- LAST REVIEWED: 19 May 2015
- LAST MODIFIED: 23 May 2012
- DOI: 10.1093/obo/9780199830060-0004
- LAST REVIEWED: 19 May 2015
- LAST MODIFIED: 23 May 2012
- DOI: 10.1093/obo/9780199830060-0004
Most people do not think of mathematics when they think of ecology. Nonetheless, mathematical ecology has a long and storied history, with mathematics playing a major role in the development of a simplifying framework for studying nature’s vastly complex ecological systems. Ecologists are often interested in how populations, communities, and ecosystems change in space and time; fortunately, there exists a branch of mathematics developed specifically to deal with dynamics, known as dynamical systems theory. Math continues to play a significant, and arguably growing, role in the development of ecology today. In this article, major papers and books that introduce the vast area of research that is mathematical ecology are identified.
The first major use of mathematics in ecology occurred in the early 1900s. From this early work, the single species logistic growth equation and models for species interactions emerged. The seminal models of Alfred Lotka (Lotka 1925) and Vito Volterra (Volterra 1926) produced basic ecological models for competition and predation—now referred to as the Lotka-Volterra models—that have formed the cornerstone for much of ecology today. Hastings 1997 conceptually introduces these models and similar models in an introductory book on population biology, while Kingsland 1995 is an engaging and thorough account of the history of population ecology, with special emphasis on the role of mathematics. Finally, a wonderful introductory book focused on the basic mathematic tools behind evolutionary and ecological models is Otto and Day 2007. In the middle of the 20th century, Robert MacArthur and colleagues bolstered the use of mathematics by using basic mathematical models to develop community and behavioral ecology (e.g., MacArthur and Pianka 1966). MacArthur used his conceptual abilities to champion the role of competition in determining the structure of ecological communities. This work led to island biogeography theory (MacArthur and Wilson 1967), a classic theory that accounts for patterns in diversity on islands of different area and distance from mainland ecosystems. Shortly after MacArthur’s seminal contributions, a cornerstone for theoretical ecology, a number of physicists entered ecology in the 1970s, and their use of mathematical tools drove a dramatic increase in dynamical systems theory in ecology. Robert May, a trained physicist, was one of the first to recognize that chaotic dynamics emerged from even simple models (May 1973), while he and others extended the basic two-species models to mathematical systems of many interacting species (May 1973). Today, the strong role of mathematical theory remains. Levin, et al. 1997 points out that increases in computational ability and the need to understand the influence of scale have led to a number of modern-day mathematical challenges that await resolution by ecologists.
Hastings, Alan. 1997. Population biology: Concepts and models. New York: Springer.
This is an introductory book that covers common models and concepts in ecology, and acts as an introductory resource for those wishing to begin understanding the use of mathematical models in ecology.
Kingsland, Sharon E. 1995. Modeling nature: Episodes in the history of population ecology. 2d ed. Chicago: Univ. of Chicago Press.
A thorough and well-told story of the history of population ecology, with special emphasis on the role of mathematics. This book is very accessible and an excellent entry point into the role, and history, of mathematics and theory in ecology up to the 1980s.
Levin, Simon A., Bryan Grenfell, Alan Hastings, and Alan S. Perelson. 1997. Mathematical and computational challenges in population biology and ecosystems science. Science 275:334–343.
This article discusses some of the major recent challenges for mathematical ecology and acts as a good reference point for understanding where mathematical ecology is presently active. Simon Levin is one of the major players in this area of ecology.
Lotka, Alfred J. 1925. Elements of physical biology. Baltimore: Williams & Wilkins.
This seminal contribution employs a mathematical framework for single species growth and interacting species, as well as the major ecosystem cycles. This important book set the stage for mathematical ecology.
MacArthur, Robert H., and Eric R. Pianka. 1966. On the optimal use of a patchy environment. American Naturalist 100:603–610.
MacArthur and Pianka developed the framework for optimal foraging theory (OFT), which states that organisms forage in such a way as to maximize their net energy intake per unit time. This seminal paper is a large part of many aspects of theoretical ecology today as well as evolutionary ecology.
MacArthur, Robert H., and Edward O. Wilson. 1967. The theory of island biogeography. Princeton, NJ: Princeton Univ. Press.
This is a major contribution to one of the more successful theories in ecology. This book details the simple assumptions behind the theory of the island biogeography model and its predictions. It remains central to understanding the geographic distribution of species diversity.
May, Robert M. 1973. Stability and complexity in model ecosystems. Princeton, NJ: Princeton Univ. Press.
This famous book added mathematics to the notion that diversity, in and of itself, drives ecosystem stability. This book serves as a good reference for this active area in ecology, arguing that diversity, if anything, tends to drive instability. May argues that inherent biological structure must lie behind the sustainability of complex ecosystems.
Otto, Sarah P., and Troy Day. 2007. A biologist’s guide to mathematical modeling in ecology and evolution. Princeton, NJ: Princeton Univ. Press.
This contribution walks students of biology through the mathematics behind common biological models. This book differs from other books in that the authors focus on giving the reader a guided tour of the basic mathematical tools behind models. Written for students of all backgrounds and quite accessible.
Volterra, Vito. 1926. Fluctuations in the abundance of a species considered mathematically. Nature 118:558–560.
The seminal paper by Vito Volterra, in which he derived the classic Lotka-Volterra equations for predator-prey dynamics. The paper, and comments by Lotka that accompanied the publication, offers an interesting look into the early work of these researchers who apparently derived similar models separately.
