Metapopulations in miniature: connectivity, subpopulation ...
Spatial Structure & Metapopulations
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Transcript of Spatial Structure & Metapopulations
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Spatial Structure&
Metapopulations
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Clematis fremontii
Erickson 1945
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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)
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Desert shrubs can be nearly regular in distribution
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Aspen in the Rocky Mountains are clonal
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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
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Clematis fremontii
Erickson 1945
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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
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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
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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
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Southern California Spotted Owl
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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
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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
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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
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The metapopoulation model
• f = fraction of sites occupied (0-1)
• I = Immigration rate (or colonization rate)
• E = Local extinction rate
• df/dt = I-E
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Probability of local colonization
• Physical conditions
• Biological conditions (preditors, pathogens, competitors)
• Patch size
• Patch isolation
• Proximity to occupied patches
• I = pi(1-f)
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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
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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)
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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]
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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)
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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.
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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
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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
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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
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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