Invasion, stability and evolution to criticality in spatially extended, artificial host—pathogen ecologies
1995; Royal Society; Volume: 259; Issue: 1354 Linguagem: Inglês
10.1098/rspb.1995.0009
ISSN1471-2954
AutoresD.A.J. Rand, Matt J. Keeling, Howard B. Wilson,
Tópico(s)Mathematical and Theoretical Epidemiology and Ecology Models
ResumoRestricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Rand D. A. , Keeling Matthew and Wilson H. B. 1995Invasion, stability and evolution to criticality in spatially extended, artificial host—pathogen ecologiesProc. R. Soc. Lond. B.25955–63http://doi.org/10.1098/rspb.1995.0009SectionRestricted accessArticleInvasion, stability and evolution to criticality in spatially extended, artificial host—pathogen ecologies D. A. Rand Google Scholar Find this author on PubMed Search for more papers by this author , Matthew Keeling Google Scholar Find this author on PubMed Search for more papers by this author and H. B. Wilson Google Scholar Find this author on PubMed Search for more papers by this author D. A. Rand Google Scholar Find this author on PubMed , Matthew Keeling Google Scholar Find this author on PubMed and H. B. Wilson Google Scholar Find this author on PubMed Published:23 January 1995https://doi.org/10.1098/rspb.1995.0009AbstractWe consider an individual-based spatial model of a generic host—pathogen system and explore the differences between such models and mean-field systems. We find a range of new dynamical and evolutionary phenomena, in particular: (i) in this system, selective pressure is substantially reduced compared with the corresponding mean-field models, and artificial suppression of the pathogen population leads to faster evolution and reduces evolutionary stability; (ii) unlike the mean-field models, there exists a critical transmissibility тcabove which the pathogen dies out; and (iii) the system displays self-evolved criticality. If the transmissibility т is allowed to mutate, it evolves to the critical value тc. Thus the system evolves to put itself at the boundary at which it can exist. Observations of the individual-based spatial model motivate an explanation for these phenomena in terms of the dynamics of host patches involving their connections and disconnections. We therefore construct a patch model of this and show that this simplified model behaves in a similar way to the individual-based spatial model.FootnotesThis text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited byBest A and Ashby B (2023) How do fluctuating ecological dynamics impact the evolution of hosts and parasites?, Philosophical Transactions of the Royal Society B: Biological Sciences, 378:1873, Online publication date: 27-Mar-2023. Gutiérrez Al‐Khudhairy O, Rossberg A and Jordan F (2022) Evolution of prudent predation in complex food webs, Ecology Letters, 10.1111/ele.13979, 25:5, (1055-1074), Online publication date: 1-May-2022. Bernstein E, Hamblen C, Junge M and Reeves L Chase-escape on the configuration model, Electronic Communications in Probability, 10.1214/22-ECP470, 27:none Wren L and Best A (2021) How Local Interactions Impact the Dynamics of an Epidemic, Bulletin of Mathematical Biology, 10.1007/s11538-021-00961-w, 83:12, Online publication date: 1-Dec-2021. Yang S, Senapati P, Wang D, Bauch C, Fountoulakis K and Althouse B (2021) Targeted pandemic containment through identifying local contact network bottlenecks, PLOS Computational Biology, 10.1371/journal.pcbi.1009351, 17:8, (e1009351) Bartlett L and Boots M (2021) The central role of host reproduction in determining the evolution of virulence in spatially structured populations, Journal of Theoretical Biology, 10.1016/j.jtbi.2021.110717, 523, (110717), Online publication date: 1-Aug-2021. Hawley D, Gibson A, Townsend A, Craft M and Stephenson J (2020) Bidirectional interactions between host social behaviour and parasites arise through ecological and evolutionary processes, Parasitology, 10.1017/S0031182020002048, 148:3, (274-288), Online publication date: 1-Mar-2021. Buendía V, di Santo S, Bonachela J and Muñoz M (2020) Feedback Mechanisms for Self-Organization to the Edge of a Phase Transition, Frontiers in Physics, 10.3389/fphy.2020.00333, 8 Ferris C, Wright R, Brockhurst M and Best A (2020) The evolution of host resistance