Advanced analytical approaches in
ecological data analysis
The world comes in fragments
Early plant succession in the Saxon (Germany) post brown coal mining area
Chicken Creak
2005
2010
Succession starts with colonising species from a regional species pool and from the initial
seed bank
Species co-occurrences
How do patterns of species co-occurrences change in time?
2005
Agrostis_capillaris
Agrostis_stolonifer
Cirsium_arvense
A1-2
0
0.1
0.1
A3-2
0
0
0.5
Basic questions
1. Which species colonise initially?
2. Is initial colonisation directional?
3. Is colonisation predictable?
A4-2
0.1
0
0
A4-3
0
0
0
B1-2
0
0
0.1
B2-1
0
0.1
0
B2-4
0
0.1
0
Starting hypothesis
1. Island biogeography predicts initial
species occurrences to be random.
2. Compretition theory predicts
equilibrium species occurrences to be
not random but driven by interspecific
competition.
Early plant succession
2011
Achillea_pannonica
Agrostis_capillaris
Agrostis_stolonifer
Agrostis_vinealis
Ajuga_genevensis
Apera_spica-venti
Arenaria_serpyllifo
A1-1
0
0
0
0
0
0
0
A1-2
0.5
0.5
0
0
0
0.4
0
A1-3
0
0
0.5
0
1.5
0
0
A1-4
0
0.5
0
2.0
0
0
0
A2-1
3.0
0.5
0
0
0
0.7
0.5
A2-2
0.1
0.5
0
0
0
0
0.5
A2-3
0
0.5
0
0
0
0
0.1
How to test for (non-) randomness?
Habitat filtering
Species
Joined absences
1
A 0
B 0
C 0
D 1
E 0
𝐶𝑙𝑢𝑚𝑝𝑖𝑛𝑔 𝑠𝑐𝑜𝑟𝑒 =
2
1
0
0
0
1
3
0
1
0
0
0
Sites
4 5
0 0
0 1
0 1
0 0
0 0
Reciprocal
segregation
Checkerboard
𝐶 − 𝑠𝑐𝑜𝑟𝑒 =
7
1
1
0
1
1
8
1
1
0
1
1
Clustered co-occurrence
Joined co-occurrence
Segregation
Competition
Reciprocal habitat
requirements
6
0
0
0
1
0
4 𝑐𝑙𝑢𝑠𝑡𝑒𝑟
𝑚𝑛(𝑚 − 1)(𝑛 − 1)
Common ecological
requirements
Habitat
engineering by the
earlier colonizer
4 𝑐ℎ𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑟𝑑𝑠
𝑚𝑛(𝑚 − 1)(𝑛 − 1)
Habitat
filtering
Niche
conservatism
Facilitation,
mutualism
Niche conservatism is
the tendency of closed
related species to have
similar ecological
requirements and life
history raits
Species
Spatial species turnover (b-diversity)
A
B
C
D
E
1
0
0
0
1
0
2
1
0
0
0
1
3
0
1
0
0
0
Sites
4 5
0 0
0 1
1 1
0 0
0 0
6
0
0
0
1
0
7
1
1
0
1
1
8
1
1
0
1
1
EV
-0.5
0.26
2.16
-0.6
-0.5
Species
EV -0.7 -0.6 0.3 2.4 1.4 -0.7 -0.4 -0.4
Sort according to the dominant
eigenvector of correspondence analysis
C1
B2
A3
E4
D5
41
1
0
0
0
0
52
1
1
0
0
0
33
0
1
0
0
0
Sites
74 85
0 0
1 1
1 1
1 1
1 1
26
0
0
1
1
0
17
0
0
0
0
1
86
0
0
0
0
1
2.4 1.4 0.3 -0.4 -0.4 -0.6 -0.7 -0.7
2.16
0.26
-0.5
-0.5
-0.6
Sorting a presenceabsence matrix
according to the
dominant
eigenvectors of
corresondence
analysis (seriation)
maximizes the
number of
occurrences along
the left to right
diagonal.
Metric for spatial
species turnover
Squared
correlation R2 of
row and column
ranks of species
occurrrences.
