Chapter 13 Part 2 Flashcards
Density dependence with time delays can cause populations to be
inherently cyclic
Populations have an inherent periodicity and tend to fluctuate up and down, although
the time required to complete a cycle differs among species
Populations behave like a swinging pendulum, which is
stable when hanging straight up and down
Gravity will force the pendulum back to the center, but
momentum causes it to overshoot the center
Populations are stable at their carrying capacity
when reductions in population sizes occur, the population responds by growing—often overshooting carrying capacity
Overshoots can occur when there is a delay between
the initiation of breeding and the time that offspring are added to the population
Population cycles can be modeled by starting with the logistic growth model:
dN/dt = rN [1 - (N/K)]
dN/dt
rate of change in population size
r
intrinsic growth rate
N
current population size at time t
K
carrying capacity
We can incorporate a delay between
a change in environmental conditions and the time the population reproduces
Delayed density dependence
when density dependence occurs based on a population density at some time in the past
We can also think about time delays for predators. When predators experience
an increase of prey,
their carrying capacity increases
We can also think about time delays for predators. When predators experience
an increase of prey, their carrying capacity increases. However,
it may take
weeks or months for the predators to convert abundant prey into higher
reproductive rates
We can also think about time delays for predators. When predators experience
an increase of prey, their carrying capacity increases. However, it may take
weeks or months for the predators to convert abundant prey into higher
reproductive rates.
By this time, the prey may no longer be abundant. The lack of prey will cause
the carrying capacity of the predator to decline just as the predator population
is increasing. In both scenarios, the population experiences a time delay in
density dependence.
To incorporate a time delay (τ) into the logistic growth model:
dN/dt = rN [1 - (Nt-t/K)
As the time delay increases,
density dependence is delayed and the population is more prone to both overshooting and undershooting K
The amount of cycling in a population depends on the product of
r and τ.