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Enhancing population stability with combined adaptive limiter control and finding the optimal harvesting-restocking balance. Theor Popul Biol 2019; 130:1-12. [PMID: 31580866 DOI: 10.1016/j.tpb.2019.09.012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2019] [Revised: 09/26/2019] [Accepted: 09/27/2019] [Indexed: 11/21/2022]
Abstract
Fluctuations in population size may have negative consequences (e.g., an increased risk of extinction or the occurrence of repeated outbreaks), and many management strategies are aimed at avoiding them by either only restocking or only harvesting the population. Two of these strategies are adaptive limiter control (ALC) and adaptive threshold harvesting (ATH). With ALC the population is controlled by only restocking and with ATH by only harvesting. We propose the strategy of combined adaptive limiter control (CALC) as the combination of ALC and ATH and study the potential advantages of CALC over ALC and ATH. We consider two different population models, namely a stochastic overcompensatory model and a host-pathogen-predator model. For the first model, our results show that the combination of restocking and harvesting under CALC improves the constancy stability of the managed populations when the harvesting and restocking intensities are high enough. Otherwise the effect is marginal or in rare cases negative. For the second model, we show that combining harvesting with restocking reduces the outbreak risk only if the harvesting intensity is low. For medium harvesting intensities the effect is marginal and for high harvesting intensities the risk of outbreaks is increased. In addition, we study the optimal harvesting-restocking balance by considering a proxy of the benefit obtained in terms of the reduction in the outbreak risk and the harvesting and restocking costs.
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Barraquand F, Louca S, Abbott KC, Cobbold CA, Cordoleani F, DeAngelis DL, Elderd BD, Fox JW, Greenwood P, Hilker FM, Murray DL, Stieha CR, Taylor RA, Vitense K, Wolkowicz GS, Tyson RC. Moving forward in circles: challenges and opportunities in modelling population cycles. Ecol Lett 2017. [DOI: 10.1111/ele.12789] [Citation(s) in RCA: 89] [Impact Index Per Article: 12.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Affiliation(s)
- Frédéric Barraquand
- Department of Arctic and Marine Biology University of Tromsø Tromsø Norway
- Integrative and Theoretical Ecology Chair, LabEx COTE University of Bordeaux Pessac France
| | - Stilianos Louca
- Institute of Applied Mathematics University of British Columbia Vancouver BC Canada
| | - Karen C. Abbott
- Department of Biology Case Western Reserve University Cleveland OH USA
| | | | - Flora Cordoleani
- Institute of Marine Science University of California Santa Cruz Santa Cruz CA USA
- Southwest Fisheries Science Center Santa Cruz CA USA
| | | | - Bret D. Elderd
- Department of Biological Sciences Lousiana State University Baton Rouge LA USA
| | - Jeremy W. Fox
- Department of Biological Sciences University of Calgary Calgary ABCanada
| | | | - Frank M. Hilker
- Institute of Environmental Systems Research, School of Mathematics/Computer Science Osnabrück University Osnabrück Germany
| | - Dennis L. Murray
- Integrative Wildlife Conservation Lab Trent University Peterborough ONCanada
| | - Christopher R. Stieha
- Department of Biology Case Western Reserve University Cleveland OH USA
- Department of Entomology Cornell University Ithaca NY USA
| | - Rachel A. Taylor
- Department of Integrative Biology University of South Florida Tampa FLUSA
| | - Kelsey Vitense
- Department of Fisheries, Wildlife, and Conservation Biology University of Minnesota Saint Paul MN USA
| | - Gail S.K. Wolkowicz
- Department of Mathematics and Statistics McMaster University Hamilton ON Canada
| | - Rebecca C. Tyson
- Department of Mathematics and Statistics University of British Columbia Okanagan Kelowna BC Canada
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Segura J, Hilker FM, Franco D. Population control methods in stochastic extinction and outbreak scenarios. PLoS One 2017; 12:e0170837. [PMID: 28151983 PMCID: PMC5289467 DOI: 10.1371/journal.pone.0170837] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2016] [Accepted: 01/11/2017] [Indexed: 11/18/2022] Open
Abstract
Adaptive limiter control (ALC) and adaptive threshold harvesting (ATH) are two related control methods that have been shown to stabilize fluctuating populations. Large variations in population abundance can threaten the constancy and the persistence stability of ecological populations, which may impede the success and efficiency of managing natural resources. Here, we consider population models that include biological mechanisms characteristic for causing extinctions on the one hand and pest outbreaks on the other hand. These models include Allee effects and the impact of natural enemies (as is typical of forest defoliating insects). We study the impacts of noise and different levels of biological parameters in three extinction and two outbreak scenarios. Our results show that ALC and ATH have an effect on extinction and outbreak risks only for sufficiently large control intensities. Moreover, there is a clear disparity between the two control methods: in the extinction scenarios, ALC can be effective and ATH can be counterproductive, whereas in the outbreak scenarios the situation is reversed, with ATH being effective and ALC being potentially counterproductive.
