1
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Ranjan R, Koffel T, Klausmeier CA. The three-species problem: Incorporating competitive asymmetry and intransitivity in modern coexistence theory. Ecol Lett 2024; 27:e14426. [PMID: 38603592 DOI: 10.1111/ele.14426] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2023] [Revised: 02/28/2024] [Accepted: 03/08/2024] [Indexed: 04/13/2024]
Abstract
While natural communities can contain hundreds of species, modern coexistence theory focuses primarily on species pairs. Alternatively, the structural stability approach considers the feasibility of equilibria, gaining scalability to larger communities but sacrificing information about dynamic stability. Three-species competitive communities are a bridge to more-diverse communities. They display novel phenomena while remaining amenable to mathematical analysis, but remain incompletely understood. Here, we combine these approaches to identify the key quantities that determine three-species competition outcomes. We show that pairwise niche overlap and fitness differences are insufficient to completely characterize competitive outcomes, which requires a strictly triplet-wise quantity: cyclic asymmetry, which underlies intransitivity. Low pairwise niche overlap stabilizes the triplet, while high fitness differences promote competitive exclusion. The effect of cyclic asymmetry on stability is complex and depends on pairwise niche overlap. In summary, we elucidate how pairwise niche overlap, fitness differences and cyclic asymmetry determine three-species competition outcomes.
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Affiliation(s)
- Ravi Ranjan
- W.K. Kellogg Biological Station, Michigan State University, Hickory Corners, Michigan, USA
- Program in Ecology, Evolution and Behavior, Michigan State University, East Lansing, Michigan, USA
- Department of Plant Biology, Michigan State University, East Lansing, Michigan, USA
- Hanse-Wissenschaftskolleg Institute for Advanced Study, Delmenhorst, Germany
| | - Thomas Koffel
- W.K. Kellogg Biological Station, Michigan State University, Hickory Corners, Michigan, USA
- Program in Ecology, Evolution and Behavior, Michigan State University, East Lansing, Michigan, USA
| | - Christopher A Klausmeier
- W.K. Kellogg Biological Station, Michigan State University, Hickory Corners, Michigan, USA
- Program in Ecology, Evolution and Behavior, Michigan State University, East Lansing, Michigan, USA
- Department of Plant Biology, Michigan State University, East Lansing, Michigan, USA
- Department of Integrative Biology, Michigan State University, East Lansing, Michigan, USA
- Department of Global Ecology, Carnegie Institution for Science, Stanford, California, USA
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2
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Song C, Spaak JW. Trophic tug-of-war: Coexistence mechanisms within and across trophic levels. Ecol Lett 2024; 27:e14409. [PMID: 38590122 DOI: 10.1111/ele.14409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2023] [Revised: 02/26/2024] [Accepted: 03/06/2024] [Indexed: 04/10/2024]
Abstract
Ecological communities encompass rich diversity across multiple trophic levels. While modern coexistence theory has been widely applied to understand community assembly, its traditional formalism only allows assembly within a single trophic level. Here, using an expanded definition of niche and fitness differences applicable to multitrophic communities, we study how diversity within and across trophic levels affects species coexistence. If each trophic level is analysed separately, both lower- and higher trophic levels are governed by the same coexistence mechanisms. In contrast, if the multitrophic community is analysed as a whole, different trophic levels are governed by different coexistence mechanisms: coexistence at lower trophic levels is predominantly limited by fitness differences, whereas coexistence at higher trophic levels is predominantly limited by niche differences. This dichotomy in coexistence mechanisms is supported by theoretical derivations, simulations of phenomenological and trait-based models, and a case study of a primeval forest ecosystem. Our work provides a general and testable prediction of coexistence mechanism operating in multitrophic communities.
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Affiliation(s)
- Chuliang Song
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, New Jersey, USA
- Department of Ecology and Evolutionary Biology, University of California, Los Angeles, California, USA
| | - Jurg W Spaak
- Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, New York, USA
- Institute for Environmental Sciences, RPTU Kaiserslautern-Landau, Landau, Germany
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3
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Liu X, Constable GWA, Pitchford JW. Feasibility and stability in large Lotka Volterra systems with interaction structure. Phys Rev E 2023; 107:054301. [PMID: 37329014 DOI: 10.1103/physreve.107.054301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Accepted: 04/14/2023] [Indexed: 06/18/2023]
Abstract
Complex system stability can be studied via linear stability analysis using random matrix theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalized Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.
