Dynamical evolution of ecosystems
Sandro Azaele1 , Simone Pigolotti2
, Jayanth R. Banavar3 & Amos Maritan1
1 Dipartimento di Fisica ‘G. Galilei’, Universita` di Padova, via Marzolo 8, 35131 Padova, Italy.
2 The Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark.
3 Department ofPhysics, The Pennsylvania State University, 104 Davey Laboratory, University Park, Pennsylvania 16802, USA.
Abstract
The assembly of an ecosystem such as a tropical forest depends crucially on the species interaction network, and the deduction of its rules is a formidably complex problem1 . In spite of this, many recent studies2–16 using Hubbell’s neutral theory of biodiversity and biogeography2 have demonstrated that the resulting emergent macroscopic behaviour of the ecosystem at or near a stationary state shows a surprising simplicity reminiscent of many physical systems17. Indeed the symmetry postulate2 , that the effective birth and death rates are species-independent within a single trophic level, allows one to make analytical predictions for various static distributions such as the relative species abundance3–12, b-diversity13–15 and the species–area relationship16. In contrast, there have only been a few studies of the dynamics and stability of tropical rain forests18–20. Here we consider the dynamical behaviour of a community, and benchmark it against the exact predictions of a neutral model near or at stationarity. In addition to providing a description of the relative species abundance, our analysis leads to a quantitative understanding of the species turnover distribution and extinction times, and a measure of the temporal scales of neutral evolution. Our model gives a very good description of the large quantity of data collected in Barro Colorado Island in Panama in the period 1990–2000 with just three ecologically relevant parameters and predicts the dynamics of extinction of the existing species.
We present an analytical model that allows one to probe the characteristic timescales of evolving tropical forests and to evaluate the consequences of anthropogenic processes. Our approach is valid for an ecosystem at or near stationarity; indeed, one would expect important deviations from our predictions when the stationarity assumption is not valid (see, for example, ref. 21). Using a neutral model, we have obtained exact solutions for the probability distribution, P(x,t), that a species has a population x at time t for arbitrary initial and boundary conditions (see Supplementary Information for details). The species are assumed to be non-interacting and are characterized by effective birth and death rates given by b(x) 5 b1x 1 b0 and d(x) 5 d1x 1 d0 respectively, where b1 and d1 are the per-capita rates and the constants b0 and d0 incorporate density dependence and result in a rare species advantage when b0 . d0 (ref. 9). To simplify the analytical treatment and for parsimony we have chosen b0 5 2d0 in our analysis.
There are three biological parameters in our framework, namely [tau] , b and D : [tau] is the characteristic timescale associated with species turnover in neutral evolution--an ecosystem close to the stationary state...
Figure 1 | Relative species abundance plot in the BCI forest from the 1990 census (Center for Tropical Forest Science website). The individuals of more than 10 cm d.b.h. in this tropical forest are binned with the method of refs 7, 29. The inset shows the same histogram for the individuals of more than 1 cm d.b.h. for the same forest and yields consistent estimates of the model parameters and temporal scales within the error bars. The estimated parameters are robust within error bars on changing the nature of binning of the empirical data to non-overlapping bins. The points are the best fits to the mean number of species with population between 2n 2 1 and 2n , as given by equation (1). The fit for large x is readily improved at the cost of introducing an additional parameter (see Supplementary Information for error analysis and other details). Note that the RSA plot for individuals of more than 10 cm d.b.h. is smoother at low abundance than the plot for individuals of more than 1 cm d.b.h. This is to be expected because younger populations are subject to larger fluctuations than older ones.
Figure 2 | STD for the interval 1990–95 in the BCI forest. The main panel shows results for individuals of more than 10 cm d.b.h., and the inset results for individuals of more than 1 cm d.b.h. (Center for Tropical Forest Science website). We have defined the new variable r 5 log(l), which is distributed as g(r) 5 e r PSTD(er ,t), where PSTD(l,t) is given by equation (2). Data are plotted with a linear binning in the r 5 log(l) axis and fitted to g(r). b/D is obtained from fitting the RSA data in 1990 (see Fig. 1). The best-fit parameter is found to be t , 4,400 years for individuals of more than 10 cm d.b.h., and t , 3,900 years for individuals of more than 1 cm d.b.h. The fits of both RSA (see Fig. 1) and STD for individuals of more than 10 cm d.b.h. are systematically better than those for individuals of more than 1 cm d.b.h.
Figure 3 | Restricted relative species abundance. Plot of the mean number of species originally present in an ecosystem with population between 2n 2 1 and 2n after time t has evolved, as given by equation (3). The circles denote the steady state at t 5 0, namely the standard RSA; the triangles correspond to t 5 100 years; the diamonds to t 5 1,000 years; and the stars to t 5 10,000 years. The parameters are those deduced from the RSA of the BCI plot in 1990 for more than 10 cm d.b.h. (see Supplementary Table 1). Note the shift of the maximum of the curve to the right and that rare species are more prone to extinction.
