Test of neutral theory predic3ons for the BCI tree community informed by regional abundance data Anne%e Ostling Cody Weinberger Devin Riley Ecology and Evolu:onary Biology University of Michigan 1
Outline 1) Background about Neutral Theory 2) Problems with exis:ng tests of Neutral Theory & Overcoming them 3) Test of Neutral Theory on BCI informed by regional abundance data
Outline 1) Background about Neutral Theory 2) Problems with exis3ng tests of Neutral Theory & Overcoming them 3) Test of Neutral Theory on BCI informed by regional abundance data
Niche or Neutral? Niche theory proposes species difference allow coexistence stable coexistence (i.e. species can invade from low abundance) niche differences means something different than just species differences in abio>c preferences, it means species differences in interac>on with regula>ng factors, enabling stable coexistence, even within one environment! Neutral theory proposes coexistence due to species similari:es stochas>c events primary shaper of community structure 4
Neutral theory as a Null Model Neutral Theory may not be true. But Niches! PaFerns in Community Structure Species richness & degree of consistency of composi:on Species abundances and the distribu:on of abundance across species (i.e. how many rare versus common species) 5
What do Neutral Models look like? Neutral Model: Local community Local community at carrying capacity J Metacommunity In each death and replacement event: a randomly chosen individual dies, and then 2 op:ons: with probability m, it is replaced with the offspring of a random individual from the regional community ( metacommunity ) or with probability (1- m) it is replaced with an offspring of a random individual in the local community m = immigra:on rate Assumes all individuals are demographically equivalent 6
What do Neutral Models look like? Neutral Model: Metacommunity Metacommunity at carrying capacity In each death and replacement event: a randomly chosen individual dies, and then 2 op:ons: with probability ν, it is replaced with an individual of a new species or with probability (1- ν) it is replaced with the offspring of a randomly chosen individual ν = specia:on rate Local community predic:ons depend on θ=2j M ν and m 7
How have ecologists been tes3ng Neutral Theory? Neutral Theory provides good fits to SADs Species Abundance Distribu:ons Local community predic:ons of species abundance distribu:on over different m Fits to tropical forest data 8 (from Hubbell 1997)
Problems with this test The parameters θ, m are essen:ally free. A stochas:c niche model might produce the same thing with that freedom. The neutral model ignores a great deal of demographic complexity that is not necessarily part of niche mechanisms or habitat filtering, e.g. spa>al structure & detailed dependence of dispersal on distance complexi>es of specia>on/history shaping metacommunity size structure community size fluctua>ons (local and meta) fitness- equalized life history varia>on Even if it had been rejected we could argue that the departure is just due to that complexity and not to the presence of those community assembly mechanisms! 9
This is also true of many other tests of neutral theory, e.g. Fails to predict spa:al synchrony in S. Ontario since retreat of the glaciers. (Clark & MacLachlan 2003) (Ostling Journal of Plant Ecology 2012) Predicts abundant taxa are older than they are. (Leigh 1999) (Nee 2005) Fails to predict large changes in rela:ve abundances in response to removal of M. californianus in inter:dal on Tatoosh (Woo%on 2005) Predicts less iner:a than observed in small mammal assemblages over deep :me (McGill, Hadly & Maurer 2005) Predicts more similarity across coral reef communi:es than observed. (Dornelas, Connolly & Hughes 2006) Fits β- diversity at intermediate (but not short or long) distances in tropical forests (Condit et al. 2001) 10
Problems with exis3ng tests of Neutral Theory When neutral theory has succeeded, seems a stochas:c niche model could do just as well When neutral theory has failed, typically easy to argue due to neutral model used ignoring demographic complexity that has li%le to do with niches 11
Overcoming these problems Figure out what differences in community structure are produced by niches species abundance distribu:ons (Rosalyn Rael) pa%erning along trait axes (Rafael D Andrea) Figure out what demographic complexity is important to neutral model predic:ons Figure out how to construct robust tests of neutral theory 12
Build demographically complex neutral models At least inform them by measurements of dispersal parameters Be%er yet, model dispersal explicitly? Consider spa:al structure of habitat? Model size structure (i.e. allometric demographic complexity) Consider fluctua:ons in community size over :me Consider fitness- equalized life history varia:on if immigra:on rates do not scale with birth rates across species 13
ShiQ the focus to the local community Use data rather than a model for the metacommunity? (Alonso et al. 2006) metacommunity P½n 1 ;...; n S jjš ¼ local community 1;...; S X P½n 1 ;...; n S jx 1 ;...; x S ; JŠ fx 1 ;...;x S g P½x 1 ;...; x S Š. Would allow us to avoid modeling demographic complexity at that scale, and to test specifically for local community processes 14
Consider species- level departures along trait axes May be hard to say much more than non- neutral from SADs. Pa%erns of departure from neutral species by species along trait axes may be more revealing of niches and habitat filtering and the mechanisms leading to them in a given community 15
Outline 1) Background about Neutral Theory 2) Problems with exis3ng tests of Neutral Theory & Overcoming them 3) Test of Neutral Theory on BCI informed by regional abundance data
Outline 1) Background about Neutral Theory 2) Problems with exis:ng tests of Neutral Theory & Overcoming them 3) Test of Neutral Theory on BCI informed by regional abundance data
