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Publications

Journal articles      Book chapters and Proceedings       Books      Other publications

(Names of supervised students are highlighted in bold face type.)

Journal articles (peer-reviewed)

  1. Hilker FM, Kolb LD, Hamelin FM (2024) Selfish grower behavior can group-optimally eradicate plant diseases caused by coinfection. International Game Theory Review, accepted. doi 
  2. Grumbach C, Reurik FN, Segura J, Franco D, Hilker FM (2023) The effect of dispersal on asymptotic total population size in discrete- and continuous-time two-patch models. Journal of Mathematical Biology 87, 60.   
  3. Hamelin FM, Hilker FM, Dumont Y (2023) Spatial spread of infectious diseases with conditional vector preferences. Journal of Mathematical Biology 87, 38.  
  4. Hilker FM, Castel PCD, Rodrigues LAD, Giardini GSY, Mistro DC, Rossato M, Maini PK (accepted) Current trends and perspectives in mathematical biology. Revista de Modelamiento Matemático de Sistemas Biológicos, to appear.  
  5. Vortkamp I, Hilker FM (2023) Farmers’ land-use decision making: A dynamical modelling approach that integrates qualitative knowledge about social norms into a quantitative model. People and Nature 5, 1147-1159.  
  6. Werner J, Pietsch T, Hilker FM, Arndt H (2022) Intrinsic nonlinear dynamics drive single-species systems. Proceedings of the National Academy of Sciences 119, e2209601119.  
  7. Lois-Prados C, Hilker FM (2022) Bifurcation sequences in a discontinuous piecewise-smooth map combining constant-catch and threshold-based harvesting strategies. SIAM Journal on Applied Dynamical Systems 21, 470-499.  
  8. DeAngelis DL, Franco D, Hastings A, Hilker FM, Lenhart S, Lutscher F, Petrovskaya N, Petrovskii S, Tyson RC (2021) Towards building a sustainable future: Positioning ecological modelling for impact in ecosystems management. Bulletin of Mathematical Biology 83, 107.   
  9. Grey S, Lenhart S, Hilker FM, Franco D (2021) Optimal control of harvesting timing in discrete population models. Natural Resource Modeling 34, e12321.  
  10. Sun AT, Hilker FM (2021) Comparison between best-response dynamics and replicator dynamics in a social-ecological model of lake eutrophication. Journal of Theoretical Biology 509, 110491.    
  11. Adamson MW, Dawes JHP, Hastings A, Hilker FM (2020) Forecasting resilience profiles of the run-up to regime shifts in nearly-one-dimensional systems. Journal of The Royal Society Interface 17, 20200566.    
  12. Adamson MW, Hilker FM (2020) Resource-harvester cycles caused by delayed knowledge of the harvested population state can be dampened by harvester forecasting. Theoretical Ecology 13, 425-434.   
  13. Hilker FM, Liz E (2020) Threshold harvesting as a conservation or exploitation strategy in population management. Theoretical Ecology 13, 519–536.  
  14. Hilker FM, Sun AT, Allen LJS, Hamelin FM (2020) Separate seasons of infection and reproduction can lead to multi-year population cycles. Journal of Theoretical Biology 489, 110158.  
  15. Segura J, Hilker FM, Franco D (2020) Degenerate period adding bifurcation structure of one-dimensional bimodal piecewise linear maps. SIAM Journal on Applied Mathematics 80, 1356-1376.  
  16. Sun AT, Hilker FM (2020) Analyzing the mutual feedbacks between lake pollution and human behaviour in a mathematical social-ecological model. Ecological Complexity 43, 100834.  
  17. Vortkamp I, Barraquand F, Hilker FM (2020) Ecological Allee effects modulate optimal strategies for conservation in agricultural landscapes. Ecological Modelling 435, 109208.   
  18. Vortkamp I, Schreiber SJ, Hastings A, Hilker FM (2020) Multiple attractors and long transients in spatially structured populations with an Allee effect. Bulletin for Mathematical Biology 82, 82.   
  19. Allen LJS, Bokil VA, Cunniffe NJ, Hamelin FM, Hilker FM, Jeger MJ (2019) Modelling vector transmission and epidemiology of co-infecting plant viruses. Viruses 11, 1153.  
  20. Bate AM, Hilker FM (2019) Preytaxis and travelling waves in an eco-epidemiological model. Bulletin of Mathematical Biology 81, 995-1030.  
  21. Bulai IM, Hilker FM (2019) Eco-epidemiological interactions with predator interference and infection. Theoretical Population Biology 130, 191-202.   