and parasite infectivity is highest in seasonal resource environments that oscillate at intermediate amplitudes, Proceedings of the Royal Society B: Biological Sciences, 287:1927, Online publication date: 27-May-2020. Su M, Chen G and Yang Y (2019) Dynamics of host-parasite interactions with horizontal and vertical transmissions in spatially heterogeneous environment, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2018.11.034, 517, (452-458), Online publication date: 1-Mar-2019. White L, Forester J, Craft M and Boulinier T (2017) Dynamic, spatial models of parasite transmission in wildlife: Their structure, applications and remaining challenges, Journal of Animal Ecology, 10.1111/1365-2656.12761, 87:3, (559-580), Online publication date: 1-May-2018. Simmons E, Drescher K, Nadell C and Bucci V (2017) Phage mobility is a core determinant of phage–bacteria coexistence in biofilms, The ISME Journal, 10.1038/ismej.2017.190, 12:2, (531-543), Online publication date: 1-Feb-2018. Saeki K, Sasaki A and Komarova N (2018) The role of spatial heterogeneity in the evolution of local and global infections of viruses, PLOS Computational Biology, 10.1371/journal.pcbi.1005952, 14:1, (e1005952) Leggett H, Wild G, West S and Buckling A (2017) Fast-killing parasites can be favoured in spatially structured populations, Philosophical Transactions of the Royal Society B: Biological Sciences, 372:1719, Online publication date: 5-May-2017. Su M and Boots M (2017) The impact of resource quality on the evolution of virulence in spatially heterogeneous environments, Journal of Theoretical Biology, 10.1016/j.jtbi.2016.12.017, 416, (1-7), Online publication date: 1-Mar-2017. Bauch C, Sigdel R, Pharaon J and Anand M (2016) Early warning signals of regime shifts in coupled human–environment systems, Proceedings of the National Academy of Sciences, 10.1073/pnas.1604978113, 113:51, (14560-14567), Online publication date: 20-Dec-2016. Nagai M and de Aguiar M (2016) Coevolution in sexually reproducing populations of predators and prey, Ecological Modelling, 10.1016/j.ecolmodel.2016.06.017, 337, (168-175), Online publication date: 1-Oct-2016. Berngruber T, Lion S, Gandon S and Brown S (2015) Spatial Structure, Transmission Modes and the Evolution of Viral Exploitation Strategies, PLOS Pathogens, 10.1371/journal.ppat.1004810, 11:4, (e1004810) Su M, Hui C and Lin Z (2015) Effects of the transmissibility and virulence of pathogens on intraguild predation in fragmented landscapes, Biosystems, 10.1016/j.biosystems.2015.02.002, 129, (44-49), Online publication date: 1-Mar-2015. Lion S and Gandon S (2015) Evolution of spatially structured host-parasite interactions, Journal of Evolutionary Biology, 10.1111/jeb.12551, 28:1, (10-28), Online publication date: 1-Jan-2015. Reluga T and Shim E (2014) Population viscosity suppresses disease emergence by preserving local herd immunity, Proceedings of the Royal Society B: Biological Sciences, 281:1796, Online publication date: 7-Dec-2014. Hartig F, Münkemüller T, Johst K, Dieckmann U and Mouquet N (2014) On the Sympatric Evolution and Evolutionary Stability of Coexistence by Relative Nonlinearity of Competition, PLoS ONE, 10.1371/journal.pone.0094454, 9:9, (e94454) Luo X, Zhang X, Sun G and Jin Z (2014) Epidemical dynamics of SIS pair approximation models on regular and random networks, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2014.05.020, 410, (144-153), Online publication date: 1-Sep-2014. Jackson D (2014) Spatial pattern as an adaptive phenotype, Ecological Complexity, 10.1016/j.ecocom.2014.04.006, 19, (59-67), Online publication date: 1-Sep-2014. Shrestha S, Bjørnstad O and King A (2014) Evolution of acuteness in pathogen metapopulations: conflicts between "classical" and invasion-persistence trade-offs, Theoretical Ecology, 10.1007/s12080-014-0219-7, 7:3, (299-311), Online publication date: 1-Aug-2014. Ashby B, Gupta S and Buckling A (2014) Spatial Structure Mitigates Fitness Costs in Host-Parasite Coevolution, The American Naturalist, 10.1086/674826, 183:3, (E64-E74), Online publication date: 1-Mar-2014. Roychoudhury P, Shrestha N, Wiss V and Krone S (2014) Fitness benefits of low infectivity in a spatially structured population of bacteriophages, Proceedings of the Royal Society B: Biological Sciences, 