1
|
Sandhu S, Mikheev V, Pasternak A, Taskinen J, Morozov A. Revisiting the role of behavior-mediated structuring in the survival of populations in hostile environments. Commun Biol 2024; 7:93. [PMID: 38216662 PMCID: PMC10786947 DOI: 10.1038/s42003-023-05731-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2022] [Accepted: 12/20/2023] [Indexed: 01/14/2024] Open
Abstract
Increasing the population density of target species is a major goal of ecosystem and agricultural management. This task is especially challenging in hazardous environments with a high abundance of natural enemies such as parasites and predators. Safe locations with lower mortality have been long considered a beneficial factor in enhancing population survival, being a promising tool in commercial fish farming and restoration of threatened species. Here we challenge this opinion and revisit the role of behavior structuring in a hostile environment in shaping the population density. We build a mathematical model, where individuals are structured according to their defensive tactics against natural enemies. The model predicts that although each safe zone enhances the survival of an individual, for an insufficient number of such zones, the entire population experiences a greater overall mortality. This is a result of the interplay of emergent dynamical behavioral structuring and strong intraspecific competition for safe zones. Non-plastic structuring in individuals' boldness reduces the mentioned negative effects. We demonstrate emergence of non-plastic behavioral structuring: the evolutionary branching of a monomorphic population into a dimorphic one with bold/shy strains. We apply our modelling approach to explore fish farming of salmonids in an environment infected by trematode parasites.
Collapse
Affiliation(s)
- Simran Sandhu
- School of Computing and Mathematical Sciences, University of Leicester, LE1 7RH, Leicester, UK
| | - Victor Mikheev
- Institute of Ecology and Evolution, Russian Academy of Sciences, Moscow, Russia
| | - Anna Pasternak
- Institute of Oceanology, Russian Academy of Sciences, Moscow, Russia
| | - Jouni Taskinen
- Department of Biological and Environmental Science, University of Jyväskylä, Jyväskylä, Finland
| | - Andrew Morozov
- School of Computing and Mathematical Sciences, University of Leicester, LE1 7RH, Leicester, UK.
- Institute of Ecology and Evolution, Russian Academy of Sciences, Moscow, Russia.
| |
Collapse
|
2
|
Nguyen AD, Do DN, Nguyen HD, Nguyen TP. Stability analysis and Hopf bifurcation of a brown planthopper–rice model under the effect of monsoon. Ecol Modell 2022. [DOI: 10.1016/j.ecolmodel.2022.109942] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
|
3
|
Kitagawa K, Nakaoka S, Asai Y, Watashi K, Iwami S. A PDE multiscale model of hepatitis C virus infection can be transformed to a system of ODEs. J Theor Biol 2018; 448:80-85. [PMID: 29634960 DOI: 10.1016/j.jtbi.2018.04.006] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2018] [Accepted: 04/04/2018] [Indexed: 12/14/2022]
Abstract
Direct-acting antivirals (DAAs) treat hepatitis C virus (HCV) by targeting its intracellular viral replication. DAAs are effective and deliver high clinical performance against HCV infection, but optimization of the DAA treatment regimen is ongoing. Different classes of DAAs are currently under development, and HCV treatments that combine two or three DAAs with different action mechanisms are being improved. To accurately quantify the antiviral effect of these DAA treatments and optimize multi-drug combinations, we must describe the intracellular viral replication processes corresponding to the action mechanisms by multiscale mathematical models. Previous multiscale models of HCV treatment have been formulated by partial differential equations (PDEs). However, estimating the parameters from clinical datasets requires comprehensive numerical PDE computations that are time consuming and often converge poorly. Here, we propose a user-friendly approach that transforms a standard PDE multiscale model of HCV infection (Guedj J et al., Proc. Natl. Acad. Sci. USA 2013; 110(10):3991-6) to mathematically identical ordinary differential equations (ODEs) without any assumptions. We also confirm consistency between the numerical solutions of our transformed ODE model and the original PDE model. This relationship between a detailed structured model and a simple model is called ``model aggregation problem'' and a fundamental important in theoretical biology. In particular, as the parameters of ODEs can be estimated by already established methods, our transformed ODE model and its modified version avoid the time-consuming computations and are broadly available for further data analysis.
