Spatial Scale Of Interactions Research Articles

A Demonstration Bench for Representing the Character of Phase Transitions of the First and Second Kind

The paper presents the description of a demonstration bench, which includes a mathematical model and analysis tools for understanding the features of phase transitions of the first and second kind. The advantage of this demonstration bench is the rejection of all phenomenology and the obvious limitation of the application of various approximations and hypotheses. The description is formed on the well-known equations of hydrodynamics, which are well-tested and are a reliable basis for the construction of realistic models. The Proctor-Sivashinsky model, which was used to describe the process of convection development in a thin layer of liquid with poorly conductive heat boundaries, is the basis for the demonstration bench. Exactly this model allows to observe phase transitions of the first and second kind. The feature of the model is that it allocates one spatial scale of interaction, leaving for the evolution of the system the possibility to choose the nature of symmetry. All spatial disturbances of the same size but of different orientation interact with each other. This allows us not to distract from the main task of this work, which is to demonstrate the process of structure formation as a result of a cascade of phase transitions. The mechanism of phase transitions associated with the presence of minimums of the interaction coefficients of modes of the spectrum of the instability. There are a large number of structural defects, which appear as attributes of phase transition. The instability spectrum modes interference is the reason of the high rate of correlations in the propagation of a new phase.

Pathways, contextual and cross-scale dynamics of science-policy-society interactions in transdisciplinary research in African cities

The United Nations’ Sustainable Development Goals (SDGs) are inherently complex. This paper contributes to the literature on co-production of knowledge at the interface of science, policy, and society in integrated, transdisciplinary research (TDR) projects. By analysing five projects of the Leading Integrated Research for Agenda 2030 in Africa (LIRA) implemented in nine African cities, the paper identifies the pathways for science-policy-society interactions (SPSI) within the TDR projects, the cross-scale and contextual dynamics influencing the interactions as well as the challenges of foregrounding the interactions. We identified four SPSI pathways: i) TDR processes, ii) explicitly conceptualising and communicating research projects in relation to mandates and policies, iii) the global sustainability agenda, and iv) relationships and networks. We argued that these pathways can be construed as important windows for foregrounding SPSI in TDR projects. Cross-scale dynamics such as the spatial scale of interactions, actors’ roles, and purposes of engagement were critical determinants of the intensity and frequency of the interactions between the project actors. The analysis suggests that being context-sensitive is key to foregrounding SPSI in TDR projects. Conceptual threshold crossing, resource intensity, power differentials, discontinuity, as well as a history of academic and practice silos present formidable challenges to SPSI in TDR projects. These challenges can be addressed through the identified pathways, adequate capability development; incentivising academics and practitioners engaged in co-production of knowledge; stimulating co-production through adequate resources; building redundancies within the project teams, ideas, and processes, and paying attention to the politics of co-production of knowledge.

Phase Transitions in Convection

The paper presents the results of the study of the models of convective instability near its threshold of thin layers of liquid and gas bounded by poorly conducting walls. These models single out one spatial scale of interaction, leaving the possibility for the evolution of the system to choose the symmetry character. This is due to the fact that the conditions for the realization of the modes of convective instability near the threshold are chosen. All spatial perturbations of the same spatial scale, but of different orientations, interact with each other. It turned out that the presence of minima of the interaction potential of the Proctor-Sivashinsky equation modes, the absolute value of the wave number vectors of which is unchanged, determines the choice of symmetry and, accordingly, the characteristics of the spatial structure. In the case of a more realistic model of convection described by the Proctor-Sivashinsky equation, it was possible to observe both the first-order phase transition and the second-order phase transition and detect the form of the state function, which is responsible for the topology of the resulting convective structures: metastable rolls and stable square cells. In this paper, it is shown that the nature of the structural-phase transition in a liquid when taking into account the dependence of viscosity on temperature in the Proctor-Sivashinsky model is similar to the case of the absence of such a dependence. The transition time turns out to be the same, despite the fact that a different structure is formed - hexagonal convective cells. As in the Swift-Hohenberg model, a hard mode for the formation of hexagonal cells in a gas medium is possible only for a sufficiently noticeable dependence of its viscosity on temperature. The phase transition times are inversely proportional to the difference in the values of this function for two consecutive states. A similar description of phase transitions did not use phenomenological approaches and various speculative considerations, which allows for a closer look at the nature of transients.

