scholarly journals Stability criteria for the consumption and exchange of essential resources

2021 ◽  
Author(s):  
Theo Gibbs ◽  
Yifan Zhang ◽  
Zachary R Miller ◽  
James P O'Dwyer
Keyword(s):  
Ecological Communities ◽  
Stability Criteria ◽  
Production Networks ◽  
Multiple Resources ◽  
Interacting Species ◽  
Pairwise Interactions ◽  
Stable Equilibria ◽  
Ecological Mechanism ◽  
Resource Environment ◽  
Stability Results

Models of pairwise interactions have informed our understanding of when ecological communities will have stable equilibria. However, these models do not explicitly include the effect of the resource environment, which has the potential to refine or modify our understanding of when a group of interacting species will coexist. Recent consumer-resource models incorporating the exchange of resources alongside competition exemplify this: such models can lead to either stable or unstable equilibria, depending on the resource supply. On the other hand, these recent models focus on a simplified version of microbial metabolism where the depletion of resources always leads to consumer growth. Here, we model an arbitrarily large system of consumers governed by Liebig's law, where species require and deplete multiple resources, but each consumer's growth rate is only limited by a single one of these multiple resources. Consumed resources that do not lead to growth are leaked back into the environment, thereby tying the mismatch between depletion and growth to cross-feeding. For this set of dynamics, we show that feasible equilibria can be either stable or unstable, once again depending on the resource environment. We identify special consumption and production networks which protect the community from instability when resources are scarce. Using simulations, we demonstrate that the qualitative stability patterns we derive analytically apply to a broader class of network structures and resource inflow profiles, including cases in which species coexist on only one externally supplied resource. Our stability criteria bear some resemblance to classic stability results for pairwise interactions, but also demonstrate how environmental context can shape coexistence patterns when ecological mechanism is modeled directly.

scholarly journals ON STABILITY CRITERIA OF FRACTAL DIFFERENTIAL SYSTEMS OF CONFORMABLE TYPE

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040009
Author(s):  
AWAIS YOUNUS ◽  
THABET ABDELJAWAD ◽  
TAZEEN GUL
Keyword(s):  
Asymptotic Stability ◽  
Control Theory ◽  
Stability Criteria ◽  
Differential Systems ◽  
Central Concern ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Stability Results

In this paper, stability results of central concern for control theory are given for finite-dimensional linear and nonlinear local fractional or fractal differential systems. The main purpose of this paper is to provide some results on stability and asymptotic stability of conformable order systems, together with some illustrating examples.

scholarly journals Phenological variation in annual timing of hibernation and breeding in nearby populations of Arctic ground squirrels

2010 ◽  
Vol 278 (1716) ◽  
pp. 2369-2375 ◽  
Author(s):  
Michael J. Sheriff ◽  
G. Jim Kenagy ◽  
Melanie Richter ◽  
Trixie Lee ◽  
Øivind Tøien ◽  
...  
Keyword(s):  
Environmental Conditions ◽  
Ground Squirrels ◽  
Ecological Communities ◽  
Physiological Mechanisms ◽  
Interacting Species ◽  
Trade Offs ◽  
Phenological Shifts ◽  
Arctic Ground Squirrels ◽  
Northern Alaska

Ecologists need an empirical understanding of physiological and behavioural adjustments that animals can make in response to seasonal and long-term variations in environmental conditions. Because many species experience trade-offs between timing and duration of one seasonal event versus another and because interacting species may also shift phenologies at different rates, it is possible that, in aggregate, phenological shifts could result in mismatches that disrupt ecological communities. We investigated the timing of seasonal events over 14 years in two Arctic ground squirrel populations living 20 km apart in Northern Alaska. At Atigun River, snow melt occurred 27 days earlier and snow cover began 17 days later than at Toolik Lake. This spatial differential was reflected in significant variation in the timing of most seasonal events in ground squirrels living at the two sites. Although reproductive males ended seasonal torpor on the same date at both sites, Atigun males emerged from hibernation 9 days earlier and entered hibernation 5 days later than Toolik males. Atigun females emerged and bred 13 days earlier and entered hibernation 9 days earlier than those at Toolik. We propose that this variation in phenology over a small spatial scale is likely generated by plasticity of physiological mechanisms that may also provide individuals the ability to respond to variation in environmental conditions over time.

