Presentation given at the Annual Plant Sciences Symposium at the University of Wisconsin, Madison, "Turning a New Leaf on Plant Evolution and Ecology". Hosted by the Plant Sciences Graduate Student Council on Friday, November 4, 2016 at the H.F. Deluca Forum in the Wisconsin Institute for Discovery (330 N Orchard St, Madison, WI 53715). http://psgsc.wisc.edu/annual-plant-sciences-symposium/

1. Turning a new leaf
with persistent
homology:
old and new ways
of analyzing leaf shape
and the topology of
plants
Dan Chitwood
Donald Danforth Plant Science Center
November 4, 2016

2. Does leaf shape contain
information?
If so, what do leaves tell
us and how do we
measure leaf shape?
A primer on leaf shape
and past morphometric
methods …

3. Does leaf shape contain
information?
If so, what do leaves tell
us and how do we
measure leaf shape?
A primer on leaf shape
and past morphometric
methods …

4. Does leaf shape contain
information?
If so, what do leaves tell
us and how do we
measure leaf shape?
A primer on leaf shape
and past morphometric
methods …

5. Chitwood & Sinha, 2016
Leaf shape varies by
evolution, genetics, development and
by present climates & ancient climates

6. Leaf shape varies by
evolution, genetics, development and
by present climates & ancient climates
Chitwood & Sinha, 2016

7. Paleomap, scotese.com
Leaf shape varies by
evolution, genetics, development and
by present climates & ancient climates
Chitwood & Sinha, 2016

8. There are many ways to measure shape:
Pseudo-landmarks
Chitwood & Sinha, 2016

9. There are many ways to measure shape:
Elliptical Fourier Descriptors
Chitwood & Sinha, 2016

10. There are many ways to measure shape:
Homologous landmarks
Chitwood & Sinha, 2016

11. There are many ways to measure shape:
All methods are comprehensive,
but they’re not equivalent
Landmarks Elliptical Fourier Descriptors
Chitwood & Sinha, 2016

12. Grapevine: discriminating
genetic, developmental, and
environmental shapes
Examples of old and new morphometric
methods for plants
Persistent homology: a
topology based
morphometric method
Leaf morphospaces & a universal
theory of plant morphology

13. Landmark-based Procrustes analysis:
Superimposed homologous coordinates

14. Landmark-based Procrustes analysis:
Superimposed homologous coordinates
Kerschbaumer and Sturmbauer (2011)
International Journal of Evol. Biol.

15. Landmark-based Procrustes analysis:
Superimposed homologous coordinates
Kerschbaumer and Sturmbauer (2011)
International Journal of Evol. Biol.
Translate

16. Landmark-based Procrustes analysis:
Superimposed homologous coordinates
Kerschbaumer and Sturmbauer (2011)
International Journal of Evol. Biol.
Translate
Scale

17. Landmark-based Procrustes analysis:
Superimposed homologous coordinates
Kerschbaumer and Sturmbauer (2011)
International Journal of Evol. Biol.
Translate
Scale
Rotate

18. Homologous landmarks:
On every grape leaf

19. Homologous landmarks:
On every grape leaf

20. Homologous landmarks:
On every grape leaf

21. Homologous landmarks:
On every grape leaf

22. Homologous landmarks:
On every grape leaf

23. Homologous landmarks:
On every grape leaf

24. Homologous landmarks:
Species differences

25. Shoot
base
Shoot
tip
Leaf number
Developmental stage
Unequal expansion
Different leaf types
Homologous landmarks:
Species differences manifest in a
developmental context

26. Shoot
base
Shoot
tip
Leaf number
Developmental stage
Unequal expansion
Different leaf types
Homologous landmarks:
Species differences manifest in a
developmental context

27. Shoot
base
Shoot
tip
Leaf number
Developmental stage
Unequal expansion
Different leaf types
Homologous landmarks:
Species differences manifest in a
developmental context

28. Evolutionary vs. developmental paths
in the leaf morphospace
Species effects
Chitwood et al., New Phytol, 2016

29. Evolutionary vs. developmental paths
in the leaf morphospace
Developmental effects
Chitwood et al., New Phytol, 2016

30. Species can be predicted
independently from development
Chitwood et al., New Phytol, 2016

31. Development can be predicted
independently from species
Chitwood et al., New Phytol, 2016

32. Vein landmarks more sensitive to development
Chitwood et al., Plant Physiol, 2016

33. Vein landmarks more sensitive to development
Chitwood et al., Plant Physiol, 2016

34. Discriminating leaves from different years:
Same vines, same developmental stages
Chitwood et al., Plant Physiol, 2016

