1
|
Lampo A, Palazzi MJ, Borge-Holthoefer J, Solé-Ribalta A. Structural dynamics of plant-pollinator mutualistic networks. PNAS NEXUS 2024; 3:pgae209. [PMID: 38881844 PMCID: PMC11177885 DOI: 10.1093/pnasnexus/pgae209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 05/21/2024] [Indexed: 06/18/2024]
Abstract
The discourse surrounding the structural organization of mutualistic interactions mostly revolves around modularity and nestedness. The former is known to enhance the stability of communities, while the latter is related to their feasibility, albeit compromising the stability. However, it has recently been shown that the joint emergence of these structures poses challenges that can eventually lead to limitations in the dynamic properties of mutualistic communities. We hypothesize that considering compound arrangements-modules with internal nested organization-can offer valuable insights in this debate. We analyze the temporal structural dynamics of 20 plant-pollinator interaction networks and observe large structural variability throughout the year. Compound structures are particularly prevalent during the peak of the pollination season, often coexisting with nested and modular arrangements in varying degrees. Motivated by these empirical findings, we synthetically investigate the dynamics of the structural patterns across two control parameters-community size and connectance levels-mimicking the progression of the pollination season. Our analysis reveals contrasting impacts on the stability and feasibility of these mutualistic communities. We characterize the consistent relationship between network structure and stability, which follows a monotonic pattern. But, in terms of feasibility, we observe nonlinear relationships. Compound structures exhibit a favorable balance between stability and feasibility, particularly in mid-sized ecological communities, suggesting they may effectively navigate the simultaneous requirements of stability and feasibility. These findings may indicate that the assembly process of mutualistic communities is driven by a delicate balance among multiple properties, rather than the dominance of a single one.
Collapse
Affiliation(s)
- Aniello Lampo
- Grupo Interdisciplinar de Sistemas Complejos (GISC), Departamento de Matemáticas, Universidad Carlos III de Madrid, Av. Universidad, 30 (edificio Sabatini), 28911 Leganés (Madrid), Spain
| | - María J Palazzi
- Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya, Rambla del Poblenou, 154 08018, Barcelona, Catalonia, Spain
| | - Javier Borge-Holthoefer
- Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya, Rambla del Poblenou, 154 08018, Barcelona, Catalonia, Spain
| | - Albert Solé-Ribalta
- Internet Interdisciplinary Institute (IN3), Universitat Oberta de Catalunya, Rambla del Poblenou, 154 08018, Barcelona, Catalonia, Spain
| |
Collapse
|
2
|
Parmentier T, Bonte D, De Laender F. A successional shift enhances stability in ant symbiont communities. Commun Biol 2024; 7:645. [PMID: 38802499 PMCID: PMC11130137 DOI: 10.1038/s42003-024-06305-3] [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: 02/09/2024] [Accepted: 05/08/2024] [Indexed: 05/29/2024] Open
Abstract
Throughout succession, communities undergo structural shifts, which can alter the relative abundances of species and how they interact. It is frequently asserted that these alterations beget stability, i.e. that succession selects for communities better able to resist perturbations. Yet, whether and how alterations of network structure affect stability during succession in complex communities is rarely studied in natural ecosystems. Here, we explore how network attributes influence stability of different successional stages of a natural network: symbiotic arthropod communities forming food webs inside red wood ant nests. We determined the abundance of 16 functional groups within the symbiont community across 51 host nests in the beginning and end stages of succession. Nest age was the main driver of the compositional shifts: symbiont communities in old nests contained more even species abundance distributions and a greater proportion of specialists. Based on the abundance data, we reconstructed interaction matrices and food webs of the symbiont community for each nest. We showed that the enhanced community evenness in old nests leads to an augmented food web stability in all but the largest symbiont communities. Overall, this study demonstrates that succession begets stability in a natural ecological network by making the community more even.
Collapse
Affiliation(s)
- Thomas Parmentier
- Terrestrial Ecology Unit, Department of Biology, University of Ghent, Ghent, Belgium.