281:1774, Online publication date: 7-Jan-2014. Tack A, Horns F and Laine A (2013) THE IMPACT OF SPATIAL SCALE AND HABITAT CONFIGURATION ON PATTERNS OF TRAIT VARIATION AND LOCAL ADAPTATION IN A WILD PLANT PARASITE, Evolution, 10.1111/evo.12239, 68:1, (176-189), Online publication date: 1-Jan-2014. Messinger S and Ostling A (2013) Predator attack rate evolution in space: The role of ecology mediated by complex emergent spatial structure and self-shading, Theoretical Population Biology, 10.1016/j.tpb.2013.08.003, 89, (55-63), Online publication date: 1-Nov-2013. Takahashi D, Brännström Å, Mazzucco R, Yamauchi A and Dieckmann U (2013) Abrupt community transitions and cyclic evolutionary dynamics in complex food webs, Journal of Theoretical Biology, 10.1016/j.jtbi.2013.08.003, 337, (181-189), Online publication date: 1-Nov-2013. Mitteldorf J and Goodnight C (2013) Post-reproductive life span and demographic stability, Biochemistry (Moscow), 10.1134/S0006297913090071, 78:9, (1013-1022), Online publication date: 1-Sep-2013. (2013) Bibliography Food Webs and Biodiversity, 10.1002/9781118502181.biblio, (349-363), Online publication date: 12-Jul-2013. Webb S, Keeling M and Boots M (2013) The role of spatial population structure on the evolution of parasites with acquired immunity and demography, Journal of Theoretical Biology, 10.1016/j.jtbi.2013.01.015, 324, (21-31), Online publication date: 1-May-2013. Webb S, Keeling M and Boots M (2013) A theoretical study of the role of spatial population structure in the evolution of parasite virulence, Theoretical Population Biology, 10.1016/j.tpb.2012.11.008, 84, (36-45), Online publication date: 1-Mar-2013. Horns F and Hood M (2012) The evolution of disease resistance and tolerance in spatially structured populations, Ecology and Evolution, 10.1002/ece3.290, 2:7, (1705-1711), Online publication date: 1-Jul-2012. Best A, Webb S, Antonovics J and Boots M (2011) Local transmission processes and disease-driven host extinctions, Theoretical Ecology, 10.1007/s12080-011-0111-7, 5:2, (211-217), Online publication date: 1-May-2012. Jones E, Webb S, Ruiz-Fons F, Albon S and Gilbert L (2010) The effect of landscape heterogeneity and host movement on a tick-borne pathogen, Theoretical Ecology, 10.1007/s12080-010-0087-8, 4:4, (435-448), Online publication date: 1-Nov-2011. Capitán J, Cuesta J, Manrubia S, Aguirre J and Moreno Y (2011) Severe Hindrance of Viral Infection Propagation in Spatially Extended Hosts, PLoS ONE, 10.1371/journal.pone.0023358, 6:8, (e23358) Best A, Webb S, White A and Boots M (2010) Host resistance and coevolution in spatially structured populations, Proceedings of the Royal Society B: Biological Sciences, 278:1715, (2216-2222), Online publication date: 22-Jul-2011. Suzuki S and Sasaki A (2011) How does the resistance threshold in spatially explicit epidemic dynamics depend on the basic reproductive ratio and spatial correlation of crop genotypes?, Journal of Theoretical Biology, 10.1016/j.jtbi.2011.02.002, 276:1, (117-125), Online publication date: 1-May-2011. Cuesta J, Aguirre J, Capitán J and Manrubia S (2011) Struggle for Space: Viral Extinction through Competition for Cells, Physical Review Letters, 10.1103/PhysRevLett.106.028104, 106:2 Boerlijst M, van Ballegooijen W and Tanaka M (2010) Spatial Pattern Switching Enables Cyclic Evolution in Spatial Epidemics, PLoS Computational Biology, 10.1371/journal.pcbi.1001030, 6:12, (e1001030) Luz P, Struchiner C, Galvani A and Brooker S (2010) Modeling Transmission Dynamics and Control of Vector-Borne Neglected Tropical Diseases, PLoS Neglected Tropical Diseases, 10.1371/journal.pntd.0000761, 4:10, (e761) Lion S and Boots M (2010) Are parasites ''prudent'' in space?, Ecology Letters, 10.1111/j.1461-0248.2010.01516.x, 13:10, (1245-1255), Online publication date: 1-Oct-2010. Willemsen J (2010) Anomalous invasion in a 2d model of chemotactic predation, Physica A: Statistical Mechanics and its Applications, 10.1016/j.physa.2010.04.017, 389:17, (3484-3495), Online publication date: 1-Sep-2010. Liu Q, Wang R, Jin Z, van de Koppel J and Alonso D (2010) Spatial self-organization in a multi-strain host–pathogen system, Journal of Statistical Mechanics: Theory and Experiment, 10.1088/1742-5468/2010/05/P05017, 2010:05, (P05017) Buckee C and Gupta S (2010) A Network Approach to Understanding Pathogen Population Structure Infectious Disease Informatics, 10.1007/978-1-4419-1327-2_8, (167-185), . Perisic A and Bauch C (2009) A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks, BMC Infectious Diseases, 10.1186/1471-2334-9-77, 9:1, Online publication date: 1-Dec-2009. Messinger S and Ostling A (2009) The Consequences of Spatial Structure for the Evolution of Pathogen Transmission Rate and Virulence, The American Naturalist, 10.1086/605375, 174:4, (441-454), Online publication date: 1-Oct-2009. Boots M, Childs D, Reuman D and Mealor M (2009) Local Interactions Lead to Pathogen-Driven Change to Host Population Dynamics, Current Biology, 10.1016/j.cub.2009.07.070, 19:19, (1660-1664), Online publication date: 1-Oct-2009. Lion S and van Baalen M (2009) The evolution of juvenile-adult interactions in populations structured in age and space, Theoretical Population Biology, 10.1016/j.tpb.2009.05.005, 76:2, (132-145), Online publication date: 1-Sep-2009. Mitteldorf J and Pepper J (2009) Senescence as an adaptation to limit the spread of disease, Journal of Theoretical Biology, 10.1016/j.jtbi.2009.05.013, 260:2, (186-195), Online publication date: 1-Sep-2009. Woodroffe R, Donnelly C, Wei G, Cox D, Bourne F, Burke T, Butlin R, Cheeseman C, Gettinby G, Gilks P, Hedges S, Jenkins H, Johnston W, McInerney J, Morrison W and Pope L (2009) Social group size affects Mycobacterium bovis infection in European badgers ( Meles meles ) , Journal of Animal Ecology, 10.1111/j.1365-2656.2009.01545.x, 78:4, (818-827), Online publication date: 1-Jul-2009. Liu Q, Wang R and Jin Z (2009) Persistence, extinction and spatio-temporal synchronization of SIRS spatial models, Journal of Statistical Mechanics: Theory and Experiment, 10.1088/1742-5468/2009/07/P07007, 2009:07, (P07007) Su M, Li W, Li Z, Zhang F and Hui C (2008) The effect of landscape heterogeneity on host–parasite dynamics, Ecological Research, 10.1007/s11284-008-0568-z, 24:4, (889-896), Online publication date: 1-Jul-2009. King A, Shrestha S, Harvill E and Bjørnstad O (2009) Evolution of Acute Infections and the Invasion‐Persistence Trade‐Off, The American Naturalist, 10.1086/597217, 173:4, (446-455), Online publication date: 1-Apr-2009. Fouchet D, Le Pendu J, Guitton J, Guiserix M, Marchandeau S and Pontier D (2009) Evolution of microparasites in spatially and genetically structured host populations: The example of RHDV infecting rabbits, Journal of Theoretical Biology, 10.1016/j.jtbi.2008.11.021, 257:2, (212-227), Online publication date: 1-Mar-2009. Perisic A, Bauch C and Meyers L (2009) Social Contact Networks and Disease Eradicability under Voluntary Vaccination, PLoS Computational Biology, 10.1371/journal.pcbi.1000280, 5:2, (e1000280) ALIZON S, HURFORD A, MIDEO N and VAN BAALEN M (2008) Virulence evolution and the trade-off hypothesis: history, current state of affairs and the future, Journal of Evolutionary Biology, 10.1111/j.1420-9101.2008.01658.x, 22:2, (245-259), Online publication date: 1-Feb-2009. Carver S, Bestall A, Jardine A and Ostfeld R (2009) Influence of Hosts on the Ecology of Arboviral Transmission: Potential Mechanisms Influencing Dengue, Murray Valley Encephalitis, and Ross River Virus in Australia, Vector-Borne and Zoonotic Diseases, 10.1089/vbz.2008.0040, 9:1, (51-64), Online publication date: 1-Feb-2009. Buice M and Cowan J (2009) Statistical mechanics of the neocortex, Progress in Biophysics and Molecular Biology, 10.1016/j.pbiomolbio.2009.07.003, 99:2-3, (53-86), Online publication date: 1-Feb-2009. Ferdy J (2009) Virulence and transmission modes in metapopulations: When group selection increases virulence, Journal of Theoretical Biology, 10.1016/j.jtbi.2008.09.032, 256:2, (286-296), Online publication date: 1-Jan-2009. Goodnight C, Rauch E, Sayama H, De Aguiar M, Baranger M and Bar-yam Y (2008) Evolution in spatial predator–prey models and the "prudent predator": The inadequacy of steady-state organism fitness and the concept of individual and group selection, Complexity, 10.1002/cplx.20209, 13:5, (23-44), Online publication date: 1-May-2008. Lion S and Baalen M (2008) Self-structuring in spatial evolutionary ecology, Ecology Letters, 10.1111/j.1461-0248.2007.01132.x, 11:3, (277-295), Online publication date: 