Download The Species-Area Relationship (SAR) in Conservation Biology

Page 1
Adam B. Smith | Missouri Botanical Garden | adamATearthskyseaDOTorg | 2011-11-04
Applications of the SAR
Upscaling
Example: Tree diversity of India’s Western Ghats
1070 species
60,000 km²
ln(Species)
0.25 ha
Upscaling based on
MaxEnt theory… ~900
32.5 species species known, with new
ones reported annually
predicted
observed
ln(Area)
Harte et al. 2009. Ecology Letters 12:789-797.
Krishnamani et al. 2004 Ecography 27:637-642.
Predicting extinctions
Assuming a power-function SAR,
Number of species = S(A) = cAz
then
∆S = S(A) - S(a) = c(Az – az)
where A is area before habitat loss and a is
area after loss. Alternatively, the proportion
remaining is
S(a)/S(A) = (a/A)z
∆S
No. species (S)
This document is available at www.earthskysea.org, “ecology resources”.
The Species-Area Relationship (SAR) in Conservation Biology
a
Area
A-a
Example: Deforestation from 1990 to 2000
Groombridge & Jenkins 2002 World Atlas of
Biodiversity, Univ Calif Press, Berkeley.
Estimated proportion of species lost
Africa
Asia
Europe
N/Cent Am
Oceania
South Am
World
∆ forest
-0.08
-0.01
+0.01
∆ species
-0.021
-0.002
+0.002
-0.01
-0.02
-0.04
-0.02
-0.003
-0.005
-0.011
-0.006
Example: Birds in biodiversity hotspots
Pimm et al. 2006 PNAS 103:10941-10946.
Page 2
Applications of the SAR
Impact assessment
Example: Effects of protected areas on fish diversity
Tittensor et al. 2007. Ecology
Letters 10:760-772.
SAR slope
Indian Ocean Sites
→ increased fishing pressure
Assessing restoration
Example: Restoring native grasslands in California
“reverse” fertilization
Sandel & Corbin 2010
Oikos 119:1281-1290.
Slope of the nativeexotic relationship
mowing
control
Area (m²)
Prioritization
Example: Identifying global plant biodiversity hotspots
Hobhom 2003 Biodiversity & Conservation 12:279-287.
Page 3
SAR Geometry
Census design
log10 ( No. species )
2.50
accumulating area by
joining adjacent cells
Scheiner 2003 Global Ecology
and Biogeography 12:441-447.
2.40
2.30
A good classification of SAR
census designs can be found
in Dengler 2009 Journal of
Biogeography 36:728-744.
2.20
2.10
2.00
3.5
4.0
4.5
5.0
5.5
log10 ( Area in m2 )
6.0
Fully nested census design
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
- -
- -
- -
- - - -
- -
- -
- -
- -
- -
- -
- - - -
- -
- -
- -
-
-
-
-
- -
- - -
- -
-
- -
- - -
-
-
-
-
- -
- - - - - - -
-
- -
- - -
- -
-
- - -
- -
-
- -
- -
- -
- -
- -
-
-
-
-
-
- -
- -
- -
-
-
-
- -
- -
- -
- -
- -
- - - -
- -
- -
- -
-
-
-
-
-
-
- -
-
-
-
-
-
- -
-
-
-
-
- - --
-- -
-
- -
- -
- -
- - -
- - - --
- --
- -
- -
-
-
-
-
-
-
--
-
- -
- -
- -
- - - -
- -
- - -
- -
-
-
-
- -
-
-
-
- -
-
- - -
- -
-
-
--
-
-
-
-
--
--
--
-
-
-
--
-
-
-
-
-
-
- -
--
-
--
-
-
-
--
-
-
2
1-m cells
-
-
-
2
-
1/4-m cells 1/16-m2 cells
-
Mean
no. species
Senicio
vulgaris
D. capitatum
Senicio
vulgaris
D. capitatum
Microseris
douglasii
Microseris douglasii
-
-
Non-power function behavior
Example: Vascular plants of the world
+ other
species
+ other
species
-
in cells of this
size
12.24
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
+ otherspecies
16.97
-
21.55
-
log ( No. species
-
)
log ( Area )
For a list of statistical models that can be fit to the
SAR, see:
Tjørve 2003 Journal of Biogeography 30:827-835.
Tjørve 2009 Journal of Biogeography 36:1435-1445.
Tjørve 2012 Journal of Biogeography 39:629-639.
Williams et al. 2009 Journal of Biogeography
36:1994-2004.
Fridley et al. 2006 American Naturalist 168:133-143.