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Affiliation(s)
- Xiaoyuan Liu
- Department of Mathematics, University of York, York, YO10 5DD, United Kingdom
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4
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Baron JW, Jewell TJ, Ryder C, Galla T. Breakdown of Random-Matrix Universality in Persistent Lotka-Volterra Communities. PHYSICAL REVIEW LETTERS 2023; 130:137401. [PMID: 37067312 DOI: 10.1103/physrevlett.130.137401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Revised: 06/17/2022] [Accepted: 03/06/2023] [Indexed: 06/19/2023]
Abstract
The eigenvalue spectrum of a random matrix often only depends on the first and second moments of its elements, but not on the specific distribution from which they are drawn. The validity of this universality principle is often assumed without proof in applications. In this Letter, we offer a pertinent counterexample in the context of the generalized Lotka-Volterra equations. Using dynamic mean-field theory, we derive the statistics of the interactions between species in an evolved ecological community. We then show that the full statistics of these interactions, beyond those of a Gaussian ensemble, are required to correctly predict the eigenvalue spectrum and therefore stability. Consequently, the universality principle fails in this system. We thus show that the eigenvalue spectra of random matrices can be used to deduce the stability of "feasible" ecological communities, but only if the emergent non-Gaussian statistics of the interactions between species are taken into account.
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Affiliation(s)
- Joseph W Baron
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain
| | - Thomas Jun Jewell
- Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Christopher Ryder
- Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Tobias Galla
- Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca, Spain
- Department of Physics and Astronomy, School of Natural Sciences, The University of Manchester, Manchester M13 9PL, United Kingdom
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5
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Rubin IN, Ispolatov Y, Doebeli M. Maximal ecological diversity exceeds evolutionary diversity in model ecosystems. Ecol Lett 2023; 26:384-397. [PMID: 36737422 DOI: 10.1111/ele.14156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Revised: 10/10/2022] [Accepted: 10/12/2022] [Indexed: 02/05/2023]
Abstract
Understanding community saturation is fundamental to ecological theory. While investigations of the diversity of evolutionary stable states (ESSs) are widespread, the diversity of communities that have yet to reach an evolutionary endpoint is poorly understood. We use Lotka-Volterra dynamics and trait-based competition to compare the diversity of randomly assembled communities to the diversity of the ESS. We show that, with a large enough founding diversity (whether assembled at once or through sequential invasions), the number of long-time surviving species exceeds that of the ESS. However, the excessive founding diversity required to assemble a saturated community increases rapidly with the dimension of phenotype space. Additionally, traits present in communities resulting from random assembly are more clustered in phenotype space compared to random, although still markedly less ordered than the ESS. By combining theories of random assembly and ESSs we bring a new viewpoint to both the saturation and random assembly literature.
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Affiliation(s)
- Ilan N Rubin
- Department of Zoology, University of British Columbia, Vancouver, British Columbia, Canada
| | - Yaroslav Ispolatov
- University of Santiago of Chile (USACH), Physics Department, Santiago, Chile
| | - Michael Doebeli
- Department of Zoology, University of British Columbia, Vancouver, British Columbia, Canada.,Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada
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6
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Song C, Fortin MJ, Gonzalez A. Metapopulation persistence can be inferred from incomplete surveys. Proc Biol Sci 2022; 289:20222029. [PMID: 36515114 PMCID: PMC9748775 DOI: 10.1098/rspb.2022.2029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2022] [Accepted: 11/17/2022] [Indexed: 12/15/2022] Open
Abstract
Habitat destruction and fragmentation are principal causes of species loss. While a local population might go extinct, a metapopulation-populations inhabiting habitat patches connected by dispersal-can persist regionally by recolonizing empty patches. To assess metapopulation persistence, two widely adopted indicators in conservation management are metapopulation capacity and patch importance. However, we face a fundamental limitation in that assessing metapopulation persistence requires that we survey or sample all the patches in a landscape: often these surveys are logistically challenging to conduct and repeat, which raises the question whether we can learn enough about the metapopulation persistence from an incomplete survey. Here, we provide a robust statistical approach to infer metapopulation capacity and patch importance by sampling a portion of all patches. We provided analytic arguments on why the metapopulation capacity and patch importance can be well predicted from sub-samples of habitat patches. Full-factorial simulations with more complex models corroborate our analytic predictions. We applied our model to an empirical metapopulation of mangrove hummingbirds (Amazilia boucardi). On the basis of our statistical framework, we provide some sampling suggestion for monitoring metapopulation persistence. Our approach allows for rapid and effective inference of metapopulation persistence from incomplete patch surveys.