1-Mar-2008. Caraco T and Wang I (2008) Free-living pathogens: Life-history constraints and strain competition, Journal of Theoretical Biology, 10.1016/j.jtbi.2007.10.029, 250:3, (569-579), Online publication date: 1-Feb-2008. Kuo C, Corby-Harris V and Promislow D (2008) The unavoidable costs and unexpected benefits of parasitism: Population and metapopulation models of parasite-mediated competition, Journal of Theoretical Biology, 10.1016/j.jtbi.2007.10.004, 250:2, (244-256), Online publication date: 1-Jan-2008. Webb S, Keeling M and Boots M (2007) Host–parasite interactions between the local and the mean-field: How and when does spatial population structure matter?, Journal of Theoretical Biology, 10.1016/j.jtbi.2007.06.013, 249:1, (140-152), Online publication date: 1-Nov-2007. Lion S and van Baalen M (2007) From Infanticide to Parental Care: Why Spatial Structure Can Help Adults Be Good Parents, The American Naturalist, 10.1086/519462, 170:2, (E26-E46), Online publication date: 1-Aug-2007. Champagnat N and Méléard S (2007) Invasion and adaptive evolution for individual-based spatially structured populations, Journal of Mathematical Biology, 10.1007/s00285-007-0072-z, 55:2, (147-188), Online publication date: 2-Jul-2007. Liu Q and Jin Z (2007) Formation of spatial patterns in an epidemic model with constant removal rate of the infectives, Journal of Statistical Mechanics: Theory and Experiment, 10.1088/1742-5468/2007/05/P05002, 2007:05, (P05002-P05002) Boots M and Mealor M (2007) Local Interactions Select for Lower Pathogen Infectivity, Science, 10.1126/science.1137126, 315:5816, (1284-1286), Online publication date: 2-Mar-2007. Webb S, Keeling M and Boots M (2007) Spatially extended host–parasite interactions: The role of recovery and immunity, Theoretical Population Biology, 10.1016/j.tpb.2006.07.010, 71:2, (251-266), Online publication date: 1-Mar-2007. Kamo M, Sasaki A and Boots M (2007) The role of trade-off shapes in the evolution of parasites in spatial host populations: An approximate analytical approach, Journal of Theoretical Biology, 10.1016/j.jtbi.2006.08.013, 244:4, (588-596), Online publication date: 1-Feb-2007. Green D, Kiss I and Kao R (2006) Parasite strain coexistence in a heterogeneous host population, Oikos, 10.1111/j.2006.0030-1299.15155.x, 115:3, (495-503), Online publication date: 1-Dec-2006. Read J and Keeling M (2006) Disease evolution across a range of spatio-temporal scales, Theoretical Population Biology, 10.1016/j.tpb.2006.04.006, 70:2, (201-213), Online publication date: 1-Sep-2006. Caraco T, Glavanakov S, Li S, Maniatty W and Szymanski B (2006) Spatially structured superinfection and the evolution of disease virulence, Theoretical Population Biology, 10.1016/j.tpb.2005.12.004, 69:4, (367-384), Online publication date: 1-Jun-2006. Lion S, van Baalen M and Wilson W (2006) The evolution of parasite manipulation of host dispersal, Proceedings of the Royal Society B: Biological Sciences, 273:1590, (1063-1071), Online publication date: 7-May-2006. Dennehy J, Friedenberg N, Holt R and Turner P (2006) Viral Ecology and the Maintenance of Novel Host Use, The American Naturalist, 10.1086/499381, 167:3, (429-439), Online publication date: 1-Mar-2006. Gilchrist M and Coombs D (2006) Evolution of virulence: Interdependence, constraints, and selection using nested models, Theoretical Population Biology, 10.1016/j.tpb.2005.07.002, 69:2, (145-153), Online publication date: 1-Mar-2006. Rauch E and Bar-Yam Y (2006) Long-range interactions and evolutionary stability in a predator-prey system, Physical Review E, 10.1103/PhysRevE.73.020903, 73:2 DeAngelis D and Mooij W (2005) Individual-Based Modeling of Ecological and Evolutionary Processes, Annual Review of Ecology, Evolution, and Systematics, 10.1146/annurev.ecolsys.36.102003.152644, 36:1, (147-168), Online publication date: 1-Dec-2005. Bauch C (2005) The spread of infectious diseases in spatially structured populations: An invasory pair approximation, Mathematical Biosciences, 10.1016/j.mbs.2005.06.005, 198:2, (217-237), Online publication date: 1-Dec-2005. Wei W and Krone S (2005) Spatial invasion by a mutant pathogen, Journal of Theoretical Biology, 10.1016/j.jtbi.2005.03.016, 236:3, (335-348), Online publication date: 1-Oct-2005. Saramäki J and Kaski K (2005) Modelling