We develop methods for quantifying habitat connectivity at multiple scales and assigning conservation priority to habitat patches based on their contribution to connectivity. By representing the habitat mosaic as a mathematical "graph," we show that percolation theory can be used to quantify connectivity at multiple scales from empirical landscape data. Our results indicate that connectivity of landscapes is highly scale dependent, exhibiting a marked transition at a characteristic distance and varying significantly for organisms with different dispersal behavior. More importantly, we show that the sensitivity and importance of landscape pattern is also scale dependent, peaking at scales associated with the percolation transition. In addition, the sensitivity analysis allows us to identify critical "stepping stone" patches that, when removed from the landscape, cause large changes in connectivity.

/pdf/detecting-critical-scales-in-fragmented-landscapes-3sy3irszcc.pdf

Detecting Critical Scales in Fragmented Landscapes

An integrated approach (i.e. lecture, computer simulation and experimental measurements) to percolation theory is discussed. The computational and experimental techniques are simple enough to make the introduction of such topics to university entrance and even high school students a realistic proposition.

http://iopscience.iop.org/article/10.1088/0143-0807/15/3/001/pdf

An introduction to percolation

Many spatial fields exhibit connectivity features that have an important influence on hydrologic behavior. Examples include high-conductivity preferred flow paths in aquifers and saturated source areas in drainage lines. Connected features can be considered as arbitrarily shaped bands or pathways of connected pixels having similar (e.g., high) values. Connectivity is a property that is not captured by standard geostatistical approaches, which assume that spatial variation occurs in the most random possible way that is consistent with the spatial correlation, nor is it captured by indicator geostatistics. An alternative approach is to use connectivity functions. In this paper we apply connectivity functions to 13 observed soil moisture patterns from the Tarrawarra catchment and two synthetic aquifer conductivity patterns. It is shown that the connectivity functions are able to distinguish between connected and disconnected patterns. The importance of the connectivity in determining hydrologic behavior is explored using rainfall-runoff simulations and groundwater transport simulations. We propose the integral connectivity scale as a measure of the presence of hydrologic connectivity. Links between the connectivity functions and integral connectivity scale and simulated hydrologic behavior are demonstrated and explained from a hydrologic process perspective. Connectivity functions and the integral connectivity scale provide promising means for characterizing features that exist in observed spatial fields and that have an important influence on hydrologic behavior. Previously, this has not been possible within a statistical framework.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000WR900241

Toward capturing hydrologically significant connectivity in spatial patterns

We are presenting techniques for simulating the motion and the deformation of cloth, fabrics or, more generally, deformable surfaces. Our main goal is to be able to simulate any kind of surface without imposing restrictions on shape or geometrical environment. In particular, we are considering difficult situations with respect to deformations and collisions, like wrinkled fabric falling on the ground. Thus, we have enhanced existing algorithms in order to cope with any possible situation. A mechanical model has been implemented to deal with any irregular triangular meshes, handle high deformations despite rough discretisation, and cope with complex interacting collisions. Thus, it should deal efficiently with situations where nonlinearities and discontinuities are really non marginal. Collision detection has also been improved to efficiently detect self-collisions, and also to correctly consider collision orientations despite the lack of surface orientation information from preset geometrical contexts, using consistency checking and correction. We illustrate these features through simulation examples.

/pdf/versatile-and-efficient-techniques-for-simulating-cloth-and-2nkld9qcqw.pdf

Versatile and efficient techniques for simulating cloth and other deformable objects

In this article, we present a self-contained review of recent work on complex biological systems which exhibit no characteristic scale. This property can manifest itself with fractals (spatial scale invariance), flicker noise or 1/f-noise where f denotes the frequency of a signal (temporal scale invariance) and power laws (scale invariance in the size and duration of events in the dynamics of the system). A hypothesis recently put forward to explain these scale-free phenomomena is criticality, a notion introduced by physicists while studying phase transitions in materials, where systems spontaneously arrange themselves in an unstable manner similar, for instance, to a row of dominoes. Here, we review in a critical manner work which investigates to what extent this idea can be generalized to biology. More precisely, we start with a brief introduction to the concepts of absence of characteristic scale (power-law distributions, fractals and 1/f-noise) and of critical phenomena. We then review typical mathematical models exhibiting such properties: edge of chaos, cellular automata and self-organized critical models. These notions are then brought together to see to what extent they can account for the scale invariance observed in ecology, evolution of species, type III epidemics and some aspects of the central nervous system. This article also discusses how the notion of scale invariance can give important insights into the workings of biological systems.

Scale invariance in biology: coincidence or footprint of a universal mechanism?

From the Publisher:
Physics is a discipline which lends itself especially well to visualization This text teaches physics through computer simulation using TrueBasic--a friendly, accessible, non-commercialized or packaged language The emphasis is on physics instruction through computer simulation as opposed to teaching programming or numerical analysis

Julia Berrisford

Papers

An Introduction to Computer Simulation Methods: Applications to Physical Systems