Spatial Structure
&
Metapopulations
Clematis fremontii
Erickson 1945
Dispersion of Individuals
within Populations
• Dispersion of individuals within a population
describes their spacing with respect to one
another.
• A variety of patterns is possible:
– clumped (individuals in discrete groups)
– evenly spaced (each individual maintains a
minimum distance from other individuals)
– random (individuals distributed independently
of others within a homogeneous area)
Desert shrubs can be nearly regular in distribution
Aspen in the Rocky Mountains are clonal
Causes of Dispersion
• Even spacing may arise from direct
interactions among individuals:
– maintenance of minimum distance between
individuals or direct competition for limited
resources may cause this pattern
• Clumped distribution may arise from:
– social predisposition to form groups
– clumped distribution of resources
– tendency of progeny to remain near parent
• Spatial pattern is scale-dependent
Clematis fremontii
Erickson 1945
Populations exist in
heterogeneous landscapes.
• Uniform habitats are the exception rather
than the rule:
– most populations are divided into subpopulations
living in suitable habitat patches
• Degree to which members of subpopulations
are isolated from one another depends on:
– distances between subpopulations
– nature of intervening environment
– mobility of the species
Metapopulation Model
• The metapopulation model views a
population as a set of subpopulations
occupying patches of a particular
habitat:
– intervening habitat is referred to as the
habitat matrix:
– the matrix is viewed only as a barrier to
movement of individuals between
subpopulations
Metapopulation models:
applications in conservation
planning and management.
• As natural populations become increasingly
fragmented by human activities, ecologists
have turned increasingly to the
metapopulation concept.
• Two kinds of processes contribute to
dynamics of metapopulations:
– growth and regulation of subpopulations within
patches
– colonization to form new subpopulations and
extinction of existing subpopulations
Southern California Spotted Owl
Connectivity determines
metapopulation dynamics
• When individuals move frequently between
subpopulations, local fluctuations are damped
out.
• At intermediate levels of movement:
– the metapopulation behaves as a shifting mosaic of
occupied and unoccupied patches
• At low levels of movement:
– the subpopulations behave independently
– as small subpopulations go extinct, they cannot be
reestablished, and the entire population eventually
goes extinct
Local extinction
• Regional extinction is the probability that
the population goes extinct.
• Local extinction is the probability that the
part of the population in an occupied patch
does extinct = pe
• Probability of persistence for n years =
probability of no extinction for n years in a
row = (1-pe)n
• pe = .7, n = 5 , survival = .00243
Regional persistence
• Consider x independent patches
• Probability of persistence in one patch
= 1 - pe
• Probability of persistence in at least
one patch is one minus probability they
are all extinct
= 1 – pe x
• pe = .7, t = 10 patches, survival = .97
The metapopoulation model
• f = fraction of sites occupied (0-1)
• I = Immigration rate (or colonization
rate)
• E = Local extinction rate
• df/dt = I-E
Probability of local colonization
• Physical conditions
• Biological conditions (preditors,
pathogens, competitors)
• Patch size
• Patch isolation
• Proximity to occupied patches
• I = pi(1-f)
Basic model
• Extinction rate is the product of
probability local extinction rate times
the fraction of sites occupied = pef
• Extinction rate is 0 if pe or f is 0
• df/dt = pi(1-f) –pef
• The simplest model
Assumptions to relax?
• Homogeneous patches (size, isolation,
quality, resource levels, etc)
• No spatial structure (no neighborhoods)
• No time lags (instantaneous response)
• Constant pe and pi
• Relationships can exist between regional
occurrence and local colonization and
extinction
• Large number of patches (no demographic
stochasticity)
Island model
• Probability of immigration is fixed.
Propagule rain fixed by a constant,
large source population.
• df/dt = pi(1-f)-pef
• df/dt = 0  pi - pif –pef = 0
• f = pi / (pi+pe) [always positive]
Internal colonization
• Only source of propagules is occupied
patches
• Pi = if where i is a measure of how
much each occupied site will
contribute to colonization.
• df/df = if(1-f)-pef
• f = 1-(pe/i)
Rescue effect
• Probability of extinction can be influenced
by immigration from occupied patches
• Pe = e(1-f) where e is a measure of the
strength of the rescue effect
• If f = 1, pe = 0, which is unrealistic
• df/dt = pi(1-f) –ef(1-f)
• f = pi/e
• Persistence if pi>0 with rescue effect, and
if e<pi then patches are saturated.
Internal colonization & rescue
• Df/dt = if(1-f) - ef(1-f)
• If i > e , population will grow to f=1
• If e > 1, population will decrease to
f=0
Connectivity determines
metapopulation dynamics.
• When individuals move frequently between
subpopulations, local fluctuations are damped
out.
• At intermediate levels of movement:
– the metapopulation behaves as a shifting mosaic of
occupied and unoccupied patches
• At low levels of movement:
– the subpopulations behave independently
– as small subpopulations go extinct, they cannot be
reestablished, and the entire population eventually
goes extinct
Source-Sink Model &
Mass effect Model
• The source-sink model recognizes
differences in quality of suitable habitat
patches:
– in source patches, where resources are
abundant:
• individuals produce more offspring than needed
to replace themselves
• surplus offspring disperse to other patches
– in sink patches, where resources are scarce:
• populations are maintained by immigration of
individuals from elsewhere
Landscape Model
• The landscape model considers effects of
differences in habitat quality within the
habitat matrix:
– the quality of a habitat patch can be affected
by the nature of the surrounding matrix
• quality is enhanced by presence of resources, such as
nesting materials or pollinators
• quality is reduced by presence of predators or
disease organisms
– some matrix habitats are more easily traversed
than others