scholarly journals Small-scale spatial structure influences large-scale invasion rates

2019 ◽  
Author(s):  
Michael J. Plank ◽  
Matthew J. Simpson ◽  
Rachelle N. Binny
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Large Scale ◽  
Spatial Scales ◽  
Mean Field ◽  
Average Density ◽  
Small Scale ◽  
Local Interactions ◽  
Mean Field Model ◽  
Species Invasions

AbstractLocal interactions among individual members of a population can generate intricate small-scale spatial structure, which can strongly influence population dynamics. The two-way interplay between local interactions and population dynamics is well understood in the relatively simple case where the population occupies a fixed domain with a uniform average density. However, the situation where the average population density is spatially varying is less well understood. This situation includes ecologically important scenarios such as species invasions, range shifts, and moving population fronts. Here, we investigate the dynamics of the spatial stochastic logistic model in a scenario where an initially confined population subsequently invades new, previously unoccupied territory. This simple model combines density-independent proliferation with dispersal, and density-dependent mortality via competition with other members of the population. We show that, depending on the spatial scales of dispersal and competition, either a clustered or a regular spatial structure develops over time within the invading population. In the short-range dispersal case, the invasion speed is significantly lower than standard predictions of the mean-field model. We conclude that mean-field models, even when they account for non-local processes such as dispersal and competition, can give misleading predictions for the speed of a moving invasion front.

The nonlinear properties of a large-scale dynamo driven by helical forcing

2002 ◽  
Vol 456 ◽  
pp. 219-237 ◽  
Author(s):  
FAUSTO CATTANEO ◽  
DAVID W. HUGHES ◽  
JEAN-CLAUDE THELEN
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Initial Conditions ◽  
Spatial Scales ◽  
Mean Field ◽  
Forced Flow ◽  
Small Scale ◽  
Dynamo Action ◽  
Initial State ◽  
The Magnetic Field

By considering an idealized model of helically forced flow in an extended domain that allows scale separation, we have investigated the interaction between dynamo action on different spatial scales. The evolution of the magnetic field is studied numerically, from an initial state of weak magnetization, through the kinematic and into the dynamic regime. We show how the choice of initial conditions is a crucial factor in determining the structure of the magnetic field at subsequent times. For a simulation with initial conditions chosen to favour the growth of the small-scale field, the evolution of the large-scale magnetic field can be described in terms of the α-effect of mean field magnetohydrodynamics. We have investigated this feature further by a series of related numerical simulations in smaller domains. Of particular significance is that the results are consistent with the existence of a nonlinearly driven α-effect that becomes saturated at very small amplitudes of the mean magnetic field.

scholarly journals Spatial moment dynamics for collective cell movement incorporating a neighbour-dependent directional bias

2015 ◽  
Vol 12 (106) ◽  
pp. 20150228 ◽  
Author(s):  
Rachelle N. Binny ◽  
Michael J. Plank ◽  
Alex James
Keyword(s):  
Spatial Structure ◽  
Mean Field ◽  
Cell Movement ◽  
Population Level ◽  
Average Density ◽  
Small Scale ◽  
Directional Bias ◽  
Field Approach ◽  
Spatial Moment ◽  
Migrating Cells

The ability of cells to undergo collective movement plays a fundamental role in tissue repair, development and cancer. Interactions occurring at the level of individual cells may lead to the development of spatial structure which will affect the dynamics of migrating cells at a population level. Models that try to predict population-level behaviour often take a mean-field approach, which assumes that individuals interact with one another in proportion to their average density and ignores the presence of any small-scale spatial structure. In this work, we develop a lattice-free individual-based model (IBM) that uses random walk theory to model the stochastic interactions occurring at the scale of individual migrating cells. We incorporate a mechanism for local directional bias such that an individual's direction of movement is dependent on the degree of cell crowding in its neighbourhood. As an alternative to the mean-field approach, we also employ spatial moment theory to develop a population-level model which accounts for spatial structure and predicts how these individual-level interactions propagate to the scale of the whole population. The IBM is used to derive an equation for dynamics of the second spatial moment (the average density of pairs of cells) which incorporates the neighbour-dependent directional bias, and we solve this numerically for a spatially homogeneous case.