R
1
1
2
2
2
2
3
3
3
4
4
4
5
5
5
5
C
1
2
2
3
4
5
4
5
6
4
5
6
4
5
7
7
Pearson
0.75
R2
0.56
Species
A nested subset pattern
A
B
C
D
E
1
1
1
1
1
1
2
1
1
1
1
0
Sites
3 4 5
1 1 1
1 1 1
1 0 0
0 0 0
0 0 0
6
1
0
0
0
0
7
1
0
0
0
0
8
1
0
0
0
0
Nestedness describes a
situation where a
species poorer site is a
true subset of the next
species richer site.
Sum
8
5
3
2
1
A presence – absence matrix
ordered according to total species
richness (marginal totals, degree
distributions)
Unexpected
absence
Unexpected
presence
Species
Sum 5 4 3 2 2 1 1 1
A
B
C
D
E
1
1
1
1
1
1
2
1
0
1
1
0
Sites
3 4 5
1 1 1
1 1 1
1 0 0
0 0 0
0 0 0
6
1
0
0
1
0
7
1
0
0
0
0
8
1
0
0
0
0
Sum 5 3 3 2 2 2 1 1
Sum
8
4
3
3
1
The measurement of nestedness
The distance concept
of nestedness.
A
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
C
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
M O P D F H K E B J N L G
1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1
D 1 1 1 1 1 1 1
0 1 1 1 1 1 1 0 1 0 1 1 0
1 1 20;P
1 1 0 0 1 1 0 1 1 0 1
1 1 0 1 1 1 1 1 0 0 0 0 0
d
1 0 1 1 1 1 1 1 0 1 1 0 0
1 0 1 0 0 1 1 0 d 1 13;J
0 1 0 0
1 0 1 1 1 1 0 1 0 1 0 0 0
1 1 X;Y
0 0 1 1 0 1 0 0 0 1 0
1 1 0 0 0 1 0 0 0 1 0 1 0
1 1 0 0 1 0 1 0 0 0 0 0 0
0 1 1 0 1 0 0 0 0 0 0 0 1
0 0 1 1 0 0 0 0 1 0 0 0 0
0 0 0 1 0 0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0 0 0 0 D0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0 0 0 0 0 0
Sum 12 11 10 10 10 10
9
9
100
1
𝑇=
0.04145 𝑚𝑛
9
8
7
𝑚
𝑛
1
1
6
6
𝑑𝑖𝑗
𝐷𝑖𝑗
6
5
2
Sum
16
16
12
11
10
9
9
9
7
6
6
6
5
3
2
1
1
1
1
1
Sort the matrix rows and columns
according to some gradient.
Define an isocline that divides the matrix
into a perfectly filled and an empty part.
The normalized squared sum of relative
distances of unexpected absences and
unexpected presences is now a metric of
nestedness the nestedness temperature.
4
Z-score
I
1
3
7
15
20
4
9
13
2
11
17
18
5
8
16
6
10
12
14
19
8
6
4
2
0
-2
-4
-6
-8
0
50
Matrix size
100
Nestedness based on Overlap and Decreasing Fill (NODF)
r1
c2
1
0
c3
1
c4
c5
1
Nestedness among columns
c1
1
r2
1
1
1
0
0
r3
0
1
1
1
0
r4
1
1
0
0
0
r5
1
1
0
0
0
Nestedness among rows
c1 c2
c1 c3
c1 c4
c1 c5
c2 c3
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
Npaired=0
Npaired=67
Npaired=50
Npaired=100
Npaired=67
c2 c4
c2 c5
c3 c4
c3 c5
c4 c5
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
Npaired=50
r1
1
0
1
1
1
r2
1
1
1
0
0
r1
1
0
1
1
1
r3
0
1
1
1
0
r1
1
0
1
1
1
r4
1
1
0
0
0
r1
1
0
1
1
1
r5
1
1
0
0
r2
0
1
1
r3
1
1
0
r2
0
1
1
1
0
r4
1
1
0
0
0
r2
1
1
0
0
0
r5
1
1
0
0
0
r3
1
1
1
0
0
r4
0
1
1
1
0
r3
1
1
1
0
0
0
r5
1
1
0
0
0
1
0
r4
1
1
1
0
0
0
0
r5
1
1
0
0
0
Npaired=67
Npaired=67
Npaired=50
Npaired=50
Npaired=50
Npaired=0
Npaired=100 Npaired=100 Npaired=100
Npaired=50
Npaired=0
Ncolumns = 63.4
Npaired=0
Nrows = 53.4
Npaired=100
NODF = 58.4
Npaired=100
2 𝑁𝑝𝑎𝑖𝑟𝑒𝑑
𝑁𝑂𝐷𝐹 =
𝑚 𝑚 − 1 + 𝑛(𝑛 − 1)
NODF is a gap based metric and more conservative than temperature.
