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Bieg C, Gellner G, McCann KS. Stability of consumer-resource interactions in periodic environments. Proc Biol Sci 2023; 290:20231636. [PMID: 37752846 PMCID: PMC10523078 DOI: 10.1098/rspb.2023.1636] [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: 07/21/2023] [Accepted: 08/31/2023] [Indexed: 09/28/2023] Open
Abstract
Periodic fluctuations in abiotic conditions are ubiquitous across a range of temporal scales and regulate the structure and function of ecosystems through dynamic biotic responses that are adapted to these external forces. Research has suggested that certain environmental signatures may play a crucial role in the maintenance of biodiversity and the stability of food webs, while others argue that coupled oscillators ought to promote chaos. As such, numerous uncertainties remain regarding the intersection of temporal environmental patterns and biological responses, and we lack a general understanding of the implications for food web stability. Alarmingly, global change is altering the nature of both environmental rhythms and biological rates. Here, we develop a general theory for how continuous periodic variation in productivity, across temporal scales, influences the stability of consumer-resource interactions: a fundamental building block of food webs. Our results suggest that consumer-resource dynamics under environmental forcing are highly complex and depend on asymmetries in both the speed of forcing relative to underlying dynamics and in local stability properties. These asymmetries allow for environmentally driven stabilization under fast forcing, relative to underlying dynamics, as well as extremely complex and unstable dynamics at slower periodicities. Our results also suggest that changes in naturally occurring periodicities from climate change may lead to precipitous shifts in dynamics and stability.
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Affiliation(s)
- Carling Bieg
- Department of Integrative Biology, University of Guelph, Guelph, Ontario, Canada N1G 2W1
- Ecology and Evolutionary Biology, Yale University, New Haven, CT, USA
| | - Gabriel Gellner
- Department of Integrative Biology, University of Guelph, Guelph, Ontario, Canada N1G 2W1
| | - Kevin S. McCann
- Department of Integrative Biology, University of Guelph, Guelph, Ontario, Canada N1G 2W1
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2
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Cant J, Reimer JD, Sommer B, Cook KM, Kim SW, Sims CA, Mezaki T, O'Flaherty C, Brooks M, Malcolm HA, Pandolfi JM, Salguero‐Gómez R, Beger M. Coral assemblages at higher latitudes favor short-term potential over long-term performance. Ecology 2023; 104:e4138. [PMID: 37458125 PMCID: PMC10909567 DOI: 10.1002/ecy.4138] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 11/10/2022] [Revised: 06/02/2023] [Accepted: 06/14/2023] [Indexed: 07/18/2023]
Abstract
The persistent exposure of coral assemblages to more variable abiotic regimes is assumed to augment their resilience to future climatic variability. Yet, while the determinants of coral population resilience across species remain unknown, we are unable to predict the winners and losers across reef ecosystems exposed to increasingly variable conditions. Using annual surveys of 3171 coral individuals across Australia and Japan (2016-2019), we explore spatial variation across the short- and long-term dynamics of competitive, stress-tolerant, and weedy assemblages to evaluate how abiotic variability mediates the structural composition of coral assemblages. We illustrate how, by promoting short-term potential over long-term performance, coral assemblages can reduce their vulnerability to stochastic environments. However, compared to stress-tolerant, and weedy assemblages, competitive coral taxa display a reduced capacity for elevating their short-term potential. Accordingly, future climatic shifts threaten the structural complexity of coral assemblages in variable environments, emulating the degradation expected across global tropical reefs.