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- Accounting for Ecological Capital
- Allocation of Reproductive Resources in Plants
- Animals, Functional Morphology of
- Animals, Reproductive Allocation in
- Animals, Thermoregulation in
- Antarctic Environments and Ecology
- Applied Ecology
- Aquatic Conservation
- Aquatic Nutrient Cycling
- Archaea, Ecology of
- Assembly Models
- Bacterial Diversity in Freshwater
- Benthic Ecology
- Biodiversity and Ecosystem Functioning
- Biodiversity Patterns in Agricultural Systms
- Biological Chaos and Complex Dynamics
- Biome, Alpine
- Biome, Boreal
- Biome, Desert
- Biome, Grassland
- Biome, Savanna
- Biome, Tundra
- Biomes, African
- Biomes, East Asian
- Biomes, Mountain
- Biomes, North American
- Biomes, South Asian
- Bryophyte Ecology
- Butterfly Ecology
- Carson, Rachel
- Chemical Ecology
- Classification Analysis
- Coastal Dune Habitats
- Communities and Ecosystems, Indirect Effects in
- Communities, Top-Down and Bottom-Up Regulation of
- Community Concept, The
- Community Ecology
- Community Genetics
- Community Phenology
- Competition and Coexistence in Animal Communities
- Competition in Plant Communities
- Complexity Theory
- Conservation Biology
- Conservation Genetics
- Coral Reefs
- Darwin, Charles
- De-Glaciation, Ecology of
- Disease Ecology
- Drought as a Disturbance in Forests
- Early Explorers, The
- Earth’s Climate, The
- Eco-Evolutionary Dynamics
- Ecological Dynamics in Fragmented Landscapes
- Ecological Informatics
- Ecology, Microbial (Community)
- Ecosystem Engineers
- Ecosystem Multifunctionality
- Ecosystem Services
- Ecosystem Services, Conservation of
- Elton, Charles
- Endophytes, Fungal
- Energy Flow
- Environments, Extreme
- Ethics, Ecological
- Facilitation and the Organization of Communities
- Fern and Lycophyte Ecology
- Fire Ecology
- Food Webs
- Foraging Behavior, Implications of
- Foraging, Optimal
- Forests, Temperate Coniferous
- Forests, Temperate Deciduous
- Freshwater Invertebrate Ecology
- Genetic Considerations in Plant Ecological Restoration
- Genomics, Ecological
- Geographic Range
- Gleason, Henry
- Greig-Smith, Peter
- Gymnosperm Ecology
- Habitat Selection
- Harper, John L.
- Heavy Metal Tolerance
- Himalaya, Ecology of the
- Host-Parasitoid Interactions
- Human Ecology
- Human Ecology of the Andes
- Hutchinson, G. Evelyn
- Insect Ecology, Terrestrial
- Introductory Sources
- Invasive Species
- Island Biogeography Theory
- Island Biology
- Kin Selection
- Landscape Dynamics
- Landscape Ecology
- Laws, Ecological
- Legume-Rhizobium Symbiosis, The
- Leopold, Aldo
- Lichen Ecology
- Life History
- Literature, Ecology and
- MacArthur, Robert H.
- Mangrove Zone Ecology
- Marine Fisheries Management
- Mathematical Ecology
- Mating Systems
- Maximum Sustainable Yield
- Metabolic Scaling Theory
- Metacommunity Dynamics
- Metapopulations and Spatial Population Processes
- Mutualisms and Symbioses
- Mycorrhizal Ecology
- Natural History Tradition, The
- Networks, Ecological
- Niche Versus Neutral Models of Community Organization
- Nutrient Foraging in Plants
- Ordination Analysis
- Organic Agriculture, Ecology of
- Parental Care, Evolution of
- Patch Dynamics
- Phenotypic Selection
- Philosophy, Ecological
- Phylogenetics and Comparative Methods
- Physiological Ecology of Nutrient Acquisition in Animals
- Physiological Ecology of Photosynthesis
- Physiological Ecology of Water Balance in Terrestrial Anim...
- Plant Disease Epidemiology
- Plant Ecological Responses to Extreme Climatic Events
- Polar Regions
- Pollination Ecology
- Population Dynamics, Density-Dependence and Single-Species
- Population Dynamics, Methods in
- Population Fluctuations and Cycles
- Population Genetics
- Population Viability Analysis
- Populations and Communities, Dynamics of Age- and Stage-St...
- Predation and Community Organization
- Predator-Prey Interactions
- Reductionism Versus Holism
- Religion and Ecology
- Remote Sensing
- Restoration Ecology
- Ricketts, Edward Flanders Robb
- Seed Ecology
- Serpentine Soils
- Shelford, Victor
- Soil Biogeochemistry
- Soil Ecology
- Spatial Pattern Analysis
- Spatial Patterns of Species Biodiversity in Terrestrial En...
- Species Extinctions
- Species Responses to Climate Change
- Species-Area Relationships
- Stability and Ecosystem Resilience, A Below-Ground Perspec...
- Stoichiometry, Ecological
- Stream Ecology
- Systems Ecology
- Tansley, Sir Arthur
- Terrestrial Resource Limitation
- Thermal Ecology of Animals
- Tragedy of the Commons
- Trophic Levels
- Vegetation Classification
- Vegetation Mapping
- Weed Ecology
- Whittaker, Robert H.
- Wildlife Ecology