Sampling e ects on beta diversity

Transcription

1 Introduction Methods Results Conclusions Sampling e ects on beta diversity Ben Bolker, Adrian Stier, Craig Osenberg McMaster University, Mathematics & Statistics and Biology UBC, Zoology University of Florida, Biology 7 August 2013 Sunday, August 4, 13 References

2 Outline 1 Introduction 2 Methods 3 Results 4 Conclusions

3 Ecological diversity (Whittaker, 1972) alpha (local), beta (cross-site), gamma (total) Spatial scale (patch, biogeographic) Diversity scale (species, phylogenetic, functional) Metrics (incidence vs. density-based, robust, partitioning-based) Disclaimer

4 Ecological diversity (Whittaker, 1972) alpha (local), beta (cross-site), gamma (total) Spatial scale (patch, biogeographic) Diversity scale (species, phylogenetic, functional) Metrics (incidence vs. density-based, robust, partitioning-based) Disclaimer

5 Ecological diversity (Whittaker, 1972) alpha (local), beta (cross-site), gamma (total) Spatial scale (patch, biogeographic) Diversity scale (species, phylogenetic, functional) Metrics (incidence vs. density-based, robust, partitioning-based) Disclaimer

6 Genesis of beta diversity SPECIES POOL ENVIRONMENTAL FILTERING COMMUNITY SIZE SAMPLE SIZE A C B D Site 1 B A C Envt. 1 A B Size 1 A Sample 1 E G pool envt size effort F H Site 2 C B D Envt. 2 B C B Size 2 Sample 2 SAMPLING EFFECTS

7 Sampling eects: alpha diversity Very well studied (Colwell et al., 2012) Parametric extrapolation (Fisher's α, lognormal... ) Rarefaction Nonparametric extrapolation Diversity vs. sample size: Realized: N = ˆN Asymptotic: N Rareed: N = N min

8 Sampling eects: alpha diversity Very well studied (Colwell et al., 2012) Parametric extrapolation (Fisher's α, lognormal... ) Rarefaction Nonparametric extrapolation Diversity vs. sample size: Realized: N = ˆN Asymptotic: N Rareed: N = N min Alpha diversity N asymptotic N realized N rare Sample size

9 Sampling eects: beta diversity (c) (d) accumulation at a large scale. spiders in compared: c) Arrábrês Guadiana. As for arthropods in Terceira; Flores Pico. he mean value of index over 10,000 (e) (f) From Cardoso et al. (2009) (also see Beck et al. (2013)) when there is undersampling, which e with the other indices that incorporate their formulae. It may seem, on a first On the other hand, many authors may not agree with this requirement of independence between diversity components. When comparing very different communities that differ both

10 Simulation protocol Dene species-abundance curves within each individual patch (number of abundance classes, species per class, rank-abundance skew) Dene mixing parameter for each abundance class 0=endemic; 1=perfectly mixed Sample (Poisson or multinomial) from resulting distributions for each patch Patch 1 Patch 2 rank-abundance skew=2 mixing = {0.5,0,1}

11 Simulation protocol Dene species-abundance curves within each individual patch (number of abundance classes, species per class, rank-abundance skew) Dene mixing parameter for each abundance class 0=endemic; 1=perfectly mixed Sample (Poisson or multinomial) from resulting distributions for each patch Patch 1 Patch 2 rank-abundance skew=2 mixing = {0.5,0,1}

12 Simulation protocol Dene species-abundance curves within each individual patch (number of abundance classes, species per class, rank-abundance skew) Dene mixing parameter for each abundance class 0=endemic; 1=perfectly mixed Sample (Poisson or multinomial) from resulting distributions for each patch Patch 1 Patch 2 rank-abundance skew=2 mixing = {0.5,0,1}

13 Simulation protocol Dene species-abundance curves within each individual patch (number of abundance classes, species per class, rank-abundance skew) Dene mixing parameter for each abundance class 0=endemic; 1=perfectly mixed Sample (Poisson or multinomial) from resulting distributions for each patch Patch 1 Patch 2 rank-abundance skew=2 mixing = {0.5,0,1}

14 Hierarchical rarefaction Alpha diversity: sample-based vs individual-based rarefaction (Colwell et al., 2012) Hierarchical rarefaction: use all samples, but rarefy them individually (sampling unit=community) Practical (maybe not optimal?) for beta diversity

15 Hierarchical rarefaction Alpha diversity: sample-based vs individual-based rarefaction (Colwell et al., 2012) Hierarchical rarefaction: use all samples, but rarefy them individually (sampling unit=community) Practical (maybe not optimal?) for beta diversity

16 Hierarchical rarefaction Alpha diversity: sample-based vs individual-based rarefaction (Colwell et al., 2012) Hierarchical rarefaction: use all samples, but rarefy them individually (sampling unit=community) Practical (maybe not optimal?) for beta diversity

17 Simulation: incidence-based (Jaccard) mixing={0.5,0.5}, 20 sites (mean pairwise Jaccard distance) rank abundance skew Local population size

18 Single abundance class pmix: 0 pmix: 0.1 pmix: 0.5 pmix: 1 beta (mean pairwise Jaccard dist) local population size # sites

19 Simulation: density-based metrics chao gower manhattan raup local population size rank abundance skew

20 Rarefaction: case studies Hawkfish Grouper Control Predator Control Predator Treatment abundance richness Jaccard rarefied Jaccard

21 Conclusions Sampling eects on beta are interesting Eects of N on variance explain sampling patterns Hierarchical rarefaction disentangles sampling eects

22 10 8 N = Future directions Hill diversity 10 6 M = Robust indices (Fontana et al., 2008) Improve rarefaction Forget rarefaction: extrapolate More interesting predation: patchy frequency-dependent context-dependent Hill diversity N = M = VMGLRIWW 7LERRSR 7MQTWSR Hill parameter Hill Figure 4 Estimated Hill diversities for in silico communities. We distribution (S ¼ 10 6, z ¼Haegeman 2) and evaluated et the al. estimators (2013) ^D a and ^D columns: M ¼ 10 2,10 4,10 6 ) and three community sizes N (in rows: N the estimation uncertainty. The true Hill diversity D a of the commun and a ¼ 2 (Simpson) are correctly estimated even for small sample siz (species richness), are characterized by large uncertainty.

23 Acknowledgements National Science Foundation Killam Foundation NSERC SHARCnet Download:

24 References Beck, J., Holloway, J.D., and Schwanghart, W., Methods in Ecology and Evolution, 4(4): ISSN X. doi: / x Cardoso, P., Borges, P.A.V., and Veech, J.A., Diversity and Distributions, 15(6): ISSN doi: /j x. Colwell, R.K., Chao, A., et al., Journal of Plant Ecology, 5(1):321. ISSN , X. doi: /jpe/rtr044. Fontana, G., Ugland, K.I., et al., Journal of Experimental Marine Biology and Ecology, 366(12): ISSN doi: /j.jembe Haegeman, B., Hamelin, J., et al., The ISME Journal, 7(6): ISSN doi: /ismej Whittaker, R.H., Taxon, 21(2/3): ISSN doi: /

25 Extra stu

26 Predation types (Ted Hart)

27 Simulation pix (1) beta (mean pairwise Jaccard dist) pmixrare: 0 pmixrare: 0.1 pmixrare: 0.5 pmixrare: local population size pmixcommon: 0 pmixcommon: 0.1 pmixcommon: 0.5 pmixcommon: 1 rank abund param # sites