Extending the concept of diversity partitioning to characterize phenotypic complexity. Zachary Marion James Fordyce Ben Fitzpatrick

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1 Extending the concept of diversity partitioning to characterize phenotypic complexity Zachary Marion James Fordyce Ben Fitzpatrick

2 Acknowledgements Fireflies Lynn Faust Raphael De Cock Kathrin Stanger-Hall Sarah Sander! Chemistry Shawn Campagna Abigail Tester! Statistics & Patience Nathan Sanders Daniel Simberloff EEB grads!!

3 Why chemistry?

4 Why chemistry?

7 "An extreme example is the subdiscipline of chemical ecology, which has taken an exceptionally reductionist, high-technology approach to studying chemically-mediated processes, such as plant defenses against herbivores (p. 11).

11 Many chemically-mediated phenotypes (chemotypes) function and evolve as complex multivariate suites

12 How can we analytically make sense of such daunting phenotypic complexity?

13 Unfortunately, many statistical approaches applied to complex chemical datasets are unsatisfying GLMM: P =.83 N= Total Amt. (sqrt) Aggressive mimicry (sequestration) Bioluminescent signaling Pheromonal signaling Lifestyle Strategy Total amount ignores qualitative variation

14 Unfortunately, many statistical approaches applied to complex chemical datasets are unsatisfying.4 RDA 2.2 r2 =. Photinus obscurellus Photinus carolinus Photinus macdermotti Photinus marginellis Photinus pyralis. Photuris -.2 Pyropyga decipiens -.4 Lucidota punctata L. atra RDA 1. Ordinations are useful for visualizing clustering patterns but can be difficult to interpret

15 Ecologists have been describing complexity for years in terms of diversity

16 Instead of a data matrix with sites as rows and species as columns Sp 1 Sp 2 Sp 3 Site 1 X X X Site 2 X X X Site 3 X X X

17 Our matrix has individuals as rows and compound peaks as columns Sp 1 Sp 2 Sp 3 Pk 1 Pk 2 Pk 3 Site 1 X X X Ind 1 X X X Site 2 X X X Ind 2 X X X Site 3 X X X Ind 3 X X X

18 Our matrix has individuals as rows and compound peaks as columns Sp 1 Sp 2 Sp 3 Pk 1 Pk 2 Pk 3 Site 1 X X X Ind Site 2 X X X Ind Site 3 X X X Ind

19 Our matrix has individuals as rows and compound peaks as columns Sp 1 Sp 2 Sp 3 Pk 1 Pk 2 Pk 3 Site 1 X X X Ind Site 2 X X X Ind x1 Site 3 X X X Ind

20 Our matrix has individuals as rows and compound peaks as columns Sp 1 Sp 2 Sp 3 Pk 1 Pk 2 Pk 3 Site 1 X X X Ind Site 2 X X X Ind Site 3 X X X Ind 3 1 1

21 We can characterize chemical complexity as the effective number of chemical compounds 2 1 Diversity Diversity order (q)

22 We can characterize chemical complexity as the effective number of chemical compounds 2 Q: Richness 1 Diversity Diversity order (q)

23 We can characterize chemical complexity as the effective number of chemical compounds 2 1 Q: Richness! Q1: Shannon entropy Diversity Diversity order (q)

24 We can characterize chemical complexity as the effective number of chemical compounds Diversity Q: Richness! Q1: Shannon entropy! Q2: Gini-Simpson index Diversity order (q)

25 We can characterize chemical complexity as the effective number of chemical compounds Diversity Q: Richness! Q1: Shannon entropy! Q2: Gini-Simpson index Diversity order (q) Effective No: Equivalent to the number of compounds in an idealized chemotype with equal abundances

26 We can characterize chemical complexity as the effective number of chemical compounds Diversity Q: Richness! Q1: Shannon entropy! Q2: Gini-Simpson index Diversity order (q) Effective No: Equivalent to the number of compounds in an idealized chemotype with equal abundances

