The Ecology Book

46

T

he predator–prey equations

are an early example of the

application of mathematics

to biology. Formulated in the 1920s

by American mathematician Alfred

J. Lotka and Italian mathematician

and physicist Vito Volterra, the

two equations—also known as

the Lotka–Volterra equations—

describe the way in which the

population of a predator species

and that of its prey fluctuate in

relation to each other.

Lotka proposed the equations

in 1910, as a way of understanding

the rates of autocatalytic chemical

reactions—chemical processes

that regulate themselves. In the

following decade, he applied

the equations to the population

dynamics of wild animals.

In 1926, Vito Volterra arrived

at the same conclusions. He had

become interested in the subject

after meeting Italian marine

biologist Umberto D’Ancona.

D’Ancona told Volterra how the

percentage of predatory fish

caught in nets in the Adriatic

Sea had greatly increased during

World War I. This change was

clearly linked to the drastic

reduction in fishing during the

PREDATOR–PREY EQUATIONS

IN CONTEXT

KEY FIGURES

Alfred J. Lotka (1880 –1949),

Vito Volterra (1860 –1940)

BEFORE

1798 British economist

Thomas Malthus shows that

the rate at which the population

changes increases as the size

of the population grows.

1871 In Lewis Carroll’s novel

Through the Looking Glass,

the Red Queen tells Alice,

“you have to run just to stay

in the same place.”

AFTER

1973 American biologist Leigh

Van Valen proposes the Red

Queen effect, which describes

the constant “arms race”

between predators and prey.

1989 The Arditi–Ginzburg

equations offer another model

of predator–prey dynamics

by including the impact of the

ratio between predator and prey.

Vito Volterra Born in 1860 in Ancona, Italy, the

son of a Jewish cloth merchant,

Vito Volterra grew up in poverty.

Despite this, in 1883, aged just 23,

he secured a position as professor

of mechanics at the University

of Pisa and began a career as

a mathematician. Further

professorships at the universities

of Turin and Rome followed. In

1900, Volterra married, fathering

six children, although only four

survived to adulthood. He was

made a senator of the Kingdom

of Italy in 1905 and worked on the

development of military airships

during World War I. In 1931,

Volterra refused to swear loyalty

to Italy’s fascist dictator Benito

Mussolini and was dismissed

from the University of Rome.

Forced to work abroad, he only

returned to Italy for a short time

before his death in 1940.

Key works

1926 “Fluctuations in the

Abundance of a Species

Considered M athematica l ly,”

Nature

1935 Les associations

biologiques au point de vue

mathématique

The prey has access to

food and its population

growth is exponential.

When prey animals meet

a predator, they

are eaten.

Eating prey results

in more predators.

More predators

results in less

prey, reducing the

number of predators.

Populations of two species,

one predator, the

other prey, interact.

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