Combining network theory and reaction–advection–diffusion modelling for predicting animal distribution in dynamic environments

Multi-mode movement decisions across widely ranging behavioral processes

Movement of organisms plays a fundamental role in the evolution and diversity of life. Animals typically move at an irregular pace over time and space, alternating among movement states. Understanding movement decisions and developing mechanistic models of animal distribution dynamics can thus be contingent to adequate discrimination of behavioral phases. Existing methods to disentangle movement states typically require a follow-up analysis to identify state-dependent drivers of animal movement, which overlooks statistical uncertainty that comes with the state delineation process. Here, we developed population-level, multi-state step selection functions (HMM-SSF) that can identify simultaneously the different behavioral bouts and the specific underlying behavior-habitat relationship. Using simulated data and relocation data from mule deer (Odocoileus hemionus), plains bison (Bison bison bison) and plains zebra (Equus quagga), we illustrated the HMM-SSF robustness, versatility, and predictive ability for animals involved in distinct behavioral processes: foraging, migrating and avoiding a nearby predator. Individuals displayed different habitat selection pattern during the encamped and the travelling phase. Some landscape attributes switched from being selected to avoided, depending on the movement phase. We further showed that HMM-SSF can detect multi-modes of movement triggered by predators, with prey switching to the travelling phase when predators are in close vicinity. HMM-SSFs thus can be used to gain a mechanistic understanding of how animals use their environment in relation to the complex interplay between their needs to move, their knowledge of the environment and navigation capacity, their motion capacity and the external factors related to landscape heterogeneity.

Emergency of Tsallis statistics in fractal networks

Scale-free networks constitute a fast-developing field that has already provided us with important tools to understand natural and social phenomena. From biological systems to environmental modifications, from quantum fields to high energy collisions, or from the number of contacts one person has, on average, to the flux of vehicles in the streets of urban centres, all these complex, non-linear problems are better understood under the light of the scale-free network’s properties. A few mechanisms have been found to explain the emergence of scale invariance in complex networks, and here we discuss a mechanism based on the way information is locally spread among agents in a scale-free network. We show that the correct description of the information dynamics is given in terms of the q-exponential function, with the power-law behaviour arising in the asymptotic limit. This result shows that the best statistical approach to the information dynamics is given by Tsallis Statistics. We discuss the main properties of the information spreading process in the network and analyse the role and behaviour of some of the parameters as the number of agents increases. The different mechanisms for optimization of the information spread are discussed.

Thermofractals, Non-Additive Entropy, and q-Calculus

Non-additive entropy is obtained through the thermodynamic description of a system with a fractal structure in its energy-momentum space, called a thermofractal. The entropic parameter, q, is determined in terms of the fractal structure parameters. The characteristics of the thermofractals are determined by two parameters associated with the number of degrees of freedom of the fractal structure and the scale. The parameter q, of non-extensive thermodynamics, has a physical meaning related to the number of degrees of freedom of the thermofractal. The two types of thermofractals are distinguished by the value of q>1 or q<1. Studying the group of transformations of the fractal system, we identify three different classes of transformations and their mathematical expressions. For one class of transformations of thermofractals, the group is isomorphic with q-calculus. Another class of transformations led to new mathematical expressions that extended the deformed q-algebra. Finally, we comment regarding the applications of the results obtained here for different areas such as QCD and scale-free networks.