scholarly journals Macroevolutionary imprints on the assembly of frugivory networks

2020 ◽  
Author(s):  
Gustavo Burin ◽  
Paulo R. Guimarães ◽  
Tiago B. Quental
Keyword(s):  
Interaction Network ◽  
Ecological Networks ◽  
Species Number ◽  
Ecological Communities ◽  
Biological Interactions ◽  
Deep Time ◽  
Interacting Species ◽  
History Of ◽  
Current Interaction ◽  
Biodiversity Changes

Biological interactions are a key aspect of ecological communities (Delmas et al., 2018). Current interaction network structures are snapshots of dynamic processes of community assembly (Thompson, 2005), and represent the product of the evolutionary history of interacting species over millions of years. Thus, assessing the deep time mechanisms affecting the assembly of ecological networks are key to better understand biodiversity changes in broader time scales (Jablonski, 2008). Here we integrate tools from macroevolutionary studies with network science to show that more central species in frugivory networks belong to lineages with higher macroevolutionary stability. This association is more pronounced in warmer, wetter, less seasonal environments, which highlights the role of environmental factors in shaping ecological networks. Furthermore, our results suggest that these environments possess a more diverse (either in species number or ecology) assemblage of species that can be sorted during network assembly. Lastly, we found evidence that the macro-evolutionary contribution to network stability changes in geographical space. This reinforces the idea that the macroevolutionary sorting mechanism acts at the regional pool of species, rather than selecting absolute paces of diversification. Hence our results suggest an interplay between ecological roles and diversification regimes in shaping the fate of lineages of plants and seed dispersing birds.

scholarly journals Dynamical persistence in resource-consumer models

2020 ◽  
Author(s):  
Itay Dalmedigos ◽  
Guy Bunin
Keyword(s):  
Fixed Points ◽  
Competitive Exclusion ◽  
Resource Competition ◽  
Exclusion Principle ◽  
Ecological Communities ◽  
Competitive Exclusion Principle ◽  
Stable Equilibria ◽  
Species Being ◽  
Abundance Fluctuations ◽  
High Diversity

We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio of realized species diversity to the number of resources. This ratio is set by competition, through the balance between species being pushed out and invading. When this ratio is smaller than one, dynamics will reach stable equilibria. When this ratio is larger than one, fixed-points are either unstable or marginally stable, as expected by the competitive exclusion principle. If they are unstable, the system is repelled from fixed points, and abundances forever fluctuate. While marginally-stable fixed points are in principle allowed and predicted by some models, they become structurally unstable at high diversity. This means that even small changes to the model, such as non-linearities in how resources combine to generate species’ growth, will result in persistent abundance fluctuations.

scholarly journals Relative contribution of ecological and biological attributes in the fine-grain structure of ant-plant networks

2015 ◽  
Author(s):  
Cecilia Díaz-Castelazo ◽  
Victor Rico-Gray
Keyword(s):  
Habitat Heterogeneity ◽  
Abiotic Factors ◽  
Grain Structure ◽  
Ecological Communities ◽  
Plant Interactions ◽  
Generalist Species ◽  
Facultative Mutualism ◽  
Interacting Species ◽  
Biotic Defense ◽  
Fine Grain

