Lotka and Volterra, the founding fathers of theoretical ecology

Google translation / Original article : http://blog.globe-expert.info/thierrylorho/2011/04/10/lotka-et-volterra-peres-fondateurs-de-lecologie-theorique/

Fifth theme devoted to the topic “THEORY OF INFORMATION AND ARTIFICIAL INTELLIGENCE” discussed at the seminar “ENVIRONMENT AND INTERNATIONAL RELATIONS” at the Catholic University of Lille.

In the first half of the twentieth century, the study of the dynamics of several interacting species grew considerably. It was then called the golden age of theoretical ecology that developed the first models were based on behaviors like competition and predator-prey relationships.

Two of these people gave their names to the most famous behavioral equations:

- The most famous Italian scientist of the time, Vito Volterra (1860-1940), nicknamed “Signor Scienza Italiana”. At 13, he already handles complex differential equations. Doctorate in physics at age 22, he will not stop writing until his death. In 1922, he opposed the fascist regime of Benito Mussolini. It is one of the signers of the Declaration on Intellectual. In 1931, he refused to sign the oath of allegiance and must resign his university position, and goes abroad. He was stripped of all his privileges and honors in Italian universities. He returned to Rome just before his death in 1940.

- Alfred J. Lotka (1880-1949). Alfred Lotka was not a scientist in the usual sense: he belonged to any university, or any scientific institution. He was supervisor of the statistical office of the Metropolitan Life Insurance Company of New York.Nevertheless, his experience in the field of population statistics and extensive knowledge of Biology and Chemistry show that he was interested, as Vito Volterra, an impressive amount of scientific topics.

In 1925 and 1926, Alfred Lotka and Vito Volterra respectively publish “Elements of Physical Biology,” which describes the coexistence of an animal population with its parasite (problem-type predator-prey) and “Variazioni e fluttuazioni” del number of individui in specie animali neighborliness. ” From there resulted a controversy about the authorship of the modeling work. Subsequently, in “Lectures on the Mathematical Theory of the Struggle for Life” in 1931 Vito. Volterra laying the foundations of population dynamics and considering all aspects of the problem:the influence of environment and pollution, the heterogeneity of individuals or classes of shares inherited ages, diffusion or migration intake by a small number of individuals, seasonality and changes in external conditions over time .

The equations of Lotka-Volterra have been continuously improved and enriched. Today, in the context of international relations, may serve to explain the behavior of crowds, armed militia in conflicts such as Rwanda (Luterbacher work of Professor EHEID of Geneva, which is involved in a forthcoming session, for example). In general, mathematical models are tools for understanding the functioning of natural systems, and predicting their evolution.These models are used in the study of population dynamics and ecosystems, but the techniques are also applied to complex systems of relationships influences, or by widening the field, spatial models, epidemiology by example. Artificial intelligence Globe-Expert uses such models to explore, analyze and simulate complex relationships, such as predator-prey, producer-consumer … etc..

Potential map Globe-Expert / Lotka-Volterra model