BCB 322:Landscape Ecology

Lecture 3: Theories & ModelsIsland biogeography, metapopulations & the

source-sink theory

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)

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

Immigration & emigration• IMMIGRATION• 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

kRPdI )(

mnSE

EIR ~

Island biogeography: criticisms• 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

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

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

Different metapopulation types.

(Farina, 1998)

mppcpdt

dp )1(

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

Turner et al., 2001

mppDcpdt

dp )1(

c

mDp 1'

m = 0.2, c = 0.6; 1- m/c = 0.666

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

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.

• 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.

Rana lessonae. http://www.reptilis.org/rana/thumbnails/tnRana-lessonae.jpg

Source-sink model• 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

Farina, 1998

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

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

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 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.

Grasshopper sparrow

http://www.ut.blm.gov/vernalrmpguide/ssimages/GrasshopperSparrow.gif

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

• 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)

Bluetithttp://img-x.fotocommunity.com/43/2153443.jpg

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

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 6:212-219

• Bascompte, J. & Sole, R.V. (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. Journal of Animal Ecology 65:465-473

• 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 46:101-105

• 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 75:1357-1367

• 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 37:306-312

• 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 53:253-264

Assignment

• Write an essay of no less than 2000 words on the implications of the metapopulation model and the special case of the source-sink model for conservation. Post this on to your weblog by no later than 10 days time.

• Spell check your document before submission.