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Affiliation(s)
- Juan Segura
- Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), Madrid, Spain
| | - Frank M. Hilker
- Institute of Environmental Systems Research, School of Mathematics / Computer Science, Osnabrück University, Osnabrück, Germany
- * E-mail:
| | - Daniel Franco
- Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), Madrid, Spain
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Segura J, Hilker FM, Franco D. Adaptive threshold harvesting and the suppression of transients. J Theor Biol 2016; 395:103-114. [PMID: 26854876 DOI: 10.1016/j.jtbi.2016.01.039] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2015] [Revised: 01/28/2016] [Accepted: 01/30/2016] [Indexed: 11/18/2022]
Abstract
Fluctuations in population size are in many cases undesirable, as they can induce outbreaks and extinctions or impede the optimal management of populations. We propose the strategy of adaptive threshold harvesting (ATH) to control fluctuations in population size. In this strategy, the population is harvested whenever population size has grown beyond a certain proportion in comparison to the previous generation. Taking such population increases into account, ATH intervenes also at smaller population sizes than the strategy of threshold harvesting. Moreover, ATH is the harvesting version of adaptive limiter control (ALC) that has recently been shown to stabilize population oscillations in both experiments and theoretical studies. We find that ATH has similar stabilization properties as ALC and thus offers itself as a harvesting alternative for the control of pests, exploitation of biological resources, or when restocking interventions required from ALC are unfeasible. We present numerical simulations of ATH to illustrate its performance in the presence of noise, lattice effect, and Allee effect. In addition, we propose an adjustment to both ATH and ALC that restricts interventions when control seems unnecessary, i.e. when population size is too small or too large, respectively. This adjustment cancels prolonged transients.
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Affiliation(s)
- Juan Segura
- Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), c/ Juan del Rosal 12, 28040, Madrid, Spain
| | - Frank M Hilker
- Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Barbarastr. 12, 49076 Osnabrück, Germany
| | - Daniel Franco
- Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia (UNED), c/ Juan del Rosal 12, 28040, Madrid, Spain.
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Stabilizing the dynamics of laboratory populations of Drosophila melanogaster through upper and lower limiter controls. ECOLOGICAL COMPLEXITY 2016. [DOI: 10.1016/j.ecocom.2015.11.003] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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Franco D, Ruiz-Herrera A. To connect or not to connect isolated patches. J Theor Biol 2015; 370:72-80. [DOI: 10.1016/j.jtbi.2015.01.029] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/27/2014] [Revised: 01/21/2015] [Accepted: 01/25/2015] [Indexed: 11/24/2022]
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Tung S, Mishra A, Dey S. A comparison of six methods for stabilizing population dynamics. J Theor Biol 2014; 356:163-73. [PMID: 24801858 DOI: 10.1016/j.jtbi.2014.04.036] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2013] [Revised: 04/25/2014] [Accepted: 04/28/2014] [Indexed: 11/17/2022]
Abstract
Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very different concepts of stability, which makes it difficult to compare their relative efficiencies. Moreover, since the dynamics of populations are dependent on the life-history of the species and its environment, it is conceivable that the stabilizing effects of control methods would also be affected by such factors, a complication that has typically not been investigated. In this study, we compare six different control methods with respect to their efficiency at inducing a common level of enhancement (defined as 50% increase) for two kinds of stability (constancy and persistence) under four different life-history/environment combinations. Since these methods have been analytically studied elsewhere, we concentrate on an intuitive understanding of realistic simulations incorporating noise, extinction probability and lattice effect. We show that for these six methods, even when the magnitude of stabilization attained is the same, other aspects of the dynamics like population size distribution can be very different. Consequently, correlated aspects of stability, like the amount of persistence for a given degree of constancy stability (and vice versa) or the corresponding effective population size (a measure of resistance to genetic drift) vary widely among the methods. Moreover, the number of organisms needed to be added or removed to attain similar levels of stabilization also varies for these methods, a fact that has economic implications. Finally, we compare the relative efficiencies of these methods through a composite index of various stability related measures. Our results suggest that Lower Limiter Control (LLC) seems to be the optimal method under most conditions, with the recently proposed Adaptive Limiter Control (ALC) being a close second.
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Affiliation(s)
- Sudipta Tung
- Population Biology Laboratory, Biology Division, Indian Institute of Science Education and Research-Pune, Dr. Homi Bhabha Road, Pune, Maharashtra 411008, India.
| | - Abhishek Mishra
- Population Biology Laboratory, Biology Division, Indian Institute of Science Education and Research-Pune, Dr. Homi Bhabha Road, Pune, Maharashtra 411008, India.
| | - Sutirth Dey
- Population Biology Laboratory, Biology Division, Indian Institute of Science Education and Research-Pune, Dr. Homi Bhabha Road, Pune, Maharashtra 411008, India.
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Capeáns R, Sabuco J, Sanjuán MA. When less is more: Partial control to avoid extinction of predators in an ecological model. ECOLOGICAL COMPLEXITY 2014. [DOI: 10.1016/j.ecocom.2014.02.002] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Sah P, Dey S. Stabilizing spatially-structured populations through adaptive Limiter Control. PLoS One 2014; 9:e105861. [PMID: 25153073 PMCID: PMC4143321 DOI: 10.1371/journal.pone.0105861] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/23/2013] [Accepted: 07/29/2014] [Indexed: 11/19/2022] Open
Abstract
Stabilizing the dynamics of complex, non-linear systems is a major concern across several scientific disciplines including ecology and conservation biology. Unfortunately, most methods proposed to reduce the fluctuations in chaotic systems are not applicable to real, biological populations. This is because such methods typically require detailed knowledge of system specific parameters and the ability to manipulate them in real time; conditions often not met by most real populations. Moreover, real populations are often noisy and extinction-prone, which can sometimes render such methods ineffective. Here, we investigate a control strategy, which works by perturbing the population size, and is robust to reasonable amounts of noise and extinction probability. This strategy, called the Adaptive Limiter Control (ALC), has been previously shown to increase constancy and persistence of laboratory populations and metapopulations of Drosophila melanogaster. Here, we present a detailed numerical investigation of the effects of ALC on the fluctuations and persistence of metapopulations. We show that at high migration rates, application of ALC does not require a priori information about the population growth rates. We also show that ALC can stabilize metapopulations even when applied to as low as one-tenth of the total number of subpopulations. Moreover, ALC is effective even when the subpopulations have high extinction rates: conditions under which another control algorithm had previously failed to attain stability. Importantly, ALC not only reduces the fluctuation in metapopulation sizes, but also the global extinction probability. Finally, the method is robust to moderate levels of noise in the dynamics and the carrying capacity of the environment. These results, coupled with our earlier empirical findings, establish ALC to be a strong candidate for stabilizing real biological metapopulations.
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Affiliation(s)
- Pratha Sah
- Population Biology Laboratory, Biology Division, Indian Institute of Science Education and Research-Pune, Pashan, Pune, Maharashtra, India
| | - Sutirth Dey
- Population Biology Laboratory, Biology Division, Indian Institute of Science Education and Research-Pune, Pashan, Pune, Maharashtra, India
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