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Takashina N. Linking multi-level population dynamics: state, role, and population. PeerJ 2022; 10:e13315. [PMID: 35582614 PMCID: PMC9107789 DOI: 10.7717/peerj.13315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2022] [Accepted: 03/31/2022] [Indexed: 01/13/2023] Open
Abstract
The dynamics of an ecological community can be described at different focal scales of the species, such as individual states or the population level. More detailed descriptions of ecological dynamics offer more information, but produce more complex models that are difficult to analyze. Adequately controlling the model complexity and the availability of multiple descriptions of the concerned dynamics maximizes our understanding of ecological dynamics. One of the central goals of ecological studies is to develop links between multiple descriptions of an ecological community. In this article, starting from a nonlinear state-level description of an ecological community (generalized McKendrick-von Foerster model), role-level and population-level descriptions (Lotka-Volterra model) are derived in a consistent manner. The role-level description covers a wider range of situations than the population-level description. However, using the established connections, it is demonstrated that the population-level description can be used to predict the equilibrium status of the role-level description. This approach connects state-, role-, and population-level dynamics consistently, and offers a justification for the multiple choices of model description.
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Xu N, Delius GW, Zhang L, Thygesen UH, Andersen KH. Spatial drivers of instability in marine size-spectrum ecosystems. J Theor Biol 2021; 517:110631. [PMID: 33600827 DOI: 10.1016/j.jtbi.2021.110631] [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: 02/18/2020] [Revised: 02/04/2021] [Accepted: 02/05/2021] [Indexed: 11/17/2022]
Abstract
Size-spectrum models are a recent class of models describing the dynamics of a whole community based on a description of individual organisms. The models are motivated by marine ecosystems where they cover the size range from multicellular plankton to the largest fish. We propose to extend the size-spectrum model with spatial components. The spatial dynamics is governed by a random motion and a directed movement in the direction of increased fitness, which we call 'fitness-taxis'. We use the model to explore whether spatial irregularities of marine communities can occur due to the internal dynamics of predator-prey interactions and spatial movements. This corresponds to a pattern-formation analysis generalized to an entire ecosystem but is not limited to one prey and one predator population. The analyses take the form of Fourier analysis and numerical experiments. Results show that diffusion always stabilizes the equilibrium but fitness-taxis destabilizes it, leading to non-stationary spatially inhomogeneous population densities, which are travelling in size. However, there is a strong asymmetry between fitness-induced destabilizing effects and diffusion-induced stabilizing effects with the latter dominating over the former. These findings reveal that fitness taxis acts as a possible mechanism behind pattern formations in ecosystems with high diversity of organism sizes, which can drive the emergence of spatial heterogeneity even in a spatially homogeneous environment.
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Affiliation(s)
- Nuo Xu
- School of Mathematical Science, Yangzhou University, Yangzhou 225002 China
| | - Gustav W Delius
- Department of Mathematics, University of York, York YO10 5DD, UK
| | - Lai Zhang
- School of Mathematical Science, Yangzhou University, Yangzhou 225002 China.