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Affiliation(s)
- James Cant
- Centre for Biological DiversityUniversity of St AndrewsSt AndrewsUK
- School of Biology, Faculty of Biological SciencesUniversity of LeedsLeedsUK
| | - James D. Reimer
- Molecular Invertebrate Systematics and Ecology LaboratoryGraduate School of Engineering and Science, University of the RyukyusNishiharaJapan
- Tropical Biosphere Research CentreUniversity of the RyukyusNishiharaJapan
| | - Brigitte Sommer
- School of Life and Environmental ScienceThe University of SydneyCamperdownNew South WalesAustralia
- School of Life SciencesUniversity of Technology SydneyUltimoNew South WalesAustralia
| | - Katie M. Cook
- School of Biology, Faculty of Biological SciencesUniversity of LeedsLeedsUK
- National Institute of Water and Atmospheric ResearchHamiltonNew Zealand
| | - Sun W. Kim
- Australian Research Council Centre of Excellence for Coral Reef Studies, School of Biological SciencesThe University of QueenslandBrisbaneQueenslandAustralia
| | - Carrie A. Sims
- Smithsonian Tropical Research InstitutePanama CityRepublic of Panama
| | - Takuma Mezaki
- Kuroshio Biological Research Foundation, Nishidomari, Otsuki‐choKochiJapan
| | | | - Maxime Brooks
- School of Biology, Faculty of Biological SciencesUniversity of LeedsLeedsUK
| | - Hamish A. Malcolm
- Fisheries Research, Department of Primary IndustriesCoffs HarbourNew South WalesAustralia
| | - John M. Pandolfi
- Australian Research Council Centre of Excellence for Coral Reef Studies, School of Biological SciencesThe University of QueenslandBrisbaneQueenslandAustralia
| | - Roberto Salguero‐Gómez
- Department of ZoologyUniversity of OxfordOxfordUK
- Centre for Biodiversity and Conservation Science, School of Biological SciencesUniversity of QueenslandBrisbaneQueenslandAustralia
- Max Planck Institute for Demographic ResearchRostockGermany
| | - Maria Beger
- School of Biology, Faculty of Biological SciencesUniversity of LeedsLeedsUK
- Centre for Biodiversity and Conservation Science, School of Biological SciencesUniversity of QueenslandBrisbaneQueenslandAustralia
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3
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Gross K, de Roos AM. Resonance in Physiologically Structured Population Models. Bull Math Biol 2021; 83:86. [PMID: 34155575 DOI: 10.1007/s11538-021-00915-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Accepted: 05/27/2021] [Indexed: 12/01/2022]
Abstract
Ecologists have long sought to understand how the dynamics of natural populations are affected by the environmental variation those populations experience. A transfer function is a useful tool for this purpose, as it uses linearization theory to show how the frequency spectrum of the fluctuations in a population's abundance relates to the frequency spectrum of environmental variation. Here, we show how to derive and to compute the transfer function for a continuous-time model of a population that is structured by a continuous individual-level state variable such as size. To illustrate, we derive, compute, and analyze the transfer function for a size-structured population model of stony corals with open recruitment, parameterized for a common Indo-Pacific coral species complex. This analysis identifies a sharp multi-decade resonance driven by space competition between existing coral colonies and incoming recruits. The resonant frequency is most strongly determined by the rate at which colonies grow, and the potential for resonant oscillations is greatest when colony growth is only weakly density-dependent. While these resonant oscillations are unlikely to be a predominant dynamical feature of degraded reefs, they suggest dynamical possibilities for marine invertebrates in more pristine waters. The size-structured model that we analyze is a leading example of a broader class of physiologically structured population models, and the methods we present should apply to a wide variety of models in this class.
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Affiliation(s)
- Kevin Gross
- Department of Statistics, North Carolina State University, Raleigh, NC, 27695, USA.
| | - André M de Roos
- Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Amsterdam, The Netherlands.,Santa Fe Institute, Santa Fe, NM, 87501, USA
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4
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Bernhardt JR, O'Connor MI, Sunday JM, Gonzalez A. Life in fluctuating environments. Philos Trans R Soc Lond B Biol Sci 2020; 375:20190454. [PMID: 33131443 PMCID: PMC7662201 DOI: 10.1098/rstb.2019.0454] [Citation(s) in RCA: 60] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
Variability in the environment defines the structure and dynamics of all living systems, from organisms to ecosystems. Species have evolved traits and strategies that allow them to detect, exploit and predict the changing environment. These traits allow organisms to maintain steady internal conditions required for physiological functioning through feedback mechanisms that allow internal conditions to remain at or near a set-point despite a fluctuating environment. In addition to feedback, many organisms have evolved feedforward processes, which allow them to adjust in anticipation of an expected future state of the environment. Here we provide a framework describing how feedback and feedforward mechanisms operating within organisms can generate effects across scales of organization, and how they allow living systems to persist in fluctuating environments. Daily, seasonal and multi-year cycles provide cues that organisms use to anticipate changes in physiologically relevant environmental conditions. Using feedforward mechanisms, organisms can exploit correlations in environmental variables to prepare for anticipated future changes. Strategies to obtain, store and act on information about the conditional nature of future events are advantageous and are evidenced in widespread phenotypes such as circadian clocks, social behaviour, diapause and migrations. Humans are altering the ways in which the environment fluctuates, causing correlations between environmental variables to become decoupled, decreasing the reliability of cues. Human-induced environmental change is also altering sensory environments and the ability of organisms to detect cues. Recognizing that living systems combine feedback and feedforward processes is essential to understanding their responses to current and future regimes of environmental fluctuations. This article is part of the theme issue ‘Integrative research perspectives on marine conservation’.