Background. Ecological communities of interacting species analyzed as complex networks, revealed that species dependence on their counterpart is more complex than expected at random. For ant-plant networks (mediated by extrafloral nectar), links among species are asymmetric (nested), forming a core of generalist species. Proposed factors affecting network organization include encounter probability (species abundances, habitat heterogeneity), behavior, phylogeny and body size. While the importance of underlying factors that influence structure of ant-plant networks have been separately explored, simultaneous contribution of several biological and ecological attributes inherent to the species, guild or habitat level have not been addressed. Methods. For a tropical seasonal site we recorded frequency of pairwise ant-plant interactions mediated by extrafloral nectaries, attributes of interacting species, habitat attributes, cover of plants with EFNs, and studied the resultant network structure. We addressed for the first time the role of mechanistic versus neutral determinants at the “fine-grain” structure (pairwise interactions) of ant-plant networks, studying the simultaneous contribution of several plant, ant, and habitat attributes in prevailing interactions as well as in overall network topology (community). Results. Our studied network was highly-nested, non-modular, with core species in general having high species strengths (higher strength values for ants than plants) and low specialization; plants had higher dependences on their counterparts. The significant factor explaining network and fine-grain structure was habitat heterogeneity in vegetation structure (open vs. shaded habitats), with no evidence of neutral (abundance) effects. Discussion. Core ant species are relevant to most plants species at the network, the latter depending more on the former, core ants showing adaptations to nectar consumption and deterrent behavior, suggestive of potential biotic defense at a community scale. At our study site spatiotemporal heterogeneity is so strong, that emerges at community-level structural properties, depicting influence of abiotic factors in facultative mutualism. Frequent occurrence of morphologically-diverse EFNs at all habitats suggests plasticity in plant strategies for biotic defense provided by ants.

scholarly journals Top-down identification of keystone species in the microbiome

2021 ◽  
Author(s):  
Guy Amit ◽  
Amir Bashan
Keyword(s):  
Native Species ◽  
Keystone Species ◽  
Metagenomic Data ◽  
Ecological Communities ◽  
Top Down ◽  
Cross Sectional ◽  
Pairwise Interactions ◽  
Total Influence ◽  
The Stability ◽  
Longitudinal Sampling

Keystone species in ecological communities are native species that play an especially important role in the stability of their ecosystem and can also be potentially used as its main drivers. However, we still lack an effective framework for identifying these species from the available metagenomic data without the notoriously difficult step of reconstructing the detailed network of inter-specific interactions. Here we propose a top-down identification framework, which detects keystones by their total influence on the rest of the species. Our method does not assume pairwise interactions or any specific underlying dynamics and is appropriate to both perturbation experiments and metagenomic cross-sectional surveys. When applied to real metagenomic data of the human gastrointestinal microbiome, we detect a set of candidate keystones and find that they are often part of a keystone module -- multiple candidate keystones species with correlated occurrence. The keystones analysis of single-time-point cross-sectional data is also later verified by evaluation of two-time-points longitudinal sampling. Our framework represents a necessary advancement towards the reliable identification of these key players of complex, real-world microbial communities.

scholarly journals Theoretical guidelines for editing ecological communities

2020 ◽  
Author(s):  
Vu Nguyen ◽  
Dervis Can Vural
Keyword(s):  
Community Resilience ◽  
Optimization Process ◽  
Community Control ◽  
Ecological Communities ◽  
Interspecies Interactions ◽  
Cost Parameter ◽  
Pairwise Interactions ◽  
Species Abundances

Having control over species abundances and community resilience is of great interest for experimental, agricultural, industrial and conservational purposes. Here, we theoretically explore the possibility of manipulating ecological communities by modifying pairwise interactions. Specifically, we establish which interaction values should be modified, and by how much, in order to alter the composition or resilience of a community towards a favorable direction. While doing so, we also take into account the experimental difficulties in making such modifications by including in our optimization process, a cost parameter, which penalizes large modifications. In addition to prescribing what changes should be made to interspecies interactions given some modification cost, our approach also serves to establish the limits of community control, i.e. how well can one approach an ecological goal at best, even when not constrained by cost.