Panama basin regional abundance data Since 1994, over 50 one- hectare plots and smaller have been established in the Panama Canal watershed. P½n 1 ;...; 1;...; n S jjšs¼ P½n 1 ;...; n S jx 1 ;...; x S ; JŠ The idea is to use observed rela:ve abundances in regional plots for these rather than averaging over predicted behavior in a neutral metacommunity model 18
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 Census 7: 222 Species, 20,803 individuals 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 19
Neutral predic3ons for BCI 50ha plot using regional abundance data For each species k, we calculated analy:cally the neutral probability distribu:on based on it s observed regional rela:ve abundance p k : P( n m, p ) k We then calculated the SAD predic:on by summing these: S(n) = S M k =1 P( n m, p ) k We find the best fit m among realis:c m values for BCI, and the overall best finng m. (0.062 to 0.089) (Chisholm and Lichstein 2009) 20
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 21
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 best fit among realis:c m ( 0.062) 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 22
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 best fit among realis:c m ( 0.062) Recall realis:c range: 0.062 to 0.089 best fit m ( 0.006) 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 23
Neutral predic3ons for BCI 50ha plot using regional abundance data More realis8c dispersal a 1 a 50ha Immigra:on (s:ll described by m) involves: - individuals from the 10ha plot around BCI 50ha w/ probability a - the rest of the region with probability (1 a). 24
Neutral predic3ons for BCI 50ha plot using regional abundance data More realis8c dispersal a 1 a 50ha P( n m, p ) k P( n m, ap 10ha + (1 a)p ) rest Note this assumes the composi:on plot surrounding BCI is fixed. 25
Neutral predic3ons for BCI 50ha plot using regional abundance data More realis8c dispersal a 1 a 50ha We calculate m, a pairs under: 1) Gaussian dispersal, and 2) Students- t dispersal. (Chisholm and Lichstein 2009) (Muller- Landau PhD Disserta:on) for mean dispersal distances in the realis:c range measured for BCI, and find the best- fit among them. 26
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 best fit among realis:c m ( 0.062) best fit m ( 0.006) 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 27
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 both for smallest realis:c dispersal distance! best fit m, a among Student- t pairs: m=0.062, a=0.70 best fit m, a among Gaussian pairs: m=0.062, a=0.88 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 28
For best fit parameter values: Sta3s3cal tests We use simula:ons to determine whether the neutral model could be rejected based S obs, χ 2 obs. Frequency across neutral communi:es 5% S obs? Species Richness 29
For best fit parameter values: Sta3s3cal tests We use simula:ons to determine whether the neutral model could be rejected based S obs, χ 2 obs. Frequency across neutral communi:es 5% χ 2 against mean neutral SAD χ 2 obs? 30
BCI 50ha species abundance distribu3on m=0.062 Number of Species 0 10 20 30 40 50 60 70 based on S obs : m=0.062, a=0.70 m=0.062, a=0.88 all with p<0.001 m=0.006 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 31
BCI 50ha species abundance distribu3on m=0.062 Number of Species 0 10 20 30 40 50 60 70 based on χ 2 obs : m=0.062, a=0.70 m=0.062, a=0.88 m=0.006 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 32
BCI 50ha species abundance distribu3on Number of Species 0 10 20 30 40 50 60 70 based on an SAD metric correc:ng for S obs : m=0.062 m=0.062, a=0.70 m=0.062, a=0.88 m=0.006 1 2 4 8 16 32 64 128 256 512 1024 2048 4096 Abundance (log 2 bins) 33
Species- level analyses We calculated n pred and the p- value for each species: n pred = J n =1 P( n p k )n p - value = n obs n =1 ( ) or P( n p ) k P n p k J n =n obs For more realis:c dispersal with m=0.062, a=0.7: 97 species had p- value < 0.025 none of 1000 neutral runs resulted in this much selec:on 34
PaFerning along a trait axis Abundance 0 500 1000 1500 2000 4 6 8 10 12 Species' Maximum Tree Height 35
PaFerning along a trait axis Simple immigra:on model: m=0.006 Observed Abundance - Predicted Abundance -500 0 500 1000 1500 4 6 8 10 12 Species' Maximum Tree Height 36
Observed Abundance - Predicted Abundance -500 0 500 1000 1500 2000 PaFerning along a trait axis More realis:c immigra:on: m=0.062, a=0.7 (Students t) Looked at nearest neighbor distances among species w/observed abundance predicted abundance > 150 individuals. Mimimum is larger than expected by chance (p=0.02). CV is low but not significantly different from random. 4 6 8 10 12 Species' Maximum Tree Height 37
Conclusions/Discussion Tests of our neutral model suggest fewer species on BCI than expected some species are being selected è filtering (either abio>c or bio>c) on BCI! fewer rare and highly abundant species more species of intermediate abundance è Difficult to draw conclusions from this SAD paxerning, but maybe niches? species with large selec:on gradient are have large minimum separa:on è suggests maximum tree height is a niche axis on BCI? 38
Conclusions/Discussion But this analysis should be redone with a neutral model that incorporates greater complexity spa:ally explicit dispersal size/age structure other? (life history tradeoffs, species- specific dispersal) Expect to find filtering predomina:ng SADs may indicate only when community is non- neutral? But pa%erning of departures from neutral along trait axes may be more sugges:ve of niches 39
Ostling lab Undergraduates: Acknowledgements Devin Riley (Univ of Michigan) Cody Weinberger (Univ of Chicago) NSF Advancing Theory in Biology Grant (1038678) BCI forest dynamics research project funded by NSF grants to Stephen P. Hubbell, support from the Center for Tropical Forest Science, the Smithsonian Tropical Research Ins:tute, the John D. and Catherine T. MacArthur Founda:on, the Mellon Founda:on, the Small World Ins:tute Fund, and numerous private individuals, and through the hard work of over 100 people from 10 countries over the past two decades. The plot project is part the Center for Tropical Forest Science, a global network of large- scale demographic tree plots. 40