27 We can characterize chemical complexity as the effective number of chemical compounds Diversity Q: Richness! Q1: Shannon entropy! Q2: Gini-Simpson index Diversity order (q) Effective No: Equivalent to the number of compounds in an idealized chemotype with equal abundances

28 We can characterize chemical complexity as the effective number of chemical compounds Diversity Q: Richness! Q1: Shannon entropy! Q2: Gini-Simpson index Diversity order (q) Effective No: Equivalent to the number of compounds in an idealized chemotype with equal abundances

29 As with communities, we can partition chemical diversity into within-group, among-group, and pooled total components

30 As with communities, we can partition chemical diversity into within-group, among-group, and pooled total components I1 I2 I3

31 As with communities, we can partition chemical diversity into within-group, among-group, and pooled total components I1 I2 I3 γ

32 As with communities, we can partition chemical diversity into within-group, among-group, and pooled total components I1! γ diversity: The total effective no. of compounds overall γ I2 I3 γ

33 As with communities, we can partition chemical diversity into within-group, among-group, and pooled total components I1! γ of compounds overall α diversity: The mean within-group chemical diversity I2 I3 γ= α

34 As with communities, we can partition chemical diversity into within-group, among-group, and pooled total components I1! γ of compounds overall β α chemical diversity! β diversity: The effective number of completely distinct chemotypes I2 I3 γ α = β

35 Using a hierarchical framework, we can partition diversity at multiple levels to address chemical complexity at different scales Bioluminescent Signaling Pheromonal Signaling Species 1 Species 2 Species 3 Species 4 Pop 1 Pop 2 Pop 3 Pop 4 Pop Pop 6 Pop 7 Pop 8 I1 I2 I3 I4 I I6 I7 I8 I9 I1 I11 I12 I13 I14 I1 I16

36 Using a hierarchical framework, we can partition diversity at multiple levels to address chemical complexity at different scales Bioluminescent Signaling Pheromonal Signaling Species 1 Species 2 Species 3 Species 4 Pop 1 Pop 2 Pop 3 Pop 4 Pop Pop 6 Pop 7 Pop 8 I1 I2 I3 I4 I I6 I7 I8 I9 I1 I11 I12 I13 I14 I1 I16 Hierarchical bootstrapping provides error estimates

37 What happens when we apply a diversity partitioning approach to the firefly chemical dataset?

38 Within populations, diurnal individuals have the highest effective diversity on average while mimics have the lowest Diversity order (q) β Diversity 7 No. unique chemotypes Effective chem. diversity α Diversity Diversity order (q) 4

39 Although sequestering mimic individuals have the lowest α-diversity, they have the highest β-diversity Diversity order (q) β Diversity 7 No. unique chemotypes Effective chem. diversity α Diversity Diversity order (q) 4

40 In conclusion, using diversity partitioning to describe chem. complexity succinctly addresses both qualitative and quantitative variation Effective chem. diversity α Diversity Diversity order (q) No. unique chemotypes β Diversity Diversity order (q)

41 Diversity partitioning simplifies the complexity without obscuring the interesting components of complexity Effective chem. diversity α Diversity Diversity order (q) No. unique chemotypes β Diversity Diversity order (q)

42 This method can be used to answer questions about other multivariate traits not just chemically-mediated phenotypes Effective chem. diversity α Diversity Diversity order (q) No. unique chemotypes β Diversity Diversity order (q)

43 This method can be used to answer questions about other multivariate traits not just chemically-mediated phenotypes Questions? Diversity order (q) β Diversity 7 No. unique chemotypes Effective chem. diversity α Diversity Diversity order (q) 4

44 Contact: Zachary Marion 69 Dabney Hall University of Tennessee Knoxville, TN 3792

Package hierdiversity

Version 0.1 Date 2015-03-11 Package hierdiversity March 20, 2015 Title Hierarchical Multiplicative Partitioning of Complex Phenotypes Author Zachary Marion, James Fordyce, and Benjamin Fitzpatrick Maintainer