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.
When rτ < 0.37, the population
approaches carrying capacity without oscillations.
When 0.37 < rτ < 1.57, the population
exhibits damped oscillations.
Damped oscillations
a pattern of population growth in which the population initially oscillates but the magnitude of the oscillations declines over time
When rτ > 1.57, the population
will exhibit a stable limit cycle
Stable limit cycle
a pattern of population growth in which the population continues to exhibit large oscillations over time
Consider a logistic model that includes a time delay in density dependence and
exhibits dampened oscillations. If the carrying capacity is increased but all other
parameters remain the same, which of the following outcomes is most likely?
The population will continue to exhibit dampened oscillations
Consider a logistic model that includes a time delay in density dependence and
exhibits dampened oscillations. If the intrinsic rate of increase is reduced but all
other parameters remain the same, which of the following outcomes is most likely?
The population will approach carrying capacity without any oscillations.
In the logistic model with delayed density dependence, an increase in the length
of the time delay will affect population dynamics by:
making it more likely that the population will oscillate.
Delayed density dependence may occur because
the organism can store energy and nutrient reserves
When populations are low and food is abundant, the water flea Daphnia galeata
stores surplus energy as lipid droplets.
When resources are less abundant, adults use
this stored energy to reproduce
Eventually, lipid reserves are used up and
the populations decline to low numbers
In contrast, Bosmina longirostris
does not store energy and does not exhibit oscillations in population size
Delayed density dependence can occur when there is
a time delay in development from one life stage to another
what can cause small populations to go extinct
chance events
Small populations are more vulnerable to extinction than
larger populations
Although data suggest that small populations are more likely to go extinct, growth models suggest that
small populations should have more rapid growth and be resistant to extinction
Although data suggest that small populations are more likely to go extinct, growth models suggest that small populations should have more rapid growth and be resistant to extinction
This contradiction can be resolved by incorporating
incorporating random variation of growth rates into growth models.
Deterministic model
a model that is designed to predict a result without accounting for random variation in population growth rate
Stochastic model
a model that incorporates random variation in population growth rate; assumes that variation in birth and death rates is due to random chance
Demographic stochasticity
variation in birth rates and death rates due to random differences among individuals
Environmental stochasticity
variation in birth rates and death rates due to random changes in the environmental conditions (e.g., changes in the weather)
what populations are more likely to go extinct
populations that randomly experience a string of years with low birth rates or high death rates
With time, there is an increased chance of having
a string of bad years
Smaller populations are at more risk of extinction if they experience
a string of bad years
When we use stochastic models, there is an average growth rate with some variation
around that average. The actual growth rate experienced by the modeled population
can
take any of the values within the range of this variation
When we use stochastic models, there is an average growth rate with some variation
around that average. The actual growth rate experienced by the modeled population
can take any of the values within the range of this variation. As a result, a population’s
growth rate may be
above or below the average growth rate
If a population experiences
a string of years with above average growth rates, it will have
faster growth
If the
population happens to have a string of years with below average growth rates, it will
have
slower growth
