THE LOTKA-VOLTERRA MODEL
Origin of the model



 
 
 
 

The Lotka-Volterra model describes interactions between two  species in an ecosystem, a predator and a prey. This simple model was developped independently by the American physical chemist Lotka in 1925 and by Italian mathematician Volterra in 1926.

For Volterra, the origin of his interest for this subject is linked to particular events.
During the first World War, Volterra had been contacted by Umberto d'Ancona who was a responsible of the italian fishing office working in Triestre at this period. D'Ancona was perplexed about statistical data. In particular, he remarked that during the war, period in which the fishing was very low, the proportion of fished sharks and other non-eatable predators was very high compared to the values noticed before the war (and also to the ones noticed after).
Here are some of these data:
 
 
Year
Percentage of predators in the fished fishes
1914
11.9%
1915
21.4%
1916
22.1%
1917
21.2%
1918
36.4%
1919
27.3%
1920
16.0%
1921
15.9%
1922
14.8%
1923
10.7%

 

It is particularly clear that there is a quite important variation during the period of the war. Those constations allow Volterra to set his model.