Transcript Nested Subsets

Community Ecology and
Conservation
• It is too costly (time and money) to use a
species-by-species approach to
conservation
• Frequently a single species in a given
habitat/ecosystem is not the only species
of conservation concern
Species Assemblages
• The ecological principle most commonly
applied to conservation biology are those
of island biogeography (e.g. MacArthur
and Wilson 1963,1967)
Species Assemblages
• At the core of island biogeography theory
is the species-area relationship
• “Given a set of islands (whether oceanic,
protected lands, or archipelagos) of
discrete sites, larger sites will support
more species than smaller sites, all else
being equal”
Species-Area Curve
Species-Area Curve
• While it lacks a certain specific predictive
power, it does have conceptual value
• Also, it focuses on species number, not
their identity
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• However, there are patterns of species
richness among islands described by the
species-area relationship and these
describe the species composition
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• Impoverished biotas are frequently nonrandom subsets of richer biotas
• This pattern, termed ‘nested subset’
(Patterson and Atmar 1986) has been
known to biogeographers for years (e.g.
Darlington 1956) and has strong potential
for conservation biologists
Nested Subsets
• Not much structure in the distributional-site
relationship
Site
• Species
1
2
3
4
5
• A
X
X
X
• B
X
X
X
• C
X
X
X
• D
X
X
X
• E
X
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X
Nested Subsets
• Perfectly nested set of biota
Site
• Species
1
2
3
4
• A
X
X
X
X
• B
X
X
X
X
• C
X
X
X
• D
X
X
• E
X
5
X
Nested Subsets
The species-area relationship is a
pervasive phenomenon (taxonomically
and geographically) and most
archipelagos show a nested structure
However, one does not necessarily imply
the other…
Nested Subsets
For example, sets of islands or habitat
patches can vary in species richness for
reasons unrelated to area (e.g.
distance)
Or a perfect species-area relationship can
fail to show a nested structure
Mechanisms of Nestedness
• Four mechanisms have been proposed to
account for a pattern of nestedness (and
the species-area relationship)
• 1) differential immigration rates
• 2) differential extinction rates
• 3) nested habitat types (diversity)
• 4) passive sampling
Mechanisms of Nestedness
immigration
• If sites vary in their distance from the
source pool of immigrant species, then
species of superior dispersal ability will be
able to colonize more sites than will less
vagile species
Mechanisms of Nestedness
extinction
• If sites represent fragments of a oncecontinuous habitat and vary in the
population sizes they can support, then
local extinctions of species at the sites
could produce a nested pattern if
extinctions occur in a deterministic
sequence
• Sites with high extinction rates would only
contain extinction-resistant species
Mechanisms of Nestedness
extinction
• Differential extinction has been suggested
to explain the strong nested patterns seen
in the biotas in habitats fragmented and
isolated by post-Pleistocene climate
change
• Similar results exist for extinctionproduced nestedness on shorter time
scales as well
Mechanisms of Nestedness
habitat distribution
• If species are habitat-specific, and the
habitats themselves have a nested
distribution among sites for geologic or
other non-biological reasons, then
nestedness of the species distributions
would be, in effect, an epiphenomenon
• The influence of habitat distribution to
nested structure remains an open question
Mechanisms of Nestedness
passive sampling
• Abundant species have a higher
probability of being represented in a given
biota than rare species, simply by chance
Nested Subsets
• Observed relationship
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Species
A
B
C
D
E
1
X
X
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X
2
X
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X
Site
3
4
X
X
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5
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Mechanisms of Nestedness
passive sampling
• Thus, passive sampling could contribute to
nested structure
• Bird fauna of montane forests in the Great
Basin show no evidence of faunal
relaxation or of isolation effects
Mechanisms of Nestedness
passive sampling
• Bird fauna of montane forests in the Great
Basin show no evidence of faunal
relaxation or of isolation effects
• Analysis indicated faunas are outlier-rich
(Ua = 4.5, Up = 9.5) whereas the
extinction-dominated mammal faunas are