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Affiliation(s)
- Chuliang Song
- Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Canada H3A 1B1
- Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, Canada M5S 3B2
| | - Marie-Josée Fortin
- Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, Canada M5S 3B2
| | - Andrew Gonzalez
- Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Canada H3A 1B1
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7
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Davies BFR, Holmes L, Bicknell A, Attrill MJ, Sheehan EV. A decade implementing ecosystem approach to fisheries management improves diversity of taxa and traits within a marine protected area in the UK. DIVERS DISTRIB 2021. [DOI: 10.1111/ddi.13451] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
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8
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Guzman LM, Chamberlain SA, Elle E. Network robustness and structure depend on the phenological characteristics of plants and pollinators. Ecol Evol 2021; 11:13321-13334. [PMID: 34646472 PMCID: PMC8495816 DOI: 10.1002/ece3.8055] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Revised: 07/07/2021] [Accepted: 08/12/2021] [Indexed: 01/07/2023] Open
Abstract
Many structural patterns have been found to be important for the stability and robustness of mutualistic plant-pollinator networks. These structural patterns are impacted by a suite of variables, including species traits, species abundances, their spatial configuration, and their phylogenetic history. Here, we consider a specific trait: phenology, or the timing of life history events. We expect that timing and duration of activity of pollinators, or of flowering in plants, could greatly affect the species' roles within networks in which they are embedded. Using plant-pollinator networks from 33 sites in southern British Columbia, Canada, we asked (a) how phenological species traits, specifically timing of first appearance in the network and duration of activity in a network, were related to species' roles within a network, and (b) how those traits affected network robustness to phenologically biased species loss. We found that long duration of activity increased connection within modules for both pollinators and plants and among modules for plants. We also found that date of first appearance was positively related to interaction strength asymmetry in plants but negatively related to pollinators. Networks were generally more robust to the loss of pollinators than plants, and robustness increased if the models allow new interactions to form when old ones are lost, constrained by overlapping phenology of plants and pollinators. Robustness declined with the loss of late-flowering plants, which tended to have higher interaction strength asymmetry. In addition, robustness declined with loss of early-flying or long-duration pollinators. These pollinators tended to be among-module connectors. Our results point to networks being limited by early-flying pollinators. If plants flower earlier due to climate change, plant fitness may decline as they will depend on early emerging pollinators, unless pollinators also emerge earlier.
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Affiliation(s)
- Laura Melissa Guzman
- Evolutionary and Behavioural Ecology Research GroupDepartment of Biological SciencesSimon Fraser UniversityBurnabyBritish ColumbiaCanada
| | - Scott A. Chamberlain
- Evolutionary and Behavioural Ecology Research GroupDepartment of Biological SciencesSimon Fraser UniversityBurnabyBritish ColumbiaCanada
| | - Elizabeth Elle
- Evolutionary and Behavioural Ecology Research GroupDepartment of Biological SciencesSimon Fraser UniversityBurnabyBritish ColumbiaCanada
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9
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Song C, Uricchio LH, Mordecai EA, Saavedra S. Understanding the emergence of contingent and deterministic exclusion in multispecies communities. Ecol Lett 2021; 24:2155-2168. [PMID: 34288350 DOI: 10.1111/ele.13846] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Revised: 04/21/2021] [Accepted: 06/23/2021] [Indexed: 12/11/2022]
Abstract
Competitive exclusion can be classified as deterministic or as historically contingent. While competitive exclusion is common in nature, it has remained unclear when multispecies communities formed by more than two species should be dominated by deterministic or contingent exclusion. Here, we take a fully parameterised model of an empirical competitive system between invasive annual and native perennial plant species to explain both the emergence and sources of competitive exclusion in multispecies communities. Using a structural approach to understand the range of parameters promoting deterministic and contingent exclusions, we then find heuristic theoretical support for the following three general conclusions. First, we find that the life-history of perennial species increases the probability of observing contingent exclusion by increasing their effective intrinsic growth rates. Second, we find that the probability of observing contingent exclusion increases with weaker intraspecific competition, and not with the level of hierarchical competition. Third, we find a shift from contingent exclusion to deterministic exclusion with increasing numbers of competing species. Our work provides a heuristic framework to increase our understanding about the predictability of species persistence within multispecies communities.