Back to the Huehnerwasser
How does species co-occurrence change during early succession?
0.008
0.006
0.5
0.4
0.3
0.004
0.2
0.002
0.1
0
2005 2006 2007 2008 2009 2010 2011
1
0.8
0.6
The degree of nestedness
is at an average level
(neithert nested nor antinested)
0
2005 2006 2007 2008 2009 2010 2011
Study year
Study year
R2
C-score
0.01
0.6
The number of
reciprocal species cooccurrences increases
in time
NODF
0.012
The degree of species
spatial turnover
decreases in time
0.4
0.2
0
2005 2006 2007 2008 2009 2010 2011
Study year
But are raw scores
reliable?
What do we expect
if colonisation were
a simple random
process?
Statistical inference using null models
Species
Species
What is random in ecology?
1
01
0
0
01
0
2
01
01
0
0
0
3
0
0
0
0
0
Sites
4 5
0 0
0
1 0
0 0
0 0
0 0
Sum 5
4
3
2
6
1
0
0
0
0
7
0
0
1
0
0
8
1
0
0
0
0
1
1
1
A
B
C
D
E
2
1
1
1
1
1
1
2
1
1
1
1
0
3
1
1
0
1
0
Sites
4 5
1 0
1 1
0 1
0 0
0 0
Sum 5
4
3
2
A
B
C
D
E
2
6
10
0
0
10
0
7
0
0
0
0
0
8
0
0
0
0
0
1
1
1
Sum
8
5
3
2
1
The proportionalproportional null model
Fill the matrix at random but
proportional to observed
marginal (row/column) totals
until the observed total
number of occurrences is
reached
The fixed - fixed null model
Sum
6
5
3
3
1
Fill the matrix at random until
for each row and each column
the observed total number of
occurrences is reached
Take a checkerboard pair and
swap. Do this 100000 times to
randomize the matrix.
Statistical inference using null models
Frequency
0.30
120
400 randomized
matrices
0.25
100
Observed
score
0.20
80
0.15
60
- SES
SES
0.10
40
0.05
20
0.00
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Score class
For each randomized matrix we calculate the
respective metric (C-score, NODF, R2).
𝑆𝐸𝑆 =
(𝑂𝑏𝑠 − 𝐸𝑥𝑝)
𝑆𝑡𝐷𝑒𝑣
Standardized effect sizes (SES) are Ztransformed scores and can be linked
to a normal distribution.
The Fisherian significance levels
P(-1 < X <+1) = 68%
P(-1.65 < X < +1.65) = 90%
P(-1.96 < X < +1.96) = 95%
P(-2.58 < X < +2.58) = 99%
P(-3.29 < X < +3.29) = 99.9%
Year
Score
Average null
distribution score
Standard
deviation
Z-score (SES)
FF null model
P(Z)
0.00009
0.00002
0.00001
0.00001
0.00001
0.00001
0.00001
0.193
1.106
3.036
4.995
4.454
7.273
10.273
0.847184
0.26857
0.002319
6E-07
7.9E-06
0
0
0.00575
0.00116
0.00171
0.00274
0.00122
0.00081
0.00089
-0.12
-1.095
-0.138
-1.358
0.083
-0.498
0.053
0.904851
0.27362
0.890053
0.174224
0.933961
0.618628
0.95803
0.02176
0.04284
0.02361
0.011
0.00509
0.00507
0.00497
-0.523
-0.168
1.238
6.025
6.705
5.463
2.488
0.601039
0.866252
0.215409
0
0
1E-07
0.012634
C-score
2005
2006
2007
2008
2009
2010
2011
0.01087
0.00106
0.00132
0.00355
0.00492
0.00756
0.00813
0.01085
0.00104
0.0013
0.00349
0.00487
0.00747
0.008
NODF
2005
2006
2007
2008
2009
2010
2011
0.05931
0.48707
0.53815
0.46488
0.49842
0.52119
0.49632
0.05999
0.48834
0.53838
0.4686
0.49832
0.52159
0.49627
R2
2005
2006
2007
2008
2009
2010
2011
0.91608
0.27526
0.20723
0.12074
0.06106
0.04678
0.02964
0.92746
0.28248
0.17799
0.05448
0.02695
0.01907
0.01728
8
6
4
2
0
2005 2006 2007 2008 2009 2010 2011
Study year
SES R2
SES C-score
10
SES NODF
12
SES scores (FF mull model)
The degree of reciprocal
0.2
species segregation
0
constantly increases
-0.2
-0.4
during early succession
-0.6
Local plant communities
-0.8
are not significantly
-1
nested during succession
-1.2
-1.4
-1.6
2005 2006 2007 2008 2009 2010 2011
Study year
8
7
Species spatial turnover
6
peaks at intermediate
5
stages of succession
4
3
2
1
In ecological research
0
raw metrics are most
-1
often meaningless!!
