The Ecology Book

48

D’Ancona’s account of a sudden

increase in the population of

predatory sea fish. One theory

to explain this discrepancy

started from the premise that the

population of predators is related

to the size of the population of their

food supply, such as prey species.

The relationship suggests that

when a lot of food is available, there

will be a large predator population.

The growing predator population

should then begin to reduce the

amount of prey, which will in

turn lead to a drop in the number

of predators. The size of both

populations will rise and fall, but

the ratio of predators to prey will

remain stable.

Such a balanced theory was still

at odds with species observations.

Through mathematical modeling,

Volterra was able to show that the

average sizes of predator and prey

populations do indeed oscillate but

the rate at which each population

is growing or declining is always

changing and almost never

matches the changes experienced

by the other population. To

eliminate variables, Volterra made

a series of assumptions: first, that

the prey and predator species have

no reproduction limits and the

rate of change in a population

is proportional to its size; second,

that the prey population—presumed

to be a herbivore—is always able

to find enough food to survive.

Next, they assumed that the prey

population is the predators’ only

source of nourishment, and that

the predators never become full

and never stop hunting. Finally,

they assumed that environmental

conditions, such as weather or

natural disasters, had no impact

on the process. The effect of the

genetic diversity of the predators

and prey animals on their ability to

survive was not taken into account.

When plotted on a graph, the

predator population trails the rise

and fall of the prey population, and

is still rising as the prey population

starts to decline. This explained

D’Ancona’s observation of the larger

proportion of predators after the

prey population had been allowed

to boom by a reduction in fishing.

The relative fluctuations of the

populations depends on the relative

reproductive rates of the two

PREDATOR–PREY EQUATIONS

species and the predation rate.

For example, oscillations in the

size of an ant population and that

of an anteater are barely noticeable

because they reproduce at such

different rates. The oscillations

in the populations of species that

breed at similar rates, such as the

Iberian lynx and rabbit, are much

more pronounced.

Nature’s arms race

The predator–prey equations

revealed that species are locked

together in a never-ending struggle,

swinging from near disaster and

extinction to times of abundance

and fertility. In this biological “arms

race,” the evolutionary pressure

on the prey species is to escape

predation and survive, so as to have

more offspring. Meanwhile, the

predator is under pressure to have

a higher predation rate in order

to provide food for more offspring.

However, neither species is

superior, responding instead

to the adaptations of the other. The

predator–prey relationship between

even-toed hoofed mammals—such

Predator–prey population cycles

The predator and prey

populations rise and fall

over time in regular cycles.

Although the degree to

which they change varies,

the cycle follows a broadly

similar pattern.

POPULATION

TIME

Prey

Predator

KEY

Mathematics without

natural history is sterile, but

natural history without

mathematics is muddled.

John Maynard Smith

British mathematician

and evolutionist

US_044-049_Predator_prey_equations.indd 48 12/11/18 6:24 PM