Data-driven competitive facilitative tree interactions and their implications on nature-based solutions

Spatio-temporal data are more ubiquitous and richer than even before and the availability of such data poses great challenges in data analytics. Ecological facilitation, the positive effect of density of individuals on the individual's survival across a stress gradient, is a complex phenomenon. A large number of tree individuals coupled with soil moisture, temperature, and water stress data across a long temporal period were followed. Data-driven analysis in the absence of hypothesis was performed. Information theoretic analysis of multiple statistical models was employed in order to quantify the best data-driven index of vegetation density and spatial scale of interactions. Sequentially, tree survival was quantified as a function of the size of the individual, vegetation density, and time at the optimal spatial interaction scale. Land surface temperature and soil moisture were also statistically explained by tree size, density, and time. Results indicated that in space both facilitation and competition co-exist in the same ecosystem and the sign and magnitude of this depend on the spatial scale. Overall, within the optimal data-driven spatial scale, tree survival was best explained by the interaction between density and year, sifting overall from facilitation to competition through time. However, small sized trees were always facilitated by increased densities, while large sized trees had either negative or no density effects. Tree size was more important predictor than density in survival and this has implications for nature-based solutions: maintaining large tree individuals or planting species that can become large-sized can safeguard against tree-less areas by promoting survival at long time periods through harsh environmental conditions. Large trees had also a significant effect in moderating land surface temperature and this effect was higher than the one of vegetation density on temperature.

Fine-scale interactions between habitat quality and genetic variation suggest an impact of grazing on the critically endangered Crau Plain grasshopper (Pamphagidae: Prionotropis rhodanica)

The Crau Plain grasshopper,PrionotropisrhodanicaUvarov, 1923 (Orthoptera: Pamphagidae: Thrinchinae), is a rare grasshopper species endemic to the Crau Plain, a steppic habitat in France with unique floristic and faunistic communities. During recent decades, the area covered by these steppic grasslands has been highly reduced and fragmented due to the development of irrigation-based agriculture, roads, as well as industrial and military complexes. The restricted distribution, low population density and poor dispersal ability ofP.rhodanica, combined with the destruction of its habitat, has led to the classification of this species as critically endangered in the IUCN Red List of Threatened Species. Decreases in habitat quality due to intensive grazing in the remnant grassland patches constitute an additional threat forP.rhodanicathat can impact population dynamics at a relatively small-scale. In this work, we focused on a small area of about 3 km2occupied by one of the largest subpopulations observed in 2000–2001. We conducted a single-time snapshot intensive survey of grasshopper density and genetic variation at 11 microsatellite markers. We used a recent method, MAPI, to visualize the spatial genetic structure as a continuous surface and to determine, with the simultaneous use of spatial cross-correlograms, whether the normalized difference vegetation index, which informs on the balance between vegetation productivity and grazing intensity, can explain grasshopper population structure at such a fine scale. We found that both population density and gene flow were strongly and positively correlated to habitat quality (higher productivity of grasslands and/or lower sheep grazing). The spatial scales of interaction between these variables were estimated to be highly similar, in the range of 812–880 meters. This result suggests thatP.rhodanicais very sensitive to the quality of the grasslands it inhabits.

Synthesis and future research directions linking tree diversity to growth, survival, and damage in a global network of tree diversity experiments

Despite considerable research demonstrating that biodiversity increases productivity in forests and regulates herbivory and pathogen damage, there remain gaps in our understanding of the shape, magnitude, and generality of these biodiversity-ecosystem functioning (BEF) relationships. Here, we review findings from TreeDivNet, a global network of 25 tree diversity experiments, on relationships between levels of biodiversity and (a) tree growth and survival and (b) damage to trees from pests and pathogens. Tree diversity often improved the survival and above- and belowground growth of young trees. The mechanistic bases of the diversity effects on tree growth and survival include both selection effects (i.e., an increasing impact of particular species in more species-rich communities) and complementary effects (e.g. related to resource differentiation and facilitation). Plant traits and abiotic stressors may mediate these relationships. Studies of the responses of invertebrate and vertebrate herbivory and pathogen damage have demonstrated that trees in more diverse experimental plots may experience more, less, or similar damage compared to conspecific trees in less diverse plots. Documented mechanisms producing these patterns include changes in concentration, frequency, and apparency of hosts; herbivore and pathogen diet breadth; the spatial scale of interactions; and herbivore and pathogen regulation by natural enemies. Our review of findings from TreeDivNet indicates that tree diversity experiments are extending BEF research across systems and scales, complementing previous BEF work in grasslands by providing opportunities to use remote sensing and spectral approaches to study BEF dynamics, integrate belowground and aboveground approaches, and trace the consequences of tree physiology for ecosystem functioning. This extension of BEF research into tree-dominated systems is improving ecologists’ capacity to understand the mechanistic bases behind BEF relationships. Tree diversity experiments also present opportunities for novel research. Since experimental tree diversity plantations enable measurements at tree, neighbourhood and plot level, they allow for explicit consideration of temporal and spatial scales in BEF dynamics. Presently, most TreeDivNet experiments have run for less than ten years. Given the longevity of trees, exciting results on BEF relationships are expected in the future.

