In this post I will again hammer wake-up calls into my own camp, researchers in the field of individual and population 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 outside the traditional community of ecologists.
These directions are pointing towards spatial models from two directions; on one hand the progress comes from physiological research on the functioning of the brain’s complex information processing. On the other hand progress comes from the field of physics dealing with models with so-called “stochastic resetting of particles”, including memory effects. I’m convinced that combining these disparate directions of research will in due course bring focus on a unification: the concept of parallel processing and the complementary theories of MRW and the Zoomer model.
Ecologists should take notice. Such a development may potentially rattle the more dogmatic framework of space use theory, for example by offering solutions to the old problems of simulating Allée effects, Taylor’s power law, pink noise spectra in population series, and long distance connectivity in population structure (complex network topology, pointing towards alternatives to classic metapopulation models).
What regards brain research, professor Marianne Fyhn, Associate Professor Torkel Hafting and their research group at the faculty of Medicine, University of Oslo, are investigating processes in the brains of awake, behaving animals in order to better understand how the brain works in real time, and reveal the mechanisms underlying perception, learning and memory. Recent progress is astonishing! The same regards the Nobel laureates and Professors May-Britt Moser and Edvard Moser at the Kavli Institute and the Centre for Neural Computation, Trondheim. They are interested in the fundamental neural computations underlying cognition and behaviour. To decipher these computations, they focus on the mechanisms for mapping of local space in the mammalian cortex. Their past work includes the discovery of grid cells. Grid cells are place-modulated neurons whose firing fields define a triangular array across the entire environment in the actual nerve system. These cells are thought to form an essential part of the brain’s coordinate system for metric navigation.
I’m sensing that these breakthroughs in brain research on memory and GPS-like functions may be approaching the concept of Parallel processing in spatio-temporal navigation at a rapid pace.
What regards the concept of stochastic resetting of particles, in a recent review Evans et al. (2019) generalize this rapidly expanding field of non-random path crossing of moving particles (i.e., a core property of MRW) to an arbitrary stochastic process (e.g. Lévy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). They also go on to discuss multi-particle systems as well as extended systems, such as fluctuating interfaces, under resetting. They consider memory effects, which implies resetting the process to some randomly selected previous time (like MRW). Finally the review gives an overview of recent developments and applications in the field. By the way, it also refers to some MRW papers (Gautestad and Mysterud 2005; 2006) as application of particle resetting in a biological context.*
*) However, the MRW model and the parallel processing concept were introduced already in my Dr. philos. thesis from 1998 and in Gautestad et al. (1998).
Evans, M. R., S. N. Majumdar, and G. Schehr. 2019. Stochastic Resetting and Applications. arXiv:1910.07993v1 [cond-mat.stat-mech].
Gautestad, A. O. and I. Mysterud. 2005. Intrinsic scaling complexity in animal dispersion and abundance. The American Naturalist 165:44-55.
Gautestad, A. O. and I. Mysterud. 2006. Complex animal distribution and abundance from memory-dependent kinetics. Ecological Complexity 3:44-55.
Gautestad, A. O., I. Mysterud, and M. R. Pelton. 1998. Complex movement and scale-free habitat use: testing the multi-scaled home range model on black bear telemetry data. Ursus 10:219-234.