Transcript Powerpoint

Populations: Variation in time
and space
Ruesink Lecture 6
Biology 356
Temporal variation
• Due to changes in the environment
(e.g., ENSO, seasons) OR
• Due to inherent dynamics
– Lag times
– Predator-prey interactions (LATER)
Oscillations occur when population growth occurs faster
than density dependence can act – population overshoots
Figure 15.11
Larval food is limited: Larvae do not have enough food
to reach metamorphosis unless larval density is low
adults
larvae
Figure
15.13
If food is limited for adults, then they cannot lay
high densities of eggs. Low densities of larvae
consistently survive.
Figure
15.14
Three reasons why populations may
fail to increase from low density
• r<0 (deterministic decline at all
densities) OR
• Depensation: individual performance
declines at low population size
(deterministic decline at low
densities) OR
• Below Minimum Viable Population:
stochastic decline
Depensation
• Form of density dependence where
individuals do worse at low population
size
– Resources are not limiting, but…
– Mates difficult to find
– Lack of neighbors may reduce foraging
or breeding success (flocking, schooling)
Deterministic decline in Pacific salmon across a wide
range of densities (r<0)
Kareiva et al. 2000
Deterministic extinction
from low population size
Passenger Pigeon
Millions to billions in
North America prior to
European arrival
1896: 250,000 in one
flock
Probably required large
flocks for successful
reproduction
1900: last record of
pigeons in wild
1914: “Martha” dies
Draw a hypothetical graph of fecundity as a function
of population size for passenger pigeons
Births/individual/year
Draw a hypothetical graph of fecundity as a function
of population size for passenger pigeons
No density
dependence
Population density (N)
Births/individual/year
Draw a hypothetical graph of fecundity as a function
of population size for passenger pigeons
Carrying
capacity
when
dN/dt/N=0
Population density (N)
Births/individual/year
Draw a hypothetical graph of fecundity as a function
of population size for passenger pigeons
Depensation
Population density (N)
Stochastic extinction
Heath hen
(Picture is related
prairie chicken)
1830: only on Martha’s
Vineyard
1908: reserve set up for
50 birds
1915: 2000 birds
1916: Fire eliminated
habitat, hard winter,
predation, poultry
disease
1928: 13 birds, just 2
females
1930: 1 bird remained
Small populations
• Dynamics governed by uncertainty
– Large populations by law of averages
• Demographic stochasticity: random
variation in sex ratio at birth, number of
deaths, number reproducing
• Environmental stochasticity: decline in
population numbers due to environmental
disasters or more minor events
Small populations
• Genetic problems also arise in small
populations
– Inbreeding depression
– Reduction in genetic diversity
• Genetic problems probably occur
slower than demographic problems at
small population sizes
Minimum viable population
• Population size that has a high
probability of persisting into the
future, given deterministic dynamics
and stochastic events
Initial population size
What is the minimum
viable population of
Bighorn Sheep, based
on model results?
Spatial variation
• No species is distributed evenly or
randomly across all space
Individuals may be clumped due to underlying
habitat heterogeneity
Figure
15.15
• Individuals may also occur in a
clumped distribution due to habitat
fragmentation by human activities
Population
• Group of regularly-interacting and
interbreeding individuals
Metapopulation
• Collection of subpopulations
• Spatially structured
– Previously we’ve talked about population
structure in terms of differences among
individuals: Age structure
Metapopulation
• Dynamics of subpopulations are
relatively independent
• Migration connects subpopulations
(Immigration and Emigration are nonzero)
• Subpopulations have finite probability
of extinction (and colonization)
Metapopulation dynamics
• Original “classic” formulation by R.
Levins 1969
• dp/dt = c p (1-p) - e p
• p = proportion of patches occupied by
species
• 1-p = proportion of patches not
occupied by species
Metapopulation dynamics
• dp/dt = c p (1-p) - e p
• c = colonization rate (probability that
an individual moves from an occupied
patch to an unoccupied patch per
time)
• e = extinction rate (probability that
an occupied patch becomes
unoccupied per time)
Metapopulation dynamics
Metapopulation dynamics
Metapopulation dynamics
Metapopulation dynamics
Metapopulation dynamics
Metapopulation dynamics
Metapopulation dynamics
Classic metapopulations
• At equilibrium, dp/dt = 0 and p =1 - e/c
• Metapopulation persists if e<c
• Specific subpopulation dynamics are
not modeled (but can be); only model
probability of extinction of entire
metapopulation
Classic metapopulations
• Lesson 1: Unoccupied patches or
disappearing subpopulations can be
rescued by immigration (Rescue
Effect)
• Lesson 2: Unoccupied patches are
necessary for metapopulation
persistence
In real populations…
• Subpopulations can vary in
– Size
– Interpatch distance
– Population growth type
• D-D or D-I
• value of r
– Quality
Figure 15.16
Figure 15.17a
Figure 15.17b
Classic metapopulation
• Subpopulations
have
independent
dynamics and
are connected
by dispersal
Mainland-Island
metapopulation
• R. MacArthur and
E.O. Wilson 1967
• 1 area persists
indefinitely and
provides colonists
to other areas that
go extinct
Source-Sink metapopulation
•
•
•
•
R. Pulliam 1988
In sources, R>1
In sinks, R<1
Sinks persist
because they
are resupplied
with individuals
from sources
Source-Sink metapopulation
• Do all
subpopulations
with high l have
high density?
• Which would
contribute more
to conservation,
high l or high
density?