Page 4
SAR Geometry
The unsolved problem of β diversity (commonality)
Example: Predicting diversity in ≥3 plots
plot a
S(a) = α
Define β diversity as the proportion of
species in plot b not in plot a:
β ac
β ab = 1 – species in common between plots a and b
α
β ab
plot b
S(a) = α
where α is mean no. species in a plot.
plot c
Species diversity in plots a and b:
S(a+b) = α + α β ab
Species diversity in plots a, b, and c:
S(a+b+c) = α + α β ab+ α β ac- α(1- β bc) + γ(a,b,c)
plot a
plot a
α
α
α β ac
α β ab
plot b
To estimate γ for plots a, b, and c you
need at least one census of plots that
have the same spatial arrangement:
plot c
α β ab
plot b
Problems:
β is minimally a function of distance between a and b
but probably also α and the abundance and spatial
distribution of each species (how estimate this?).
γ is as β, but also minimally the distances between a,
b, and c.
δ, ε, etc. for four-. five-, etc.-way joins are as γ, but
even more complicated!
Satellite image of deforestation in Amazonia
Assumes isotropy in diversity!
So estimation of extinctions due to realistic
patterns of habitat loss and accumulation of
species as noncontiguous protected area increases
require practicably inestimable relationships
between n parcels with incredibly complex spatial
arrangements that probably cannot be replicated
in a non-exhaustive census design. It also cannot
be estimated without extreme extrapolation or
assuming a spatial and species-abundance
distribution.
Skole et al. 1994 BioScience 44:314-322.
S(a) = α
β bc
Page 5
SAR Geometry
Effects of subplot shape
log10( No. species )
Long parcels will
almost always have
more species than
short parcels of the
same area.
2.2
2.2
Portion of the Barro
Colorado Island 50-ha
plot’s SAR… difference
at smallest scale is ~10
species
2.1
2.1
2.0
Long, thin cells
2.0
Square cells
1.9
3.0
3.5
log10 ( Area in m2 )
4.0
The endemics-area relationship (EAR)
slope is < 1 in log-log space
slope is ≥ 1 in loglog space
He & Hubbell 2011 Nature 473:368-371.
Smith 2010 Biological Conservation
143:555-564.
NB: Defining “endemic” relative to entire study region, not necessarily the world!
EAR first presented in:
Harte, J. and A.P. Kinzig. 1997. On the implications of species-area relationships for
endemism, spatial turnover, and food web patterns. Oikos 80:417-427.
Kinzig, A.P. and J. Harte. 2000. Implications of endemics-area relationships for
estimates of species extinctions. Ecology 81:3305-3311.
These references assume a particular spatial distribution of individuals (community-level
self-similarity), but their conclusions about EARs are not dependent on this distribution!
Page 6
The SAR in Systematic Conservation Planning
The Return on Investment (ROI) Method
Wilson et al. 2007 PLOS Biology 5:1850-1861
Example: Allocating $100M among different conservation actions in 17 Mediterranean
ecosystems (51 action-region combinations)
Calculate SARs for areas affected by each kind of threat
not to be treated
already treated
to be treated
Calculate species-investment relationships (SIRs)
(= area × cost of treatment to address threat)
not to be spent
already spent
Assumptions:
• Threats don’t interact
(addressable).
• Power function SAR.
• Ensuring preservation of just one
individual per species is adequate
(should use EAR).
Smith 2010 Biological Conservation
143:555-564.
• Area affected by treatment is
contiguous and nicely-shaped (the
problem of β diversity).
See also:
Bode et al. Bulletin of Mathematical Biology 70:2039-2054.
Wilson et al. 2006 Nature 440:337-340.
to be spent
Page 7
Using the SAR and EAR to Predict Species Loss
He and Hubbell 2011 Species-area relationships always overestimate extinction rates from
habitat loss. Nature 473:368-371.
Assertion: “Species-area relationships always overestimate extinction rates
from habitat loss” (title) and “[The] backward SAR systematically overestimates
extinction rates” (p. 369).
Response: “For the power-law SAR model, the backward method always
overestimates extinction rates. However, this is not always true if other SAR
models are used. For example . . .” (their online supplement, section C)
He & Hubbell’s Figure S2: Expected
extinction probability for a species
with 20 individuals and a clustered
distribution
“backwards” SAR
EAR
The extinction rate is not
always higher using the SAR!
half of total area
Assertion: “…the most widely used method of estimating species extinction
rates due to habitat loss, the backward SAR calculation, is not correct” (p. 370).
Map of all trees/lianas in BCI’s
50-ha plot with dbh ≥1 cm
pattern of deforestation
500
SAR is accurate!
450
400
350
300
250
500 m
200
150
100
50
0
0
100
200
300
400
500
600
700
800
900
1000
pattern of deforestation
1000
1000 m
m
SAR inaccurate
pattern of deforestation
pattern of deforestation
EAR accurate
EAR inaccurate
Smith 2010 Biological Conservation
143:555-564.
See also Pereia et al 2012 Nature 482:E3-E6.