At what scales does aggregated dispersal lead to coexistence?

Aggregation during dispersal can allow persistence of weak competitors, by creating conditions where stronger competitors are more likely to interact with conspecifics than with heterospecifics. However, aggregation mechanisms operate over a wide range of spatial scales, and species experience space in very different ways. The net effect of dispersal aggregation on coexistence will depend on how these scales interact. We show that it is possible to approximate the effects of aggregated dispersal on coexistence by considering three empirically measurable parameters: the spatial scale of interaction (how strongly competition drops off with distance), the spatial scale of aggregation (how large propagule packets are), and the temporal scale of aggregation (how frequently packets arrive). We use a novel metacommunity moment closure based on this approximation and stochastic simulations to show that aggregated dispersal allows for coexistence only when the stronger competitor is both aggregated and interacts at the same or a smaller spatial scale than the weaker competitor. When species interact and are aggregated at the same scales, coexistence outcomes are only weakly sensitive to the absolute scales of interaction and aggregation, as long as the scale of interaction is smaller than the scale of aggregation. However, coexistence is sensitive to the time‐scale of aggregation: increasing the frequency of packet arrival substantially reduces the region of fitness inequalities where both species persist. Finally, coexistence is less likely and global extinction of both competitors is more frequent when aggregation is fixed (with a constant number of propagules per packet), compared to density‐dependent (number of propagules increases with adult density).

Spatial scales of interactions among bacteria and between bacteria and the leaf surface.

Microbial life on plant leaves is characterized by a multitude of interactions between leaf colonizers and their environment. While the existence of many of these interactions has been confirmed, their spatial scale or reach often remained unknown. In this study, we applied spatial point pattern analysis to 244 distribution patterns of Pantoea agglomerans and Pseudomonas syringae on bean leaves. The results showed that bacterial colonizers of leaves interact with their environment at different spatial scales. Interactions among bacteria were often confined to small spatial scales up to 5–20 μm, compared to interactions between bacteria and leaf surface structures such as trichomes which could be observed in excess of 100 μm. Spatial point-pattern analyses prove a comprehensive tool to determine the different spatial scales of bacterial interactions on plant leaves and will help microbiologists to better understand the interplay between these interactions.

Evolution of pathogen specialisation in a host metapopulation: joint effects of host and pathogen dispersal.

Metapopulation processes are important determinants of epidemiological and evolutionary dynamics in host-pathogen systems, and are therefore central to explaining observed patterns of disease or genetic diversity. In particular, the spatial scale of interactions between pathogens and their hosts is of primary importance because migration rates of one species can affect both spatial and temporal heterogeneity of selection on the other. In this study we developed a stochastic and discrete time simulation model to specifically examine the joint effects of host and pathogen dispersal on the evolution of pathogen specialisation in a spatially explicit metapopulation. We consider a plant-pathogen system in which the host metapopulation is composed of two plant genotypes. The pathogen is dispersed by air-borne spores on the host metapopulation. The pathogen population is characterised by a single life-history trait under selection, the infection efficacy. We found that restricted host dispersal can lead to high amount of pathogen diversity and that the extent of pathogen specialisation varied according to the spatial scale of host-pathogen dispersal. We also discuss the role of population asynchrony in determining pathogen evolutionary outcomes.

Synchronisation and stability in river metapopulation networks

Spatial structure in landscapes impacts population stability. Two linked components of stability have large consequences for persistence: first, statistical stability as the lack of temporal fluctuations; second, synchronisation as an aspect of dynamic stability, which erodes metapopulation rescue effects. Here, we determine the influence of river network structure on the stability of riverine metapopulations. We introduce an approach that converts river networks to metapopulation networks, and analytically show how fluctuation magnitude is influenced by interaction structure. We show that river metapopulation complexity (in terms of branching prevalence) has nonlinear dampening effects on population fluctuations, and can also buffer against synchronisation. We conclude by showing that river transects generally increase synchronisation, while the spatial scale of interaction has nonlinear effects on synchronised dynamics. Our results indicate that this dual stability - conferred by fluctuation and synchronisation dampening - emerges from interaction structure in rivers, and this may strongly influence the persistence of river metapopulations.