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Affiliation(s)
- Chuliang Song
- Department of Civil and Environmental Engineering, MIT, Cambridge, MA, USA.,Department of Biology, McGill University, Montreal, Canada.,Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, ON, Canada
| | - Lawrence H Uricchio
- Department of Integrative Biology, University of California, Berkeley, Berkeley, CA, USA
| | | | - Serguei Saavedra
- Department of Civil and Environmental Engineering, MIT, Cambridge, MA, USA
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10
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Gjini E, Madec S. The ratio of single to co-colonization is key to complexity in interacting systems with multiple strains. Ecol Evol 2021; 11:8456-8474. [PMID: 34257910 PMCID: PMC8258234 DOI: 10.1002/ece3.7259] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2020] [Revised: 12/16/2020] [Accepted: 01/12/2021] [Indexed: 11/06/2022] Open
Abstract
The high number and diversity of microbial strains circulating in host populations have motivated extensive research on the mechanisms that maintain biodiversity. However, much of this work focuses on strain-specific and cross-immunity interactions. Another less explored mode of pairwise interaction is via altered susceptibilities to co-colonization in hosts already colonized by one strain. Diversity in such interaction coefficients enables strains to create dynamically their niches for growth and persistence, and "engineer" their common environment. How such a network of interactions with others mediates collective coexistence remains puzzling analytically and computationally difficult to simulate. Furthermore, the gradients modulating stability-complexity regimes in such multi-player endemic systems remain poorly understood. In a recent study (Madec & Gjini, Bulletin of Mathematical Biology, 82), we obtained an analytic representation for N-type coexistence in an SIS epidemiological model with co-colonization. We mapped multi-strain dynamics to a replicator equation using timescale separation. Here, we examine what drives coexistence regimes in such co-colonization system. We find the ratio of single to co-colonization, µ, critically determines the type of equilibrium and number of coexisting strains, and encodes a trade-off between overall transmission intensity R 0 and mean interaction coefficient in strain space, k. Preserving a given coexistence regime, under fixed trait variation, requires balancing between higher mean competition in favorable environments, and higher cooperation in harsher environments, and is consistent with the stress gradient hypothesis. Multi-strain coexistence tends to steady-state attractors for small µ, whereas as µ increases, dynamics tend to more complex attractors. Following strain frequencies, evolutionary dynamics in the system also display contrasting patterns with µ, interpolating between multi-stable and fluctuating selection for cooperation and mean invasion fitness, in the two extremes. This co-colonization framework could be applied more generally, to study invariant principles in collective coexistence, and to quantify how critical shifts in community dynamics get potentiated by mean-field and environmental gradients.
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Affiliation(s)
- Erida Gjini
- Instituto Gulbenkian de CiênciaOeirasPortugal
- Center for Computational and Stochastic MathematicsInstituto Superior TécnicoUniversity of LisbonLisbonPortugal
| | - Sten Madec
- Institut Denis PoissonUniversity of ToursToursFrance
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11
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Zhao N, Saavedra S, Liu YY. Impact of colonization history on the composition of ecological systems. Phys Rev E 2021; 103:052403. [PMID: 34134331 PMCID: PMC8217719 DOI: 10.1103/physreve.103.052403] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Accepted: 04/21/2021] [Indexed: 11/07/2022]
Abstract
Observational studies of ecological systems have shown that different species compositions can arise from distinct species arrival orders during community assembly-also known as colonization history. The presence of multiple interior equilibria in the positive orthant of the state space of the population dynamics will naturally lead to history dependency of the final state. However, it is still unclear whether and under which conditions colonization history will dominate community composition in the absence of multiple interior equilibria. Here, by considering that only one species can invade at a time and there are no recurrent invasions, we show clear evidence that the colonization history can have a big impact on the composition of ecological systems even in the absence of multiple interior equilibria. In particular, we first derive two simple rules to determine whether the composition of a community will depend on its colonization history in the absence of multiple interior equilibria and recurrent invasions. Then we apply them to communities governed by generalized Lotka-Volterra (gLV) dynamics and propose a numerical scheme to measure the probability of colonization history dependence. Finally, we show, via numerical simulations, that for gLV dynamics with a single interior equilibrium, the probability that community composition is dominated by colonization history increases monotonically with community size, network connectivity, and the variation of intrinsic growth rates across species. These results reveal that in the absence of multiple interior equilibria and recurrent invasions, community composition is a probabilistic process mediated by ecological dynamics via the interspecific variation and the size of regional pools.
