BCB 322: Landscape Ecology

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

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 • IMMIGRATION • d= distance tomainland 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. 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

6. Metapopulation model • Most populations have a finite probability of extinction mwhich 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

7. 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)

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. 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 http://www.ut.blm.gov/vernalrmpguide/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.

15. 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 http://img-x.fotocommunity.com/43/2153443.jpg • 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)

16. 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

17. 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 Ecology6:212-219 • Bascompte, J. & Sole, R.V. (1996) Habitat fragmentation and extinction thresholds in spatially explicit models. Journal of Animal Ecology65:465-473 • 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. Oecologia46:101-105 • 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. Ecology75:1357-1367 • 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. Oikos37:306-312 • 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 Conservation53:253-264

18. 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.