scholarly journals When are bacteria really gazelles? Comparing patchy ecologies with dimensionless numbers

2021 ◽  
Author(s):  
Samuel S Urmy ◽  
Alli N Cramer ◽  
Tanya L Rogers ◽  
Jenna Sullivan-Stack ◽  
Marian Louise Schmidt ◽  
...  
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Natural Populations ◽  
Mean Field ◽  
Dimensionless Numbers ◽  
Mean Field Model ◽  
Spatially Explicit Models ◽  
Mean Fields ◽  
Resource Patches ◽  
Blue Whales

From micro to planetary scales, spatial heterogeneity - patchiness - is ubiquitous in ecological systems, defining the environments in which organisms move and interact. While this fact has been recognized for decades, most large-scale ecosystem models still use spatially averaged "mean fields" to represent natural populations, while fine-scale, spatially explicit models are mostly restricted to particular organisms or systems. In a conceptual paper, Grunbaum (2012, Interface Focus 2: 150-155) introduced a heuristic framework, based on three dimensionless ratios quantifying movement, reproduction, and resource consumption, to characterize patchy ecological interactions and identify when mean-field assumptions are justifiable. In this paper, we calculated Grunbaum's dimensionless numbers for 33 real interactions between consumers and their resource patches in terrestrial, aquatic, and aerial environments. Consumers ranged in size from bacteria to blue whales, and patches lasted from minutes to millennia, spanning spatial scales of mm to hundreds of km. We found that none of the interactions could be accurately represented by a purely mean-field model, though 26 of them (79%) could be partially simplified by averaging out movement, reproductive, or consumption dynamics. Clustering consumer-resource pairs by their non-dimensional ratios revealed several unexpected dynamic similarities between disparate interactions. For example, bacterial Pseudoalteromonas exploit nutrient plumes in a similar manner to Mongolian gazelles grazing on ephemeral patches of steppe vegetation. Our findings suggest that dimensional analysis is a valuable tool for characterizing ecological patchiness, and can link the dynamics of widely different systems into a single quantitative framework.

scholarly journals Magnetic helicity fluxes in αΩ dynamos

2010 ◽  
Vol 6 (S274) ◽  
pp. 464-466
Author(s):  
Simon Candelaresi ◽  
Axel Brandenburg
Keyword(s):  
Magnetic Fields ◽  
Large Scale ◽  
Field Model ◽  
Mean Field ◽  
Reynolds Numbers ◽  
Magnetic Helicity ◽  
Small Scale ◽  
Mean Field Model ◽  
One Dimensional

AbstractIn turbulent dynamos the production of large-scale magnetic fields is accompanied by a separation of magnetic helicity in scale. The large- and small-scale parts increase in magnitude. The small-scale part can eventually work against the dynamo and quench it, especially at high magnetic Reynolds numbers. A one-dimensional mean-field model of a dynamo is presented where diffusive magnetic helicity fluxes within the domain are important. It turns out that this effect helps to alleviate the quenching. Here we show that internal magnetic helicity fluxes, even within one hemisphere, can be important for alleviating catastrophic quenching.

scholarly journals Analysis of 220 Years of Floodplain Population Dynamics in the US at Different Spatial Scales

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 141
Author(s):  
Firoza Akhter ◽  
Maurizio Mazzoleni ◽  
Luigia Brandimarte
Keyword(s):  
Population Dynamics ◽  
Large Scale ◽  
Spatial Scales ◽  
National Level ◽  
State Level ◽  
Economic Activities ◽  
Protection Measures ◽  
Management Planning ◽  
The Us ◽  
Over Time

In this study, we explore the long-term trends of floodplain population dynamics at different spatial scales in the contiguous United States (U.S.). We exploit different types of datasets from 1790–2010—i.e., decadal spatial distribution for the population density in the US, global floodplains dataset, large-scale data of flood occurrence and damage, and structural and nonstructural flood protection measures for the US. At the national level, we found that the population initially settled down within the floodplains and then spread across its territory over time. At the state level, we observed that flood damages and national protection measures might have contributed to a learning effect, which in turn, shaped the floodplain population dynamics over time. Finally, at the county level, other socio-economic factors such as local flood insurances, economic activities, and socio-political context may predominantly influence the dynamics. Our study shows that different influencing factors affect floodplain population dynamics at different spatial scales. These facts are crucial for a reliable development and implementation of flood risk management planning.

scholarly journals On the Throughput Optimization in Large-Scale Batch-Processing Systems

2021 ◽  
Vol 48 (3) ◽  
pp. 128-129
Author(s):  
Sounak Kar ◽  
Robin Rehrmann ◽  
Arpan Mukhopadhyay ◽  
Bastian Alt ◽  
Florin Ciucu ◽  
...  
Keyword(s):  
Large Scale ◽  
Mean Field ◽  
Queueing Network ◽  
Processing System ◽  
Batch Size ◽  
System Throughput ◽  
Throughput Optimization ◽  
Mean Field Model ◽  
Optimal Batch Size ◽  
Globally Attractive

We analyze a data-processing system with n clients producing jobs which are processed in batches by m parallel servers; the system throughput critically depends on the batch size and a corresponding sub-additive speedup function that arises due to overhead amortization. In practice, throughput optimization relies on numerical searches for the optimal batch size which is computationally cumbersome. In this paper, we model this system in terms of a closed queueing network assuming certain forms of service speedup; a standard Markovian analysis yields the optimal throughput in w n4 time. Our main contribution is a mean-field model that has a unique, globally attractive stationary point, derivable in closed form. This point characterizes the asymptotic throughput as a function of the batch size that can be calculated in O(1) time. Numerical settings from a large commercial system reveal that this asymptotic optimum is accurate in practical finite regimes.

scholarly journals Mean-Field Models for EEG/MEG: From Oscillations to Waves

2021 ◽  
Author(s):  
Áine Byrne ◽  
James Ross ◽  
Rachel Nicks ◽  
Stephen Coombes
Keyword(s):  
Gap Junction ◽  
Large Scale ◽  
Mean Field ◽  
Coarse Grained ◽  
Neural Mass Model ◽  
Neuron Network ◽  
Mass Model ◽  
Mean Field Model ◽  
Neural Mass ◽  
The Rich

AbstractNeural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological considerations they are phenomenological in nature, and cannot hope to recreate some of the rich repertoire of responses seen in real neuronal tissue. Here we consider a simple spiking neuron network model that has recently been shown to admit an exact mean-field description for both synaptic and gap-junction interactions. The mean-field model takes a similar form to a standard neural mass model, with an additional dynamical equation to describe the evolution of within-population synchrony. As well as reviewing the origins of this next generation mass model we discuss its extension to describe an idealised spatially extended planar cortex. To emphasise the usefulness of this model for EEG/MEG modelling we show how it can be used to uncover the role of local gap-junction coupling in shaping large scale synaptic waves.

scholarly journals Enhancing ecosystem restoration efficiency through spatial and temporal coordination

2015 ◽  
Vol 112 (19) ◽  
pp. 6236-6241 ◽  
Author(s):  
Thomas M. Neeson ◽  
Michael C. Ferris ◽  
Matthew W. Diebel ◽  
Patrick J. Doran ◽  
Jesse R. O’Hanley ◽  
...  
Keyword(s):  
Great Lakes ◽  
Large Scale ◽  
Expert Knowledge ◽  
Spatial Scales ◽  
Small Scale ◽  
Space And Time ◽  
Ecosystem Connectivity ◽  
Breeding Grounds ◽  
Local Expert ◽  
Conservation Projects

