Download ppt

Population Ecology
I. Attributes
II.Distribution
III. Population Growth – changes in size through time
IV. Species Interactions
V. Dynamics of Consumer-Resource Interactions
Population Ecology
I. Attributes
II.Distribution
III. Population Growth – changes in size through time
IV. Species Interactions
V. Dynamics of Consumer-Resource Interactions
A. Like Limiting Resources, Predators Reduce Population Size/Growth
Predators
“Top down”
Target Species
“Bottom up”
Limiting Resources
Opuntia introduced into Australia for “living fenceposts”… quickly spread
Cactoblastus catorum introduced from Argentina – 95% reduction in 20
years.
Introduced in Africa and West Indies, and has invaded Florida and is wiping
out several native species.
Cyclamen mites:
Important crop pests
(strawberries, in
particular). Females
reproduce
parthenogenetically
and produce 10-40
offspring/day.
If prey increase when
predators are removed,
then predators were
limiting population growth
Cattle excluded
Cattle grazing
Kelp and Urchins In 1940's:
Kelp and Urchins In 1940's:
As urchin density increases, kelp beds
“retreat” (negative displacement) at a
rate of meters/month
Moose and Wolves - Isle Royale
Moose and Wolves - Isle Royale
1930's - Moose population = ~2400 on Isle Royale
1930's - Moose population about 2400 on Isle Royale
1949 - Wolves cross on an ice bridge; studied since 1958
1930's - Moose population about 2400 on Isle Royale
1949 - Wolves cross on an ice bridge; studied since 1958
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern – Why?
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern – Why?
Specialist predators and time lags between food
consumption and increase in predator population
(gestation)
A refuge where prey can hide and increase their population
(seasonal, here): Voles and Owls in Sweden – Damped Oscillations:
Decrease in snow pack makes voles susceptible to owls all year,
reducing the lag and reducing the amplitude of oscillations
Winter refuge for voles
beneath the snow
In parasites where hosts develop immunity, the parasite can only increase
after a population of susceptible hosts (babies) are produced.
Measles in London: 1948-1968 (before vaccine).
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern
C. Models
1. Host-Pathogen Models
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern
C. Models
1. Host-Pathogen Models
Dependent on:
a. the rate of transmission (b)
(“infectability”)
b. the rate of recovery (g) (inversely related to the period during
which the host is contagious)
c. the number of susceptible (S), infectious, and recovered hosts
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern
C. Models
1. Host-Pathogen Models
Dependent on:
a. the rate of transmission (b)
b. the rate of recovery (g) (inversely related to the period during
which the host is contagious)
c. the number of susceptible (S), infectious, and recovered hosts
The reproductive ratio of the pathogen, R =(b/g)S
so a pathogen population will grow (R > 1, epidemic) if :
the rate of transmission is high (infectious)
recovery is slow (creating a long period of contagion)
susceptible individuals are common.
In this case, each infected individual infects more than one new host and the
disease spreads.
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern
C. Models
1. Host-Pathogen Models
As a disease proceeds and the number of susceptible individuals declines, R
 < 1 and the epidemic declines.
In the simplest version of this model (single generation), oscillations don’t
occur because there is no production of new susceptible people and
immunity after recovery is permanent.
However, if you add the production of susceptible newborns or susceptible
immigrants, or allow for vertical transmission from parent to offspring, or add
a latency period, or allow for reinfection (and not lifetime immunity),
oscillations and cyclic epidemic occur because the number of susceptible
people can increase… driving R > 1.
so a pathogen population will grow (R > 1, epidemic) if :
the rate of transmission is high
recovery is slow (creating a long period of contagion)
or susceptible individuals are common.
In this case, each infected individual infects more than one new host and the
disease spreads.
Cold and Flu:
Transmission rate “low” - 34%
Recovery slow, favoring spread
(Viral integrity is greatest under low humidity,
and particles remain small (don’t take on water
and fall out of the air column). Cool temps
reduce ciliary beating in nasal and respiratory
mucosa, favoring viral reproduction. Both
cause higher transmission rates in winter.
Lowen, et al. 2007.
http://www.plospathogens.org/article/info%3Adoi%2F10.1371%2Fjournal.ppat.0030151
so a pathogen population will grow (R > 1, epidemic) if :
the rate of transmission is high
recovery is slow (creating a long period of contagion)
or susceptible individuals are common.
In this case, each infected individual infects more than one new host and the
disease spreads.
Ebola:
Transmission rate “high” ~75%
99% fatality rate – short contagious period
Deadly pathogens need a high transmission
rate to persist, or a very dense population (S).
so a pathogen population will grow (R > 1, epidemic) if :
the rate of transmission is high
recovery is slow (creating a long period of contagion)
or susceptible individuals are common.
In this case, each infected individual infects more than one new host and the
disease spreads.
1918 Flu Epidemic (H1N1):
Killed 50-100 million people; 3-5% of the global
population
Transmission rate was high because of high
density of susceptible hosts (military), and
movement of carriers across Europe (military
and migrating refugees).