Collapse
Affiliation(s)
- Kosaku Kitagawa
- Mathematical Biology Laboratory, Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan
| | - Shinji Nakaoka
- PRESTO, JST, Saitama 332-0012, Japan; Institute of Industrial Sciences, The University of Tokyo, Meguro-ku, Tokyo 153-0041, Japan
| | - Yusuke Asai
- Graduate School of Medicine, Hokkaido University, Kita 15 Jo Nishi 7 Chome, Kita-ku, Sapporo-shi, Hokkaido 060-8638, Japan; CREST, JST, Saitama 332-0012, Japan.
| | - Koichi Watashi
- CREST, JST, Saitama 332-0012, Japan; Department of Virology II, National Institute of Infectious Diseases, Tokyo 162-8640, Japan; Department of Applied Biological Sciences, Tokyo University of Science, Noda 278-8510, Japan.
| | - Shingo Iwami
- Mathematical Biology Laboratory, Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka 812-8581, Japan; PRESTO, JST, Saitama 332-0012, Japan; CREST, JST, Saitama 332-0012, Japan.
| |
Collapse
|
4
|
MA ZHIHUI, WANG SHUFAN, WANG TINGTING, TANG HAOPENG, LI ZIZHEN. A GENERALIZED PREDATOR–PREY SYSTEM WITH HABITAT COMPLEXITY. J BIOL SYST 2017. [DOI: 10.1142/s0218339017500231] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
This paper presents a generalized predator–prey system and considers the effect of habitat complexity on the dynamical consequences. The results show that habitat complexity has a major impact on the dynamical consequences of the considered system. On the one hand, habitat complexity has a stabilizing impact under certain conditions. A numerical simulation in our study and in experiments conducted in the published studies elaborate on this stabilizing effect. On the other hand, the most interesting and open issue is that a destabilizing effect of habitat complexity is found theoretically. All results are explained and illustrated from the ecological viewpoint.
Collapse
Affiliation(s)
- ZHIHUI MA
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
| | - SHUFAN WANG
- School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730000, P. R. China
| | - TINGTING WANG
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
| | - HAOPENG TANG
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
| | - ZIZHEN LI
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, P. R. China
| |
Collapse
|
5
|
Perez-Saez J, Mari L, Bertuzzo E, Casagrandi R, Sokolow SH, De Leo GA, Mande T, Ceperley N, Froehlich JM, Sou M, Karambiri H, Yacouba H, Maiga A, Gatto M, Rinaldo A. A Theoretical Analysis of the Geography of Schistosomiasis in Burkina Faso Highlights the Roles of Human Mobility and Water Resources Development in Disease Transmission. PLoS Negl Trop Dis 2015; 9:e0004127. [PMID: 26513655 PMCID: PMC4625963 DOI: 10.1371/journal.pntd.0004127] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2015] [Accepted: 09/08/2015] [Indexed: 12/28/2022] Open
Abstract
We study the geography of schistosomiasis across Burkina Faso by means of a spatially explicit model of water-based disease dynamics. The model quantitatively addresses the geographic stratification of disease burden in a novel framework by explicitly accounting for drivers and controls of the disease, including spatial information on the distributions of population and infrastructure, jointly with a general description of human mobility and climatic/ecological drivers. Spatial patterns of disease are analysed by the extraction and the mapping of suitable eigenvectors of the Jacobian matrix subsuming the stability of the disease-free equilibrium. The relevance of the work lies in the novel mapping of disease burden, a byproduct of the parametrization induced by regional upscaling, by model-guided field validations and in the predictive scenarios allowed by exploiting the range of possible parameters and processes. Human mobility is found to be a primary control at regional scales both for pathogen invasion success and the overall distribution of disease burden. The effects of water resources development highlighted by systematic reviews are accounted for by the average distances of human settlements from water bodies that are habitats for the parasite's intermediate host. Our results confirm the empirical findings about the role of water resources development on disease spread into regions previously nearly disease-free also by inspection of empirical prevalence patterns. We conclude that while the model still needs refinements based on field and epidemiological evidence, the proposed framework provides a powerful tool for large-scale public health planning and schistosomiasis management.