1. Montoya, J. M., Pimm, S. L. & Sole´, R. Ecological networks and their fragility. Nature 442, 259–264 (2006).
2. Hubbell, S. P. The Unified Neutral Theory of Biodiversity and Biogeography (Princeton Univ., New Jersey, 2001).
3. Bell, G. Neutral macroecology. Science 293, 2413–2418 (2001).
4. Chave, J. Neutral theory and community ecology. Ecol. Lett. 7, 241–253 (2004).
5. Bell, G. The distribution of abundance in neutral communities. Am. Nat. 155, 606–617 (2000).
6. McKane, A., Alonso, D. & Sole´, R. V. Mean-field stochastic theory for species-rich assembled communities. Phys. Rev. E 62, 8466–8484 (2000).
7. Volkov, I., Banavar, J. R., Hubbell, S. P. & Maritan, A. Neutral theory and relative species abundance in ecology. Nature 424, 1035–1037 (2003).
8. Pigolotti, S., Flammini, A. & Maritan, A. Stochastic model for the species abundance problem in an ecological community. Phys. Rev. E 70, 011916 (2004).
9. Volkov, I., Banavar, J. R., He, F., Hubbell, S. P. & Maritan, A. Density dependence explains tree species abundance and diversity in tropical forests. Nature 438, 658–661 (2005).
10. Alonso, D. & McKane, A. Sampling Hubbell’s neutral theory of biodiversity. Ecol. Lett. 7, 911–914 (2004).
11. Alonso, D., Etienne, R. S. & McKane, A. J. The merits of neutral theory. Trends Ecol. Evol. 21, 451–457 (2006).
12. Etienne, R. S. & Alonso, D. A dispersal-limited sampling theory for species and alleles. Ecol. Lett. 8, 1147–1156 (2005).
13. Chave, J. & Leigh, E. G. Jr. A spatially-explicit model of b-diversity. Theor. Popul. Biol. 62, 153–168 (2002).
14. Condit, R. et al. Beta-diversity in tropical forest trees. Science 295, 666–669 (2002).
15. Zillio, T., Volkov, I., Banavar, J. R., Hubbell, S. P. & Maritan, A. Spatial scaling in model plant communities. Phys. Rev. Lett. 95, 098101 (2005).
16. Durrett, R. & Levin, S. A. Spatial models for species area curves. J. Theor. Biol. 179, 119–127 (2002).
17. Harte, J. Tail of death and resurrection. Nature 424, 1006–1007 (2003).
18. Clark, J. S. & McLachlan, J. S. Stability of forest biodiversity. Nature 423, 635–638 (2003).
19. Condit, R. et al. Dynamics of the forest communities at Pasoh and Barro Colorado: comparing two 50-ha plots. Phil. Trans. R. Soc. Lond. B 354, 1739–1748 (1999).
20. Sheil, D., Jennings, S. & Savill, P. Long-term plot observations of vegetation dynamics in Budongo, a Uganda rain forest. J. Trop. Ecol. 16, 765–800 (2000).
21. Gilbert, B., Laurance, W. F., Leigh, E. G. Jr & Nascimento, H. E. M. Can neutral theory predict the responses of amazonian tree communities to forest fragmentation? Am. Nat. 168, 304–317 (2006).
22. Gonzalez, A., Lawton, J. H., Gilbert, F. S., Blackburn, T. M. & Evans-Freke, I. I. Metapopulation dynamics, abundance, and distribution in a microsystem. Science 281, 2045–2047 (1998).
23. Abramowitz, M. & Stegun, I. A. Handbook of Mathematical Functions (National Bureau of Standards, Gaithersburg, Maryland, 1964).
24. Foster, D. R. & Zebrick, T. M. Long-term vegetation dynamics and disturbance history of a Tsuga -dominated forest in New England. Ecology 74, 982–998 (1993).
25. Bush, M. B., Silman, M. R. & Urrego, D. H. 48,000 years of climate and forest change in a biodiversity hot spot. Science 303, 827–829 (2004).
26. Pimm, S. L., Russell, G. J., Gittleman, J. L. & Brooks, T. M. The future of biodiversity. Science 269, 347–350 (1995).
27. Adler, P. B. Neutral models fail to reproduce observed species–area and species–time relationships in Kansas grasslands. Ecology 85, 1265–1272 (2004).
28. Hilborn, R. & Mangel, M. The Ecological Detective. Confronting Models with Data (Princeton Univ. Press, Princeton, New Jersey, 1997).
29. Preston, F. W. The commonness and rarity of species. Ecology 29, 254–283 (1948).
ليست هناك تعليقات:
إرسال تعليق