1. BCB 322: Landscape Ecology
Lecture 3: Theories & Models
Island biogeography, metapopulations & the source-sink theory

2. Island biogeography theory
Developed originally in 1963 by MacArthur & Wilson, & further developed by these & others
Influenced understanding of spatial influences on organisms
For a while, it was the principle design paradigm for conservation reserves
“The number of species on an island will reach an equilibrium that is positively related to island size & negatively related to distance from mainland”
Hence, large islands have more species
Islands distant from the mainland have fewer species (far from the source of new colonists)

3. Island biogeography
Originally applied to islands, but works for any population in a fragmented landscape.
In this case, a fragment is the “island”, & the mainland is the nearest large contiguous source.
Species richness in the island is related to immigration rate to the island & extinction rate on the island.
Immigration rate is a linear function of distance from mainland & is related to size of mainland population.
Extinction rate is dependent on available resources on island. Should be proportional to island size if all islands are similar.
Prison Island, Zanzibar

4. Immigration & emigration
d = distance to mainland source
P = number of species on mainland
R = number of species on island
k = island-specific parameter , dependent on species community
EXTINCTION
S = island size
n,m = parameters fitted from regression data

5. Effects of distance

6. Effects of size &distance

7. Effects of size &distance

8. Effects of distance Real World

9. Island biogeography: criticisms
assumption of equilibrium (can take a long time)
Other factors may affect diversity on a fragment:
resistance to invasion (eg: heathland remnants: Webb & Vermaat, 1990)
habitat quality/ interspecific competition (Hanski, 1981)
catastrophes (eg: hurricanes) may dominate extinction rates, independent of size (Ehrlich et al., 1980)
trophic dynamics. (eg): Bahamian spider distributions follow IB predictions unless predatory lizards are present. Otherwise predation drives extinction rates (Toft & Schoener, 1983)
Despite this, IB was the primary concept in reserve design until the evolution of metapopulation models in the 1980s

10. Metapopulation model
Most populations have a finite probability of extinction m which is greater than 0
This implies that all populations will go extinct on a large enough time frame
Fragmentation can therefore benefit a species, allowing recolonization from neighbouring populations
This creates a locally dynamic, but regionally stable population
This regional population, or collection of local populations, was termed a metapopulation by Levins (1969)
This depends on the ability to maintain an exchange of species

11. Metapopulation model p = proportion of locations colonized at time t
c = probability of colonization
m = probability of extinction
Populations persist regionally only if m < c
This model allows assessment of damage to regional populations by habitat destruction
Levin’s metapopulation
Core – satellite metapopulation
Patchy metapopulation
Non-equilibrium metapopulation
Combination of types b & c (Harrison, 1991)
Different metapopulation types.
(Farina, 1998)

12. Metapopulation model
If the fraction of occupied sites is assumed to decrease in proportion to the number of destroyed sites (D), we get
Hence, the estimate of expected colonized sites (equilibrium solution)
The extinction threshold occurs when the fraction of available sites(1-D) <= m/c
This means a population will disappear long before the final patches are removed
m = 0.2, c = 0.6; 1- m/c = 0.666
Turner et al., 2001

13. Metapopulation model
Early metapopulation models assumed all patches have a similar likelihood of colonization or extinctions, regardless of the distance between them
Bascompte & Sole (1996) use a spatially explicit model to examine the effect of limited dispersal
The models are more or less identical when there is no habitat destruction.
However, limited dispersal exacerbates the effect of habitat destruction
Hence, near the extinction threshold, spatially explicit models demonstrate an increased probability of extinction
Bascompte & Sole, 1996

14. Metapopulation model
Example: in Rana lessonae populations (Gulve, 1994) the rate of extinction depends of deterministic & stochastic effects.
Deterministic extinction is through drainage of ponds or natural succession.
Rana lessonae.
Permanent ponds experience extinction through population stochastic effects (random dry periods, over predation by migrant species, low seasonal birth success)
However, extinction in permanent ponds is low (<=8.5%), indicating migration between ponds and consequent reduction in local extinctions.
DETERMINISTIC: an event that is directly caused by another event or process; an event that is part of a long-term process
STOCHASTIC: an event that occurs randomly, or through a random set of variables

15. Source-sink model
Farina, 1998
The metapopulation model assumes all patches are of the same quality, & hence birth/death rates are the same across the landscape
A special-case model was proposed (Pulliam, 1988) in which local populations have unique demographics in response to local variation in habitat quality
This naturally gives rise to the source-sink concept (Dias, 1996)
Areas with greater reproductive success than death rates must have a net excess of individuals, making the areas sources
Other areas, where local mortality is greater than birth rates, have a net deficit in individuals, making them a sink