Collapse
Affiliation(s)
- Javier Perez-Saez
- Laboratory of Ecohydrology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Lorenzo Mari
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Enrico Bertuzzo
- Laboratory of Ecohydrology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Renato Casagrandi
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Susanne H. Sokolow
- Hopkins Marine Station, Stanford University, Pacific Grove, California, United States of America
- Marine Science Institute, University of California Santa Barbara, California, United States of America
| | - Giulio A. De Leo
- Hopkins Marine Station, Stanford University, Pacific Grove, California, United States of America
- Woods Institute for the Environment, Stanford University, California, United States of America
| | - Theophile Mande
- Laboratory of Ecohydrology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Natalie Ceperley
- Laboratory of Ecohydrology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Jean-Marc Froehlich
- Laboratory of Ecohydrology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
| | - Mariam Sou
- Institute International d’Ingénierie de l’Eau et de l’Environment, Ouagadougou, Burkina Faso
| | - Harouna Karambiri
- Institute International d’Ingénierie de l’Eau et de l’Environment, Ouagadougou, Burkina Faso
| | - Hamma Yacouba
- Institute International d’Ingénierie de l’Eau et de l’Environment, Ouagadougou, Burkina Faso
| | - Amadou Maiga
- Institute International d’Ingénierie de l’Eau et de l’Environment, Ouagadougou, Burkina Faso
| | - Marino Gatto
- Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy
| | - Andrea Rinaldo
- Laboratory of Ecohydrology, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
- Dipartimento ICEA, Università di Padova, Padova, Italy
| |
Collapse
|
6
|
Marie G, Simioni G. Extending the use of ecological models without sacrificing details: a generic and parsimonious meta-modelling approach. Methods Ecol Evol 2014. [DOI: 10.1111/2041-210x.12250] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Affiliation(s)
- Guillaume Marie
- INRA, UR 629 Ecologie des Forêts Méditerranêennes; URFM, Domaine Saint Paul, site Agroparc; CS 40509 - 89914 Avignon cedex 9 France
| | - Guillaume Simioni
- INRA, UR 629 Ecologie des Forêts Méditerranêennes; URFM, Domaine Saint Paul, site Agroparc; CS 40509 - 89914 Avignon cedex 9 France
| |
Collapse
|
7
|
Jana D, Bairagi N. Habitat complexity, dispersal and metapopulations: Macroscopic study of a predator–prey system. ECOLOGICAL COMPLEXITY 2014. [DOI: 10.1016/j.ecocom.2013.11.006] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
8
|
Scaling up the predator functional response in heterogeneous environment: When Holling type III can emerge? J Theor Biol 2013; 336:200-8. [DOI: 10.1016/j.jtbi.2013.07.011] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2012] [Revised: 04/29/2013] [Accepted: 07/15/2013] [Indexed: 11/24/2022]
|
9
|
Samanta S, Chowdhury T, Chattopadhyay J. Mathematical modeling of cascading migration in a tri-trophic food-chain system. J Biol Phys 2013; 39:469-87. [PMID: 23860921 DOI: 10.1007/s10867-013-9311-2] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2012] [Accepted: 03/04/2013] [Indexed: 11/26/2022] Open
Abstract
Diel vertical migration is a behavioral antipredator defense that is shaped by a trade-off between higher predation risk in surface waters and reduced growth in deeper waters. The strength of migration of zooplankton increases with a rise in the abundance of predators and their exudates (kairomone). Recent studies span multiple trophic levels, which lead to the concept of coupled vertical migration. The migrations that occur at one trophic level can affect the vertical migration of the next lower trophic level, and so on, throughout the food chain. This is called cascading migration. In this paper, we introduce cascading migration in a well-known model (Hastings and Powell, Ecology 73:896-903, 1991). We represent the dynamics of the system as proposed by Hastings and Powell as a phytoplankton-zooplankton-fish (prey-middle predator-top predator) model where fish affect the migrations of zooplankton, which in turn affect the migrations of motile phytoplankton. The system under cascading migration enhances system stability and population coexistence. It is also observed that for a higher rate of cascading migration, the system shows chaotic behavior. We conclude that the observations of Hastings and Powell remain true if the cascading migration rate is high enough.