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Affiliation(s)
- Joey R Bernhardt
- Department of Aquatic Ecology, Eawag: Swiss Federal Institute of Aquatic Science and Technology, Überlandstrasse 133, 8600 Dübendorf, Switzerland.,Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Canada H3A 1B1
| | - Mary I O'Connor
- Department of Zoology and Biodiversity Research Centre, University of British Columbia, 6270 University Boulevard, Vancouver, Canada V6T 1Z4
| | - Jennifer M Sunday
- Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Canada H3A 1B1
| | - Andrew Gonzalez
- Department of Biology, Quebec Centre for Biodiversity Science, McGill University, Montreal, Canada H3A 1B1
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5
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Frequency content of environmental variability and extinction risk of age-structured populations: Chinook salmon (Oncorhynchus tschawytscha) as an example. THEOR ECOL-NETH 2018. [DOI: 10.1007/s12080-018-0401-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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6
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Schmidt AE, Botsford LW, Patrick Kilduff D, Bradley RW, Jahncke J, Eadie JM. Changing environmental spectra influence age-structured populations: increasing ENSO frequency could diminish variance and extinction risk in long-lived seabirds. THEOR ECOL-NETH 2018. [DOI: 10.1007/s12080-018-0372-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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7
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Eager EA, Pilson D, Alexander HM, Tenhumberg B. Assessing the Influence of Temporal Autocorrelations on the Population Dynamics of a Disturbance Specialist Plant Population in a Random Environment. Am Nat 2017; 190:570-583. [DOI: 10.1086/692911] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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8
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Guiver C, Mueller M, Hodgson D, Townley S. Robust set-point regulation for ecological models with multiple management goals. J Math Biol 2016; 72:1467-529. [PMID: 26242360 PMCID: PMC4823387 DOI: 10.1007/s00285-015-0919-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2014] [Revised: 07/02/2015] [Indexed: 11/26/2022]
Abstract
Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering, such set-point regulation problems are commonly tackled using multi-input, multi-output proportional and integral (PI) feedback controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multi-objective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, both described in the paper, and illustrate the theory with examples. Our results apply more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.
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Affiliation(s)
- Chris Guiver
- />Environment and Sustainability Institute, College of Engineering Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Penryn, Cornwall TR10 9FE UK
| | - Markus Mueller
- />Environment and Sustainability Institute, College of Engineering Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Penryn, Cornwall TR10 9FE UK
| | - Dave Hodgson
- />Centre for Ecology and Conservation, College of Life and Environmental Sciences, University of Exeter, Penryn Campus, Penryn, Cornwall TR10 9FE UK
| | - Stuart Townley
- />Environment and Sustainability Institute, College of Engineering Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Penryn, Cornwall TR10 9FE UK
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9
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Warren M, Mcgeoch MA, Chown SL. The detection of spatial structure in populations and communities: An empirical case study. ECOSCIENCE 2015. [DOI: 10.2980/16-1-3185] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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10
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11
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Wilson White J, Botsford LW, Hastings A, Holland MD. Stochastic models reveal conditions for cyclic dominance in sockeye salmon populations. ECOL MONOGR 2014. [DOI: 10.1890/12-1796.1] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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12
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Ezard THG, Prizak R, Hoyle RB. The fitness costs of adaptation via phenotypic plasticity and maternal effects. Funct Ecol 2014. [DOI: 10.1111/1365-2435.12207] [Citation(s) in RCA: 66] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Thomas H. G. Ezard
- Department of Mathematics Faculty of Engineering and Physical Sciences University of Surrey Guildford SurreyGU2 7XHUK
- Centre for Biological Sciences University of Southampton Life Sciences Building 85 Highfield Campus Southampton SO17 1BJUK
| | - Roshan Prizak
- Department of Mathematics Faculty of Engineering and Physical Sciences University of Surrey Guildford SurreyGU2 7XHUK
- Department of Electrical Engineering Indian Institute of Technology Bombay Powai Mumbai400076India
- Institute of Science and Technology Austria Am Campus 1 Klosterneuburg A‐3400Austria
| | - Rebecca B. Hoyle
- Department of Mathematics Faculty of Engineering and Physical Sciences University of Surrey Guildford SurreyGU2 7XHUK
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13
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Ruokolainen L, McCann K. Environmental weakening of trophic interactions drives stability in stochastic food webs. J Theor Biol 2013; 339:36-46. [DOI: 10.1016/j.jtbi.2013.08.021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2012] [Revised: 07/05/2013] [Accepted: 08/21/2013] [Indexed: 10/26/2022]
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14
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Mustin K, Dytham C, Benton TG, Travis JMJ. Red noise increases extinction risk during rapid climate change. DIVERS DISTRIB 2013. [DOI: 10.1111/ddi.12038] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
Affiliation(s)
| | - Calvin Dytham
- Department of Biology; University of York; York; YO10 5DD; UK
| | - Tim G. Benton
- Institute of Integrative and Comparative Biology; University of Leeds; Leeds; LS2 9JT; UK
| | - Justin M. J. Travis
- Institute of Biological and Environmental Sciences; University of Aberdeen; Zoology Building, Tillydrone Avenue; Aberdeen; AB24 2TZ; UK
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15
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Mischaracterising density dependence biases estimated effects of coloured covariates on population dynamics. POPUL ECOL 2012. [DOI: 10.1007/s10144-012-0347-0] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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16
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Ruokolainen L, Ripa J. The strength of species interactions modifies population responses to environmental variation in competitive communities. J Theor Biol 2012; 310:199-205. [PMID: 22781554 DOI: 10.1016/j.jtbi.2012.06.035] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2012] [Revised: 06/26/2012] [Accepted: 06/27/2012] [Indexed: 11/17/2022]
Abstract
The life-history parameters of most living organisms are modified by fluctuations in environmental conditions. The impact of environmental autocorrelation on population persistence is well understood in single species systems. However, in multi-species communities the impact of stochasticity is complicated by the possibility of different species having differing intrinsic responses to the environment (environmental correlation). Previous work has shown that whether increasing between-species environmental correlation stabilises population fluctuations or not, depends on an interaction between density-dependence and environmental autocorrelation. Here we derive analytical conditions for how this interaction in turn depends on the strength of interspecific competition. Under relatively weak between-species interactions, increasing environmental autocorrelation always dampens population fluctuations, while increasing autocorrelation destabilises strongly interacting populations. In contrast, under intermediate interaction strengths, increasing autocorrelation destabilises (stabilises) population dynamics when populations respond independently (similarly) to environmental fluctuations. These results apply to a wide range of competitive communities and also have some relevance to consumer-resource systems. The results presented here help us better understand population responses to environmental fluctuations under different conditions.
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Affiliation(s)
- Lasse Ruokolainen
- Department of Biosciences, University of Helsinki, Viikinkaari 1, P. O. Box 65, FI-00014 Helsingin yliopisto, Finland.
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17
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Hoyle RB, Ezard THG. The benefits of maternal effects in novel and in stable environments. J R Soc Interface 2012; 9:2403-13. [PMID: 22572028 DOI: 10.1098/rsif.2012.0183] [Citation(s) in RCA: 53] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Natural selection favours phenotypes that match prevailing ecological conditions. A rapid process of adaptation is therefore required in changing environments. Maternal effects can facilitate such responses, but it is currently poorly understood under which circumstances maternal effects may accelerate or slow down the rate of phenotypic evolution. Here, we use a quantitative genetic model, including phenotypic plasticity and maternal effects, to suggest that the relationship between fitness and phenotypic variance plays an important role. Intuitive expectations that positive maternal effects are beneficial are supported following an extreme environmental shift, but, if too strong, that shift can also generate oscillatory dynamics that overshoot the optimal phenotype. In a stable environment, negative maternal effects that slow phenotypic evolution actually minimize variance around the optimum phenotype and thus maximize population mean fitness.