- Research Unit of Environmental and Evolutionary Biology, naXys, ILEE, University of Namur, Namur, Belgium.
| | - Dries Bonte
- Terrestrial Ecology Unit, Department of Biology, University of Ghent, Ghent, Belgium
| | - Frederik De Laender
- Research Unit of Environmental and Evolutionary Biology, naXys, ILEE, University of Namur, Namur, Belgium
| |
Collapse
|
3
|
Almaraz P, Kalita P, Langa JA, Soler-Toscano F. Structural stability of invasion graphs for Lotka-Volterra systems. J Math Biol 2024; 88:64. [PMID: 38630280 PMCID: PMC11023985 DOI: 10.1007/s00285-024-02087-8] [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: 10/04/2022] [Revised: 03/11/2024] [Accepted: 03/19/2024] [Indexed: 04/19/2024]
Abstract
In this paper, we study in detail the structure of the global attractor for the Lotka-Volterra system with a Volterra-Lyapunov stable structural matrix. We consider the invasion graph as recently introduced in Hofbauer and Schreiber (J Math Biol 85:54, 2022) and prove that its edges represent all the heteroclinic connections between the equilibria of the system. We also study the stability of this structure with respect to the perturbation of the problem parameters. This allows us to introduce a definition of structural stability in ecology in coherence with the classical mathematical concept where there exists a detailed geometrical structure, robust under perturbation, that governs the transient and asymptotic dynamics.
Collapse
Affiliation(s)
- Pablo Almaraz
- Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Campus Reina Mercedes, 41012, Sevilla, Spain
- Grupo de Oceanografía de Ecosistemas, Instituto de Ciencias Marinas de Andalucía (ICMAN-CSIC), Campus Universitario de Puerto Real, Puerto Real, 11519, Spain
| | - Piotr Kalita
- Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Campus Reina Mercedes, 41012, Sevilla, Spain.
- Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348, Kraków, Poland.
| | - José A Langa
- Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, Campus Reina Mercedes, 41012, Sevilla, Spain
| | - Fernando Soler-Toscano
- Departamento de Filosofía, Lógica y Filosofía de la Ciencia, Universidad de Sevilla, C/ Camillo José Cela, s/n, 41018, Sevilla, Spain
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
Miller ZR, Clenet M, Della Libera K, Massol F, Allesina S. Coexistence of many species under a random competition-colonization trade-off. Proc Natl Acad Sci U S A 2024; 121:e2314215121. [PMID: 38261621 PMCID: PMC10835059 DOI: 10.1073/pnas.2314215121] [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: 08/17/2023] [Accepted: 12/14/2023] [Indexed: 01/25/2024] Open
Abstract
The competition-colonization (CC) trade-off is a well-studied coexistence mechanism for metacommunities. In this setting, it is believed that the coexistence of all species requires their traits to satisfy restrictive conditions limiting their similarity. To investigate whether diverse metacommunities can assemble in a CC trade-off model, we study their assembly from a probabilistic perspective. From a pool of species with parameters (corresponding to traits) sampled at random, we compute the probability that any number of species coexist and characterize the set of species that emerges through assembly. Remarkably, almost exactly half of the species in a large pool typically coexist, with no saturation as the size of the pool grows, and with little dependence on the underlying distribution of traits. Through a mix of analytical results and simulations, we show that this unlimited niche packing emerges as assembly actively moves communities toward overdispersed configurations in niche space. Our findings also apply to a realistic assembly scenario where species invade one at a time from a fixed regional pool. When diversity arises de novo in the metacommunity, richness still grows without bound, but more slowly. Together, our results suggest that the CC trade-off can support the robust emergence of diverse communities, even when coexistence of the full species pool is exceedingly unlikely.
