The document discusses methods for measuring tree diversity, including richness, evenness, and Rényi diversity profiles. It describes how Rényi profiles can order communities based on differences in diversity by considering both richness and evenness. Examples are provided to illustrate how the profiles can reveal differences in these aspects of diversity between sites.

1. Roeland Kindt
senior ecologist
World Agroforestry Centre (ICRAF)
R.Kindt@CGIAR.org
Tree Diversity Analysis:
Application to sentinel landscape data
Introduction to BiodiversityR

2. How to measure diversity?
• Richness: species number
• Diversity: richness and evenness
• Sample size effects (hierarchical
structure)
• Differences in species composition:
ordination and cluster analysis

3. Diversity: richness and evenness
Less diverse More diverse
richness
evenness

4. Rényi diversity profiles
• One of several methods for
diversity ordering
• Considers richness and evenness
• Based on proportional abundance
for each species
α
α
α
−
=
∑=
1
)ln(
1
S
i
ip
H

5. Rényi diversity profiles
S1
S2
Site A
Site D
S1 S2 S2
Site C
Site B
S3
S1
S2
S3S4
S5
S3
S1
S1
S1
S1 S1
S2
S3 S3
0 0.25 0.5 1 2 4 8 Inf
scale
0.0
0.5
1.0
1.5
Renyidiversity
Community A
Community B
Community C
Community D
Scale parameter changes influence of richness
and evenness on diversity measurement
Diversity
profile ranks
communities
according to
differences
in diversity
B
A = D
C
EVENNESSRICHNESS
DIVERSITY

6. Rényi diversity profiles
S1
S2
Site A
Site D
S1 S2 S2
Site C
Site B
S3
S1
S2
S3S4
S5
S3
S1
S1
S1
S1 S1
S2
S3 S3
0 0.25 0.5 1 2 4 8 Inf
scale
0.0
0.5
1.0
1.5
Renyidiversity
Community A
Community B
Community C
Community D
ln(richness)
Shannon ln(1/Simpson) ln(1/BergerParker)
B
A = D
C

7. Rényi diversity profiles
0 0.25 0.5 1 2 4 8 Inf
scale
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Renyidiversity
Community A
Community B
Community C
1 2 3 4 5
0
5
10
15
20
25
30
35 33
29
5
28
5
Community A
1 2 3 4 5 6
0
5
10
15
20
25
30
35
40
45
42
Community B
30
8
10
55
1 2 3 4 5 6 7
0
5
10
15
20
25
30
35
32
Community C21
12
16
4
9
6
Partial ordering:
one community is richer
but with lower evenness
than a second community

8. Rényi diversity profiles
1 2 3 4
0
5
10
10
Community A
6
1
4
1 2 3 4 5 6 7 8
0
5
10
10
Community B
10
66
1
4 4
1
1 2 3 4 5 6 7 8
0
5
10
15
17
Community C
1 11 11 1 1
1 2 3 4
0
5
10
15
10
Community D
10 1010
1 2 3 4 5 6 7 8
0
5
10
15
20
25
30
35
35
Community E
1 11 11 1 1
0 0.25 0.5 1 2 4 8 Inf
scale
0.0
0.5
1.0
1.5
2.0
Renyidiversity
Community A
Community B
Community C
Community D
Community E

9. 0 0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.5 3 10 100 inf.
alpha
0
1
2
3
4
5
6
H
boundary
fruit
firewood
medicine
timber
construction
shade
soil fertility
beverage
charcoal
fodder
ornamental
all
1.0
1.6
2.7
4.5
7.4
12.2
20.1
33.1
54.6
90.0
148.4
244.7
403.4
EXP(H)
Kindt R, Van Damme P, Simons AJ. 2006.
Tree diversity in western Kenya: using profiles to characterise
richness and evenness.
Biodiversity and Conservation 15: 1253-1270.

10. 0 0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.5 3 10 100 inf.
alpha
0
1
2
3
4
5H
1.0
1.6
2.7
4.5
7.4
12.2
20.1
33.1
54.6
90.0
148.4
EXP(H)
spices
fruit
firewood
medicine
stimuli
construction
shade
soil fertility
tools
gums
fodder
drugs
vegetables
all
0 0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.5 3 10 100 inf.
alpha
0
1
2
3
4
5
6
H
boundary
fruit
firewood
medicine
timber
construction
shade
soil fertility
beverage
charcoal
fodder
ornamental
all
1.0
1.6
2.7
4.5
7.4
12.2
20.1
33.1
54.6
90.0
148.4
244.7
403.4
EXP(H)
0 0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.5 3 10 100 inf.
alpha
0
1
2
3
4
5
6
H
1.0
1.6
2.7
4.5
7.4
12.2
20.1
33.1
54.6
90.0
148.4
244.7
403.4
EXP(H)
boundary
fruit
firewood
medicine
timber
construction
shade
soil fertility
leaves
charcoal
fodder
ornamental
stakes
all
0 0.1 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.5 3 10 100 inf.
alpha
0
1
2
3
4
5
6
H
boundary
fruit/nut
firewood
medicine
timber
construction
shade
cash
plant support
charcoal
fodder
animal traps
ornamentals
tool handles
all
1.0
1.6
2.7
4.5
7.4
12.2
20.1
33.1
54.6
90.0
148.4
244.7
403.4
EXP(H)
Cameroon Mabira
MeruW-Kenya