Central V4 Receptive Fields Are Scaled by the V1 Cortical Magnification and Correspond to a Constant-Sized Sampling of the V1 Surface

The mapping of the topographic representation of the visual field onto cortical areas changes throughout the hierarchy of cortical visual areas. The changes are believed to reflect the establishment of modules with different spatial processing emphasis. The receptive fields (RFs) of neurons within these modules, however, may not be governed by the same spatial topographic map parameters. Here it is shown that the RFs of area V4 neurons (centered 1-12 degrees in eccentricity) are based on a circularly symmetric sampling of the primary visual cortical retinotopic map. No eccentricity dependent magnification beyond that observed in V1 is apparent in the V4 neurons. The size and shape of V4 RFs can be explained by a simple, constant sized, two-dimensional Gaussian sample of visual input from the retinotopic map laid out across the surface of V1. Inferences about the spatial scale of interactions within the receptive fields of neurons cannot be based on a visual area's apparent cortical magnification derived from topographic mapping.

Invasiveness in plant communities with feedbacks

The detrimental effects of invasive plant species on ecosystems are well documented. While much research has focused on discovering ecological influences associated with invasiveness, it remains unclear how these influences interact, causing some introduced exotic species to become invasive threats. Here we develop a framework that incorporates the influences of propagule pressure, frequency independent growth rates, feedback relationships, resource competition and spatial scale of interactions. Our results show that these ecological influences interact in complex ways, resulting in expected outcomes ranging from inability to establish, to naturalization, to conditional invasion dependent on quantity and spatial distribution of propagules, to unconditional takeover. We propose a way to predict the likelihood of these four possible outcomes, for a species recently introduced into a given target community. Such information could enable conservation biologists to craft strategies and target remediation efforts more efficiently and effectively in order to help maintain biodiversity in ecological communities.

A multiple-scale analysis of metazoan meiofaunal distribution in the deep Mediterranean Sea

In order to identify environmental factors driving the distribution and functioning of deep-sea fauna and the spatial scales of interactions, we carried out a multiple-scale investigation in the Mediterranean basin in which we compared two bathyal plains, located at the same depth (ca. 3000 m), but characterised by contrasting trophic conditions. We investigated meiofaunal abundance, biomass, community structure and biodiversity (expressed as richness of taxa) in relation to sediment characteristics, downward fluxes and food availability in the sediment. Samples were collected at all spatial scales (from small to macroscale) in two seasons. Our results indicated that deep-sea systems with different trophic conditions displayed different responses to the distribution of available energy and its spatio-temporal variability in the sediment. The analysis at a macroscale (>1000 km) indicated that meiofauna were controlled primarily by the trophic inputs to the deep-sea system. Spatial variability of meiofaunal parameters at a mesoscale (>50 km) was highest in the eastern Mediterranean and lowest in the western Mediterranean. Such differences are the consequence of the unpredictable inputs of organic matter in the oligotrophic eastern Mediterranean versus a more homogeneous distribution of food inputs in the mesotrophic western Mediterranean. At a smaller scale (local scale 7 km), in the western Mediterranean, the distribution of meiofaunal parameters was highly homogeneous, reflecting the homogeneous distribution of the food availability in the sediment. Our results indicated that the highly variable input and distribution of food sources in the deep eastern Mediterranean did not provide any “insurance” for the sustainability of the deep-sea faunal assemblages in the long term, thus leading to an uncoupling between resource availability and distribution of organisms. We conclude that the influence of energy availability on the deep-sea faunal distributions change at different spatial scales and that the analysis of spatial variability at mesoscales is crucial for understanding the relationships between deep-sea benthic fauna and environmental drivers.