Collapse
Affiliation(s)
- Zachary R. Miller
- Department of Ecology & Evolution, University of Chicago, Chicago, IL60637
- Department of Plant Biology, University of Illinois, Urbana, IL, 61801
| | - Maxime Clenet
- Laboratoire d’Informatique Gaspard-Monge, UMR 8049, CNRS, Université Gustave Eiffel, Marne-la-Vallée77454, France
| | - Katja Della Libera
- Department of Ecology & Evolution, University of Chicago, Chicago, IL60637
| | - François Massol
- Université Lille, CNRS, INSERM, CHU Lille, Institut Pasteur de Lille, U1019–UMR 9017–Center for Infection and Immunity of Lille, LilleF-59000, France
| | - Stefano Allesina
- Department of Ecology & Evolution, University of Chicago, Chicago, IL60637
| |
Collapse
|
6
|
Deng J, Taylor W, Levin SA, Saavedra S. On the limits to invasion prediction using coexistence outcomes. J Theor Biol 2024; 577:111674. [PMID: 38008157 DOI: 10.1016/j.jtbi.2023.111674] [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: 04/20/2023] [Revised: 11/01/2023] [Accepted: 11/14/2023] [Indexed: 11/28/2023]
Abstract
The dynamics of ecological communities in nature are typically characterized by probabilistic processes involving invasion dynamics. Because of technical challenges, however, the majority of theoretical and experimental studies have focused on coexistence dynamics. Therefore, it has become central to understand the extent to which coexistence outcomes can be used to predict analogous invasion outcomes relevant to systems in nature. Here, we study the limits to this predictability under a geometric and probabilistic Lotka-Volterra framework. We show that while individual survival probability in coexistence dynamics can be fairly closely translated into invader colonization probability in invasion dynamics, the translation is less precise between community persistence and community augmentation, and worse between exclusion probability and replacement probability. These results provide a guiding and testable theoretical framework regarding the translatability of outcomes between coexistence and invasion outcomes when communities are represented by Lotka-Volterra dynamics under environmental uncertainty.
Collapse
Affiliation(s)
- Jie Deng
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA.
| | - Washington Taylor
- Center for Theoretical Physics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
| | - Simon A Levin
- Department of Ecology & Evolutionary Biology, Princeton University, Princeton, NJ 08544, USA; High Meadows Environmental Institute, Princeton University, Princeton, NJ 08544, USA
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA; Santa Fe Institute, 1399 Hyde Park Rd, Santa Fe, NM 87501, USA
| |
Collapse
|
7
|
Fagan B, Pitchford JW, Stepney S, Thomas CD. Increased dispersal explains increasing local diversity with global biodiversity declines. GLOBAL CHANGE BIOLOGY 2023; 29:6713-6726. [PMID: 37819684 DOI: 10.1111/gcb.16948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/16/2023] [Revised: 08/11/2023] [Accepted: 08/28/2023] [Indexed: 10/13/2023]
Abstract
The narrative of biodiversity decline in response to human impacts is overly simplistic because different aspects of biodiversity show different trajectories at different spatial scales. It is also debated whether human-caused biodiversity changes lead to subsequent, accelerating change (cascades) in ecological communities, or alternatively build increasingly robust community networks with decreasing extinction rates and reduced invasibility. Mechanistic approaches are needed that simultaneously reconcile different aspects of biodiversity change, and explore the robustness of communities to further change. We develop a trophically structured, mainland-archipelago metacommunity model of community assembly. Varying the parameters across model simulations shows that local alpha diversity (the number of species per island) and regional gamma diversity (the total number of species in the archipelago) depend on both the rate of extirpation per island and on the rate of dispersal between islands within the archipelago. In particular, local diversity increases with increased dispersal and heterogeneity between islands, but regional diversity declines because the islands become biotically similar and local one-island and few-island species are excluded (homogenisation, or reduced beta diversity). This mirrors changes observed empirically: real islands have gained species (increased local and island-scale community diversity) with increased human-assisted transfers of species, but global diversity has declined with the loss of endemic species. However, biological invasions may be self-limiting. High-dispersal, high local-diversity model communities become resistant to subsequent invasions, generating robust species-community networks unless dispersal is extremely high. A mixed-up world is likely to lose many species, but the resulting ecological communities may nonetheless be relatively robust.
