under a coherent biophysics framework. It also forces upon us a need to differentiate between mechanistic dynamics (the M-floor) and non-mechanistic dynamics (the PP-ceiling).

As a supplement to my book presentation I have published a series of posts on this theme, where its unfamiliar nature has b…

On the Paradox of Mechanistic Movement Models

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Mechanistic design is still dominating animal space use modelling. As the readers of my papers, book and blog have understood I’m very critical to this framework. In particular, because both mechanics and standard statistical mechanics – due to their dependence on Markovian dynamics seem to be unable to implement memory-influenced movement in a realistic manner. Thus, paradoxes abound. Unfortunately most theoreticians in movement ecology either do not care or do not know how to approach this issue. In this post I seek to pinpoint the most basic challenge, and how it may be potentially resolved by exploring a qualitatively new direction of modelling.

Consider the standard, simplified illustration of animal foraging, which takes up much of an individual’s focus during a day. At each time increment the behaviour adheres to rules under the mathematical framework of a low order Markovian process. A similar diagram could have been shown for other behavioural modes; like looking for a mate,…

Intraspecific Cohesion From Conspecific Attraction, Part III: A Simple Test

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In the real world, animals typically tend to congregate at the landscape scale, even when they show repellence at finer scales (territorial behaviour). In contrast, one of the basic assumptions of the vast majority of mathematical population models is independent space use by individuals. In other words, it is assumed that the individuals do not show conspecific attraction but adhere to “full mixing” from independent space use. A strange assumption, indeed! Using the part of the Parallel processing theory (PP) that was summarized in Part I and Part II it is a simple statistical exercise to test if a given population’s dispersion obeys the full mixing assumption (the Paradigm); or alternatively, indicating a positive feedback tendency from PP-compliant space use (the Zoomer model).

The concept of conspecific attraction is verified among many species and taxa of animals. For example, lizards prefer to settle near conspecifics, even when unoccupied habitat is available nearby (Stamps 1…

Intraspecific Cohesion from Conspecific Attraction, Part II: Paradox Resolved

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I briefly mentioned in Part I that the combination of spatial memory utilization and scale-free space use under the Parallel processing conjecture (PP) may lead to a fractal compliant population dispersion of intrinsic origin, given the additional condition of conspecific attraction. Below I elaborate on heterogeneous population dispersion as expected under the Paradigmatic framework (Markovian process, mean field compliance) and the contrasting PP kind of space use. In particular, one may find that two locations with different population density under the PP condition may reveal similar intensity of space use! Under the Paradigm such a result will appear paradoxical. Under the PP framework (the MRW and the Zoomer model) the paradox is resolved.

Before switching to empirical results, consider the following crucial question for ecological theory of space use. What is the driving force behind the typical pattern of a shifting mosaic of population abundance over a range of spatial scale…

Intraspecific Cohesion From Conspecific Attraction, Part I: Overview

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Animal survival requires some kind of intraspecific cohesion (“population glue”); an intrinsically driven tendency to counteract the diffusion effect from free dispersal. Populations of most species live in an open environment. Thus, without some kind of behavioural capacity to continuously or periodically seek and maintain contact with conspecifics only the most extreme and bizarre kind of environmental constraint would be required for the species’ long term survival. Despite the general agreement on this basic requirement, ecological models for individual movement and population dynamics have for a century maintained a different paradigm, a stubborn assumption that the animals follow the basic principles of mechanistic (Markovian) movement at the individual level and diffusion-advection laws at the population level. Fueled by empirical results and – in my view – common sense the Paradigm has from some researchers come under attack for many years, but mostly in vain. Ecological model…

Conservation Biology and SLOSS , Part II: Parallel Processing and Network Topology

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Consider the following two system conditions and theoretical assumptions. First, a large nature reserve has a smaller periphery than several small ones with the same total area. Thus, all other factors equal, a smaller periphery pr. unit area of a large reserve implies a higher implicit survival rate for its embedded species. Fewer animals are “lost in space” due to accidentally diffusing out of their reserve. Consequently, a larger reserve is expected to have a proportionally larger species abundance of animals than a fragmented mosaic of smaller reserves, right? Second, again considering all other factors equal, distant reserves are functionally less connected. In other words, the population dynamics of two reserves in close proximity are assumed to be more in sync or anti-sync from intra-population dynamics than more distant ones, right? The conventional answers are obviously “yes”, but…

In my previous post I referred to empirical results on snail kite Rostrhamus sociabilis plumbe…

Conservation Biology and SLOSS , Part I: Time to Challenge System Assumptions

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The contrasting ideas of a single large or several small (SLOSS) habitat reserves ignited a heated debate in conservation biology (Diamond 1975; Simberloff and Abele 1982). The recent development in movement ecology – in particular the theoretical aspects of spatial memory and scale-free space use of individuals – makes time ripe to initiate a study of the SLOSS concept under this contemporary perspective. In order to produce realistic predictions community, population and individual processes need to be understood from a coherent system theory involving all levels of system abstraction. Under this premise the original SLOSS concept seems to fall apart.

A single large reserve was argued to be preferable to several smaller reserves whose total areas were equal to the larger (Diamond 1975). On the other hand, if the smaller reserves had unshared species it was possible that two smaller reserves it sum could have more species than a single large reserve of the same total area (Simberlof…

Parallel Processing – How to Verify It

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In my previous post I contrasted the qualitative difference between animal space use under parallel processing (PP) and the standard, mechanistic approach. In this post I take the illustration one step further by illustrating how PP – in contrast to the mechanistic approach – allows for the simultaneous execution of responses and goals at different time scales. This architecture is substantially different from the traditional mechanistic models, which are locked into a serial processing kind of dynamics. This crucial difference in modelling dynamics allows for a simple statistical test to differentiate between true scale-free movement and look-alike variants; for example, composite random walk that is fine-tuned towards producing apparently scale-free movement.

First, recall that I make a clear distinction between a mechanistic model and a dynamic model. The former is a special case of a dynamic model, which is broader in scope by including true scale-free processing; i.e., PP. In m…

The Inner Working of Parallel Processing

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The concept of scale-free animal space use becomes increasingly difficult to avoid in modeling and statistical analysis of data. The empirical support for power law distributions continue to pile up, whether the pattern appears in GPS fixes of black bear movement or in the spatial dispersion of a population of sycamore aphids. What is the general class of mechanism, if any? In my approach into this challenging and often frustrating field of research on complex systems, one particular conjecture – parallel processing (PP) – percolates the model architecture. PP requires a non-mechanistic kind of dynamics. Sounding like a contradiction in terms? To illustrate PP in a simple graph, let’s roll dice!

The basic challenge regards how to model a process that consists of a mixture of short term tactics and longer time (coarser scale) strategic goals. Consider that the concept of “now” for a tactical response regards a temporally finer-grained event than “now” at the time scale for executing a …