Collapse
Affiliation(s)
- S Samanta
- Agricultural and Ecological Research Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108, India
| | | | | |
Collapse
|
10
|
Sen M, Banerjee M, Morozov A. Bifurcation analysis of a ratio-dependent prey–predator model with the Allee effect. ECOLOGICAL COMPLEXITY 2012. [DOI: 10.1016/j.ecocom.2012.01.002] [Citation(s) in RCA: 103] [Impact Index Per Article: 8.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
11
|
Morozov A, Poggiale JC. From spatially explicit ecological models to mean-field dynamics: The state of the art and perspectives. ECOLOGICAL COMPLEXITY 2012. [DOI: 10.1016/j.ecocom.2012.04.001] [Citation(s) in RCA: 36] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
12
|
Morozov A, Sen M, Banerjee M. Top-down control in a patchy environment: Revisiting the stabilizing role of food-dependent predator dispersal. Theor Popul Biol 2012; 81:9-19. [DOI: 10.1016/j.tpb.2011.10.003] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2011] [Revised: 10/08/2011] [Accepted: 10/27/2011] [Indexed: 11/29/2022]
|
13
|
Gibbons J, Wood A, Craigon J, Ramsden S, Crout N. Semi-automatic reduction and upscaling of large models: A farm management example. Ecol Modell 2010. [DOI: 10.1016/j.ecolmodel.2009.11.006] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
14
|
Auger P, de la Parra RB, Poggiale J, Sánchez E, Sanz L. Aggregation methods in dynamical systems and applications in population and community dynamics. Phys Life Rev 2008. [DOI: 10.1016/j.plrev.2008.02.001] [Citation(s) in RCA: 49] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
|
15
|
Simplifying a physiologically structured population model to a stage-structured biomass model. Theor Popul Biol 2008; 73:47-62. [PMID: 18006030 DOI: 10.1016/j.tpb.2007.09.004] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/19/2006] [Revised: 07/20/2007] [Accepted: 09/25/2007] [Indexed: 11/22/2022]
|
16
|
Boulain N, Simioni G, Gignoux J. Changing scale in ecological modelling: A bottom up approach with an individual based vegetation model. Ecol Modell 2007. [DOI: 10.1016/j.ecolmodel.2006.11.024] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
17
|
Ratzé C, Gillet F, Müller JP, Stoffel K. Simulation modelling of ecological hierarchies in constructive dynamical systems. ECOLOGICAL COMPLEXITY 2007. [DOI: 10.1016/j.ecocom.2007.02.014] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
18
|
Mchich R, Bergam A, Raïssi N. Effects of density dependent migrations on the dynamics of a predator prey model. Acta Biotheor 2006; 53:331-40. [PMID: 16583273 DOI: 10.1007/s10441-005-4883-2] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/22/2005] [Accepted: 10/22/2005] [Indexed: 10/24/2022]
Abstract
We study the effects of density dependent migrations on the stability of a predator-prey model in a patchy environment which is composed with two sites connected by migration. The two patches are different. On the first patch, preys can find resource but can be captured by predators. The second patch is a refuge for the prey and thus predators do not have access to this patch. We assume a repulsive effect of predator on prey on the resource patch. Therefore, when the predator density is large on that patch, preys are more likely to leave it to return to the refuge. We consider two models. In the first model, preys leave the refuge to go to the resource patch at constant migration rates. In the second model, preys are assumed to be in competition for the resource and leave the refuge to the resource patch according to the prey density. We assume two different time scales, a fast time scale for migration and a slow time scale for population growth, mortality and predation. We take advantage of the two time scales to apply aggregation of variables methods and to obtain a reduced model governing the total prey and predator densities. In the case of the first model, we show that the repulsive effect of predator on prey has a stabilizing effect on the predator-prey community. In the case of the second model, we show that there exists a window for the prey proportion on the resource patch to ensure stability.