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Affiliation(s)
- Rebecca B Hoyle
- Department of Mathematics, University of Surrey, Guildford, Surrey GU2 7XH, UK
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18
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Wikström A, Ripa J, Jonzén N. The role of harvesting in age-structured populations: disentangling dynamic and age truncation effects. Theor Popul Biol 2012; 82:348-54. [PMID: 22227065 DOI: 10.1016/j.tpb.2011.12.008] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2011] [Revised: 12/12/2011] [Accepted: 12/19/2011] [Indexed: 11/16/2022]
Abstract
Understanding the processes generating fluctuations of natural populations lies at the very heart of academic ecology. It is also very important for applications such as fisheries management and pest control. We are interested in the effect of harvesting on population fluctuations and for that purpose we develop and analyze an age-structured model where recruitment is a stochastic process and the adult segment of the population is harvested. When a constant annual harvest is taken the coefficient of variation of the adult population increases for most parameter values due to the age truncation effect, i.e. an increased variability in a juvenescent population due to the removal of older individuals. However, if a constant proportion of the adults is harvested the age truncation effect is sometimes counteracted by a stabilizing dynamic effect of harvesting. Depending on parameter values mirroring different life histories, proportional harvest can either increase or decrease the relative fluctuations of an exploited population. When there is a demographic Allee effect the ratio of juveniles to adults may actually decrease with harvesting. We conclude that, depending on life history and harvest strategy, harvesting can either reinforce or dampen population fluctuations due to the relative importance of stabilizing dynamic effects and the age truncation effect. The strength of the latter is highly dependent on the fished population's endogenous, age-structured dynamics. More specifically, we predict that populations with strong and positively autocorrelated dynamics will show stronger age truncation effect, a testable prediction that offers a simple rule-of-thumb assessment of a population's vulnerability to exploitation.
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Affiliation(s)
- Anders Wikström
- Department of Biology (Theoretical Population Ecology and Evolution Group), Ecology Building, Lund University, SE-223 62 Lund, Sweden.
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19
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Greenman J, Pasour V. Phase control of resonant systems: Interference, chaos and high periodicity. J Theor Biol 2011; 278:74-86. [DOI: 10.1016/j.jtbi.2011.03.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2010] [Revised: 03/02/2011] [Accepted: 03/03/2011] [Indexed: 10/18/2022]
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20
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García-Carreras B, Reuman DC. An empirical link between the spectral colour of climate and the spectral colour of field populations in the context of climate change. J Anim Ecol 2011; 80:1042-8. [PMID: 21466552 DOI: 10.1111/j.1365-2656.2011.01833.x] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
1. The spectral colour of population dynamics and its causes have attracted much interest. The spectral colour of a time series can be determined from its power spectrum, which shows what proportion of the total variance in the time series occurs at each frequency. A time series with a red spectrum (a negative spectral exponent) is dominated by low-frequency oscillations, and a time series with a blue spectrum (a positive spectral exponent) is dominated by high-frequency oscillations. 2. Both climate variables and population time series are characterised by red spectra, suggesting that a population's environment might be partly responsible for its spectral colour. Laboratory experiments and models have been used to investigate this potential link. However, no study using field data has directly tested whether populations in redder environments are redder. 3. This study uses the Global Population Dynamics Database together with climate data to test for this effect. We found that the spectral exponent of mean summer temperatures correlates positively and significantly with population spectral exponent. 4. We also found that over the last century, temperature climate variables on most continents have become bluer. 5. Although population time series are not long or abundant enough to judge directly whether their spectral colours are changing, our two results taken together suggest that population spectral colour may be affected by the changing spectral colour of climate variables. Population spectral colour has been linked to extinction; we discuss the potential implications of our results for extinction probability.
