Spatial Structure & Metapopulations

1. Spatial Structure& Metapopulations

2. Clematis fremontii Erickson 1945

3. 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)

4. Desert shrubs can be nearly regular in distribution

5. Aspen in the Rocky Mountains are clonal

6. 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

7. Clematis fremontii Erickson 1945

8. 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

9. 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

10. Metapopulation models: applications in conservation planning and management. • As natural populations become increasingly fragmented by human activities, ecologists have turned increasingly to the metapopulationconcept. • 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

11. Southern California Spotted Owl

12. 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

13. 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

14. 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 – pex • pe = .7, t = 10 patches, survival = .97

16. The metapopoulation model • f = fraction of sites occupied (0-1) • I = Immigration rate (or colonization rate) • E = Local extinction rate • df/dt = I-E

17. Probability of local colonization • Physical conditions • Biological conditions (preditors, pathogens, competitors) • Patch size • Patch isolation • Proximity to occupied patches • I = pi(1-f)

18. 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

19. 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)

20. 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]

21. 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)

22. 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.

23. 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

25. 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

26. 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

30. 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