Collapse
Affiliation(s)
- Rachid Mchich
- Ecole Nationale de Commerce et de Gestion, B.P. 1255, 90000, Tanger, Morocco.
| | | | | |
Collapse
|
19
|
Komuro R, Ford ED, Reynolds JH. The use of multi-criteria assessment in developing a process model. Ecol Modell 2006. [DOI: 10.1016/j.ecolmodel.2006.03.033] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|
20
|
Chambon-Dubreuil E, Auger P, Gaillard JM, Khaladi M. Effect of aggressive behaviour on age-structured population dynamics. Ecol Modell 2006. [DOI: 10.1016/j.ecolmodel.2005.09.005] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
|
21
|
Pichancourt JB, Burel F, Auger P. Assessing the effect of habitat fragmentation on population dynamics: An implicit modelling approach. Ecol Modell 2006. [DOI: 10.1016/j.ecolmodel.2005.07.027] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
|
22
|
Angelini R, Agostinho AA. Food web model of the Upper Paraná River Floodplain: description and aggregation effects. Ecol Modell 2005. [DOI: 10.1016/j.ecolmodel.2004.06.025] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
23
|
Borsuk ME, Stow CA, Reckhow KH. A Bayesian network of eutrophication models for synthesis, prediction, and uncertainty analysis. Ecol Modell 2004. [DOI: 10.1016/j.ecolmodel.2003.08.020] [Citation(s) in RCA: 246] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
24
|
Abstract
Biological systems are composed of different levels of organization. Usually, one considers the atomic, molecular, cellular, individual, population, community and ecosystem levels. These levels of organization also correspond to different levels of observation of the system, from microscopic to macroscopic, i.e., to different time and space scales. The more microscopic the level is, the faster the time scale and the smaller the space scale are. The dynamics of the complete system is the result of the coupled dynamical processes that take place in each of its levels of organization at different time scales. Variables aggregation methods take advantage of these different time scales to reduce the dimension of mathematical models such as a system of ordinary differential equations. We are going to study the dynamics of a system which is hierarchically organized in the sense that it is composed of groups of elements that can be themselves divided into further smaller sub-groups and so on. The hierarchical structure of the system results from the fact that the intra-group interactions are assumed to be larger than inter-group ones. We present aggregation methods that allow one to build a reduced model that governs a few global variables at the slow time scale.
Collapse
Affiliation(s)
- Pierre Auger
- Laboratoire de biométrie et biologie évolutive, UMR CNRS 5558, université Claude-Bernard, Lyon-1, 43, bd du 11-Novembre-1918, 69622 Villeurbanne, France.
| | | |
Collapse
|
25
|
Lett C, Auger P, Bravo de la Parra R. Migration frequency and the persistence of host-parasitoid interactions. J Theor Biol 2003; 221:639-54. [PMID: 12713946 DOI: 10.1006/jtbi.2003.3213] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
This paper analyses the effect of migration frequency on the stability and persistence of a host-parasitoid system in a two-patch environment. The hosts and parasitoids are allowed to move from one patch to the other a certain number of times within a generation. When this number is low, i.e. when the time-scales associated with migration and demography are of the same order, host-parasitoid interactions are usually not persistent. When this number is high, however, persistence is more likely. Moreover, in this situation, aggregation methods can be used to simplify the proposed initial model into an aggregated model describing the dynamics of both the total host and parasitoid populations. Analysis of the aggregated model shows that the system reaches a stable steady state for some regions of the parameter domain. Persistence occurs when the movement of the parasitoids is asymmetrical, i.e. they move preferentially to one of the two patches. We show that the growth rate of the host population is a key parameter in determining which migration strategies of the parasitoids lead to persistent host-parasitoid interactions.