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Affiliation(s)
- Nannan Zhao
- Channing Division of Network Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, 02115, USA
- Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710129, China
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA
| | - Yang-Yu Liu
- Channing Division of Network Medicine, Brigham and Women’s Hospital and Harvard Medical School, Boston, MA, 02115, USA
- Center for Cancer Systems Biology, Dana Farber Cancer Institute, Boston, MA, 02115, USA
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12
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Song C, Saavedra S. Bridging parametric and nonparametric measures of species interactions unveils new insights of non‐equilibrium dynamics. OIKOS 2021. [DOI: 10.1111/oik.08060] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
Affiliation(s)
- Chuliang Song
- Dept of Biology, McGill Univ. Montreal Canada
- Dept of Ecology and Evolutionary Biology, Univ. of Toronto Toronto Canada
| | - Serguei Saavedra
- Dept of Civil and Environmental Engineering, MIT Cambridge MA USA
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13
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Medeiros LP, Song C, Saavedra S. Merging dynamical and structural indicators to measure resilience in multispecies systems. J Anim Ecol 2021; 90:2027-2040. [PMID: 33448053 DOI: 10.1111/1365-2656.13421] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2021] [Accepted: 12/09/2020] [Indexed: 11/30/2022]
Abstract
Resilience is broadly understood as the ability of an ecological system to resist and recover from perturbations acting on species abundances and on the system's structure. However, one of the main problems in assessing resilience is to understand the extent to which measures of recovery and resistance provide complementary information about a system. While recovery from abundance perturbations has a strong tradition under the analysis of dynamical stability, it is unclear whether this same formalism can be used to measure resistance to structural perturbations (e.g. perturbations to model parameters). Here, we provide a framework grounded on dynamical and structural stability in Lotka-Volterra systems to link recovery from small perturbations on species abundances (i.e. dynamical indicators) with resistance to parameter perturbations of any magnitude (i.e. structural indicators). We use theoretical and experimental multispecies systems to show that the faster the recovery from abundance perturbations, the higher the resistance to parameter perturbations. We first use theoretical systems to show that the return rate along the slowest direction after a small random abundance perturbation (what we call full recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before losing any species (what we call full resistance). We also show that the return rate along the second fastest direction after a small random abundance perturbation (what we call partial recovery) is negatively correlated with the largest random parameter perturbation that a system can withstand before at most one species survives (what we call partial resistance). Then, we use a dataset of experimental microbial systems to confirm our theoretical expectations and to demonstrate that full and partial components of resilience are complementary. Our findings reveal that we can obtain the same level of information about resilience by measuring either a dynamical (i.e. recovery) or a structural (i.e. resistance) indicator. Irrespective of the chosen indicator (dynamical or structural), our results show that we can obtain additional information by separating the indicator into its full and partial components. We believe these results can motivate new theoretical approaches and empirical analyses to increase our understanding about risk in ecological systems.
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Affiliation(s)
- Lucas P Medeiros
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Chuliang Song
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.,Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Quebec, Canada.,Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, Ontario, Canada
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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14
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Ho HC, Tylianakis JM, Pawar S. Behaviour moderates the impacts of food-web structure on species coexistence. Ecol Lett 2020; 24:298-309. [PMID: 33205909 DOI: 10.1111/ele.13643] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2020] [Revised: 10/06/2020] [Accepted: 10/07/2020] [Indexed: 11/29/2022]
Abstract
How species coexistence (mathematical 'feasibility') in food webs emerges from species' trophic interactions remains a long-standing open question. Here we investigate how structure (network topology and body-size structure) and behaviour (foraging strategy and spatial dimensionality of interactions) interactively affect feasibility in food webs. Metabolically-constrained modelling of food-web dynamics based on whole-organism consumption revealed that feasibility is promoted in systems dominated by large-eat-small foraging (consumers eating smaller resources) whenever (1) many top consumers are present, (2) grazing or sit-and-wait foraging strategies are common, and (3) species engage in two-dimensional interactions. Congruently, the first two conditions were associated with dominance of large-eat-small foraging in 74 well-resolved (primarily aquatic) real-world food webs. Our findings provide a new, mechanistic understanding of how behavioural properties can modulate the effects of structural properties on species coexistence in food webs, and suggest that 'being feasible' constrains the spectra of behavioural and structural properties seen in natural food webs.
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Affiliation(s)
- Hsi-Cheng Ho
- Department of Life Sciences, Imperial College London, Silwood Park Campus, Ascot, SL5 7PY, UK
| | - Jason M Tylianakis
- School of Biological Sciences, University of Canterbury, Private Bag 4800, Christchurch, New Zealand
| | - Samraat Pawar
- Department of Life Sciences, Imperial College London, Silwood Park Campus, Ascot, SL5 7PY, UK
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15
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AlAdwani M, Saavedra S. Ecological models: higher complexity in, higher feasibility out. J R Soc Interface 2020; 17:20200607. [PMID: 33202176 PMCID: PMC7729046 DOI: 10.1098/rsif.2020.0607] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 10/28/2020] [Indexed: 11/12/2022] Open
Abstract
Finding a compromise between tractability and realism has always been at the core of ecological modelling. The introduction of nonlinear functional responses in two-species models has reconciled part of this compromise. However, it remains unclear whether this compromise can be extended to multispecies models. Yet, answering this question is necessary in order to differentiate whether the explanatory power of a model comes from the general form of its polynomial or from a more realistic description of multispecies systems. Here, we study the probability of feasibility (the existence of at least one positive real equilibrium) in complex models by adding higher-order interactions and nonlinear functional responses to the linear Lotka-Volterra model. We characterize complexity by the number of free-equilibrium points generated by a model, which is a function of the polynomial degree and system's dimension. We show that the probability of generating a feasible system in a model is an increasing function of its complexity, regardless of the specific mechanism invoked. Furthermore, we find that the probability of feasibility in a model will exceed that of the linear Lotka-Volterra model when a minimum level of complexity is reached. Importantly, this minimum level is modulated by parameter restrictions, but can always be exceeded via increasing the polynomial degree or system's dimension. Our results reveal that conclusions regarding the relevance of mechanisms embedded in complex models must be evaluated in relation to the expected explanatory power of their polynomial forms.