Collapse
Affiliation(s)
- Brennen Fagan
- Leverhulme Centre for Anthropocene Biodiversity, University of York, York, UK
- Department of Mathematics, University of York, York, UK
| | - Jon W Pitchford
- Department of Mathematics, University of York, York, UK
- Department of Biology, University of York, York, UK
| | - Susan Stepney
- Department of Computer Science, University of York, York, UK
| | - Chris D Thomas
- Leverhulme Centre for Anthropocene Biodiversity, University of York, York, UK
- Department of Biology, University of York, York, UK
| |
Collapse
|
8
|
Arya S, George AB, O’Dwyer JP. Sparsity of higher-order landscape interactions enables learning and prediction for microbiomes. Proc Natl Acad Sci U S A 2023; 120:e2307313120. [PMID: 37991947 PMCID: PMC10691334 DOI: 10.1073/pnas.2307313120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/16/2023] [Indexed: 11/24/2023] Open
Abstract
Microbiome engineering offers the potential to leverage microbial communities to improve outcomes in human health, agriculture, and climate. To translate this potential into reality, it is crucial to reliably predict community composition and function. But a brute force approach to cataloging community function is hindered by the combinatorial explosion in the number of ways we can combine microbial species. An alternative is to parameterize microbial community outcomes using simplified, mechanistic models, and then extrapolate these models beyond where we have sampled. But these approaches remain data-hungry, as well as requiring an a priori specification of what kinds of mechanisms are included and which are omitted. Here, we resolve both issues by introducing a mechanism-agnostic approach to predicting microbial community compositions and functions using limited data. The critical step is the identification of a sparse representation of the community landscape. We then leverage this sparsity to predict community compositions and functions, drawing from techniques in compressive sensing. We validate this approach on in silico community data, generated from a theoretical model. By sampling just [Formula: see text]1% of all possible communities, we accurately predict community compositions out of sample. We then demonstrate the real-world application of our approach by applying it to four experimental datasets and showing that we can recover interpretable, accurate predictions on composition and community function from highly limited data.
Collapse
Affiliation(s)
- Shreya Arya
- Department of Physics, University of Illinois, Urbana-Champaign, Urbana, IL61801
| | - Ashish B. George
- Center for Artificial Intelligence and Modeling, Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Broad Institute of Massachusetts Institute of Technology and Harvard, Cambridge, MA0214
- Department of Plant Biology, University of Illinois, Urbana-Champaign, Urbana, IL61801
| | - James P. O’Dwyer
- Center for Artificial Intelligence and Modeling, Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Department of Plant Biology, University of Illinois, Urbana-Champaign, Urbana, IL61801
| |
Collapse
|
9
|
Cosme M, Thomas C, Gaucherel C. On the History of Ecosystem Dynamical Modeling: The Rise and Promises of Qualitative Models. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1526. [PMID: 37998218 PMCID: PMC10670156 DOI: 10.3390/e25111526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Revised: 10/25/2023] [Accepted: 10/25/2023] [Indexed: 11/25/2023]
Abstract
Ecosystem modeling is a complex and multidisciplinary modeling problem which emerged in the 1950s. It takes advantage of the computational turn in sciences to better understand anthropogenic impacts and improve ecosystem management. For that purpose, ecosystem simulation models based on difference or differential equations were built. These models were relevant for studying dynamical phenomena and still are. However, they face important limitations in data-poor situations. As a response, several formal and non-formal qualitative dynamical modeling approaches were independently developed to overcome some limitations of the existing methods. Qualitative approaches allow studying qualitative dynamics as relevant abstractions of those provided by quantitative models (e.g., response to press perturbations). Each modeling framework can be viewed as a different assemblage of properties (e.g., determinism, stochasticity or synchronous update of variable values) designed to satisfy some scientific objectives. Based on four stated objectives commonly found in complex environmental sciences ((1) grasping qualitative dynamics, (2) making as few assumptions as possible about parameter values, (3) being explanatory and (4) being predictive), our objectives were guided by the wish to model complex and multidisciplinary issues commonly found in ecosystem modeling. We then discussed the relevance of existing modeling approaches and proposed the ecological discrete-event networks (EDEN) modeling framework for this purpose. The EDEN models propose a qualitative, discrete-event, partially synchronous and possibilistic view of ecosystem dynamics. We discussed each of these properties through ecological examples and existing analysis techniques for such models and showed how relevant they are for environmental science studies.