2005 2006 2007 2008 2009 2010 2011
Study year
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
FF
-1.4
-1.6
2005 2006 2007 2008 2009 2010 2011
3
2
1
0
-1
-2
2005 2006 2007 2008 2009 2010 2011
Study year
12
1
10
0.5
SES C-score
SES C-score
Study year
8
6
4
2
FF
0
2005 2006 2007 2008 2009 2010 2011
Study year
PP
4
SES NODF
SES NODF
Different null assumptions give different answers
0
-0.5
-1
-1.5
PP
-2
2005 2006 2007 2008 2009 2010 2011
Study year
Study year
The FF null model assumes that
sites are filled with species and
that each species occupies the
maximal number of sites.
5
4
3
SES R2
SES R2
8
7
6
5
4
3
2
1
0
FF
-1
2005 2006 2007 2008 2009 2010 2011
2
1
0
-1
PP
-2
2005 2006 2007 2008 2009 2010 2011
Study year
The PP null model assumes that
sites might differ dynamically in
species richness and that each
species might occupy a variable
number of sites.
The PP null model points often to a random pattern in species occupancy.
Idiosyncratic species are those that deviate in their patterns of occurrences
Total
NODF ExpNODF SpResult Z-SpResu DeltaSpC
Occ
Cirsium_arvense
11 56.618 63.431
6.087
0.864
-2.229
Chenopodium_album_agg. 7 69.118 69.402
5.975
1.049
-1.146
Species 2005
6
6
6
75
91.176
66.912
74.615
79.348
80.944
5.409
5.365
6.245
-0.529
-0.607
3.091
-1.452
-1.382
-0.536
3
86.029
86.852
5.919
1.163
-0.05
3
94.118
85.908
5.311
-1.004
-0.841
Arenaria_serpyllifolia_agg.
Festuca_rubra_agg.
Daucus_carota
Agrostis_capillaris
Carex_ericetorum
Bromus_tectorum
Robinia_pseudoacacia
Lupinus_luteus
Poa_palustris
Rubus_fruticosus_agg.
2
2
2
2
2A
2
B
1
C
1
D
1
E
0
92.647
85.294
92.647
92.647
1 2
98.529
1 1
92.647
1 1
92.647
1 1
92.647
1 1
92.647
1 0
100
90.293
90.795
92.899
Sites
3 91.203
4 5 6
1 91.166
1 1 1
1 91.345
1 1 0
96.805
1 1 0 0
0 96.949
0 0 1
94.787
0 0 0 0
100
5.859
5.97
5.505
75.831
8
15.792
1
05.822
0
5.838
0 0
15.789
0
5.816
0 1
5.629
1.341
1.683
-0.527
1.133
1.035
0.806
1.672
1.126
1.269
0
-0.008
0.075
-0.383
-0.092
-0.133
-0.092
0.075
0.075
0.075
0.075
Species
Agrostis_stolonifera_agg.
Crepis_tectorum
Echium_vulgare
Rumex_acetosella_var._te
nuifoliu
Calamagrostis_epigejos
Cirsium arvense
increases
(DeltaC < 0)
the degree of
nestedness
None of the
species
decreases the
nestedness
pattern. There
are few
unexpected
occurrences .
All species
behave similar.