Introduction to the analysis of community data Vojtech Novotny Czech Academy of Science, University of South Bohemia & New Guinea Binatang Research Center

Ecological analysis of community samples typical data format:

Some of the questions you can ask about the samples: How many species? How many individuals? What species are common / rare? How different are the sites in their species composition? How different are the species in their distribution?

Presence – absence characteristics: number of species and sites

Species accumulation curve

How many species? Corrected estimate for missing species Chao1 S + singletons2/(2*doubletons) S – number of species sampled

Courtesy Jonathan Coddington .

Courtesy Jonathan Coddington

No. of species often depends on the number of individuals: samples with more individuals have also more species Rarefraction: Comparing the number of species in a random selection of the same number of individuals from each sample

describing distribution of individuals among species Diversity measures: describing distribution of individuals among species Simpson’s index: the probability that two individuals chosen from your sample will belong to the same species Berger-Parker’s index: share of the most common species

Diversity estimate: Simpson’s diversity: 1- ∑[ni(ni-1)/N(N-1)] ni – number of individuals from species i, N – total number of individ. Berger-Parker’s Index: nmax/N nmax = abundance of the most common species, N – total no. of individ.

Na = (p1a + p2a + ... + pna)1/(1-a) Diversity: Hill’s numbers Na = (p1a + p2a + ... + pna)1/(1-a) a = Hill’s number p1, ... , pn = proportional abundance of species 1, 2, ... n N-∞ = reciprocal of the proportional abundance of the rarest species N0 = number of species N1 = eH where H = Shannon diversity index N2 = 1/D where D = Simpson’s index N∞ = reciprocal of the proportional abundance of the commonest species

Alpha, beta and gamma diversity alpha diversity beta diversity gamma diversity  = avg +  avg = 16.6  = 20 = 20 - 16.6 = 3.4 α β γ

X Y Community similarity estimate: Jaccard similarity: shared species/[total species X + Y] Jaccard similarity = A/(A+B+C) X, Y - samples X Y

Similarity indices Koleff et al. 2003 J anim Ecol 72:367

incorporate differences in species richness Jaccard Sorensen "Broad sense" measures incorporate differences in species richness as well as differences in composition Lennon et al. "Narrow sense" measures independent of differences in species richness 1- Example 1 a = 10, b = 10, c = 100 Jaccard = 10/120 = 0.08 Sorensen = 20/130 = 0.15 Lennon = 1- 10/20 = 0.5 Example 2 a = 10, b = 10, c = 1000 Jaccard = 10/1020 = 0.010 Sorensen = 20/1030 = 0.019 Lennon = 1- 10/20 = 0.5 Koleff et al. 2003 J anim Ecol 72:367

EstimateS data format, saved as TXT file

CJ = a / (a + b + c) CS = 2a / (2a + b +c) Chao1 S + singletons2/(2*doubletons) S = number of species sampled Jaccard CJ CJ = a / (a + b + c) a = richness in first site, b = richness in second site, j = shared species Sorenson CS CS = 2a / (2a + b +c) Simpson's Index (D) measures the probability that two individuals randomly selected from a sample will belong to the same species

Jaccard Coefficient number of shared species as proportion of total number of species in the two SUs ranges from 0 (no species in common) to 1 (the SUs have identical species lists) SU 2 Present Absent SU 1 a b c d

Sørenson Coefficient like Jaccard, ignores shared absences SU 2 Present Absent SU 1 a b c d

Quantitative Version of Sørenson (Bray-Curtis) Similarity

Morisita-Horn CmH Not influenced by sample size & richness Highly sensitive to the abundance of common spp. CmH = 2S(ani * bni) / (da + db)(aN)(bN) aN = total # of indiv in site A ani = # of individuals in ith species in site A da = Sani2 / aN2