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21
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Ernebjerg M, Kishony R. Dynamic phenotypic clustering in noisy ecosystems. PLoS Comput Biol 2011; 7:e1002017. [PMID: 21445229 PMCID: PMC3060162 DOI: 10.1371/journal.pcbi.1002017] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2010] [Accepted: 01/29/2011] [Indexed: 11/18/2022] Open
Abstract
In natural ecosystems, hundreds of species typically share the same environment and are connected by a dense network of interactions such as predation or competition for resources. Much is known about how fixed ecological niches can determine species abundances in such systems, but far less attention has been paid to patterns of abundances in randomly varying environments. Here, we study this question in a simple model of competition between many species in a patchy ecosystem with randomly fluctuating environmental conditions. Paradoxically, we find that introducing noise can actually induce ordered patterns of abundance-fluctuations, leading to a distinct periodic variation in the correlations between species as a function of the phenotypic distance between them; here, difference in growth rate. This is further accompanied by the formation of discrete, dynamic clusters of abundant species along this otherwise continuous phenotypic axis. These ordered patterns depend on the collective behavior of many species; they disappear when only individual or pairs of species are considered in isolation. We show that they arise from a balance between the tendency of shared environmental noise to synchronize species abundances and the tendency for competition among species to make them fluctuate out of step. Our results demonstrate that in highly interconnected ecosystems, noise can act as an ordering force, dynamically generating ecological patterns even in environments lacking explicit niches.
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Affiliation(s)
- Morten Ernebjerg
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America
| | - Roy Kishony
- Department of Systems Biology, Harvard Medical School, Boston, Massachusetts, United States of America
- School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts, United States of America
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22
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Worden L, Botsford LW, Hastings A, Holland MD. Frequency responses of age-structured populations: Pacific salmon as an example. Theor Popul Biol 2010; 78:239-49. [DOI: 10.1016/j.tpb.2010.07.004] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2009] [Revised: 07/16/2010] [Accepted: 07/27/2010] [Indexed: 10/19/2022]
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23
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Jonsson T, Karlsson P, Jonsson A. Trophic interactions affect the population dynamics and risk of extinction of basal species in food webs. ECOLOGICAL COMPLEXITY 2010. [DOI: 10.1016/j.ecocom.2009.05.013] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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24
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Ezard TH, Coulson T. How sensitive are elasticities of long-run stochastic growth to how environmental variability is modelled? Ecol Modell 2010. [DOI: 10.1016/j.ecolmodel.2009.09.017] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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25
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Downing AL, Brown BL, Perrin EM, Keitt TH, Leibold MA. ENVIRONMENTAL FLUCTUATIONS INDUCE SCALE‐DEPENDENT COMPENSATION AND INCREASE STABILITY IN PLANKTON ECOSYSTEMS. Ecology 2008; 89:3204-3214. [DOI: 10.1890/07-1652.1] [Citation(s) in RCA: 54] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/11/2007] [Revised: 02/01/2008] [Accepted: 03/13/2008] [Indexed: 11/18/2022]
Affiliation(s)
- Amy L. Downing
- Department of Zoology, Ohio Wesleyan University, Delaware, Ohio 43015 USA
| | - Bryan L. Brown
- Department of Forestry and Natural Resources, Clemson University, Clemson, South Carolina 29634 USA
| | | | - Timothy H. Keitt
- Section of Integrative Biology, University of Texas, 1 University Station C0930, Austin, Texas 78712 USA
| | - Mathew A. Leibold
- Section of Integrative Biology, University of Texas, 1 University Station C0930, Austin, Texas 78712 USA
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26
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Reuman DC, Costantino RF, Desharnais RA, Cohen JE. Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations. Ecol Lett 2008; 11:820-30. [PMID: 18479454 DOI: 10.1111/j.1461-0248.2008.01194.x] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
Populations fluctuate because of their internal dynamics, which can be nonlinear and stochastic, and in response to environmental variation. Theory predicts how the colour of environmental stochasticity affects population means, variances and correlations with the environment over time. The theory has not been tested for cycling populations, commonly observed in field systems. We applied noise of different colours to cycling laboratory beetle populations, holding other statistical properties of the noise fixed. Theory was largely validated, but failed to predict observations in sufficient detail. The main period of population cycling was shifted up to 33% by the colour of environmental stochasticity. Noise colour affected population means, variances and dominant periodicities differently for populations that cycled in different ways without noise. Our results show that changes in the colour of climatic variability, partly caused by humans, may affect the main periodicity of cycling populations, possibly impacting industry, pest management and conservation.
