Access the full text.
Sign up today, get DeepDyve free for 14 days.
M. Begon, R. Bowers, N. Kadianakis, D. Hodgkinson (1992)
Disease and Community Structure: The Importance of Host Self-Regulation in a Host-Host-Pathogen ModelThe American Naturalist, 139
Paul Ewald (1995)
The evolution of virulence: a unifying link between parasitology and ecology.The Journal of parasitology, 81 5
T. Yates, J. Mills, C. Parmenter, T. Ksiazek, R. Parmenter, John Castle, C. Calisher, S. Nichol, K. Abbott, J. Young, M. Morrison, B. Beaty, J. Dunnum, R. Baker, J. Salazar-Bravo, C. Peters (2002)
The Ecology and Evolutionary History of an Emergent Disease: Hantavirus Pulmonary Syndrome, 52
P. Moorcroft, G. Hurtt, S. Pacala (2001)
A METHOD FOR SCALING VEGETATION DYNAMICS: THE ECOSYSTEM DEMOGRAPHY MODEL (ED)Ecological Monographs, 71
P. Chesson (1985)
Coexistence of Competitors in Spatially and Temporally Varying Environments: A Look at the Combined Effects of Different Sorts of VariabilityTheoretical Population Biology, 28
R. Macarthur, R. Levins (1967)
The Limiting Similarity, Convergence, and Divergence of Coexisting SpeciesThe American Naturalist, 101
M. Boots, A. Sasaki (1999)
‘Small worlds’ and the evolution of virulence: infection occurs locally and at a distanceProceedings of the Royal Society of London. Series B: Biological Sciences, 266
C. Clark (1993)
Mathematical Bioeconomics: The Optimal Management of Renewable Resources.Biometrics, 49
S. Gandon, M. Mackinnon, S. Nee, A. Read (2001)
Imperfect vaccines and the evolution of pathogen virulenceNature, 414
G. Hurtt, R. Armstrong (1999)
A pelagic ecosystem model calibrated with BATS and OWSI data, 46
R. Monson, J. Ehleringer, C. Field (1995)
Scaling Physiological Processes: Leaf to GlobeBioScience
Jessica Green, A. Hastings, P. Arzberger, F. Ayala, K. Cottingham, K. Cuddington, F. Davis, J. Dunne, M. Fortin, L. Gerber, M. Neubert (2005)
Complexity in Ecology and Conservation: Mathematical, Statistical, and Computational Challenges, 55
M. Mackinnon, A. Read (1999)
Selection for high and low virulence in the malaria parasiteProceedings of the Royal Society of London. Series B: Biological Sciences, 266
O. Bjørnstad, B. Grenfell (2001)
Noisy Clockwork: Time Series Analysis of Population Fluctuations in AnimalsScience, 293
J. Sanchirico, J. Wilen (2001)
A Bioeconomic Model of Marine Reserve CreationJournal of Environmental Economics and Management, 42
A. Osterhaus (2000)
[Circulation of virus and interspecies contamination in wild animals].Bulletin de la Societe de pathologie exotique, 93 3
P. Reich, M. Walters, D. Ellsworth (1997)
From tropics to tundra: global convergence in plant functioning.Proceedings of the National Academy of Sciences of the United States of America, 94 25
M. Mackinnon, A. Read (1999)
GENETIC RELATIONSHIPS BETWEEN PARASITE VIRULENCE AND TRANSMISSION IN THE RODENT MALARIA PLASMODIUM CHABAUDIEvolution, 53
L. Pitelka, R. Gardner, J. Ash, S. Berry, H. Gitay, I. Noble, A. Saunders, R. Bradshaw, L. Brubaker, J. Clark, M. Davis, S. Sugita, James Dyer, R. Hengeveld, G. Hope, B. Huntley, G. King, S. Lavorel, R. Mack, G. Malanson, M. McGlone, I. Prentice, M. Rejmánek (1997)
Plant migration and climate changeAmerican Scientist, 85
W. Parton, J. Scurlock, D. Ojima, D. Schimel, D. Hall (1995)
Impact of climate change on grassland production and soil carbon worldwideGlobal Change Biology, 1
Botsford, Gaines (2001)
Dependence of sustainability on the configuration of marine reserves and larval dispersal distanceEcology Letters, 4
L. Segel (2001)
Controlling the immune system: diffuse feedback via a diffuse informational network.Novartis Foundation symposium, 239
G. Leo, A. Dobson (1996)
Allometry and simple epidemic models for microparasitesNature, 379
A. Lotka (1925)
Elements of Physical Biology.Nature, 116
A. Allen, James Brown, James Gillooly (2002)
Global Biodiversity, Biochemical Kinetics, and the Energetic-Equivalence RuleScience, 297
James Brown, James Gillooly, A. Allen, V. Savage, G. West (2004)
Toward a metabolic theory of ecologyEcology, 85
Alan Hastings, L. Botsford (1999)