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Affiliation(s)
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
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16
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Saavedra S, Medeiros LP, AlAdwani M. Structural forecasting of species persistence under changing environments. Ecol Lett 2020; 23:1511-1521. [PMID: 32776667 DOI: 10.1111/ele.13582] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Revised: 06/07/2020] [Accepted: 07/08/2020] [Indexed: 12/15/2022]
Abstract
The persistence of a species in a given place not only depends on its intrinsic capacity to consume and transform resources into offspring, but also on how changing environmental conditions affect its growth rate. However, the complexity of factors has typically taken us to choose between understanding and predicting the persistence of species. To tackle this limitation, we propose a probabilistic approach rooted on the statistical concepts of ensemble theory applied to statistical mechanics and on the mathematical concepts of structural stability applied to population dynamics models - what we call structural forecasting. We show how this new approach allows us to estimate a probability of persistence for single species in local communities; to understand and interpret this probability conditional on the information we have concerning a system; and to provide out-of-sample predictions of species persistence as good as the best experimental approaches without the need of extensive amounts of data.
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Affiliation(s)
- Serguei Saavedra
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Av, 02139, Cambridge, MA, USA
| | - Lucas P Medeiros
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Av, 02139, Cambridge, MA, USA
| | - Mohammad AlAdwani
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Av, 02139, Cambridge, MA, USA
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17
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Tabi A, Pennekamp F, Altermatt F, Alther R, Fronhofer EA, Horgan K, Mächler E, Pontarp M, Petchey OL, Saavedra S. Species multidimensional effects explain idiosyncratic responses of communities to environmental change. Nat Ecol Evol 2020; 4:1036-1043. [PMID: 32572220 DOI: 10.1038/s41559-020-1206-6] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2019] [Accepted: 04/15/2020] [Indexed: 01/30/2023]
Abstract
Environmental change can alter species' abundances within communities consistently; for example, increasing all abundances by the same percentage, or more idiosyncratically. Here, we show how comparing effects of temperature on species grown in isolation and when grown together helps our understanding of how ecological communities more generally respond to environmental change. In particular, we find that the shape of the feasibility domain (the parameter space of carrying capacities compatible with positive species' abundances) helps to explain the composition of experimental microbial communities under changing environmental conditions. First, we introduce a measure to quantify the asymmetry of a community's feasibility domain using the column vectors of the corresponding interaction matrix. These column vectors describe the effects each species has on all other species in the community (hereafter referred to as species' multidimensional effects). We show that as the asymmetry of the feasibility domain increases the relationship between species' abundance when grown together and when grown in isolation weakens. We then show that microbial communities experiencing different temperature environments exhibit patterns consistent with this theory. Specifically, communities at warmer temperatures show relatively more asymmetry; thus, the idiosyncrasy of responses is higher compared with that in communities at cooler temperatures. These results suggest that while species' interactions are typically defined at the pairwise level, multispecies dynamics can be better understood by focusing on the effects of these interactions at the community level.
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Affiliation(s)
- Andrea Tabi
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.
| | - Frank Pennekamp
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland
| | - Florian Altermatt
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.,Department of Aquatic Ecology, Eawag, Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
| | - Roman Alther
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.,Department of Aquatic Ecology, Eawag, Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
| | - Emanuel A Fronhofer
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.,Department of Aquatic Ecology, Eawag, Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland.,ISEM, Université de Montpellier, CNRS, IRD, EPHE, Montpellier, France
| | - Katherine Horgan
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland
| | - Elvira Mächler
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland.,Department of Aquatic Ecology, Eawag, Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland
| | - Mikael Pontarp
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland
| | - Owen L Petchey
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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18
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Duthie AB. Component response rate variation underlies the stability of highly complex finite systems. Sci Rep 2020; 10:8296. [PMID: 32427891 PMCID: PMC7237446 DOI: 10.1038/s41598-020-64401-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/13/2019] [Accepted: 04/15/2020] [Indexed: 11/08/2022] Open
Abstract
The stability of a complex system generally decreases with increasing system size and interconnectivity, a counterintuitive result of widespread importance across the physical, life, and social sciences. Despite recent interest in the relationship between system properties and stability, the effect of variation in response rate across system components remains unconsidered. Here I vary the component response rates (γ) of randomly generated complex systems. I use numerical simulations to show that when component response rates vary, the potential for system stability increases. These results are robust to common network structures, including small-world and scale-free networks, and cascade food webs. Variation in γ is especially important for stability in highly complex systems, in which the probability of stability would otherwise be negligible. At such extremes of simulated system complexity, the largest stable complex systems would be unstable if not for variation in γ. My results therefore reveal a previously unconsidered aspect of system stability that is likely to be pervasive across all realistic complex systems.
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Affiliation(s)
- A Bradley Duthie
- Biological and Environmental Sciences, University of Stirling, Stirling, FK9 4LA, UK.
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19
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Song C, Von Ahn S, Rohr RP, Saavedra S. Towards a Probabilistic Understanding About the Context-Dependency of Species Interactions. Trends Ecol Evol 2020; 35:384-396. [PMID: 32007296 DOI: 10.1016/j.tree.2019.12.011] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Revised: 12/11/2019] [Accepted: 12/20/2019] [Indexed: 01/10/2023]
Abstract
Observational and experimental studies have shown that an interaction class between two species (be it mutualistic, competitive, antagonistic, or neutral) may switch to a different class, depending on the biotic and abiotic factors within which species are observed. This complexity arising from the evidence of context-dependencies has underscored a difficulty in establishing a systematic analysis about the extent to which species interactions are expected to switch in nature and experiments. Here, we propose an overarching theoretical framework, by integrating probabilistic and structural approaches, to establish null expectations about switches of interaction classes across environmental contexts. This integration provides a systematic platform upon which it is possible to establish new hypotheses, clear predictions, and quantifiable expectations about the context-dependency of species interactions.
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Affiliation(s)
- Chuliang Song
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Av., Cambridge 02139, MA, USA
| | - Sarah Von Ahn
- Department of Mathematics, MIT, 77 Massachusetts Av., Cambridge 02139, MA, USA
| | - Rudolf P Rohr
- Department of Biology - Ecology and Evolution, University of Fribourg Chemin du Musée 10, Fribourg CH-1700, Switzerland
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Av., Cambridge 02139, MA, USA.
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20
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Gornish ES, Shaw J, Gillespie BM. Using strip seeding to test how restoration design affects randomness of community assembly. Restor Ecol 2019. [DOI: 10.1111/rec.12988] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Elise S. Gornish
- School of Natural Resources and the EnvironmentUniversity of Arizona, Tucson Tucson AZ 85721 U.S.A
| | - Julea Shaw
- Plant SciencesUniversity of California, Davis Davis CA 95616 U.S.A
| | - Breahna M. Gillespie
- Plant SciencesUniversity of California, Davis Davis CA 95616 U.S.A
- Department of BiologySan Diego State University San Diego CA 92182 U.S.A
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21
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Fischer SM, Huth A. An Approach to Study Species Persistence in Unconstrained Random Networks. Sci Rep 2019; 9:14110. [PMID: 31575980 PMCID: PMC6773691 DOI: 10.1038/s41598-019-50373-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/25/2019] [Accepted: 08/21/2019] [Indexed: 11/19/2022] Open
Abstract
The connection between structure and stability of ecological networks has been widely studied in the last fifty years. A challenge that scientists continue to face is that in-depth mathematical model analysis is often difficult, unless the considered systems are specifically constrained. This makes it challenging to generalize results. Therefore, methods are needed that relax the required restrictions. Here, we introduce a novel heuristic approach that provides persistence estimates for random systems without limiting the admissible parameter range and system behaviour. We apply our approach to study persistence of species in random generalized Lotka-Volterra systems and present simulation results, which confirm the accuracy of our predictions. Our results suggest that persistence is mainly driven by the linkage density, whereby additional links can both favour and hinder persistence. In particular, we observed "persistence bistability", a rarely studied feature of random networks, leading to a dependency of persistence on initial species densities. Networks with this property exhibit tipping points, in which species loss can lead to a cascade of extinctions. The methods developed in this paper may facilitate the study of more general models and thereby provide a step forward towards a unifying framework of network architecture and stability.