development of epidemics with dynamic small-world networks, Journal of Theoretical Biology, 10.1016/j.jtbi.2004.12.003, 234:3, (413-421), Online publication date: 1-Jun-2005. Kamo M and Sasaki A (2005) Evolution toward multi-year periodicity in epidemics, Ecology Letters, 10.1111/j.1461-0248.2005.00734.x, 8:4, (378-385), Online publication date: 1-Apr-2005. De Castro F and Bolker B (2004) Mechanisms of disease-induced extinction, Ecology Letters, 10.1111/j.1461-0248.2004.00693.x, 8:1, (117-126) Keeling M (2005) EXTENSIONS TO MASS-ACTION MIXING Ecological Paradigms Lost, 10.1016/B978-012088459-9/50008-X, (107-142), . van Ballegooijen W and Boerlijst M (2004) Emergent trade-offs and selection for outbreak frequency in spatial epidemics, Proceedings of the National Academy of Sciences, 10.1073/pnas.0405682101, 101:52, (18246-18250), Online publication date: 28-Dec-2005. Kamo M and Boots M (2004) The curse of the pharaoh in space: free-living infectious stages and the evolution of virulence in spatially explicit populations, Journal of Theoretical Biology, 10.1016/j.jtbi.2004.07.005, 231:3, (435-441), Online publication date: 1-Dec-2004. Salzberg C, Antony A and Sayama H (2004) Evolutionary dynamics of cellular automata-based self-replicators in hostile environments, Biosystems, 10.1016/j.biosystems.2004.07.004, 78:1-3, (119-134), Online publication date: 1-Dec-2004. McKane A and Newman T (2004) Stochastic models in population biology and their deterministic analogs, Physical Review E, 10.1103/PhysRevE.70.041902, 70:4 Gudelj I and White K (2004) Spatial heterogeneity, social structure and disease dynamics of animal populations, Theoretical Population Biology, 10.1016/j.tpb.2004.04.003, 66:2, (139-149), Online publication date: 1-Sep-2004. Werfel J and Bar-Yam Y (2004) The evolution of reproductive restraint through social communication, Proceedings of the National Academy of Sciences, 10.1073/pnas.0305059101, 101:30, (11019-11024), Online publication date: 27-Jul-2004. Keeling M, Brooks S and Gilligan C (2004) Using conservation of pattern to estimate spatial parameters from a single snapshot, Proceedings of the National Academy of Sciences, 10.1073/pnas.0400335101, 101:24, (9155-9160), Online publication date: 15-Jun-2004. Boots M, Hudson P and Sasaki A (2004) Large Shifts in Pathogen Virulence Relate to Host Population Structure, Science, 10.1126/science.1088542, 303:5659, (842-844), Online publication date: 6-Feb-2004. Boots M and Bowers R (2003) Baseline criteria and the evolution of hosts and parasites: D0, R0 and competition for resources between strains, Journal of Theoretical Biology, 10.1016/S0022-5193(03)00105-X, 223:3, (361-365), Online publication date: 1-Aug-2003. Brown D and Hastings A (2003) Resistance may be futile: dispersal scales and selection for disease resistance in competing plants, Journal of Theoretical Biology, 10.1016/S0022-5193(03)00044-4, 222:3, (373-388), Online publication date: 1-Jun-2003. Read J and Keeling M (2003) Disease evolution on networks: the role of contact structure, Proceedings of the Royal Society of London. Series B: Biological Sciences, 270:1516, (699-708), Online publication date: 7-Apr-2003. de Aguiar M, Rauch E and Bar-Yam Y (2003) Mean-field approximation to a spatial host-pathogen model, Physical Review E, 10.1103/PhysRevE.67.047102, 67:4 RAUCH E, SAYAMA H and BAR-YAM Y (2003) Dynamics and Genealogy of Strains in Spatially Extended Host–Pathogen Models, Journal of Theoretical Biology, 10.1006/jtbi.2003.3127, 221:4, (655-664), Online publication date: 1-Apr-2003. Boots M and Sasaki A (2003) Parasite evolution and extinctions, Ecology Letters, 10.1046/j.1461-0248.2003.00426.x, 6:3, (176-182), Online publication date: 1-Mar-2003. Levin S and Pacala S (2003) Ecosystem Dynamics Environmental Degradation and Institutional Responses, 10.1016/S1574-0099(03)01007-6, (61-95), . Norman R and Shankland C (2003) Developing the Use of Process Algebra in the Derivation and Analysis of Mathematical Models of Infectious Disease Computer Aided Systems Theory - EUROCAST 2003, 10.1007/978-3-540-45210-2_37, (404-414), . Hixon M, Pacala S and Sandin S (2002) POPULATION REGULATION: HISTORICAL CONTEXT AND CONTEMPORARY CHALLENGES OF OPEN VS. CLOSED SYSTEMS, Ecology, 10.1890/0012-9658(2002)083[1490:PRHCAC]2.0.CO;2, 