Lotka (1880-1949) was an American mathematical biologist (and later actuary) who formulated many of the same models as Volterra, independently and at about the same time. The first and simplest of these models is the subject of this module.Īlfred J. In a matter of months, Volterra developed a series of models for interactions of two or more species. Having no biological or ecological explanation for this phenomenon, D'Ancona asked Volterra if he could come up with a mathematical model that might explain what was going on. He concluded that the predator-prey balance was at its natural state during the war, and that intense fishing before and after the war disturbed this natural balance - to the detriment of predators. D'Ancona observed that the highest percentages of predators occurred during and just after World War I (as we now call it), when fishing was drastically curtailed. Percentages of predators in the Fiume fish catchĪs we did with Canadian furs, we may assume that proportions within the "harvested" population reflect those in the total population. The percentages of predator species (sharks, skates, rays, etc.) in the Fiume catch are shown in the following table: In 1926 D'Ancona completed a statistical study of the numbers of each species sold on the fish markets of three ports: Fiume, Trieste, and Venice. His son-in-law, Humberto D'Ancona, was a biologist who studied the populations of various species of fish in the Adriatic Sea. Vito Volterra (1860-1940) was a famous Italian mathematician who retired from a distinguished career in pure mathematics in the early 1920s. However, we will ignore that in our subsequent development. In areas of Canada where lynx died out completely, there is evidence that the snowshoe hare population continued to oscillate - which suggests that lynx were not the only effective predator for hares. To be candid, things are never as simple in nature as we would like to assume in our models.
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