35. Discriminating leaves from different years:
Same vines, same developmental stages
Chitwood et al., Plant Physiol, 2016

36. Climate interannual variability:
2014/15 was colder & drier than 2012/13
Chitwood et al., Plant Physiol, 2016

37. Climate interannual variability:
2014/15 was colder & drier than 2012/13
Chitwood et al., Plant Physiol, 2016

38. Climate interannual variability:
Plasticity and evolutionary changes in leaf shape
go in the same direction?
Chitwood et al., Plant Physiol, 2016

39. Measuring future climates:
To California, wine grapes, and rootstocks!

40. The Vitis Underground:
Adapting perennial crops for climate change:
Graft transmissible effects of rootstocks on grapevine
shoots
Allison Miller, Saint Louis University
Jason Londo, USDA-ARS, Geneva, NY
Anne Fennel, South Dakota State University
Misha Kwasinewski, Mizzou
Laszlo Kovacs, Missouri State University
Peter Cousins, E&J Gallo Winery

41. Grapevine: discriminating
genetic, developmental, and
environmental shapes
Examples of old and new morphometric
methods for plants
Persistent homology: a
topology based
morphometric method
Leaf morphospaces & a universal
theory of plant morphology

42. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

43. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

44. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

45. These slides made by:
Mao Li
Donald Danforth Plant Science Center
Chitwood Lab & Topp Lab
Persistent homology: a
tool to universally
measure
plant morphologies across
organs and scales

46. Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

47. r
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

48. r
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

49. r
Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?

50. Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
How many groups are there? 3? 10? 1?
It depends on scale!

51. Verri et al. Biological Cybernetics, 1993
Carlsson, Bulletin AMS, 2009
Edelsbrunner et al., AMS, 2010
Persistent Homology, WHY? WHAT?
Another example

52. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

53. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

54. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

55. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

56. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

57. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

58. Sublevel Set Filtration:
Blue Red
A Persistent Homology Primer
How to get a nest sequence of shapes

59. Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes

60. Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes

61. Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes

62. Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes

63. Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes

64. Superlevel Set Filtration:
Red Blue
A Persistent Homology Primer
How to get a nest sequence of shapes

65. r
Persistent Homology, HOW?
Persistence Barcode

66. r
Persistent Homology, HOW?
Persistence Barcode

67. r
Persistent Homology, HOW?
Persistence Barcode

68. r
Persistent Homology, HOW?
Persistence Barcode

69. r
Persistent Homology, HOW?
Persistence Barcode

70. r
Persistent Homology, HOW?
Persistence Barcode
#connectedcomponents r

71. r
Persistent Homology, HOW?
Persistence Barcode
#connectedcomponents r
Now, apply!

72. tomato introgression lines
Eshed et al. , Genetic, 1999
Chitwood et al., The Plant Cell 2013
(domesticated, cv. M82) (wild)
IL4_3
• Significant difference is caused by the gene in the small region
• The difference is usually subtle

74. 16 annulus (rings) density estimator
A tool: Local and smooth side view
Blind to size, position, and orientation

75. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

76. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

77. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

78. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

79. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

80. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

81. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

82. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

83. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

84. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

85. • A robust metric between barcodes: bottleneck distance
plane height
(level value)
connectedcomponent

86. CV1
• Our approach integrates very different morphological characteristics
into a single descriptor.
Leaf Shape QTL
Statistical techniques: Multidimensional scaling (MDS, reduce dimension)
Canonical variate analysis (CVA, feature that most distinguish groups)

87. Result
Leaf Shape QTL

89. Coarse approximation
Elliptical Fourier Transform
http://haitham.ece.illinois.edu
First harmonics 5 harmonics 10 harmonics 20 harmonics

90. Euler characteristics = # connected component - # loops
level

91. Euler characteristics = # connected component - # loops
level

92. Leaf Serrations QTL
level

93. Result
Leaf Serrations QTL

97. Root Architecture QTL

98. Result
Root Architecture QTL

99. Persistent homology detects concerted changes in shoot and root architecture
Leaf Shape Root Architecture Serrations

100. Persistent homology detects concerted changes in shoot and root architecture
median values plots

101. Persistent Homology
• robust to noise
• invariant with respect to orientation
• capable of application across diverse scales
• compatible with diverse functions to quantify
disparate plant morphologies, architectures, and
textures

