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