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1、Developments in Neutral theory1Three Assumptions in Neutral Community EcologyNeutrality assumption Zero-Sum assumptionPoint mutuation assumptionHubbell, S. P. 2001. The unified neutral theory of biodiversityand biogeography. - Princeton University Press.2Relax zero-sum assumptionEtienne et al. (2007
2、): zero-sum and non-zero-sum formulations of neutral theory have exactly the same sampling formula when the community is in equilibrium.Conlisk et al.(2010): a simple colonization rule can yield Hubbells local abundance distribution with weeker assumption (relaxing zero-sum assumption).Etienne RS, A
3、lonso D, McKane AJ (2007a) The zero-sum assumption in neutral biodiversity theory. J Theor Biol 248:522536.Conlisk J, Conlisk E, Harte J (2010) Hubbells local abundance distribution: insights from a simple colonization rule. Oikos 119:379383.3Relax point mutuation assumption- random fission speciati
4、onHubbell (2001) stated that the equilibrium metacommunity SAD resulting from random fission speciation is a zero-sum multinomial.Ricklefs (2003) provided some approximate formulas for the total species richness in the metacommunity under random fission speciation.Etienne and Haegeman (2010) derive
5、analytical expressions for the distribution of abundances according to the neutral model with recruitment (i.e., dispersal and establishment) limitation and random fission speciation.4Relax point mutuation assumption- random fission speciationEtienne, R.S. and Bart, Haegeman, 2010. The neutral theor
6、y biodiversity with random fission speciation.Theor EcolFigure 5 shows the abundance distributions with the fitted models. Clearly the model with random fission speciation never performs significantly better than the point mutationmodel.5Relax point mutuation assumption- random fission speciationThe
7、 metacommunity abundance distribution under random fission is identical to the broken-stick abundance distribution, and thus provides a dynamical explanation for this grand old lady of abundance distributions.The metacommunity abundance distribution under random fission :6Relax point mutuation assum
8、ption- speciation rate proportional to abundance Etienne RS, Apol MEF, Olff H, Weissing FJ (2007b) Modes of speciation and the neutral theory of biodiversity. Oikos116:241258.7Relax point mutuation assumption- Protracted speciationProtracted speciation: by modeling speciation as a gradual, protracte
9、d, process rather than an instantaneous event.Speciation rate: , where u is general speciation-initiation rate.Protracted speciation: by modeling speciation as a gradual, protracted, process rather than an instantaneous event.Speciation rate: , where u is general speciation-initiation rate.8Relax po
10、int mutuation assumption- Protracted speciationRosindell et al.,2010. Protracted speciation revitalizes the neutral theory of biodiversity. Ecol. Lett. 13:716-727.9Relax point mutuation assumption- Protracted speciationRosindell et al.,2010. Protracted speciation revitalizes the neutral theory of bi
11、odiversity. Ecol. Lett. 13:716-727.10Three Assumptions in Neutral Community EcologyWhile the neutrality assumption is the heart of the neutral theory, the other two assumptions are assumptions of particular model implementations of the theory, allowing for analytical expressions for diversity measur
12、es, rather than the fundamental assumption of the theory itself. A mismatch between observes and theoretical predictions can, be due to these additional assumptions and therefore cannot be immediately interpreted as calling for a rejection of the neutral theory as a whole.Rampal EtienneEtienne, R.S.
13、 and Bart, Haegeman, 2010. The neutral theory biodiversity with random fission speciation.Theor Ecol11Further study niche-ovlappedHowever, the degree to which real ecological communites are acttually neutral is a more open question (Gotelli and McGill, 2006). That is, what is a distribution of ecolo
14、gical communities along a continuum form purely neutral, througth weekly nich-structured, to strongly niche-structured (Adler, HilleRisLambers & Levine 2007)? - Different but equal: the implausible assumption at the heart of neutral theory, 2011.In the present case, our question is: when is the limi
15、ted complexity of the neutral model sufficient to provide a useful approximation to a model of biodiversity with simple niche structure? -Theory predicts a rapid transition from niche-structured to neutral biodiversity patterns across a speciation-rate gradient, 2011.12Further study niche-ovlappedCh
16、ishom and Palaca (2010) present an analytical proof that, in the limit as diversity becomes large, a strong niche model give rises to exactly the same asymptotic form of SAD as the neutral model.Haegeman and Etienne (2011) argue that their result is an artefact because their model for high diversity
17、 is equivalent to an independent-species model. they analyse this independent-species model, and show that its SADs are identical to neutral predictions for all levels of diversity.13Further study niche-ovlappedChishom and Palaca (2011) : As the speciation rate in the hybrid model increases, we obse
18、rve a surprisingly rapid transition from an ecosystem in which diversity is almost entirely governed by niche structure to one in which diversity is statistically indistinguishable from that of the neutral model.Posterior probability that an observed species abundance distribution from the hybrid mo
19、del comes from a neutral model, given an uninformative dichotomous prior that specifies equal probabilities for the neutral model and the pure (broken-stick) niche model (P (neutral) = P(broken stick)=0.5), for different values of the speciation rate. Other parameters are m=0.1, J=20,000, JM=1012, K
20、=16. See text for model details. Dashed lines show 95% confidence intervals (estimated from 20 simulations)14Further study Relax neutrality assumptionZhou and Zhang (2008): The neutral theory can be extended to explain these observations by allowing species to differ slightly in their competitive ab
21、ility (fitness).15Further study Relax neutrality assumptionZhang et al.(2011) demonstrate how such a weaker form of symmetry can generate significant macroecological diversity patterns, leading to a very different interpretation of the relation between Fishers a and Hubbells fundamental biodiversity
22、 number., where16Further study Relax neutrality assumption Zhang et al (2011) invoke the weaker form of ecological symmetry by assuming fitness equivalence so that the ratio of the percapita birth rate to the per-capita death rate is invariant across species, that is, bi/di=C for any species i.Question:What if C N(0, 1 or others) or other distributions?17Further study - some questions Species distribution in niche overlapped area; fitting for common species； Nearly neutral theory model; Speciation and species abundace distributions;Species abundance distrubution in 2-D space;18The end19