102. Grapevine: discriminating
genetic, developmental, and
environmental shapes
Examples of old and new morphometric
methods for plants
Persistent homology: a
topology based
morphometric method
Leaf morphospaces & a universal
theory of plant morphology

103. 2,392
9,619
4,765
34,637
2,885
17,859
865
5,733
3,301
866
84,859
5,814
2,422
176,017 leaves!
Demarcating a
leaf morphospace

104. 2,392
9,619
4,765
34,637
2,885
17,859
865
5,733
3,301
866
84,859
5,814
2,422
176,017 leaves!
Demarcating a
leaf morphospace

105. Discriminating
leaves:
Across
flowering
plant
families

106. Discriminating
leaves:
Across
sites
around
the world

107. “Transect” and Leafsnap data
Transect data
Dana Royer, Wesleyan University
Daniel Peppe, Baylor University
Peter Wilf, Penn State
Huff PM, Wilf P, Azumah EJ. 2003. Digital future
for paleoclimate estimation from fossil leaves?
Preliminary results. Palaios 18: 266-274.
Royer DL, Wilf P, Janesko DA, Kowalski EA, Dilcher
DL. 2005. Correlations of climate and plant ecology
to leaf size and shape: potential proxies for the
fossil record. American Journal of Botany 92: 1141-
1151.
Peppe DJ, Royer DL, Cariglino B, Oliver SY,
Newman S, Leight E, Enikolopov G, Fernandez-
Burgos M, Herrera F, Adams JM, Correa E, Currano
ED, Erickson JM, Hinojosa LF, Iglesias A, Jaramillo
CA, Johnson KR, Jordan GJ, Kraft N, Lovelock EC,
Lusk CH, Niinemets U, Penuelas J, Rapson G, Wing
SL, Wright IJ. 2011. Sensitivity of leaf size and
shape to climate: global patterns and paleoclimatic
applications. New Phytologist, 190: 724-739.
Leafsnap: A Computer Vision System for Automatic
Plant Species Identification
Neeraj Kumar, Peter N. Belhumeur, Arijit Biswas,
David W. Jacobs, W. John Kress, Ida C. Lopez, João V.
B. Soares
Proceedings of the 12th European Conference on
Computer Vision (ECCV), October 2012

108. The leaf morphospace group
Analysis
Mao Li, Danforth Center
Isolation
Rebekah Mohn, Miami University
Potato
Shelley Jansky, USDA, Wisconsin-Madison
Diego Fajardo, National Center to Genome Resources
Pepper
Allen van Deynze, UC Davis
Theresa Hill, UC Davis
Tomato
Viktoriya Coneva, Danforth Center
Margaret Frank, Danforth Center
Chris Topp, Danforth Center
Grape
Allison Miller, Saint Louis University
Jason Londo, USDA/ARS, Geneva, NY
Laura Klein, Saint Louis University
Passiflora
Wagner Otoni, Universidade Federal de Vicosa
Arabidopsis
Ruthie Angelovici, University of Missouri, Columbia
Batushansky Albert, University of Missouri, Columbia
Clement Bagaza, University of Missouri, Columbia
Edmond Riffer, University of Missouri, Columbia
Braden Zink, University of Missouri, Columbia
Brassica
J. Chris Pires, University of Missouri, Columbia
Hong An, University of Missouri, Columbia
Sarah Gebken, University of Missouri, Columbia
Cotton
Vasu Kuraparthy, North Carolina State University
Viburnum
Erika Edwards, Brown University
Elizabeth Spriggs, Yale University
Michael Donoghue, Yale University
Sam Schmerler, American Museum of Natural History
Grasses
Lynn Clark, Iowa State
Timothy Gallaher, Iowa State
Phillip Klahs, Iowa State

109. A universal theory of plant morphology:
Persistent homology and plant topology
Chris Topp, Keith Duncan, Ni Jiang, Mao Li

110. A universal theory of plant morphology:
Persistent homology and plant topology
Chris Topp, Keith Duncan, Ni Jiang, Mao Li

111. Chris Topp, Keith Duncan, Ni Jiang, Mao Li
A universal theory of plant morphology:
Persistent homology and plant topology

112. Chris Topp, Keith Duncan, Ni Jiang, Mao Li
A universal theory of plant morphology:
Persistent homology and plant topology

113. Acknowledgments
FSU
Mio Lab
Donald Danforth Plant Science Center
Topp Lab
Donald Danforth Plant
Science Center
Chitwood Lab