High density selected for more aggressive and
lethal form
Reduce Transmission Rate:
- stay clean
- stay home
Reduce Contagious Period:
- stay healthy; get well soon
Reduce # of Susceptible Hosts:
- get vaccinated
C. Models
1. Host-Pathogen Model
2. Lotka-Volterra Models
Goal - create a model system in which there are oscillations of predator and
prey populations that are out-of-phase with one another.
Basic Equations:
a. Prey (V = ‘victim’)
Equation: dV/dt = rV - cVP where
rV defines the maximal, exponential rate
c = predator foraging efficiency: % eaten
P = number of predators V= number of prey, so PV = number
of encounters and cPV = number of prey killed (consumed)
So, the formula describes the maximal growth rate, minus the number of prey
individuals lost by predation.
The Prey Isocline
dV/dt = 0 when rV = cPV; when P = r/c. Curious dynamic.
There is a particular number of predators that can limit prey growth; below
this number of predators, REGARDLESS OF THE NUMBER OF PREY, prey
increase. Greater than this number of predators, REGARDLESS OF THE
NUMBER OF PREY, and the prey declines. Prey's rate of growth is
independent of its own density (rather unrealistic).
r/c
V
C. Models
2. Lotka-Volterra Models
b. Predator
The Equation: dP/dt = a(cPV) - dP where
cPV equals the number of prey consumed, and
a = the rate at which food energy is converted to offspring.
So, a(cVP) = number of predator offspring produced.
d = mortality rate, and P = # of predators, so dP = number of
predators dying.
So, the equation boils down to the birth rate (determined by
energy "in" and conversion rate to offspring) minus the death rate.
The Predator's Isocline
dP/dt = 0 when dP = a(cPV); or when V = d/ac
Again, Predator's growth is independent of its own density. There is a
critical number of prey which can support a predator population of any size;
below this number, the predator population declines - above this number and
the population can increase.
V
d/ac
Basic Equations:
1. Prey
2. Predator
3. Dynamics
d/ac
1.
4.
1.
2. 3.
4.
V
r/c
2.
3.
OSCILLATIONS!!!
(V)
1.
Curiously, the model predicts that an
increase in the growth rate of prey (r to r’)
(favorable change in the environment?)
should NOT change equilibrial PREY
density (d/ac), but instead should cause
PREDATOR population to grow to higher
equilibrium (r’/c).
Experimental Support:
- Increase sugar to E. coli bacteria, and
their population did not increase much
as the predators (T4 phage) increased.
- Criticisms of the L-V model:
1. No time lags – instantaneous conversion of food to predator offspring
2. No density dependence in prey, even at low predator densities when prey
populations should be large.
3. Constant predation rate (functional response)
V. Dynamics of Consumer-Resource Interactions
A. Predators can limit the growth of prey populations
B. Oscillations are a Common Pattern
C. Models
D. Lab Experiments
1. Gause
P. caudatum (prey) and Didinium nasutum (predator)
P. caudatum (prey) and Didinium nasutum (predator)
In initial experiments, Paramecium populations would increase,
followed by a pulse of Didinium, and then they would crash.
P. caudatum (prey) and Didinium nasutum (predator)
In initial experiments, Paramecium populations would increase,
followed by a pulse of Didinium, and then they would crash.
He added glass wool to the bottom, creating a REFUGE that the
predator did not enter.
He induced oscillations by adding Paramecium as 'immigrants'
D. Laboratory Experiments
1. Gause
2. Huffaker
six-spotted mite (Eotetranychus sexmaculatus) was prey - SSM
Predatory mite (Typhlodromus occidentalis) was predator - PM
D. Laboratory Experiments
1. Gause
2. Huffaker
3. Holyoak and Lawler-1996
Holyoak and Lawler-1996
Used a bacteriovore ciliate, Colpidium striatum as the prey and our old friend
Didinium nasutum as the predator.
3. Holyoak and Lawler-1996
Set up replicate 30mL bottles, linked together by tubes, and single flask
systems.
D. Complexities and Applications
1. Achieving Stable Dynamics
- inefficient predators: - both populations equilibrate at high density
- alternate prey: - Pred’s high, prey low (but not extinct if predator
switches)
- prey refuge: - prey population dependent on size of the refuge
- time lags: - reduced lag allows predator population to equilibrate
with changes in prey, and less likely to go extinct
by a crash.
D. Complexities and Applications
2. Multiple State States
Consider a Type III functional response, where the predation rate is
highest at intermediate prey densities, and density dependent birth rate of
prey.
Birth rate
Predation Rate
V
D. Complexities and Applications
2. Multiple State States
Consider a Type III functional response, where the predation rate is
highest at intermediate prey densities, and density dependent birth rate of
prey.
Two stable Equilibria, at
high and low prey
densities. One unstable
equilibrium at
intermediate density.
Birth rate
Predation Rate
V