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Affiliation(s)
- Daniel C Reuman
- Laboratory of Populations, The Rockefeller University, Box 20, 1230 York Avenue, New York, NY 10065, USA.
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Smith MJ, White A, Sherratt JA, Telfer S, Begon M, Lambin X. Disease effects on reproduction can cause population cycles in seasonal environments. J Anim Ecol 2007; 77:378-89. [PMID: 18005128 PMCID: PMC2408661 DOI: 10.1111/j.1365-2656.2007.01328.x] [Citation(s) in RCA: 42] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
Abstract
Recent studies of rodent populations have demonstrated that certain parasites can cause juveniles to delay maturation until the next reproductive season. Furthermore, a variety of parasites may share the same host, and evidence is beginning to accumulate showing nonindependent effects of different infections. We investigated the consequences for host population dynamics of a disease-induced period of no reproduction, and a chronic reduction in fecundity following recovery from infection (such as may be induced by secondary infections) using a modified SIR (susceptible, infected, recovered) model. We also included a seasonally varying birth rate as recent studies have demonstrated that seasonally varying parameters can have important effects on long-term host–parasite dynamics. We investigated the model predictions using parameters derived from five different cyclic rodent populations. Delayed and reduced fecundity following recovery from infection have no effect on the ability of the disease to regulate the host population in the model as they have no effect on the basic reproductive rate. However, these factors can influence the long-term dynamics including whether or not they exhibit multiyear cycles. The model predicts disease-induced multiyear cycles for a wide range of realistic parameter values. Host populations that recover relatively slowly following a disease-induced population crash are more likely to show multiyear cycles. Diseases for which the period of infection is brief, but full recovery of reproductive function is relatively slow, could generate large amplitude multiyear cycles of several years in length. Chronically reduced fecundity following recovery can also induce multiyear cycles, in support of previous theoretical studies. When parameterized for cowpox virus in the cyclic field vole populations (Microtus agrestis) of Kielder Forest (northern England), the model predicts that the disease must chronically reduce host fecundity by more than 70%, following recovery from infection, for it to induce multiyear cycles. When the model predicts quasi-periodic multiyear cycles it also predicts that seroprevalence and the effective date of onset of the reproductive season are delayed density-dependent, two phenomena that have been recorded in the field.
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Affiliation(s)
- Matthew J Smith
- Department of Mathematics and the Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK.
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Greenman JV, Norman RA. Environmental forcing, invasion and control of ecological and epidemiological systems. J Theor Biol 2007; 247:492-506. [PMID: 17475284 DOI: 10.1016/j.jtbi.2007.03.031] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2006] [Revised: 02/08/2007] [Accepted: 03/26/2007] [Indexed: 10/23/2022]
Abstract
Destabilising a biological system through periodic or stochastic forcing can lead to significant changes in system behaviour. Forcing can bring about coexistence when previously there was exclusion; it can excite massive system response through resonance, it can offset the negative effect of apparent competition and it can change the conditions under which the system can be invaded. Our main focus is on the invasion properties of continuous time models under periodic forcing. We show that invasion is highly sensitive to the strength, period, phase, shape and configuration of the forcing components. This complexity can be of great advantage if some of the forcing components are anthropogenic in origin. They can be turned into instruments of control to achieve specific objectives in ecology and disease management, for example. Culling, vaccination and resource regulation are considered. A general analysis is presented, based on the leading Lyapunov exponent criterion for invasion. For unstructured invaders, a formula for this exponent can typically be written down from the model equations. Whether forcing hinders or encourages invasion depends on two factors: the covariances between invader parameters and resident populations and the shifts in average resident population levels brought about by the forcing. The invasion dynamics of a structured invader are much more complicated but an analytic solution can be obtained in quadratic approximation for moderate forcing strength. The general theory is illustrated by a range of models drawn from ecology and epidemiology. The relationship between periodic and stochastic forcing is also considered.
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Affiliation(s)
- J V Greenman
- Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, Scotland, UK.
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Reuman DC, Desharnais RA, Costantino RF, Ahmad OS, Cohen JE. Power spectra reveal the influence of stochasticity on nonlinear population dynamics. Proc Natl Acad Sci U S A 2006; 103:18860-5. [PMID: 17116860 PMCID: PMC1693752 DOI: 10.1073/pnas.0608571103] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2006] [Indexed: 11/18/2022] Open
Abstract
Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.
