Download BCB322: Landscape Ecology

BCB 322:
Landscape Ecology
Lecture 3: Theories & Models
Island 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
R ~ I E
• IMMIGRATION
• d = distance to mainland source
• P = number of species on
k
mainland
I d(PR)
• R = number of species on island
• k = island-specific parameter ,
dependent on species community
E  nS
m
• EXTINCTION
• S = island size
• n,m = parameters fitted from
regression data
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
dp

cp
(
1

p
)
mp locations colonized at
dt
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)
Metapopulation model
• If the fraction of occupied sites is
assumed to decrease in proportion
to the number of destroyed sites
(D), we get
m = 0.2, c = 0.6;
1- m/c = 0.666
dp

cp
(
1

D

p
)

mp
dt
• Hence, the estimate of expected
colonized sites (equilibrium
solution)
m
p'1D
c
• 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
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
Rana lessonae.
http://www.reptilis.org/rana/thumbnails/tnRananatural succession.
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.
Source-sink model
• The metapopulation model
assumes all patches are of
the same quality, & hence
birth/death rates are the
same across the
landscape
Farina,
1998
• 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
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)
Grasshopper sparrow
• Typified in many humanhttp://www.ut.blm.gov/vernalrmpguide
/ssimages/GrasshopperSparrow.gif
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.
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
Bluetit
forest
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)
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
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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 pp4566
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
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.