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Affiliation(s)
- Samuel M Fischer
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
| | - Andreas Huth
- UFZ - Helmholtz Centre for Environmental Research, Department of Ecological Modelling, Permoserstraße 15, 04318, Leipzig, Germany
- Institute of Environmental Systems Research, Osnabrück University, Barbarastraße 12, 49076, Osnabrück, Germany
- iDiv - German Centre for Integrative Biodiversity Research Halle-Jena-Leipzig, Deutscher Platz 5e, 04103, Leipzig, Germany
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22
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Boyé A, Thiébaut É, Grall J, Legendre P, Broudin C, Houbin C, Le Garrec V, Maguer M, Droual G, Gauthier O. Trait‐based approach to monitoring marine benthic data along 500 km of coastline. DIVERS DISTRIB 2019. [DOI: 10.1111/ddi.12987] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Aurélien Boyé
- CNRS IRD Ifremer LEMAR Univ Brest Plouzane France
- Département de Sciences Biologiques Université de Montréal Montréal QC Canada
| | - Éric Thiébaut
- Laboratoire Adaptation et Diversité en Milieu Marin UMR 7144 CNRS Station Biologique de Roscoff Sorbonne Université Roscoff Cedex France
| | - Jacques Grall
- CNRS IRD Ifremer LEMAR Univ Brest Plouzane France
- CNRS UMS 3113 Observatoire Marin Suivis Habitats Benthiques OSU‐IUEM Université de Brest Plouzané France
| | - Pierre Legendre
- Département de Sciences Biologiques Université de Montréal Montréal QC Canada
| | - Caroline Broudin
- CNRS Station Biologique de Roscoff FR 2424 Sorbonne Université Roscoff France
| | - Céline Houbin
- CNRS Station Biologique de Roscoff FR 2424 Sorbonne Université Roscoff France
| | - Vincent Le Garrec
- CNRS UMS 3113 Observatoire Marin Suivis Habitats Benthiques OSU‐IUEM Université de Brest Plouzané France
| | - Marion Maguer
- CNRS UMS 3113 Observatoire Marin Suivis Habitats Benthiques OSU‐IUEM Université de Brest Plouzané France
| | - Gabin Droual
- CNRS UMS 3113 Observatoire Marin Suivis Habitats Benthiques OSU‐IUEM Université de Brest Plouzané France
| | - Olivier Gauthier
- CNRS IRD Ifremer LEMAR Univ Brest Plouzane France
- CNRS UMS 3113 Observatoire Marin Suivis Habitats Benthiques OSU‐IUEM Université de Brest Plouzané France
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23
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AlAdwani M, Saavedra S. Is the addition of higher-order interactions in ecological models increasing the understanding of ecological dynamics? Math Biosci 2019; 315:108222. [PMID: 31260670 DOI: 10.1016/j.mbs.2019.108222] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2018] [Revised: 06/26/2019] [Accepted: 06/26/2019] [Indexed: 11/19/2022]
Abstract
Recent work has shown that higher-order terms in population dynamics models can increase the stability, promote the diversity, and better explain the dynamics of ecological systems. While it is known that these perceived benefits come from an increasing number of alternative solutions given by the nature of multivariate polynomials, this mathematical advantage has not been formally quantified. Here, we develop a general method to quantify the mathematical advantage of adding higher-order interactions in ecological models based on the number of free-equilibrium points that can emerge in a system (i.e., equilibria that can be feasible or unfeasible as a function of model parameters). We apply this method to calculate the number of free-equilibrium points in Lotka-Volterra dynamics. While it is known that Lotka-Volterra models without higher-order interactions only have one free-equilibrium point regardless of the number of parameters, we find that by adding higher-order terms this number increases exponentially with the dimension of the system. Hence, the number of free-equilibrium points can be used to compare more fairly between ecological models. Our results suggest that while adding higher-order interactions in ecological models may be good for prediction purposes, they cannot provide additional explanatory power of ecological dynamics if model parameters are not ecologically restricted.
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Affiliation(s)
- Mohammad AlAdwani
- Department of Civil and Environmental Engineering, MIT 77 Massachusetts Avenue, Cambridge 02139, MA, USA
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, MIT 77 Massachusetts Avenue, Cambridge 02139, MA, USA.
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24
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Song C, Rohr RP, Saavedra S. A guideline to study the feasibility domain of multi-trophic and changing ecological communities. J Theor Biol 2018; 450:30-36. [DOI: 10.1016/j.jtbi.2018.04.030] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2017] [Revised: 04/18/2018] [Accepted: 04/19/2018] [Indexed: 11/30/2022]
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