Collapse
Affiliation(s)
- Christophe Lett
- Laboratoire de Biométrie et Biologie Evolutive, UMR CNRS 5558 - Université Claude Bernard Lyon I, 43, boulevard du 11 novembre 1918, 69622, Villeurbanne Cedex, France.
| | | | | |
Collapse
|
26
|
Use of genetic algorithms to select input variables in decision tree models for the prediction of benthic macroinvertebrates. Ecol Modell 2003. [DOI: 10.1016/s0304-3800(02)00260-0] [Citation(s) in RCA: 70] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
27
|
Kooi B, Poggiale J, Auger P, Kooijman S. Aggregation methods in food chains with nutrient recycling. Ecol Modell 2002. [DOI: 10.1016/s0304-3800(02)00217-x] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
|
28
|
Charles S, Morand S, Chassé JL, Auger P. Host patch selection induced by parasitism: basic reproduction ratio r(0) and optimal virulence. Theor Popul Biol 2002; 62:97-109. [PMID: 12167350 DOI: 10.1006/tpbi.2002.1598] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
The effects of parasites on the behavior of their hosts are well documented. For example, parasites may affect the habitat selection of the host individual. We used variables aggregation methods to investigate the way in which parasites affect the spatial pattern of susceptible hosts. We developed a simple epidemiological model, taking into account both the reproduction processes of hosts (density-dependent birth and death) and infection, considered separately on two different patches, and the migration of susceptible hosts between these two patches. We used the complete model of three equations to generate an aggregated model describing the dynamics of the combined susceptible and infected host populations. We obtained the basic reproduction ratio (R(0)) from the aggregated model, and then studied the effect of the migratory behavior of susceptible hosts on the ability of the parasite to invade the system. We also used the basic reproduction ratio to investigate the evolution of parasite virulence in relation to the migration decisions of susceptible hosts. We found that host investment in avoidance of the infected patch leads to an increase in optimal virulence if host investment is costly.
Collapse
Affiliation(s)
- S Charles
- Université Claude Bernard-Lyon 1, Biométrie - Biologie Evolutive, UMR CNRS 5558, 43 Bd du 11 Novembre 1918, 69522 Villeurbanne, Cedex, France
| | | | | | | |
Collapse
|
29
|
|
30
|
Scaling-up an autoregressive time-series model (of spruce budworm population dynamics) changes its qualitative behavior. Ecol Modell 2002. [DOI: 10.1016/s0304-3800(01)00519-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
|
31
|
Schnell S, Maini P. Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations. ACTA ACUST UNITED AC 2002. [DOI: 10.1016/s0895-7177(01)00156-x] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
|
32
|
Aggregation of an individual-based space-dependent model of forest dynamics into distribution-based and space-independent models. Ecol Modell 2001. [DOI: 10.1016/s0304-3800(01)00380-5] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
33
|
Auger P, Bravo de la Parra R. Methods of aggregation of variables in population dynamics. COMPTES RENDUS DE L'ACADEMIE DES SCIENCES. SERIE III, SCIENCES DE LA VIE 2000; 323:665-74. [PMID: 11019360 DOI: 10.1016/s0764-4469(00)00182-7] [Citation(s) in RCA: 36] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Abstract
In ecology, we are faced with modelling complex systems involving many variables corresponding to interacting populations structured in different compartmental classes, ages and spatial patches. Models that incorporate such a variety of aspects would lead to systems of equations with many variables and parameters. Mathematical analysis of these models would, in general, be impossible. In many real cases, the dynamics of the system corresponds to two or more time scales. For example, individual decisions can be rapid in comparison to growth of the populations. In that case, it is possible to perform aggregation methods that allow one to build a reduced model that governs the dynamics of a lower dimensional system, at a slow time scale. In this article, we present a review of aggregation methods for time continuous systems as well as for discrete models. We also present applications in population dynamics. A first example concerns a continuous time model of a single population distributed on a system of two connected patches (a logistic source and a sink), by fast migration. It is shown that under a certain condition, the total equilibrium population can be larger than the carrying capacity of the logistic source. A second example concerns a discrete model of a population distributed on two patches, still a source and a sink, connected by fast migration. The use of aggregation methods permits us to conclude that density-dependent migration can stabilize the total population.
Collapse
Affiliation(s)
- P Auger
- UMR CNRS 5558, université Claude-Bernard-Lyon-1, Villeurbanne, France.
| | | |
Collapse
|