In many large ecosystems, conservation projects are selected by a diverse set of actors operating independently at spatial scales ranging from local to international. Although small-scale decision making can leverage local expert knowledge, it also may be an inefficient means of achieving large-scale objectives if piecemeal efforts are poorly coordinated. Here, we assess the value of coordinating efforts in both space and time to maximize the restoration of aquatic ecosystem connectivity. Habitat fragmentation is a leading driver of declining biodiversity and ecosystem services in rivers worldwide, and we simultaneously evaluate optimal barrier removal strategies for 661 tributary rivers of the Laurentian Great Lakes, which are fragmented by at least 6,692 dams and 232,068 road crossings. We find that coordinating barrier removals across the entire basin is nine times more efficient at reconnecting fish to headwater breeding grounds than optimizing independently for each watershed. Similarly, a one-time pulse of restoration investment is up to 10 times more efficient than annual allocations totaling the same amount. Despite widespread emphasis on dams as key barriers in river networks, improving road culvert passability is also essential for efficiently restoring connectivity to the Great Lakes. Our results highlight the dramatic economic and ecological advantages of coordinating efforts in both space and time during restoration of large ecosystems.

scholarly journals Population dynamics with spatial structure and an Allee effect

2020 ◽  
Author(s):  
Anudeep Surendran ◽  
Michael Plank ◽  
Matthew Simpson
Keyword(s):  
Population Dynamics ◽  
Spatial Structure ◽  
Short Range ◽  
Allee Effect ◽  
Mean Field ◽  
Mean Field Approximation ◽  
Continuum Approximation ◽  
Spatial Moment ◽  
Mean Field Models ◽  
The Mean

AbstractAllee effects describe populations in which long-term survival is only possible if the population density is above some threshold level. A simple mathematical model of an Allee effect is one where initial densities below the threshold lead to population extinction, whereas initial densities above the threshold eventually asymptote to some positive carrying capacity density. Mean field models of population dynamics neglect spatial structure that can arise through short-range interactions, such as short-range competition and dispersal. The influence of such non mean-field effects has not been studied in the presence of an Allee effect. To address this we develop an individual-based model (IBM) that incorporates both short-range interactions and an Allee effect. To explore the role of spatial structure we derive a mathematically tractable continuum approximation of the IBM in terms of the dynamics of spatial moments. In the limit of long-range interactions where the mean-field approximation holds, our modelling framework accurately recovers the mean-field Allee threshold. We show that the Allee threshold is sensitive to spatial structure that mean-field models neglect. For example, we show that there are cases where the mean-field model predicts extinction but the population actually survives and vice versa. Through simulations we show that our new spatial moment dynamics model accurately captures the modified Allee threshold in the presence of spatial structure.

Mycorrhizal fungal community relationship to root nitrogen concentration over a regional atmospheric nitrogen deposition gradient in the northeastern USA

2008 ◽  
Vol 38 (5) ◽  
pp. 1260-1266 ◽  
Author(s):  
Erik A. Lilleskov ◽  
Philip M. Wargo ◽  
Kristiina A. Vogt ◽  
Daniel J. Vogt
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Nitrogen Concentration ◽  
N Deposition ◽  
Small Scale ◽  
N Availability ◽  
Cenococcum Geophilum ◽  
Ectomycorrhizal Morphotypes ◽  
Deposition Gradient ◽  
Northeastern Usa

Increased nitrogen (N) input has been found to alter ectomycorrhizal fungal communities over short deposition gradients and in fertilization experiments; however, its effects over larger spatial scales have not been determined. To address this gap, we reanalyzed data from a study originally designed to examine the effects of soil aluminum/calcium (Al/Ca) ratios on the vitality of red spruce fine roots over a regional acid and N deposition gradient in the northeastern USA. We used root N as an indicator of stand N availability and examined its relationship with the abundance of ectomycorrhizal morphotypes. The dominant morphotypes changed in relative abundance as a function of stand N availability. As root N concentrations increased, Piloderma spp. - like, Cenococcum geophilum Fr., and other unidentified mycorrhizal morphotypes declined in abundance, while other smooth-mantled morphotypes increased. Root N concentration in the 1–2 mm diameter class was the best predictor of the abundance of multiple morphotypes. The morphotype responses were consistent with those found in experimental and small-scale studies, suggesting that N availability is altering ectomycorrhizal communities over broad spatial scales in this region. This finding provides an impetus to conduct a more detailed characterization of mycorrhizal community responses to N deposition across large-scale gradients.

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