The Species-Area Relationship (SAR) in Conservation Biology

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1 No. (S) S This document is available at ecology resources. ln(species) The SpeciesArea Relationship (SAR) in Conservation Biology Adam B. Smith Missouri Botanical Garden adamatearthskyseadotorg Applications of the SAR Page 1 Upscaling Example: Tree diversity of India s Western Ghats ,000 km² 0.25 ha 32.5 Upscaling based on MaxEnt theory ~900 known, with new ones reported annually predicted observed ln(area) Harte et al Ecology Letters 12: Krishnamani et al Ecography 27: Predicting extinctions a Area A a Assuming a powerfunction SAR, Number of = S(A) = ca z then S = S(A) S(a) = c(a z a z ) 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 Example: Deforestation from 1990 to 2000 Groombridge & Jenkins 2002 World Atlas of Biodiversity, Univ Calif Press, Berkeley. Example: Birds in biodiversity hotspots Pimm et al PNAS 103: Estimated proportion of lost forest Africa Asia Europe N/Cent Am Oceania South Am World

2 SAR slope Applications of the SAR Page 2 Impact assessment Example: Effects of protected areas on fish diversity Indian Ocean Sites Tittensor et al Ecology Letters 10: increased fishing pressure Assessing restoration Example: Restoring native grasslands in California Slope of the nativeexotic relationship reverse fertilization mowing control Sandel & Corbin 2010 Oikos 119: Area (m²) Prioritization Example: Identifying global plant biodiversity hotspots Hobhom 2003 Biodiversity & Conservation 12:

3 2 1m cells 2 1/4m cells 2 1/16m cells log10 ( No. ) SAR Geometry Page 3 Census design Microseris douglasii Scheiner 2003 Global Ecology and Biogeography 12: Fully nested census design log10 ( Area in m2 ) Microseris D. capitatum douglasii Senicio D. capitatum vulgaris Senicio vulgaris accumulating area by joining adjacent cells Mean no. in cells of this size other A good classification of SAR census designs can be found in Dengler 2009 Journal of Biogeography 36: other other Nonpower function behavior log ( No. ) Example: Vascular plants of the world log ( Area ) For a list of statistical models that can be fit to the SAR, see: Tjørve 2003 Journal of Biogeography 30: Tjørve 2009 Journal of Biogeography 36: Tjørve 2012 Journal of Biogeography 39: Williams et al Journal of Biogeography 36: Fridley et al American Naturalist 168:

4 Skole et al BioScience 44: SAR Geometry Page 4 The unsolved problem of β diversity (commonality) Example: Predicting diversity in 3 plots plot a S(a) = α β ac Define β diversity as the proportion of in plot b not in plot a: plot b β ab β ab = 1 in common between plots a and b α S(a) = α β bc S(a) = α plot c where α is mean no. in a plot. 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 α plot a α plot c plot b α β ab plot b α β α β ac ab To estimate γ for plots a, b, and c you need at least one census of plots that have the same spatial arrangement: Assumes isotropy in diversity! Problems: β is minimally a function of distance between a and b but probably also α and the abundance and spatial distribution of each (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 So estimation of extinctions due to realistic patterns of habitat loss and accumulation of as noncontiguous protected area increases require practicably inestimable relationships between n parcels with incredibly complex spatial arrangements that probably cannot be replicated in a nonexhaustive census design. It also cannot be estimated without extreme extrapolation or assuming a spatial and abundance distribution.

5 log 10 ( No. ) SAR Geometry Page 5 Effects of subplot shape Long parcels will almost always have more than short parcels of the same area Long, thin cells 2.0 Square cells log 10 ( Area in m 2 ) Portion of the Barro Colorado Island 50ha plot s SAR difference at smallest scale is ~10 The endemicsarea relationship (EAR) slope is < 1 in loglog space slope is 1 in loglog space He & Hubbell 2011 Nature 473: Smith 2010 Biological Conservation 143: NB: Defining endemic relative to entire study region, not necessarily the world! EAR first presented in: Harte, J. and A.P. Kinzig On the implications of area relationships for endemism, spatial turnover, and food web patterns. Oikos 80: Kinzig, A.P. and J. Harte Implications of endemicsarea relationships for estimates of extinctions. Ecology 81: These references assume a particular spatial distribution of individuals (communitylevel selfsimilarity), but their conclusions about EARs are not dependent on this distribution!

6 See also: Bode et al. Bulletin of Mathematical Biology 70: Wilson et al Nature 440: The SAR in Systematic Conservation Planning The Return on Investment (ROI) Method Wilson et al PLOS Biology 5: Page 6 Example: Allocating $100M among different conservation actions in 17 Mediterranean ecosystems (51 actionregion combinations) Calculate SARs for areas affected by each kind of threat already treated not to be treated to be treated Calculate investment relationships (SIRs) (= area cost of treatment to address threat) not to be spent already spent to be spent Smith 2010 Biological Conservation 143: Assumptions: Threats don t interact (addressable). Power function SAR. Ensuring preservation of just one individual per is adequate (should use EAR). Area affected by treatment is contiguous and nicelyshaped (the problem of β diversity).

7 500 m Using the SAR and EAR to Predict Species Loss Page 7 He and Hubbell 2011 Speciesarea relationships always overestimate extinction rates from habitat loss. Nature 473: Assertion: Speciesarea relationships always overestimate extinction rates from habitat loss (title) and [The] backward SAR systematically overestimates extinction rates (p. 369). Response: For the powerlaw 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 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 extinction rates due to habitat loss, the backward SAR calculation, is not correct (p. 370). Map of all trees/lianas in BCI s 50ha plot with dbh 1 cm SAR is accurate! 1000 m SAR inaccurate EAR accurate EAR inaccurate Smith 2010 Biological Conservation 143: See also Pereia et al 2012 Nature 482:E3E6.