Equivalence in yield from marine reserves and traditional fisheries managementScience, 284 5419
James Miller, M. Turner, E. Smithwick, C. Dent, E. Stanley (2004)
Spatial Extrapolation: The Science of Predicting Ecological Patterns and Processes, 54
U. Dieckmann, J. Metz, M. Sabelis, K. Sigmund (2002)
Adaptive Dynamics of Infectious Diseases: List of Boxes
A. Ives, B. Dennis, K. Cottingham, S. Carpenter (2003)
ESTIMATING COMMUNITY STABILITY AND ECOLOGICAL INTERACTIONS FROM TIME‐SERIES DATAEcological Monographs, 73
S. Burrows, S. Gower, M. Clayton, D. Mackay, D. Ahl, J. Norman, G. Diak (2002)
Application of Geostatistics to Characterize Leaf Area Index (LAI) from Flux Tower to Landscape Scales Using a Cyclic Sampling DesignEcosystems, 5
H. Fitz, E. DeBellevue, R. Costanza, R. Boumans, T. Maxwell, L. Wainger, F. Sklar (1996)
Development of a general ecosystem model for a range of scales and ecosystemsEcological Modelling, 88
O. Bjørnstad, B. Finkenstädt, B. Grenfell (2002)
Dynamics of measles epidemics: Estimating scaling of transmission rates using a time series sir modelEcological Monographs, 72
P. Valpine (2003)
BETTER INFERENCES FROM POPULATION-DYNAMICS EXPERIMENTS USING MONTE CARLO STATE-SPACE LIKELIHOOD METHODSEcology, 84
A. Ives, R. May (1985)
Competition within and between species in a patchy environment: Relations between microscopic and macroscopic modelsJournal of Theoretical Biology, 115
C. Bernacchi, J. Coleman, F. Bazzaz, K. McConnaughay (2000)
Biomass allocation in old‐field annual species grown in elevated CO2 environments: no evidence for optimal partitioningGlobal Change Biology, 6
S. Kooijman (2000)
Dynamic Energy and Mass Budgets in Biological Systems
S. Frank (1996)
Models of Parasite VirulenceThe Quarterly Review of Biology, 71
A. Huppert, B. Blasius, L. Stone (2002)
A Model of Phytoplankton BloomsThe American Naturalist, 159
M. Keeling, C. Gilligan (2000)
Bubonic plague: a metapopulation model of a zoonosisProceedings of the Royal Society of London. Series B: Biological Sciences, 267
K. Schmidt, R. Ostfeld (2001)
BIODIVERSITY AND THE DILUTION EFFECT IN DISEASE ECOLOGYEcology, 82
L. Benda, L. Poff, C. Tague, M. Palmer, J. Pizzuto, S. Cooper, E. Stanley, G. Moglen (2002)
How to Avoid Train Wrecks When Using Science in Environmental Problem Solving, 52
F. Müller (1997)
State-of-the-art in ecosystem theoryEcological Modelling, 100
S. Reid, C. Herbelin, Alyssa Bumbaugh, R. Selander, T. Whittam (2000)
Parallel evolution of virulence in pathogenic Escherichia coliNature, 406
F. Müller (1992)
Hierarchical approaches to ecosystem theoryEcological Modelling, 63
U. Sommer (1991)
A comparison of the Droop and the Monod models of nutrient limited growth applied to natural populations of phytoplanktonFunctional Ecology, 5
M. Pace, P. Groffman (1998)
Successes, Limitations, and Frontiers in Ecosystem Science: Reflections on the Seventh Cary ConferenceEcosystems, 1
R. Lenski, R. May (1994)
The evolution of virulence in parasites and pathogens: reconciliation between two competing hypotheses.Journal of theoretical biology, 169 3
AbstractUsing a carefully chosen set of examples, we illustrate the importance and ubiquity of quantitative reasoning in the biological sciences. The examples range across many different levels of biological organization, from diseases through ecosystems, and the problems addressed range from basic to applied. In addition to the overall theme that mathematical and statistical approaches are essential for understanding biological systems, three particular and interacting mathematical themes emerge. First, nonlinearity is pervasive; second, inclusion of stochasticity is essential; and third, issues of scale are common to all applications of quantitative approaches. Future progress in understanding many biological systems will depend on continued applications and developments in these three areas, and on understanding how nonlinearity, stochasticity, and scale interact.
BioScience – Oxford University Press
Published: Jun 1, 2005
Keywords: Keywords mathematics ecosystems evolution mathematical biology nonlinearity
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.