  22. Hamelin FM, Allen LJS, Bokil VA, Gross LJ, Hilker FM, Jeger MJ, Manore CA, Power AG, Rúa MA, Cunniffe NJ (2019) Co-infections by non-interacting pathogens are not independent and require new tests of interaction. PLoS Biology 17, e3000551.  
  23. Hilker FM, Liz E (2019) Proportional threshold harvesting in discrete-time population models. Journal of Mathematical Biology 79, 1927-1951.  
  24. Schakau V, Hilker FM, Lewis MA (2019) Fish disease dynamics in changing rivers: Salmonid Ceratomyxosis in the Klamath River. Ecological Complexity 40, 100776.   
  25. Segura J, Hilker FM, Franco S (2019) Enhancing population stability with combined adaptive limiter control and finding the optimal harvesting-restocking balance. Theoretical Population Biology 130, 1-12.   
  26. Weide V, Varriale MC, Hilker FM (2019) Hydra effect and paradox of enrichment in discrete-time predator-prey models. Mathematical Biosciences 310, 120-127.   
  27. Francomano E, Hilker FM, Paliaga M, Venturino E (2018) Separatrix reconstruction to identify tipping points in an eco-epidemiological model. Applied Mathematics and Computation 318, 80-91.    
  28. 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 GSK, Tyson RC (2017) Moving forward in circles: challenges and opportunities in modeling population cycles. Ecology Letters 20, 1074-1092.   
  29. Hamelin FM, Hilker FM, Sun AT, Jeger MJ, Hajimorad MR, Allen LJS, Prendeville HR (2017) The evolution of parasitic and mutualistic plant-virus symbioses through transmission-virulence trade-offs. Virus Research 241, 77-87.     
  30. Hilker FM, Allen LJS, Bokil VA, Briggs CJ, Feng Z, Garrett KA, Gross LJ, Hamelin FM, Jeger MJ, Manore CA, Power AG, Redinbaugh MG, Rua MA, Cunniffe NJ (2017) Modelling virus coinfection to inform management of maize lethal necrosis in Kenya. Phytopathology 107, 1095-1108.   
  31. Hilker FM, Paliaga M, Venturino E (2017) Diseased social predators. Bulletin of Mathematical Biology 79, 2175-2196.    
  32. Numfor E, Hilker FM, Lenhart S (2017) Optimal culling and biocontrol in a predator-prey model. Bulletin of Mathematical Biology 79, 88-116.  
  33. Segura J, Hilker FM, Franco D (2017) Population control methods in stochastic extinction and outbreak scenarios. PLoS ONE 12, e0170837.  
  34. Teixeira Alves M, Hilker FM (2017) Hunting cooperation and Allee effects in predators. Journal of Theoretical Biology 419, 13-22.  
  35. Bengfort M, Malchow H, Hilker FM (2016) The Fokker-Planck law of diffusion and pattern formation in heterogeneous environments. Journal of Mathematical Biology 73, 683-704.  
  36. Segura J, Hilker FM, Franco D (2016) Adaptive threshold harvesting and the suppression of transients. Journal of Theoretical Biology 395, 103-114. 
  37. Bate AM, Hilker FM (2014) Disease in group-defending prey can benefit predators. Theoretical Ecology 7, 87-100.   
  38. Bengfort M, Feudel U, Hilker FM, Malchow H (2014) Plankton blooms and patchiness generated by heterogeneous physical environments. Ecological Complexity 20, 185-194.  
  39. Cid B, Hilker FM, Liz E (2014) Harvest timing and its population dynamic consequences in a discrete single-species model. Mathematical Biosciences 248, 78-87.  
  40. Franco D, Hilker FM (2014) Stabilizing populations with adaptive limiters: prospects and fallacies. SIAM Journal on Applied Dynamical Systems 13, 447-465.   
  41. Jin Y, Hilker FM, Steffler PM, Lewis MA (2014) Seasonal invasion dynamics in a spatially heterogeneous river with fluctuating flows. Bulletin of Mathematical Biology 76, 1522-1565.  
  42. Sherratt JA, Dagbovie AS, Hilker FM (2014) A mathematical biologist's guide to absolute and convective instability. Bulletin of Mathematical Biology 76, 1-26.   
  43. Sieber M, Malchow H, Hilker FM (2014) Disease-induced modification of prey competition in eco-epidemiological models. Ecological Complexity 18, 74-82.  
  44. Bate AM, Hilker FM (2013) Complex dynamics in an eco-epidemiological model. Bulletin of Mathematical Biology 75, 2059-2078.  
  45. Bate AM, Hilker FM (2013) Predator-prey oscillations can shift when diseases become endemic. Journal of Theoretical Biology 316, 1-8.  
  46. Franco D, Hilker FM (2013) Adaptive limiter control of unimodal population maps. Journal of Theoretical Biology 337, 161-173.   
  47. Hilker FM, Liz E (2013) Harvesting, census timing and "hidden" hydra effects. Ecological Complexity 14, 95-107.  