16. Source-sink model
Individuals will tend to move from sources to sinks to avoid overpopulation of their areas, despite the poorer quality of sinks
Patch quality is often related to size – the source effect is greater for large patches with increased per capita production.
Long-term studies needed to determine whether a patch is source or sink:
Stochastic events (high rainfall) in a generally unfavourable site (desert) may give a false impression that it is a source
There are a number of observable special cases of the source-sink model that can lead to erroneous assumptions of carrying capacity of the area

17. Source-sink: Pseudo-sinks
Occurs where two adjacent areas are favourable, but one has a better carrying capacity
The poorer site becomes overpopulated because the net immigration rate is higher than the birth/death rate
This site may falsely be identified as a sink
In a true sink the population becomes extinct if immigration is removed
In a pseudo-sink, reduced immigration will reduce the population to a more sustainable level
This effectively increases the viability of individuals in the population, due to better resource availability

18. Source-sink: Traps
Some habitats may appear extremely favourable to a species, but lack the resources to ensure a full reproductive cycle
Effectively, a trap is a sink the looks like a source (Pulliam, 1996)
Typified in many human- influenced regions, particularly due to agriculture
Grasshopper sparrow
/ssimages/GrasshopperSparrow.gif
Grasshopper sparrows (Ammodramus savannarum) are attracted by hayfields in early spring due to high food levels
In summer, the fields are mowed before the sparrows have completed their breeding cycle, and the absence of food means that chicks may starve.

19. Source-sink: Stable maladaptation
Exemplified by bluetit (Parus caerulus) populations breeding in deciduous and evergreen oak (Blondel et al, 1992)
Birds synchronise laying dates with food availability in deciduous forest
Bluetit
In evergreen forest, the food availability is 3 weeks later, giving lower bird fertility
Birds adapted to deciduous forest, but emigrate to evergreen forest in a patchy landscape
In Corsica (all evergreen), the same species of bird is adapted to the altered timing, because it is an island population (gradual speciation through evolutionary adaptation)

20. Summary
Island biogeography: The number of species on an island is a function of island size and proximity to the main population body
Metapopulation: locally dynamic but regionally stable population. Migration between fragments may allow species to repopulate areas after local extinctions
Source: Area with a net surplus of individuals, from which migration occurs
Sink: Area with net deficit in the growth rate that receives immigrants.
Pseudo-sink: optimal area with lower carrying capacity that receives too many immigrants, lowering overall species fitness locally
Traps: an area appears beneficial but is unable to sustain a full species life cycle
Stable maladaptation: occurs where migration into suboptimal patches from an optimal matrix is common

21. References
Blondel, J., Perret, P., Maistre, M., & Dias, P.C. (1992) Do harlequin Mediterranean environments function as source-sink for Blue Tits (Parus caeruleus L.)? Landscape Ecology 6:
Bascompte, J. & Sole, R.V. (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. Journal of Animal Ecology 65:
Ehrlich, P.R., Murphy, D.D., Singer,M.C., Sherwood, C.B., White, R.R. & Brown, I.L. (1980) Extinction, reduction, stability, and increase: the responses of the checkerspot butterfly (Euphydras) populations to the California drought. Oecologia 46:
Farina, A. (1998) Principles and Methods in Landscape Ecology. Chapman & Hall, London
Gulve, P.S. (1994) Distribution and extinction patterns within a northern metapopulation of the pond frog, Rana lessonae. Ecology 75:
MacArthur, R.H. & Wilson, E.O. (1967) The Theory of Island Biogeography. Princeton University Press, Oxford, UK
Hanski, I. (1981) Coexistence of competitors in patchy environments with and without predation. Oikos 37:
Pulliam, H.R. (1996) Sources and sinks: Empirical evidence and population consequences. In: Rhodes, O.E., Chesser, R.K. & Smith, M.E. (eds) Population dynamics in ecological space and time. University of Chicago Press, Chicago pp45- 66
Toft, C.A. & Schoener, T.W. (1983) Perspectives on Landscape Ecology. Proceedings of the International Congress of the Netherlands Society for Landscape Ecology. PUDOC, Wageningen, The Netherlands
Turner, M.G., Gardner, R.H. & O’Neill, R.V. (2001) Landscape Ecology in Theory and Practice: Pattern and Process. Springer-Verlag, New York 401pp
Webb, N.R. & Vermaat, A.H. (1990) Changes in vegetational diversity on remnant heathland fragments. Biological Conservation 53: