The wartime fishing puzzle
In the years following World War I, Italian marine biologist Umberto D'Ancona noticed a strange pattern in the fish markets of the Northern Adriatic, including Trieste, Fiume (now Rijeka), and Venice. During the war years from 1914 to 1918, fishing activity had dramatically decreased. D'Ancona's statistical surveys showed that the percentage of predatory fish—cartilaginous fish like sharks and rays (selachians)—in the total catch had increased. This was counterintuitive; with less fishing pressure, he expected the population of prey fish, the preferred catch, to rebound most noticeably. Unable to explain this ecological puzzle, he presented the problem to his fiancée's father, the distinguished mathematician Vito Volterra.
From fish to formulas
Vito Volterra was a physicist and mathematician, not a biologist. He approached D'Ancona's data as a problem of dynamics. He proposed a system of two first-order, non-linear differential equations to describe the relationship between a predator population (y) and a prey population (x).
The prey population's growth is described as dx/dt = αx - βxy. The population grows exponentially on its own (αx), but this growth is limited by the rate of predation, which depends on the frequency of encounters between predators and prey (βxy).
The predator population's change is dy/dt = δxy - γy. Its growth depends entirely on consuming prey (δxy), while its population naturally declines through death or emigration (γy).
Volterra reasoned that the wartime reduction in fishing acted as a uniform decrease in pressure on both populations. His model demonstrated that this condition disproportionately benefits the predator. With fewer prey being removed by fishermen, the predators have a more abundant food source, allowing their population to grow more significantly than the prey's. This mathematical result perfectly explained D'Ancona's observations from the Adriatic fish markets. Volterra published his findings in a 1926 paper, "Fluctuations in the Abundance of a Species, Considered Mathematically". These equations, independently developed by American biomathematician Alfred J. Lotka, are now known as the Lotka-Volterra equations and are the basis of mathematical ecology.