Collapse
Affiliation(s)
- Maximilien Cosme
- UMR AMAP, INRAE, University of Montpellier (Faculté des Sciences), IRD, CIRAD, CNRS, 34398 Montpellier, France
- UMR DECOD, Institut Agro Rennes-Angers (Campus Rennes), 65 rue de Saint-Brieuc, 35042 Rennes, France
| | - Colin Thomas
- IBISC, University of Evry, 91025 Evry, France (C.G.)
| | | |
Collapse
|
10
|
Spaak JW, Schreiber SJ. Building modern coexistence theory from the ground up: The role of community assembly. Ecol Lett 2023; 26:1840-1861. [PMID: 37747362 DOI: 10.1111/ele.14302] [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: 01/23/2023] [Revised: 08/06/2023] [Accepted: 08/12/2023] [Indexed: 09/26/2023]
Abstract
Modern coexistence theory (MCT) is one of the leading methods to understand species coexistence. It uses invasion growth rates-the average, per-capita growth rate of a rare species-to identify when and why species coexist. Despite significant advances in dissecting coexistence mechanisms when coexistence occurs, MCT relies on a 'mutual invasibility' condition designed for two-species communities but poorly defined for species-rich communities. Here, we review well-known issues with this component of MCT and propose a solution based on recent mathematical advances. We propose a clear framework for expanding MCT to species-rich communities and for understanding invasion resistance as well as coexistence, especially for communities that could not be analysed with MCT so far. Using two data-driven community models from the literature, we illustrate the utility of our framework and highlight the opportunities for bridging the fields of community assembly and species coexistence.
Collapse
Affiliation(s)
- Jurg W Spaak
- Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, New York, USA
- Institute for Environmental Sciences, Rheinland-Pfälzische Technische Univerität Kaiserslautern-Landau, Landau, Germany
| | - Sebastian J Schreiber
- Department of Evolution and Ecology and Center for Population Biology, University of California, Davis, California, USA
| |
Collapse
|
11
|
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.
Collapse
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
| |
Collapse
|
12
|
Permanence via invasion graphs: incorporating community assembly into modern coexistence theory. J Math Biol 2022; 85:54. [PMID: 36255477 PMCID: PMC9579112 DOI: 10.1007/s00285-022-01815-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Revised: 07/30/2022] [Accepted: 09/06/2022] [Indexed: 11/18/2022]
Abstract
To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$$-i$$\end{document}-i communities, i.e., communities without species i where all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence.
Collapse
|
13
|
The geometry of evolved community matrix spectra. Sci Rep 2022; 12:14668. [PMID: 36038623 PMCID: PMC9530164 DOI: 10.1038/s41598-022-17379-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Accepted: 07/25/2022] [Indexed: 11/18/2022] Open
Abstract
Random matrix theory has been applied to food web stability for decades, implying elliptical eigenvalue spectra and that large food webs should be unstable. Here we allow feasible food webs to self-assemble within an evolutionary process, using simple Lotka–Volterra equations and several elementary interaction types. We show that, as complex food webs evolve under \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsbsy}
\usepackage{mathrsfs}
\usepackage{upgreek}
\setlength{\oddsidemargin}{-69pt}
\begin{document}$${10^5}$$\end{document}105 invasion attempts, the community matrix spectra become bi-modal, rather than falling onto elliptical geometries. Our results raise questions as to the applicability of random matrix theory to the analysis of food web steady states.
