1. Estimating Extinction Rates: Habitat loss, species-area curves, and the “extinction-debt” Fangliang He In collaboration with Stephen Hubbell

2. Known Species (evolved over 3.8 billion years) Source: A. Alonso, F. Dallmeier, E. Granek and P. Raven. 2001. Biodiversity: connecting with the tapestry of life. Smithsonian Institution/Monitoring & Assessment of Biodiversity Program and President’s Committee of Advisors on Science and Technology, Washington, D.C. How many species on Earth? 5 ~ 10 millions Virus 5,000 Bacteria 4,000 Fungi 70,000 Plants 270,000 Invertebrates (excluding insects) 400,000 Insects (of which 600,00 are beetles) 960,000 Fishes 22,000 Birds 10,000 Amphibians and reptiles 12,000 Mammals 4,500 Total 1.8 million

4. “ Guessed” Extinction Rates by the End of the Millennium Source: Lugo, A. E. 1988. Estimating reductions in the diversity of tropical forest species. In Biodiversity, ed. E. O. Wilson. National Academy Press, Washington, DC. Estimate Basis of estimate Source 1 species/day to 1 species/hr Unknown Myers, 1979 33-50% of all species between the 1970’s & 2000 An exponential model for species loss over time due to forest area loss Lovejoy, 1980 A million species or more by 2000 If present land-use trends continue NRC, 1980 As high as 20% of all species Unknown Lovejoy, 1981 50% of species by 2000 An exponential loss Ehrlich & Ehrlich, 1981 25-30% of all species, or from 0.5 to several million by 2000 Unknown Myers, 1983 0.75 million species by 2000 All tropical forests will disappear & half of their species will become extinct Raven, 1986 15% of all plant species and 2% of all plant families by 2000 Forest regression will proceed as predicted until 2000 and then stop completely Simberloff, 1986

5. Millennium Prediction of Extinction Rates

7. But Extinction rates estimated from the species-area relationship have not been observed. It is widely recognized that SAR-estimated extinction rates are too high to be true.

9. A Problematic Extrapolation of SAR The use of SAR in estimating extinction rates is based on the premise that the backward extrapolation of SAR is valid, implying that the loss of species due to habitat reduction is of the same rate as the discovery of species.

11. Species-Area Curve Sampling species • • • • • • • • • • • • • • • • • • • area Number of species Species-area curve

12. Extinction Rates due to Habitat Destruction A 0 A n The # of species in the entire area The # of species removed due to logging  = extinction rate x = deforestation rate The # of species in the intact area • • • • • • • • • • • • • • •

13. SAR looks a perfectly valid method, but why extinction rates are overestimated? To answer this question, it is essential to understand how spatial distribution of species would affect the backward inference of extinction. Specifically, we want to prove that SAR method is only valid when species are randomly distributed. Otherwise, it inflates extinction rates.

15. x y 0 20 40 60 80 100 20 40 60 80 100 x r i r i r i Nearest Neighbor Distances

16. Nearest Neighbor Distance for Poisson Distribution Assume a population of organisms randomly distributed with intensity  , the probability of x individuals falling in a circle of radius r follows a Poisson distribution with mean   r 2 is r x = 0, 1, 2, …, ∞ • • • • •

17. The probability for the nn distance r can be derived as follows. p ( r )  p (circle r is empty, but individuals occur in the annulus) = p (circle r is empty)  p (individuals occur in the annulus) Therefore, r r 1 • • • •

18. The probability for the nn distance r is obtained by assuming r 1  r : Thus, the pdf for the nn distance r is a Weibull distribution: Mean: Variance:

20. Hubbell, S.P. et al. 2008. How many tree species are there in the Amazon and how many of them will go extinct? PNAS 105S:11498-11504.

21. Nearest Neighbor Distance for Binomial Distribution Assume N trees randomly fall in an area of fixed size A , the probability of x individuals falling in a circle of radius r follows a Binomial distribution with mean   r 2 is r x = 0, 1, 2, …, N • • • • •

22. The area required to encounter the n th tree has distribution: Distributions of area encountering the 1 st and N th nearest neighbor: Eberhardt, L.L. 1967. Some developments in ‘distance sampling. Biometrics 23:207-216.

23. Cumulative distributions of a 1 and a N : Species-area curve (forward model): Endemics-area curve:

24. It is easy to show that species loss calculated from species-area curve is the same as the endemics-area curve Therefore, the forward and backward models are equivalent under random distribution. A a • • • • • • • • • • • • • • •

25. The average area encountering the 1 st and N th nearest neighbor: The areas encountering the 1 st individual and the last individual are complementary – mirror image. a 1 a N

26. But for non-randomly distributed species, the forward and backward methods are not the same. The mirror image relationship does not hold in this case:

27. CTFS Plots – A Global Network

29. Yasuni BCI Blue curves: Red curves:

30. Pasoh Lambir

31. HKK Changbai

32. Extinction rates if 50% of individuals are removed: Endemics-Area Curve

33. A Conclusion without Conclusions But a Question

34. Why the random placement endemics-area curve works for nonrandom species, but not SAR?