11. Rényi evenness profiles
• Based on shape of diversity
profiles: when richness is equal
then differences in diversity reflect
differences in evenness
• Expansion of measurement of
evenness of Shannon index
• Transforms evenness defined for
Hill diversity series
0ln HHE −= αα

12. Rényi evenness profiles
1 2 3 4
0
5
10
10
Community A
6
1
4
1 2 3 4 5 6 7 8
0
5
10
10
Community B
10
66
1
4 4
1
1 2 3 4 5 6 7 8
0
5
10
15
17
Community C
1 11 11 1 1
1 2 3 4
0
5
10
15
10
Community D
10 1010
1 2 3 4 5 6 7 8
0
5
10
15
20
25
30
35
35
Community E
1 11 11 1 1
0 0.25 0.5 1 2 4 8 Inf
scale
-2.0
-1.5
-1.0
-0.5
0.0
Renyievenness
Community A
Community B
Community C
Community D
Community E
0 0.25 0.5 1 2 4 8 Inf
scale
0.0
0.5
1.0
1.5
2.0
Renyidiversity
Community A
Community B
Community C
Community D
Community E
A = B

13. 1 10 100
Number of farms
1
10
100
Numberofspecies boundary
fruit
firewood
medicine
timber
construction
shade
soil fertility
beverage
charcoal
fodder
ornamental
all
W-Kenya
Species accumulation curves
Kindt R, Van Damme P, Simons AJ. 2006. Patterns of Species Richness at
Varying Scales in western Kenya: Planning for Agroecosystem Diversification.
Biodiversity and Conservation 15: 3235-3249.

14. n = 35 n = 35
n = 35
Cameroon Mabira
W-Kenya
Meru
Diversity accumulation surfaces

15. Analysis of differences in species
composition
• Diversity only depends on
frequencies, not on identities of the
species
• Various ecological distance
measures for pairwise differences in
species composition
• Various ordination and cluster
methods to summarize or analyze
distances
Kindt R, Van Damme P, Simons AJ, Beeckman H. 2006. Planning tree species
diversification in Kenya based on differences in tree species composition
between farms. I. Study of Tree Uses. Agroforestry Systems 67: 215-228.

16. A
B
C
Euclidean distance often problematic
for species composition
A B C

17. BiodiversityR
A free manual
and software for
biodiversity and
community
ecology analysis

19. http://cran.r-project.org/web/packages/BiodiversityR/
http://cran.r-project.org/web/packages/vegan/

27. 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵. 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 = 𝜋𝜋 𝑟𝑟2
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶. 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴
= 𝜋𝜋
𝑅𝑅1 +𝑅𝑅2
2
2

29. All trees, basal area
CA = DD: NO TREES

30. All trees, crown area

31. FIREWOOD
Frequencies calculated from basal area
CHARCOAL TIMBER
FODDER SHADE LIFE FENCE

32. FIREWOOD
Frequencies calculated from crown area
CHARCOAL TIMBER
FODDER SHADE LIFE FENCE

33. … short
commercial
break

34. AUC = 0.8775
Ensemble suitability modelling

35. ∑
∑=
mod
modmod )(
w
Pw
Pensemble
Ensemble = (weighted) average of different
Modeling algorithms such as random forests
(RF), Maximum Entropy (MAXENT) or Support
Vector Machines (SVM, SVME)

36. VECEA: A higher resolution map for 7 countries in eastern Africa
(Ethiopia, Kenya, Malawi, Rwanda, Uganda, Tanzania and Zambia)
http://www.vegetationmap4africa.org
Application domains:
• Climate change modelling
• Species selection
• Seed source selection
• (agro)ecological zonation
• Protected area evaluation
• Species distribution
mapping
http://www.vegetationmap4africa.org

37. Seed sources and seed zones
http://www.vegetationmap4africa.org

38. Agroforestry Species Switchboard
http://www.worldagroforestry.org/our_products/databases/switchboard