Collapse
|
14
|
Thomas C, Cosme M, Gaucherel C, Pommereau F. Model-checking ecological state-transition graphs. PLoS Comput Biol 2022; 18:e1009657. [PMID: 35666771 PMCID: PMC9203009 DOI: 10.1371/journal.pcbi.1009657] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2021] [Revised: 06/16/2022] [Accepted: 05/08/2022] [Indexed: 11/18/2022] Open
Abstract
Model-checking is a methodology developed in computer science to automatically assess the dynamics of discrete systems, by checking if a system modelled as a state-transition graph satisfies a dynamical property written as a temporal logic formula. The dynamics of ecosystems have been drawn as state-transition graphs for more than a century, ranging from state-and-transition models to assembly graphs. Model-checking can provide insights into both empirical data and theoretical models, as long as they sum up into state-transition graphs. While model-checking proved to be a valuable tool in systems biology, it remains largely underused in ecology apart from precursory applications. This article proposes to address this situation, through an inventory of existing ecological STGs and an accessible presentation of the model-checking methodology. This overview is illustrated by the application of model-checking to assess the dynamics of a vegetation pathways model. We select management scenarios by model-checking Computation Tree Logic formulas representing management goals and built from a proposed catalogue of patterns. In discussion, we sketch bridges between existing studies in ecology and available model-checking frameworks. In addition to the automated analysis of ecological state-transition graphs, we believe that defining ecological concepts with temporal logics could help clarify and compare them.
Collapse
Affiliation(s)
- Colin Thomas
- IBISC, Univ. Évry, Univ. Paris-Saclay, 91020 Évry-Courcouronne, France
- AMAP, Univ. Montpellier, INRAE, CIRAD, CNRS, IRD, Montpellier, France
| | - Maximilien Cosme
- AMAP, Univ. Montpellier, INRAE, CIRAD, CNRS, IRD, Montpellier, France
| | - Cédric Gaucherel
- AMAP, Univ. Montpellier, INRAE, CIRAD, CNRS, IRD, Montpellier, France
| | - Franck Pommereau
- IBISC, Univ. Évry, Univ. Paris-Saclay, 91020 Évry-Courcouronne, France
| |
Collapse
|
15
|
Song C, Fukami T, Saavedra S. Untangling the complexity of priority effects in multispecies communities. Ecol Lett 2021; 24:2301-2313. [PMID: 34472694 DOI: 10.1111/ele.13870] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2021] [Revised: 05/23/2021] [Accepted: 08/09/2021] [Indexed: 11/28/2022]
Abstract
The history of species immigration can dictate how species interact in local communities, thereby causing historical contingency in community assembly. Since immigration history is rarely known, these historical influences, or priority effects, pose a major challenge in predicting community assembly. Here, we provide a graph-based, non-parametric, theoretical framework for understanding the predictability of community assembly as affected by priority effects. To develop this framework, we first show that the diversity of possible priority effects increases super-exponentially with the number of species. We then point out that, despite this diversity, the consequences of priority effects for multispecies communities can be classified into four basic types, each of which reduces community predictability: alternative stable states, alternative transient paths, compositional cycles and the lack of escapes from compositional cycles to stable states. Using a neural network, we show that this classification of priority effects enables accurate explanation of community predictability, particularly when each species immigrates repeatedly. We also demonstrate the empirical utility of our theoretical framework by applying it to two experimentally derived assembly graphs of algal and ciliate communities. Based on these analyses, we discuss how the framework proposed here can help guide experimental investigation of the predictability of history-dependent community assembly.
Collapse
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
| | - Tadashi Fukami
- Department of Biology, Stanford University, Stanford, CA, USA
| | - Serguei Saavedra
- Department of Civil and Environmental Engineering, MIT, Cambridge, MA, USA
| |
Collapse
|
16
|
Coexistence holes characterize the assembly and disassembly of multispecies systems. Nat Ecol Evol 2021; 5:1091-1101. [PMID: 34045718 DOI: 10.1038/s41559-021-01462-8] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 04/07/2021] [Indexed: 11/08/2022]
Abstract
A central goal of ecological research has been to understand the limits on the maximum number of species that can coexist under given constraints. However, we know little about the assembly and disassembly processes under which a community can reach such a maximum number, or whether this number is in fact attainable in practice. This limitation is partly due to the challenge of performing experimental work and partly due to the lack of a formalism under which one can systematically study such processes. Here, we introduce a formalism based on algebraic topology and homology theory to study the space of species coexistence formed by a given pool of species. We show that this space is characterized by ubiquitous discontinuities that we call coexistence holes (that is, empty spaces surrounded by filled space). Using theoretical and experimental systems, we provide direct evidence showing that these coexistence holes do not occur arbitrarily-their diversity is constrained by the internal structure of species interactions and their frequency can be explained by the external factors acting on these systems. Our work suggests that the assembly and disassembly of ecological systems is a discontinuous process that tends to obey regularities.