83:6, (1490-1508), Online publication date: 1-Jun-2002. Boots M and Sasaki A (2002) Parasite‐Driven Extinction in Spatially Explicit Host‐Parasite Systems, The American Naturalist, 10.1086/339996, 159:6, (706-713), Online publication date: 1-Jun-2002. O'Keefe K and Antonovics J (2002) Playing by Different Rules: The Evolution of Virulence in Sterilizing Pathogens, The American Naturalist, 10.1086/339990, 159:6, (597-605), Online publication date: 1-Jun-2002. Solé R, Levin S, Pascual M, Roy M, Guichard F and Flierl G (2002) Cluster size distributions: signatures of self–organization in spatial ecologies, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 357:1421, (657-666), Online publication date: 29-May-2002. NAUG D and CAMAZINE S (2002) The Role of Colony Organization on Pathogen Transmission in Social Insects, Journal of Theoretical Biology, 10.1006/jtbi.2001.2524, 215:4, (427-439), Online publication date: 1-Apr-2002. Sato K, Yoshida N and Konno N (2002) Parity law for population dynamics of N-species with cyclic advantage competitions, Applied Mathematics and Computation, 10.1016/S0096-3003(00)00155-7, 126:2-3, (255-270), Online publication date: 1-Mar-2002. Pels B, de Roos A and Sabelis M (2002) Evolutionary Dynamics of Prey Exploitation in a Metapopulation of Predators, The American Naturalist, 10.1086/324788, 159:2, (172-189), Online publication date: 1-Feb-2002. Sasaki A, Kawaguchi I and Yoshimori A (2002) Spatial Mosaic and Interfacial Dynamics in a Müllerian Mimicry System, Theoretical Population Biology, 10.1006/tpbi.2001.1552, 61:1, (49-71), Online publication date: 1-Feb-2002. Keeling M, Wilson H and Pacala S (2002) Deterministic Limits to Stochastic Spatial Models of Natural Enemies, The American Naturalist, 10.1086/324119, 159:1, (57-80), Online publication date: 1-Jan-2002. Young W, Roberts A and Stuhne G (2001) Reproductive pair correlations and the clustering of organisms, Nature, 10.1038/35085561, 412:6844, (328-331), Online publication date: 1-Jul-2001. Caraco T, Duryea M, Glavanakov S, Maniatty W and Szymanski B (2001) Host Spatial Heterogeneity and the Spread of Vector-Borne Infection, Theoretical Population Biology, 10.1006/tpbi.2000.1517, 59:3, (185-206), Online publication date: 1-May-2001. YU D (2008) Parasites of mutualisms, Biological Journal of the Linnean Society, 10.1111/j.1095-8312.2001.tb01336.x, 72:4, (529-546), Online publication date: 1-Apr-2001. Socolar J, Richards S and Wilson W (2001) Evolution in a spatially structured population subject to rare epidemics, Physical Review E, 10.1103/PhysRevE.63.041908, 63:4 Keeling M and Rand D (2001) Spatial Correlations and Local Fluctuations in Host-Parasite Models From Finite to Infinite Dimensional Dynamical Systems, 10.1007/978-94-010-0732-0_2, (5-57), . DURRETT R and LEVIN S (2000) Lessons on Pattern Formation from Planet WATOR, Journal of Theoretical Biology, 10.1006/jtbi.2000.2061, 205:2, (201-214), Online publication date: 1-Jul-2000. Boots and Sasaki (2000) The evolutionary dynamics of local infection and global reproduction in host-parasite interactions, Ecology Letters, 10.1046/j.1461-0248.2000.00139.x, 3:3, (181-185), Online publication date: 1-May-2000. HARAGUCHI Y and SASAKI A (2000) The Evolution of Parasite Virulence and Transmission Rate in a Spatially Structured Population, Journal of Theoretical Biology, 10.1006/jtbi.1999.1065, 203:2, (85-96), Online publication date: 1-Mar-2000. Keeling M (2000) Evolutionary trade–offs at two time–scales: competition versus persistence, Proceedings of the Royal Society of London. Series B: Biological Sciences, 267:1441, (385-391), Online publication date: 22-Feb-2000.Richards S, Wilson W and Socolar J (1999) Selection for intermediate mortality and reproduction rates in a spatially structured population, Proceedings of the Royal Society of London. Series B: Biological Sciences, 266:1436, (2383-2388), Online publication date: 7-Dec-1999.Boots M and Sasaki A (1999) 'Small worlds' and the evolution of virulence: infection occurs locally and at a distance, Proceedings of the Royal Society of London. Series B: Biological Sciences, 266:1432, (1933-1938), Online publication date: 7-Oct-1999. Wallinga J, Edmunds W and Kretzschmar M (1999) Perspective: human contact patterns and the