Spatio-temporal community dynamics induced by frequency dependent interactions

A mathematical model incorporating the effects of possibly asymmetric frequency dependent interactions is proposed. Model predictions for an idealized two-species annual plant community with asymmetric linear frequency dependence are explored using (i) analytic mean field equilibrium predictions, (ii) deterministic, discrete-time, finite-population, mean field predictions, and (iii) stochastic, discrete-time, cellular automata predictions for a variety of sizes of the spatial interaction and dispersal neighborhoods. We define species interaction factors, ranging from 0 to 1, which incorporate both frequency independent and frequency dependent terms. The maximum competitive ability of a species is reduced unless species frequency is optimal based on species-specific frequency dependence coefficients, ranging from −1 to +1. Assuming that maximum competitive ability is identical for two species, they can coexist indefinitely when they have equal absolute magnitude or both have sufficiently negative frequency dependence. Although smaller scales of spatial interactions reduce the region of the parameter space in which stable coexistence is predicted, the time to extinction of one species can be significantly increased or decreased by the locality of interactions, depending on whether the losing species has positive or negative frequency dependence, respectively. The sensitivity to initial conditions in the community at large is dramatically reduced as the spatial scale of interactions is decreased. As a consequence, smaller spatial interaction neighborhoods increase the ability of introduced species to invade established communities in regions of the parameter space not predicted by mean field approximations. In the “loser positive, winner positive” regions, smaller scales of interaction dramatically increased invasiveness. In the “loser positive, winner negative” regions of the parameter space, invasion success decreases, but time to extinction of the resident species during successful invasions increases, with an increase in the spatial scale of interactions. The “loser negative, winner positive” regions were relatively insensitive to initial conditions, so invasion success was relatively high at a variety of spatial scales. Surprisingly, invasions in parts of this region are most often successful with intermediate neighborhood sizes, although the maximum time that the losing species could persist before being driven to extinction increases with an increase in the spatial scale of interactions. These results are explained by understanding cluster formation and density and the relative local inter-specific dynamics in cluster interiors, exteriors, and boundaries. In summary, frequency dependent interactions, and the spatial scale on which these interactions occur, can have a big impact on spatio-temporal community dynamics, with implications regarding species coexistence and invasiveness. The model proposed herein provides a theoretical framework for studying frequency dependent interactions that may shed light on spatio-temporal dynamics in real ecological communities.

Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey

We study interactions of predators and prey that are characterized by a scale difference in their use of space. Prey are assumed to occupy patches, forming a metapopulation with low migration among patches. Predators are homogeneously distributed over these patches, due to broad-scale foraging behavior or long-range juvenile dispersal. The predator population thus exerts a globally uniform predation pressure on the prey subpopulations. Under these conditions a nonlinear predator functional response depending on local prey density leads to multiple equilibria that can occur for the same parameter values. These equilibria differ in the fraction of prey patches that are (nearly) empty. Equilibria with a larger fraction of empty prey patches are more stable. The system tends to approach equilibria with a sufficiently high number of empty prey patches, so that local and global population dynamics are stable. If unstable dynamics are observed at all, the fluctuations in local prey density exhibit predictable characteristics. Our main conclusion is that a nonlinear functional response of the predator to local prey density can induce the formation of static patterns in prey density and, hence, lead to stable local and global dynamics. It is shown that these results are sufficiently general to carry over to situations in which prey migration between patches does occur or the spatial domain occupied by the prey population is continuous instead of subdivided into patches.

Scales of aboveground and below‐ground competition in a semi‐arid woodland detected from spatial pattern

Abstract. Semi‐arid woodlands are two‐phase mosaics of canopy and inter‐canopy patches. We hypothesized that both aboveground competition (within canopy patches), and below‐ground competition (between canopy patches), would be important structuring processes in these communities. We investigated the spatial pattern of trees in a Pinus edulis‐Juniperus monosperma woodland in New Mexico using Ripley's K‐function. We found strong aggregation of trees at scales of 2 to 4 m, which indicates the scale of canopy patches. Canopy patches were composed of individuals of both species. Crown centers of both species were always less aggregated than stem centers at scales less than canopy patch size, indicating morphological plasticity of competing crowns. In the smallest size classes of both species, aggregation was most intense, and occurred over a larger range of scales; aggregation decreased with increasing size as is consistent with density‐dependent mortality from intraspecific competition. Within canopy patches, younger trees were associated with older trees of the other species. At scales larger than canopy patches, younger trees showed repulsion from older conspecifics, indicating below‐ground competition. Hence, intraspecific competition was stronger than interspecific competition, probably because the species differ in rooting depth. Woodland dynamics depend on the scale and composition of canopy patches, aggregated seed deposition and facilitation, above‐ and below‐ground competition, and temporal changes in the spatial scale of interactions. This woodland is intermediate in a grassland‐forest continuum (a gradient of increasing woody canopy cover) and hence we expected, and were able to detect, the effects of both above‐ and below‐ground competition.