Theory of Elastic Stability

(1970). A Computer Movie Simulating Urban Growth in the Detroit Region. Economic Geography: Vol. 46, PROCEEDINGS International Geographical Union Commission on Quantitative Methods, pp. 234-240.

https://www.jstor.org/stable/pdfplus/143141.pdf

A Computer Movie Simulating Urban Growth in the Detroit Region

https://www.wsl.ch/staff/niklaus.zimmermann/papers/ecomod135_147.pdf

Predictive habitat distribution models in ecology

Metabolism provides a basis for using first principles of physics, chemistry, and biology to link the biology of individual organisms to the ecology of populations, communities, and ecosystems. Metabolic rate, the rate at which organisms take up, transform, and expend energy and materials, is the most fundamental biological rate. We have developed a quantitative theory for how metabolic rate varies with body size and temperature. Metabolic theory predicts how metabolic rate, by setting the rates of resource uptake from the environment and resource allocation to survival, growth, and reproduction, controls ecological processes at all levels of organization from individuals to the biosphere. Examples include: (1) life history attributes, including devel- opment rate, mortality rate, age at maturity, life span, and population growth rate; (2) population interactions, including carrying capacity, rates of competition and predation, and patterns of species diversity; and (3) ecosystem processes, including rates of biomass production and respiration and patterns of trophic dynamics. Data compiled from the ecological literature strongly support the theoretical predictions. Even- tually, metabolic theory may provide a conceptual foundation for much of ecology, just as genetic theory provides a foundation for much of evolutionary biology.

/pdf/toward-a-metabolic-theory-of-ecology-1dxmg8xr3n.pdf

Toward a metabolic theory of ecology

Every form of behavior is shaped by trial and error. Such stepwise adaptation can occur through individual learning or through natural selection, the basis of evolution. Since the work of Maynard Smith and others, it has been realized how game theory can model this process. Evolutionary game theory replaces the static solutions of classical game theory by a dynamical approach centered not on the concept of rational players but on the population dynamics of behavioral programs. In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities. Replicator equations describe how successful strategies spread and thereby create new conditions that can alter the basis of their success, i.e., to enable us to understand the strategic and genetic foundations of the endless chronicle of invasions and extinctions that punctuate evolution. In short, evolutionary game theory describes when to escalate a conflict, how to elicit cooperation, why to expect a balance of the sexes, and how to understand natural selection in mathematical terms.

 Comprehensive treatment of ecological and game theoretic dynamics
 Invasion dynamics and permanence as key concepts
 Explanation in terms of games of things like competition between species

/pdf/evolutionary-games-and-population-dynamics-pax1uk4ywa.pdf

Evolutionary games and population dynamics

Leçons sur la théorie mathématique de la lutte pour la vie

In the above letter from Dr. Lotka, which is in accordance with our preceding correspondence, following upon the publication of my article in NATURE, he justly observes that he had obtained the differential equations in the case of two species, one of which feeds upon the other, that he had given, as well as myself, the same diagram of the integral, and also the period in the case of small fluctuations. In this I recognize his priority, and am sorry not to have known his work, and therefore not to have been able to mention it.

Fluctuations in the Abundance of a Species considered Mathematically

Theory of Functionals and of Integral and Integro-Differential Equations

/pdf/sur-l-equilibre-des-corps-elastiques-multiplement-connexes-hbx8qdf5dy.pdf

Sur l'équilibre des corps élastiques multiplement connexes

https://projecteuclid.org/download/pdf_1/euclid.acta/1485882051

Vito Volterra

Papers

Leçons sur la théorie mathématique de la lutte pour la vie

Fluctuations in the Abundance of a Species considered Mathematically

Theory of Functionals and of Integral and Integro-Differential Equations

Sur l'équilibre des corps élastiques multiplement connexes

Sur la théorie des variations des latitudes