hole-rich (Ua = 11, Up = 5)
Mechanisms of Nestedness
passive sampling
• Bolger (1991) tested for the effects of
passive sampling in bird faunas of
chaparral fragments (and compared them
to unfragmented ‘mainland’ habitat)
• The fragments were hole-rich (extinction)
whereas the mainland plots showed an
outlier-rich pattern, although not significant
SLOSS
• Results are not consistent as to how much
nestedness will resolve the SLOSS debate
• Is likely system-specific and can be
calculated
Nested Subsets: Statistics
• Although several statistics have been generated,
the N index of Patterson and Atmar (1986)
• N is calculated in the following way:
• (1) the smallest biota in which a given species is
located
• (2) all larger biotas lacking this species are
tallied
• (3) the tallies for all the individual species in the
matrix are summed
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calculating species lacking
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• Consequently, N is a measure of how
much a matrix deviates from perfect
nestedness
• Cutler (1991) and Wright and Reeves
(1992) suggested a complimentary metric
• (1) locate the largest biota lacking a given
species and counting all smaller biotas
lacking a given species and counting all
smaller biotas in which it occurs (N2)
Nested Subsets
• If most of the deviations are in the form of
‘holes’ in the pattern (e.g. widespread
species unexpectedly missing from large
biotas), then N2 > N
• Conversely if most of the deviations are in
the form of ‘outliers’ on the pattern (e.g.
rare or restricted species unexpectedly
present in small biotas) then N > N2
Nested Subsets
• There is also the U metric that takes into
account both holes and outliers
• Two subscores, Ua and Up, tally
unexpected absences (holes) and
unexpected presences (outliers)
• Hence, the U index counts the minimum
number of steps required to transform an
imperfectly nested pattern into a perfectly
nested pattern
Nested Subsets
Holes
Outliers
1
Hole or Outlier?
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• However, some degree of nestedness is to
be expected by chance (a species-rich
biota has a higher probability of including
any given species than does a speciespoor one), the statistical significance of N,
N2 and U must be assessed
• Solution: Monte Carlo simulation of a large
number of randomized matrices where the
metrics are calculated and tested (t-test)
Nested Subsets
• The programs (RANDOM 0 and RANDOM
1) were developed by Patterson and Atmar
(1986) to generate random archipelagos
• In both programs, the number of sites,
species richness and size of species pool
are constrained to match the observed
matrix
Nested Subsets
• However, in RANDOM0, all species have
an equal probability of being assigned to a
site by the program
• In RANDOM1, the species occurrence
probabilities are weighted according to the
actual number of occurrences recorded for
a given species
Nestedness Calculator
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• Based upon the concept of the orderliness
of species extinction
• Statistical stochasticity is a concept is a
concept closely related to heat,
information, noise, order and disorder
• Hence the measure is heat of disorder to
describe the historical biography of an
archipelago
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• The system ‘temperature’ of an
archipelago can be visualized as follows:
• In a perfectly ‘cold’ system, each species
would go extinct in turn as each species
falls below its minimum sustainable
population size, and that order would not
change no matter how many times the
experiment were repeated
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• A matrix that is
perfectly cool
• Species H will
not occur on
islands smaller
than size X
H
X
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• But if the system temperature is raised (0100o), extinction order would
concomitantly become less determined
due to the increasing influence of random
processes acting on the individuals
populations and islands
• Species extinction order will no longer be
perfectly replicable
Nestedness Calculator
• Small mammal
communities on
Rocky Mountains
appear to be holerich (extinction
driven)
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• Compared to Queen
Charolotte Island landbirds,
which are not extinction
driven (subsequent
analysis suggests nested
habitat)
• Also provides insight into
which species are
disorderly (autecology)
Nestedness Calculator
• The RANDOM0
and RANDOM1
matrices for the
same data set
• Provides an
estimate of the
amount of
random variation
(vs. ‘coherent’
noise)