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Affiliation(s)
- Daniel C. Reuman
- *Laboratory of Populations, The Rockefeller University, Box 20, 1230 York Avenue, New York, NY 10021
| | - Robert A. Desharnais
- Department of Biological Sciences, California State University, Los Angeles, CA 90032
| | - Robert F. Costantino
- Department of Ecology and Evolutionary Biology, University of Arizona, Tucson, AZ 85721
| | - Omar S. Ahmad
- Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, NY 10021; and
| | - Joel E. Cohen
- *Laboratory of Populations, The Rockefeller University, Box 20, 1230 York Avenue, New York, NY 10021
- Laboratory of Sensory Neuroscience, The Rockefeller University, 1230 York Avenue, New York, NY 10021; and
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Benton TG. Revealing the ghost in the machine: using spectral analysis to understand the influence of noise on population dynamics. Proc Natl Acad Sci U S A 2006; 103:18387-8. [PMID: 17130444 PMCID: PMC1693673 DOI: 10.1073/pnas.0609323103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Affiliation(s)
- Tim G Benton
- Institute of Integrative and Comparative Biology, University of Leeds, Leeds LS2 9JT, United Kingdom.
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Benton TG, Plaistow SJ, Coulson TN. Complex population dynamics and complex causation: devils, details and demography. Proc Biol Sci 2006; 273:1173-81. [PMID: 16720388 PMCID: PMC1560275 DOI: 10.1098/rspb.2006.3495] [Citation(s) in RCA: 181] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/22/2005] [Accepted: 01/23/2006] [Indexed: 11/12/2022] Open
Abstract
Population dynamics result from the interplay of density-independent and density-dependent processes. Understanding this interplay is important, especially for being able to predict near-term population trajectories for management. In recent years, the study of model systems-experimental, observational and theoretical-has shed considerable light on the way that the both density-dependent and -independent aspects of the environment affect population dynamics via impacting on the organism's life history and therefore demography. These model-based approaches suggest that (i) individuals in different states differ in their demographic performance, (ii) these differences generate structure that can fluctuate independently of current total population size and so can influence the dynamics in important ways, (iii) individuals are strongly affected by both current and past environments, even when the past environments may be in previous generations and (iv) dynamics are typically complex and transient due to environmental noise perturbing complex population structures. For understanding population dynamics of any given system, we suggest that 'the devil is in the detail'. Experimental dissection of empirical systems is providing important insights into the details of the drivers of demographic responses and therefore dynamics and should also stimulate theory that incorporates relevant biological mechanism.
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Affiliation(s)
- Tim G Benton
- University of Leeds Institute of Integrative and Comparative Biology Leeds LS2 9JT, UK.
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Greenman JV, Benton TG. The impact of environmental fluctuations on structured discrete time population models: Resonance, synchrony and threshold behaviour. Theor Popul Biol 2005; 68:217-35. [PMID: 16182329 DOI: 10.1016/j.tpb.2005.06.007] [Citation(s) in RCA: 46] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2004] [Revised: 06/13/2005] [Accepted: 06/20/2005] [Indexed: 11/24/2022]
Abstract
External forcing of a discrete time ecological system does not just add variation to existing dynamics but can change the dynamics. We study the mechanisms that can bring this about, focusing on the key concepts of excitation and suppression which emerge when analysing the power spectra of the system in linear approximation. Excitation, through resonance between the system dynamics and the external forcing, is the greater the closer the system is to the boundary of the stability region. This amplification means that the extinction of populations becomes possible sooner than expected and, conversely, invasion can be significantly delayed. Suppression and the consequent redistribution of power within the spectrum proves to be a function both of the connectivity of the network graph of the system and the way that external forcing is applied to the system. It is also established that colour in stochastic forcing can have a major impact, by enhancing resonance and by greater redistribution of power. This can mean a higher risk of extinction through larger fluctuations in population numbers and a higher degree of synchrony between populations. The implications of external forcing for stage-structured species, for populations in competition and for trophic web systems are studied using the tools and concepts developed in the paper.
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Affiliation(s)
- J V Greenman
- Department of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, Scotland, UK.
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