  48. Anderson KE, Hilker FM, Nisbet RM (2012) Directional biases and resource-dependence in dispersal generate spatial patterning in a consumer-producer model. Ecology Letters 15, 209-217.  
  49. Bate AM, Hilker FM (2012) Rabbits protecting birds: hypopredation and limitations of hyperpredation. Journal of Theoretical Biology 297, 103-115.  
  50. Fronhofer EA, Kubisch A, Hilker FM, Hovestadt T, Poethke HJ (2012) Why are metapopulations so rare? Ecology 93, 1967-1978.  
  51. Sieber M, Hilker FM (2012) The hydra effect in predator-prey models. Journal of Mathematical Biology 64, 341-360.  
  52. Dattani J, Blake JCH, Hilker FM (2011) Target-oriented chaos control. Physics Letters A 375, 3986-3992.  
  53. Sieber M, Hilker FM (2011) Prey, predators, parasites: intraguild predation or simpler community modules in disguise? Journal of Animal Ecology 80, 414-421.  
  54. Hilker FM, Lewis MA (2010) Predator-prey systems in streams and rivers. Theoretical Ecology 3, 175-193.  
  55. Hilker FM (2010) Population collapse to extinction: the catastrophic combination of parasitism and Allee effect. Journal of Biological Dynamics 4, 86-101.  
  56. Oliveira NM, Hilker FM (2010) Modelling disease introduction as biological control of invasive predators to preserve endangered prey. Bulletin of Mathematical Biology 72, 444-468.  
  57. Stollenwerk N, van Noort S, Martins J, Aguiar M, Hilker F, Pinto A, Gomes G (2010) A spatially stochastic epidemic model with partial immunization shows in mean field approximation the reinfection threshold. Journal of Biological Dynamics 4, 634-649.  
  58. Hilker FM, Langlais M, Malchow H (2009) The Allee effect and infectious diseases: extinction, multistability, and the (dis-)appearance of oscillations. American Naturalist 173(1), 72-88.  
  59. Hilker FM, Schmitz K (2008) Disease-induced stabilization of predator-prey oscillations. Journal of Theoretical Biology 255(3), 299-306.  
  60. Gomes MGM, Rodrigues P, Hilker FM, Mantilla-Beniers NB, Muehlen M, Paulo ACAS, Medley GF (2007) Implications of partial immunity on the prospects for tuberculosis control by post-exposure interventions. Journal of Theoretical Biology 248(4), 608-617.  
  61. Hilker FM, Westerhoff FH (2007) Preventing extinction and outbreaks in chaotic populations. American Naturalist 170(2), 232-241.  
  62. Hilker FM, Langlais M, Petrovskii SV, Malchow H (2007). A diffusive SI model with Allee effect and application to FIV. Mathematical Biosciences 206(1), 61-80.  
  63. Hilker FM, Westerhoff FH (2007) Triggering crashes in chaotic dynamics. Physics Letters A 362(5-6), 407-411.  
  64. Hilker FM, Hinsch M, Poethke HJ (2006) Parameterizing, evaluating and comparing metapopulation models with data from individual-based simulations. Ecological Modelling 199(4), 476-485.  
  65. Hilker FM, Malchow H (2006) Strange periodic attractors in a prey-predator system with infected prey. Mathematical Population Studies 13(3), 119-134.  
  66. Hilker FM, Malchow H, Langlais M, Petrovskii SV (2006) Oscillations and waves in a virally infected plankton system: Part II: Transition from lysogeny to lysis. Ecological Complexity 3(3), 200-208.  
  67. Hilker FM, Westerhoff FH (2006) Paradox of simple limiter control. Physical Review E 73(5), 052901.  
  68. Becks L, Hilker FM, Malchow H, Jürgens K, Arndt H (2005) Experimental demonstration of chaos in a microbial food web. Nature 435, 1226-1229.  
  69. Hilker FM, Lewis MA, Seno H, Langlais M, Malchow H (2005) Pathogens can slow down or reverse invasion fronts of their hosts. Biological Invasions 7(5), 817-832.  
  70. Malchow H, Hilker FM, Sarkar RR, Brauer K (2005) Spatiotemporal patterns in an excitable plankton system with lysogenic viral infection. Mathematical and Computer Modelling 42(9-10), 1035-1048.  
  71. Petrovskii SV, Malchow H, Hilker FM, Venturino E (2005) Patterns of patchy spread in deterministic and stochastic models of biological invasion and biological control. Biological Invasions 7(5), 771-793.  
  72. Malchow H, Hilker FM, Petrovskii SV (2004) Noise and productivity dependence of spatiotemporal pattern formation in a prey-predator system. Discrete and Continuous Dynamical Systems B 4(3), 705-711.  
  73. Malchow H, Hilker FM, Petrovskii SV, Brauer K (2004) Oscillations and waves in a virally infected plankton system: Part I: The lysogenic stage. Ecological Complexity 1(3), 211-223.  