Collapse
|
17
|
Estrela S, Sanchez-Gorostiaga A, Vila JCC, Sanchez A. Nutrient dominance governs the assembly of microbial communities in mixed nutrient environments. eLife 2021; 10:e65948. [PMID: 33877964 PMCID: PMC8057819 DOI: 10.7554/elife.65948] [Citation(s) in RCA: 38] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Accepted: 04/02/2021] [Indexed: 12/12/2022] Open
Abstract
A major open question in microbial community ecology is whether we can predict how the components of a diet collectively determine the taxonomic composition of microbial communities. Motivated by this challenge, we investigate whether communities assembled in pairs of nutrients can be predicted from those assembled in every single nutrient alone. We find that although the null, naturally additive model generally predicts well the family-level community composition, there exist systematic deviations from the additive predictions that reflect generic patterns of nutrient dominance at the family level. Pairs of more-similar nutrients (e.g. two sugars) are on average more additive than pairs of more dissimilar nutrients (one sugar-one organic acid). Furthermore, sugar-acid communities are generally more similar to the sugar than the acid community, which may be explained by family-level asymmetries in nutrient benefits. Overall, our results suggest that regularities in how nutrients interact may help predict community responses to dietary changes.
Collapse
Affiliation(s)
- Sylvie Estrela
- Department of Ecology & Evolutionary Biology and Microbial Sciences Institute, Yale UniversityNew HavenUnited States
| | - Alicia Sanchez-Gorostiaga
- Department of Ecology & Evolutionary Biology and Microbial Sciences Institute, Yale UniversityNew HavenUnited States
- Department of Microbial Biotechnology, Centro Nacional de Biotecnología, CSIC, CantoblancoMadridSpain
| | - Jean CC Vila
- Department of Ecology & Evolutionary Biology and Microbial Sciences Institute, Yale UniversityNew HavenUnited States
| | - Alvaro Sanchez
- Department of Ecology & Evolutionary Biology and Microbial Sciences Institute, Yale UniversityNew HavenUnited States
| |
Collapse
|
18
|
Estrela S, Sánchez Á, Rebolleda-Gómez M. Multi-Replicated Enrichment Communities as a Model System in Microbial Ecology. Front Microbiol 2021; 12:657467. [PMID: 33897672 PMCID: PMC8062719 DOI: 10.3389/fmicb.2021.657467] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Accepted: 03/15/2021] [Indexed: 12/21/2022] Open
Abstract
Recent advances in robotics and affordable genomic sequencing technologies have made it possible to establish and quantitatively track the assembly of enrichment communities in high-throughput. By conducting community assembly experiments in up to thousands of synthetic habitats, where the extrinsic sources of variation among replicates can be controlled, we can now study the reproducibility and predictability of microbial community assembly at different levels of organization, and its relationship with nutrient composition and other ecological drivers. Through a dialog with mathematical models, high-throughput enrichment communities are bringing us closer to the goal of developing a quantitative predictive theory of microbial community assembly. In this short review, we present an overview of recent research on this growing field, highlighting the connection between theory and experiments and suggesting directions for future work.
Collapse
Affiliation(s)
- Sylvie Estrela
- Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT, United States
| | - Álvaro Sánchez
- Department of Ecology and Evolutionary Biology, Yale University, New Haven, CT, United States
| | | |
Collapse
|