| | - Uffe H Thygesen
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark; Center for Ocean Life, National Institute of Aquatic Resources, Technical University of Denmark, Denmark
| | - Ken H Andersen
- Center for Ocean Life, National Institute of Aquatic Resources, Technical University of Denmark, Denmark
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3
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Heneghan RF, Everett JD, Sykes P, Batten SD, Edwards M, Takahashi K, Suthers IM, Blanchard JL, Richardson AJ. A functional size-spectrum model of the global marine ecosystem that resolves zooplankton composition. Ecol Modell 2020. [DOI: 10.1016/j.ecolmodel.2020.109265] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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4
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Zakharova L, Meyer K, Seifan M. Trait-based modelling in ecology: A review of two decades of research. Ecol Modell 2019. [DOI: 10.1016/j.ecolmodel.2019.05.008] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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5
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Blanchard JL, Heneghan RF, Everett JD, Trebilco R, Richardson AJ. From Bacteria to Whales: Using Functional Size Spectra to Model Marine Ecosystems. Trends Ecol Evol 2017; 32:174-186. [DOI: 10.1016/j.tree.2016.12.003] [Citation(s) in RCA: 126] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2016] [Revised: 12/05/2016] [Accepted: 12/10/2016] [Indexed: 11/28/2022]
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6
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Nakazawa T. Individual interaction data are required in community ecology: a conceptual review of the predator–prey mass ratio and more. Ecol Res 2016. [DOI: 10.1007/s11284-016-1408-1] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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7
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Guiet J, Poggiale JC, Maury O. Modelling the community size-spectrum: recent developments and new directions. Ecol Modell 2016. [DOI: 10.1016/j.ecolmodel.2016.05.015] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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8
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The efficacy of fisheries closure in rebuilding depleted stocks: Lessons from size-spectrum modeling. Ecol Modell 2016. [DOI: 10.1016/j.ecolmodel.2016.04.001] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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Tsai C, Hsieh C, Nakazawa T. Predator–prey mass ratio revisited: does preference of relative prey body size depend on individual predator size? Funct Ecol 2016. [DOI: 10.1111/1365-2435.12680] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Cheng‐Han Tsai
- AIMS@JCU Australian Institute of Marine Science and College of Marine and Environmental Sciences DB17‐063 James Cook University Townsville Queensland 4811 Australia
| | - Chih‐hao Hsieh
- Institute of Oceanography and Institute of Ecology and Evolutionary Biology National Taiwan University No.1, Sec. 4, Roosevelt Road Taipei 106 Taiwan
| | - Takefumi Nakazawa
- Department of Life Sciences National Cheng Kung University No.1, University Road Tainan 701 Taiwan
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10
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Gravel D, Albouy C, Thuiller W. The meaning of functional trait composition of food webs for ecosystem functioning. Philos Trans R Soc Lond B Biol Sci 2016; 371:20150268. [PMID: 27114571 PMCID: PMC4843690 DOI: 10.1098/rstb.2015.0268] [Citation(s) in RCA: 83] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 02/28/2016] [Indexed: 11/12/2022] Open
Abstract
There is a growing interest in using trait-based approaches to characterize the functional structure of animal communities. Quantitative methods have been derived mostly for plant ecology, but it is now common to characterize the functional composition of various systems such as soils, coral reefs, pelagic food webs or terrestrial vertebrate communities. With the ever-increasing availability of distribution and trait data, a quantitative method to represent the different roles of animals in a community promise to find generalities that will facilitate cross-system comparisons. There is, however, currently no theory relating the functional composition of food webs to their dynamics and properties. The intuitive interpretation that more functional diversity leads to higher resource exploitation and better ecosystem functioning was brought from plant ecology and does not apply readily to food webs. Here we appraise whether there are interpretable metrics to describe the functional composition of food webs that could foster a better understanding of their structure and functioning. We first distinguish the various roles that traits have on food web topology, resource extraction (bottom-up effects), trophic regulation (top-down effects), and the ability to keep energy and materials within the community. We then discuss positive effects of functional trait diversity on food webs, such as niche construction and bottom-up effects. We follow with a discussion on the negative effects of functional diversity, such as enhanced competition (both exploitation and apparent) and top-down control. Our review reveals that most of our current understanding of the impact of functional trait diversity on food web properties and functioning comes from an over-simplistic representation of network structure with well-defined levels. We, therefore, conclude with propositions for new research avenues for both theoreticians and empiricists.
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Affiliation(s)
- Dominique Gravel
- Département de biologie, Université de Sherbrooke, 2500 Boulevard de l'Université, Sherbrooke, Quebec, Canada J1K 2R1 Québec Centre for Biodiversity Science, Institute of Terrestrial Ecosystems, ETH Zurich, Zurich, Switzerland
| | - Camille Albouy
- Landscape Ecology, Institute of Terrestrial Ecosystems, ETH Zurich, Zurich, Switzerland Swiss Federal Research Institute WSL, Birmensdorf 8903, Switzerland
| | - Wilfried Thuiller
- Laboratoire d'Écologie Alpine (LECA), Université de Grenoble Alpes, Grenoble 38000, France CNRS, Laboratoire d'écologie Alpine (LECA), Grenoble 38000, France
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11
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Brose U, Blanchard JL, Eklöf A, Galiana N, Hartvig M, R Hirt M, Kalinkat G, Nordström MC, O'Gorman EJ, Rall BC, Schneider FD, Thébault E, Jacob U. Predicting the consequences of species loss using size-structured biodiversity approaches. Biol Rev Camb Philos Soc 2016; 92:684-697. [PMID: 26756137 DOI: 10.1111/brv.12250] [Citation(s) in RCA: 78] [Impact Index Per Article: 8.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2014] [Revised: 12/03/2015] [Accepted: 12/14/2015] [Indexed: 11/28/2022]
Abstract
Understanding the consequences of species loss in complex ecological communities is one of the great challenges in current biodiversity research. For a long time, this topic has been addressed by traditional biodiversity experiments. Most of these approaches treat species as trait-free, taxonomic units characterizing communities only by species number without accounting for species traits. However, extinctions do not occur at random as there is a clear correlation between extinction risk and species traits. In this review, we assume that large species will be most threatened by extinction and use novel allometric and size-spectrum concepts that include body mass as a primary species trait at the levels of populations and individuals, respectively, to re-assess three classic debates on the relationships between biodiversity and (i) food-web structural complexity, (ii) community dynamic stability, and (iii) ecosystem functioning. Contrasting current expectations, size-structured approaches suggest that the loss of large species, that typically exploit most resource species, may lead to future food webs that are less interwoven and more structured by chains of interactions and compartments. The disruption of natural body-mass distributions maintaining food-web stability may trigger avalanches of secondary extinctions and strong trophic cascades with expected knock-on effects on the functionality of the ecosystems. Therefore, we argue that it is crucial to take into account body size as a species trait when analysing the consequences of biodiversity loss for natural ecosystems. Applying size-structured approaches provides an integrative ecological concept that enables a better understanding of each species' unique role across communities and the causes and consequences of biodiversity loss.
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Affiliation(s)
- Ulrich Brose
- German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, 04103, Leipzig, Germany.,Faculty of Biology and Pharmacy, Institute of Ecology, Friedrich Schiller University Jena, 07743, Jena, Germany
| | - Julia L Blanchard
- Institute for Marine and Antarctic Studies and Centre for Marine Socioecology, University of Tasmania, 20 Castray Esplanade, Battery Point TAS 7004, Australia
| | - Anna Eklöf
- Theoretical Biology, Department of Physics, Chemistry and Biology, Linköping University, SE-581 83, Linköping, Sweden
| | - Nuria Galiana
- Ecological Networks and Global Change Group, Experimental Ecology Station, Centre National de la Recherche Scientifique, 09200, Moulis, France
| | - Martin Hartvig
- Center for Macroecology, Evolution and Climate, Natural History Museum of Denmark, University of Copenhagen, DK-2100, Copenhagen, Denmark.,National Institute of Aquatic Resources, Technical University of Denmark, DK-2920, Charlottenlund, Denmark.,Systemic Conservation Biology Group, J.F. Blumenbach Institute of Zoology and Anthropology, Georg-August University of Göttingen, 37073, Göttingen, Germany
| | - Myriam R Hirt
- German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, 04103, Leipzig, Germany.,Faculty of Biology and Pharmacy, Institute of Ecology, Friedrich Schiller University Jena, 07743, Jena, Germany
| | - Gregor Kalinkat
- Department of Biology and Ecology of Fishes, Leibniz-Institute of Freshwater Ecology and Inland Fisheries, 12587, Berlin, Germany.,Department of Fish Ecology and Evolution, Eawag, 6047, Kastanienbaum, Switzerland
| | - Marie C Nordström
- Environmental and Marine Biology, Åbo Akademi University, FI-20520, Åbo, Finland
| | - Eoin J O'Gorman
- Imperial College London, Silwood Park Campus, Buckhurst Road, Ascot, Berkshire, SL5 7PY, UK
| | - Björn C Rall
- German Centre for Integrative Biodiversity Research (iDiv) Halle-Jena-Leipzig, 04103, Leipzig, Germany.,Faculty of Biology and Pharmacy, Institute of Ecology, Friedrich Schiller University Jena, 07743, Jena, Germany
| | - Florian D Schneider
- Institut des Sciences de l'Evolution, Université Montpellier, CNRS, IRD, EPHE, CC065, 34095, Montpellier Cedex 05, France
| | - Elisa Thébault
- Institute of Ecology and Environmental Sciences - Paris, UMR 7618 (UPMC, CNRS, IRD, INRA, UPEC, Paris Diderot), Université Pierre et Marie Curie, 75005, Paris, France
| | - Ute Jacob
- Department of Biology, Institute for Hydrobiology and Fisheries Science, Center for Earth System Research and Sustainability (CEN), KlimaCampus, University of Hamburg, 22767, Hamburg, Germany
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12
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Zhang L, Pedersen M, Lin Z. Stability patterns for a size-structured population model and its stage-structured counterpart. Math Biosci 2015; 267:109-23. [PMID: 26187293 DOI: 10.1016/j.mbs.2015.06.014] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2014] [Revised: 04/17/2015] [Accepted: 06/08/2015] [Indexed: 11/27/2022]
Abstract
In this paper we compare a general size-structured population model, where a size-structured consumer feeds upon an unstructured resource, to its simplified stage-structured counterpart in terms of equilibrium stability. Stability of the size-structured model is understood in terms of an equivalent delayed system consisting of a renewal equation for the consumer population birth rate and a delayed differential equation for the resource. Results show that the size- and stage-structured models differ considerably with respect to equilibrium stability, although the two models have completely identical equilibrium solutions. First, when adult consumers are superior foragers to juveniles, the size-structured model is more stable than the stage-structured model while the opposite occurs when juveniles are the superior foragers. Second, relatively large juvenile (adult) mortality tends to stabilise (destabilise) the size-structured model but destabilise (stabilise) the stage-structured model. Third, the stability pattern is sensitive to the adult-offspring size ratio in the size-structured model but much less sensitive in the stage-structured model. Finally, unless the adult-offspring size ratio is sufficiently small, the stage-structured model cannot satisfactorily capture the dynamics of the size-structured model. We conclude that caution must be taken when the stage-structured population model is applied, although it can consistently translate individual life history and stage-specific differences to the population level.
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Affiliation(s)
- Lai Zhang
- Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187 Umeå, Sweden.
| | - Michael Pedersen
- Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800, Denmark
| | - Zhigui Lin
- School of Mathematical Science, Yangzhou University, Yangzhou 225002, China
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13
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14
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Zhang L, Thygesen UH, Banerjee M. Size-dependent diffusion promotes the emergence of spatiotemporal patterns. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:012904. [PMID: 25122357 DOI: 10.1103/physreve.90.012904] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/09/2013] [Indexed: 06/03/2023]
Abstract
Spatiotemporal patterns, indicating the spatiotemporal variability of individual abundance, are a pronounced scenario in ecological interactions. Most of the existing models for spatiotemporal patterns treat species as homogeneous groups of individuals with average characteristics by ignoring intraspecific physiological variations at the individual level. Here we explore the impacts of size variation within species resulting from individual ontogeny, on the emergence of spatiotemporal patterns in a fully size-structured population model. We found that size dependency of animal's diffusivity greatly promotes the formation of spatiotemporal patterns, by creating regular spatiotemporal patterns out of temporal chaos. We also found that size-dependent diffusion can substitute large-amplitude base harmonics with spatiotemporal patterns with lower amplitude oscillations but with enriched harmonics. Finally, we found that the single-generation cycle is more likely to drive spatiotemporal patterns compared to predator-prey cycles, meaning that the mechanism of Hopf bifurcation might be more common than hitherto appreciated since the former cycle is more widespread than the latter in case of interacting populations. Due to the ubiquity of individual ontogeny in natural ecosystems we conclude that diffusion variability within populations is a significant driving force for the emergence of spatiotemporal patterns. Our results offer a perspective on self-organized phenomena, and pave a way to understand such phenomena in systems organized as complex ecological networks.