    Book chapters and Proceedings (peer-reviewed)

  74. Francomano E, Hilker FM, Paliaga M, Venturino E (2017) An efficient method to reconstruct invariant manifolds of saddle points. Dolomites Research Notes on Approximation 10, 25-30.    
  75. Francomano E, Hilker FM, Paliaga M, Venturino E (2016) On basins of attraction for a predator-prey model via meshless approximation. AIP Conference Proceedings 1776(1), 070007.  
  76. Liz E, Hilker FM (2014) Harvesting and dynamics in some one-dimensional population models. In Theory and Applications of Difference Equations and Discrete Dynamical Systems (AlSharawi Z, Cushing J, Elaydi S, eds.). Springer Proceedings in Mathematics & Statistics 102, 61-73.   
  77. Stone L, Hilker FM, Katriel G (2012) SIR models. In Encyclopedia of Theoretical Ecology (Hastings A, Gross L, eds.). University of California Press, Berkeley, pp. 648-658.
  78. Hilker FM (2009) Epidemiological models with demographic Allee effect. In Biomat 2008: International Symposium on Mathematical and Computational Biology (Mondaini RP, ed.). World Scientific, Singapore, pp. 52-77. doi:10.1142/9789814271820_0003
  79. Malchow H, Hilker FM, Siekmann I, Petrovskii SV, Medvinsky AB (2008) Mathematical models of pattern formation in planktonic predation-diffusion systems: a review. In Aspects of Mathematical Modelling (Hosking RJ, Venturino E, eds.). Birkhäuser, Basel, pp. 1-26.
  80. Malchow H, Hilker FM (2007) Pattern formation in models of nonlinear plankton dynamics: a minireview. In Multiple Scales in Ecology (Schröder B, Reuter H, Reineking B, eds.), Theorie in der Ökologie, vol. 13, Peter Lang Verlag, Frankfurt/M., pp. 3-20.
  81. Hilker FM, Hinsch M, Poethke HJ (2004) How to compare different conceptual approaches to metapopulation modelling. In Complexity and Integrated Resources Management (Pahl-Wostl C, Schmidt S, Rizzoli AE, Jakeman AT, eds.). Transactions of the 2nd Biennial Meeting of the International Environmental Modelling and Software Society, Volume 2, pp. 902-907. International Environmental Modelling and Software Society, Manno, Switzerland, ISBN 88-900787-1-5.   
  82. Malchow H, Petrovskii SV, Hilker FM (2003) Models of spatiotemporal pattern formation in plankton dynamics. Nova Acta Leopoldina NF 88(332), 325-340.


    Books

  83. Hilker FM (2005) Spatiotemporal patterns in models of biological invasion and epidemic spread. Logos Verlag, Berlin, ISBN 3-8325-1050-8.


    Other publications

  84. Hilker FM, Dal Castel PC, Díaz Rodrigues LA, Giardini GSY, Mistro DC, Rossato M, Maini PK (2023) Current trends and perspectives in mathematical biology. Revista de Modelamiento Matemático de Sistemas Biológicos 3, 15-24. (invited)    
  85. Hilker FM, Westerhoff FH (2005) Control of chaotic population dynamics: Ecological and economic considerations. Beiträge des Instituts für Umweltsystemforschung (Matthies M, ed.), No. 32, ISSN 1433-3805.  
  86. Hilker FM (2003) Parametrisierung von Metapopulationsmodellen. Beiträge des Instituts für Umweltsystemforschung (Matthies M, ed.), No. 25, ISSN 1433-3805.

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