Diffusion and Ecological Problems: Modern Perspectives

By A. Ōkubo, Simon A. Levin. 2013

1,090 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/24a2061b40fdf6a896096aed9d55ce592c15b843

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In Environmental Engineering

Citations in the corpus

Megafauna extinction, tree species range reduction, and carbon storage in Amazonian forests (2016, background): “In general, diffusivity can be derived from a random walk (Skellam 1951, Okubo and Levin 2001, Ovaskainen and Crone 2009).”
State-space models for bio-loggers: A methodological road map (2013, methodology): “As such, process models employed in bio-logging situations tend to be well-known movement models which have a long history in ecology (Okubo and Levin, 2001; Turchin, 1998).”
Bifurcation analysis of a diffusive ratio-dependent predator–prey model (2014, background): “The importance of spatialmodels has been recognized by the biologists for a long time and has been one of the dominant themes in both ecology and mathematical ecology [8,22,31,32].”
The Spotting Distribution of Wildfires (2016, background): “where z ≥ H + d ≈ H, u∗ is the friction velocity, κ is von Karman’s constant, z0 is the zero-datum displacement, where H is the canopy height and d is the distance above the canopy where horizontal winds begin [49].”
Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations (2011, methodology): “Mathematical modeling of the collective behavior of individuals, such as swarming, has also been treated by continuum models steaming from discrete particle models [33] [14] [41] [34] [42] [15] [36] [13] [21] [23] [16] [17].”
Concentration boundary layers around complex assemblages of macroalgae: Implications for the effects of ocean acidification on understory coralline algae (2013, background): “CBLs act on a scale of micrometers to millimeters, but it is also possible that in regions of reduced flow within macrophyte canopies, larger concentration gradients may develop, known as canopy boundary layers (Okubo et al. 2002).”
Existence and non-existence of spatial patterns in a ratio-dependent predator–prey model (2015, neutral): “The reaction–diffusion models of population interaction with appropriate initial and boundary conditions are capable to produce spatial patterns due to Turing instability (Murray, 2002; Malchow et al., 2008; Okubo and Levin, 2001).”
Diffusive spatial movement with memory and maturation delays (2019, neutral): “Reaction–diffusion equations have been widely used in mathematical modeling of many disciplines, such as physics, chemistry and biology [6, 17, 19].”
Random walks and diffusion on networks (2016, methodology): “RW models have also been applied in various domains, ranging from locomotion and foraging of animals [9–12], the dynamics of neuronal firing [13, 14] and decision-making in the brain [15, 16] to population genetics [17], polymer chains [18, 19], descriptions of financial markets [20, 21], evolution ”
Global Existence and Uniform Boundedness of Smooth Solutions to a Cross-Diffusion System with Equal Diffusion Rates (2015, background): “, population density and environmental condition at the departure location [19].”
Integrated step selection analysis: bridging the gap between resource selection and animal movement (2015, background): “Here we shall make the assumption that, in the absence of habitat selection, step lengths follow either an exponential, half-normal, gamma or log-normal distribution.”
Diffusive Spatial Movement with Memory (2020, methodology): “It was first used to describe the heat conduction in early nineteenth century, and since then it has been used in numerous movement processes in physics, chemistry and biology [7,15,16].”