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Affiliation(s)
- Lai Zhang
- Department of Mathematics and Mathematical Statistics, Umeå University, SE-90187, Umeå, Sweden
| | - Uffe Høgsbro Thygesen
- National Institute of Aquatic Resources, Technical University of Denmark, Charlottenlund Slot, Jægerborg Allé 1, DK-2910 Charlottenlund, Denmark
| | - Malay Banerjee
- Department of Mathematics and Statistics, Indian Institute of Technology, Kanpur, Kanpur-208016, India
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15
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Jacobsen NS, Gislason H, Andersen KH. The consequences of balanced harvesting of fish communities. Proc Biol Sci 2013; 281:20132701. [PMID: 24307676 DOI: 10.1098/rspb.2013.2701] [Citation(s) in RCA: 92] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Balanced harvesting, where species or individuals are exploited in accordance with their productivity, has been proposed as a way to minimize the effects of fishing on marine fish communities and ecosystems. This calls for a thorough examination of the consequences balanced harvesting has on fish community structure and yield. We use a size- and trait-based model that resolves individual interactions through competition and predation to compare balanced harvesting with traditional selective harvesting, which protects juvenile fish from fishing. Four different exploitation patterns, generated by combining selective or unselective harvesting with balanced or unbalanced fishing, are compared. We find that unselective balanced fishing, where individuals are exploited in proportion to their productivity, produces a slightly larger total maximum sustainable yield than the other exploitation patterns and, for a given yield, the least change in the relative biomass composition of the fish community. Because fishing reduces competition, predation and cannibalism within the community, the total maximum sustainable yield is achieved at high exploitation rates. The yield from unselective balanced fishing is dominated by small individuals, whereas selective fishing produces a much higher proportion of large individuals in the yield. Although unselective balanced fishing is predicted to produce the highest total maximum sustainable yield and the lowest impact on trophic structure, it is effectively a fishery predominantly targeting small forage fish.
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Affiliation(s)
- Nis S Jacobsen
- Centre for Ocean Life, DTU AQUA, , Charlottenlund Castle, 2920 Charlottenlund, Denmark
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16
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Hartvig M, Andersen KH. Coexistence of structured populations with size-based prey selection. Theor Popul Biol 2013; 89:24-33. [DOI: 10.1016/j.tpb.2013.07.003] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2013] [Revised: 06/26/2013] [Accepted: 07/13/2013] [Indexed: 10/26/2022]
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17
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Poisot T, Péquin B, Gravel D. High-throughput sequencing: a roadmap toward community ecology. Ecol Evol 2013; 3:1125-39. [PMID: 23610649 PMCID: PMC3631419 DOI: 10.1002/ece3.508] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2012] [Revised: 01/22/2013] [Accepted: 01/23/2013] [Indexed: 11/11/2022] Open
Abstract
High-throughput sequencing is becoming increasingly important in microbial ecology, yet it is surprisingly under-used to generate or test biogeographic hypotheses. In this contribution, we highlight how adding these methods to the ecologist toolbox will allow the detection of new patterns, and will help our understanding of the structure and dynamics of diversity. Starting with a review of ecological questions that can be addressed, we move on to the technical and analytical issues that will benefit from an increased collaboration between different disciplines.
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Affiliation(s)
- Timothée Poisot
- Département de biologie, chimie et géographie, Université du Québec à Rimouski300 Allée des Ursulines, Rimouski, QC, G5L 3A1, Canada
- Québec Centre for Biodiversity Sciences, Stewart Biological Sciences Building1205 Dr. Penfield Avenue, Montréal, QC, H3A 1B1, Canada
| | - Bérangère Péquin
- Département de Biologie, Université LavalQuébec, QC, G1V 0A6, Canada
- Québec-OcéanQuébec, QC, G1V 0A6, Canada
- Institut de Biologie Intégrative et des (IBIS) SystèmesQuébec, QC, G1V 0A6, Canada
| | - Dominique Gravel
- Département de biologie, chimie et géographie, Université du Québec à Rimouski300 Allée des Ursulines, Rimouski, QC, G5L 3A1, Canada
- Québec Centre for Biodiversity Sciences, Stewart Biological Sciences Building1205 Dr. Penfield Avenue, Montréal, QC, H3A 1B1, Canada
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