spread of airborne infectious diseases, Trends in Microbiology, 10.1016/S0966-842X(99)01546-2, 7:9, (372-377), Online publication date: 1-Sep-1999. GANDHI A, LEVIN S and ORSZAG S (1999) Nucleation and Relaxation from Meta-stability in Spatial Ecological Models, Journal of Theoretical Biology, 10.1006/jtbi.1999.0978, 200:2, (121-146), Online publication date: 1-Sep-1999. Keeling M (1999) Correlation equations for endemic diseases: externally imposed and internally generated heterogeneity, Proceedings of the Royal Society of London. Series B: Biological Sciences, 266:1422, (953-960), Online publication date: 7-May-1999. KEELING M, MILNER-GULLAND E and CLAYTON L (2008) SPATIAL DYNAMICS OF TWO HARVESTED WILD PIG POPULATIONS, Natural Resource Modeling, 10.1111/j.1939-7445.1999.tb00007.x, 12:1, (147-169) Durrett R (1999) Stochastic Spatial Models, SIAM Review, 10.1137/S0036144599354707, 41:4, (677-718), Online publication date: 1-Jan-1999. Durrett R (1999) Stochastic spatial models Mathematics Inspired by Biology, 10.1007/BFb0092375, (39-94), . de Roos A, McCauley E and Wilson W (1998) Pattern Formation and the Spatial Scale of Interaction between Predators and Their Prey, Theoretical Population Biology, 10.1006/tpbi.1997.1345, 53:2, (108-130), Online publication date: 1-Apr-1998. Durrett R and Levin S (1998) Spatial Aspects of Interspecific Competition, Theoretical Population Biology, 10.1006/tpbi.1997.1338, 53:1, (30-43), Online publication date: 1-Feb-1998. Savill N and Hogeweg P (1998) Spatially induced speciation prevents extinction: the evolution of dispersal distance in oscillatory predator-prey models, Proceedings of the Royal Society of London. Series B: Biological Sciences, 265:1390, (25-32), Online publication date: 7-Jan-1998.Keeling M, Mezić I, Hendry R, McGlade J and Rand D (1997) Characteristic length scales of spatial models in ecology via fluctuation analysis, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 352:1361, (1589-1601), Online publication date: 29-Nov-1997.Rhodes C, Jensen H and Anderson R (1997) On the critical behaviour of simple epidemics, Proceedings of the Royal Society of London. Series B: Biological Sciences, 264:1388, (1639-1646), Online publication date: 22-Nov-1997. Rhodes C and Anderson R (1997) Epidemic Thresholds and Vaccination in a Lattice Model of Disease Spread, Theoretical Population Biology, 10.1006/tpbi.1997.1323, 52:2, (101-118), Online publication date: 1-Oct-1997. Wilson H and Hassell M (1997) Host–parasitoid spatial models: the interplay of demographic stochasticity and dynamics, Proceedings of the Royal Society of London. Series B: Biological Sciences, 264:1385, (1189-1195), Online publication date: 22-Aug-1997. Savill N and Hogeweg P (1997) Evolutionary Stagnation Due to Pattern-Pattern Interactions in a Coevolutionary Predator-Prey Model, Artificial Life, 10.1162/artl.1997.3.2.81, 3:2, (81-100), Online publication date: 1-Apr-1997. Rhodes C and Anderson R (1997) A scaling analysis of measles epidemics in a small population, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 351:1348, (1679-1688), Online publication date: 29-Dec-1997.Swinton J and Gilligan C (1997) Dutch elm disease and the future of the elm in the U.K.: a quantitative analysis, Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, 351:1340, (605-615), Online publication date: 29-May-1996.May R and Nowak M (1997) Coinfection and the evolution of parasite virulence, Proceedings of the Royal Society of London. Series B: Biological Sciences, 261:1361, (209-215), Online publication date: 22-Aug-1995.Rand D and Wilson H (1997) Using spatio-temporal chaos and intermediate-scale determinism to quantify spatially extended ecosystems, Proceedings of the Royal Society of London. Series B: Biological Sciences, 259:1355, (111-117), Online publication date: 22-Feb-1995. This Issue23 January 1995Volume 259Issue 1354 Article InformationDOI:https://doi.org/10.1098/rspb.1995.0009Published by:Royal SocietyPrint ISSN:0962-8452Online ISSN:1471-2954History: Manuscript received26/07/1994Manuscript accepted06/09/1994Published online01/01/1997Published in print23/01/1995 License:Scanned images copyright © 2017, Royal Society Citations and impact Large datasets are available through Proceedings B's partnership with Dryad
Referência(s)