scholarly journals Stability Criteria for Complex Microbial Communities

2018 ◽  
Author(s):  
Stacey Butler ◽  
James O’Dwyer
Keyword(s):  
Microbial Communities ◽  
Microbial Ecology ◽  
Positive Equilibrium ◽  
Central Question ◽  
Stability Criteria ◽  
Small Perturbations ◽  
Pairwise Interactions ◽  
Abiotic Resources ◽  
Mutualistic Interactions ◽  
The Face

AbstractCompetition and mutualism are inevitable processes in microbial ecology, and a central question is which and how many taxa will persist in the face of these interactions. Ecological theory has demonstrated that when direct, pairwise interactions among a group of species are too numerous, or too strong, then the coexistence of these species will be unstable to any slight perturbation. This instability worsens when mutualistic interactions complement competition. Here, we refine and to some extent overturn that understanding, by considering explicitly the resources that microbes consume and produce. In contrast to more complex organisms, microbial cells consume primarily abiotic resources, and mutualistic interactions are often mediated by these same abiotic resources through the mechanism of cross-feeding. Our model therefore considers the consumption and production of a set of abiotic resources by a group of microbial species. We show that if microbes consume, but do not produce resources, then any positive equilibrium will always be stable to small perturbations. We go on to show that in the presence of crossfeeding, stability is no longer guaranteed. However, stability still holds when mutualistic interations are either symmetric, or sufficiently weak.

Species richness and redundancy promote persistence of exploited mutualisms in yeast

Science ◽  
2020 ◽  
Vol 370 (6514) ◽  
pp. 346-350 ◽  
Author(s):  
Mayra C. Vidal ◽  
Sheng Pei Wang ◽  
David M. Rivers ◽  
David M. Althoff ◽  
Kari A. Segraves
Keyword(s):  
Species Richness ◽  
Interspecific Interactions ◽  
Functional Redundancy ◽  
Ecological Communities ◽  
Negative Effects ◽  
Community Members ◽  
Pairwise Interactions ◽  
Essential Question ◽  
Diverse Communities ◽  
High Species Richness

Mutualisms, or reciprocally beneficial interspecific interactions, constitute the foundation of many ecological communities and agricultural systems. Mutualisms come in different forms, from pairwise interactions to extremely diverse communities, and they are continually challenged with exploitation by nonmutualistic community members (exploiters). Thus, understanding how mutualisms persist remains an essential question in ecology. Theory suggests that high species richness and functional redundancy could promote mutualism persistence in complex mutualistic communities. Using a yeast system (Saccharomyces cerevisiae), we experimentally show that communities with the greatest mutualist richness and functional redundancy are nearly two times more likely to survive exploitation than are simple communities. Persistence increased because diverse communities were better able to mitigate the negative effects of competition with exploiters. Thus, large mutualistic networks may be inherently buffered from exploitation.

Global stability of time-dependent flows. Part 2. Modulated fluid layers

1974 ◽  
Vol 62 (2) ◽  
pp. 387-403 ◽  
Author(s):  
George M. Homsy
Keyword(s):  
Global Stability ◽  
Time Dependent ◽  
Computational Results ◽  
Stability Criteria ◽  
Wide Range ◽  
Fluid Layers ◽  
Arbitrary Amplitude ◽  
Stability Limits ◽  
Rayleigh Numbers ◽  
Stability Results

The method of energy is used to develop two stability criteria for a large class of modulated Bénard problems. Both criteria give stability limits which hold for disturbances of arbitrary amplitude. The first of these, designated as strong global stability, requires the energy of all disturbances to decay monotonically and exponentially in time. Application of this criterion results in a prediction of Rayleigh numbers below which the diffusive stagnant solution to the Bous-sinesq equations is unique. The second criterion requires only that disturbances decay asymptotically to zero over many cycles of modulation, and is a weaker concept of stability. Computational results using both criteria are given for a wide range of specific cases for which linear asymptotic stability results are available, and it is seen that the energy and linear limits often lie close to one another.

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