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
Outline 1 Introduction 2 Methods 3 Results 4 Conclusions
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
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
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
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
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
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
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
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}
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}
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}
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}
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
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
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
Simulation: incidence-based (Jaccard) mixing={0.5,0.5}, 20 sites (mean pairwise Jaccard distance) 0.75 0.50 0.25 rank abundance skew 2 5 20 50 0.00 10 1 10 2 10 3 10 4 Local population size
Single abundance class pmix: 0 pmix: 0.1 pmix: 0.5 pmix: 1 beta (mean pairwise Jaccard dist) 0.75 0.50 0.25 0.00 10 1 10 3 10 1 10 3 10 1 10 3 10 1 10 3 local population size # sites 5 10 20
Simulation: density-based metrics 0.075 0.050 0.025 0.000 chao 0.015 0.010 0.005 0.000 gower 10 1 10 2 10 3 10 4 10 1 10 2 10 3 10 4 manhattan raup 1.8 0.06 1.6 1.4 0.04 1.2 1.0 0.02 0.00 10 1 10 2 10 3 10 4 10 1 10 2 10 3 10 4 local population size rank abundance skew 2 5 20 50
Rarefaction: case studies 100 75 50 25 12.5 10.0 7.5 5.0 0.50 0.45 0.40 0.35 0.55 0.45 0.35 0.25 Hawkfish Grouper Control Predator Control Predator Treatment abundance richness Jaccard rarefied Jaccard
Conclusions Sampling eects on beta are interesting Eects of N on variance explain sampling patterns Hierarchical rarefaction disentangles sampling eects
10 8 N = 10 15 Future directions Hill diversity 10 6 M = 10 2 10 4 10 2 Robust indices (Fontana et al., 2008) Improve rarefaction Forget rarefaction: extrapolate More interesting predation: patchy frequency-dependent context-dependent Hill diversity 10 0 10 8 10 6 10 4 10 2 N = 10 20 M = 10 2 10 0 0 0.5 1 1.5 2 0 0.5 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.
Acknowledgements National Science Foundation Killam Foundation NSERC SHARCnet Download: http://goo.gl/h4bft3
References Beck, J., Holloway, J.D., and Schwanghart, W., 2013. Methods in Ecology and Evolution, 4(4):370382. ISSN 2041-210X. doi:10.1111/2041-210x.12023. Cardoso, P., Borges, P.A.V., and Veech, J.A., 2009. Diversity and Distributions, 15(6):10811090. ISSN 1472-4642. doi:10.1111/j.1472-4642.2009.00607.x. Colwell, R.K., Chao, A., et al., 2012. Journal of Plant Ecology, 5(1):321. ISSN 1752-9921, 1752-993X. doi:10.1093/jpe/rtr044. Fontana, G., Ugland, K.I., et al., 2008. Journal of Experimental Marine Biology and Ecology, 366(12):104108. ISSN 0022-0981. doi:10.1016/j.jembe.2008.07.014. Haegeman, B., Hamelin, J., et al., 2013. The ISME Journal, 7(6):10921101. ISSN 1751-7362. doi:10.1038/ismej.2013.10. Whittaker, R.H., 1972. Taxon, 21(2/3):213251. ISSN 0040-0262. doi:10.2307/1218190.
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Predation types (Ted Hart)
Simulation pix (1) beta (mean pairwise Jaccard dist) 1.00 0.75 0.50 0.25 0.00 1.00 0.75 0.50 0.25 0.00 1.00 0.75 0.50 0.25 0.00 1.00 0.75 0.50 0.25 0.00 pmixrare: 0 pmixrare: 0.1 pmixrare: 0.5 pmixrare: 1 10 2 10 4 10 2 10 4 10 2 10 4 10 2 10 4 local population size pmixcommon: 0 pmixcommon: 0.1 pmixcommon: 0.5 pmixcommon: 1 rank abund param 2 5 20 50 # sites 5 10 20