Advanced analytical approaches in ecological data analysis
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Advanced analytical approaches in ecological data analysis The world comes in fragments
description
Advanced analytical approaches in ecological data analysis. The world comes in fragments. Early plant succession in the Saxon (Germany) post brown co a l mining area Chicken Creak. 2005. 2010. - PowerPoint PPT Presentation
Transcript of Advanced analytical approaches in ecological data analysis
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 A1-2 A3-2 A4-2 A4-3 B1-2 B2-1 B2-4Agrostis_capillaris 0 0 0.1 0 0 0 0Agrostis_stolonifer 0.1 0 0 0 0 0.1 0.1Cirsium_arvense 0.1 0.5 0 0 0.1 0 0
2011 A1-1 A1-2 A1-3 A1-4 A2-1 A2-2 A2-3Achillea_pannonica 0 0.5 0 0 3.0 0.1 0Agrostis_capillaris 0 0.5 0 0.5 0.5 0.5 0.5Agrostis_stolonifer 0 0 0.5 0 0 0 0Agrostis_vinealis 0 0 0 2.0 0 0 0Ajuga_genevensis 0 0 1.5 0 0 0 0Apera_spica-venti 0 0.4 0 0 0.7 0 0Arenaria_serpyllifo 0 0 0 0 0.5 0.5 0.1
Early plant succession
Starting hypothesis1. 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.
Basic questions1. Which species colonise initially?2. Is initial colonisation directional?3. Is colonisation predictable?
How to test for (non-) randomness?
Sites1 2 3 4 5 6 7 8
Species
A 0 1 0 0 0 0 1 1B 0 0 1 0 1 0 1 1C 0 0 0 0 1 0 0 0D 1 0 0 0 0 1 1 1E 0 1 0 0 0 0 1 1
Clustered co-occurrence
Joined co-occurrence
SegregationReciprocal segregation
Checkerboard
Common ecological requirements
Habitat filtering
Niche conservatism
Competition
Reciprocal habitat requirements
Facilitation, mutualism
Habitat engineering by the
earlier colonizer
Joined absences
Habitat filtering
𝐶−𝑠𝑐𝑜𝑟𝑒=4∑ h𝑐 𝑒𝑐𝑘𝑒𝑟𝑏𝑜𝑎𝑟𝑑𝑠𝑚𝑛(𝑚−1)(𝑛−1)
𝐶𝑙𝑢𝑚𝑝𝑖𝑛𝑔𝑠𝑐𝑜𝑟𝑒=4∑𝑐𝑙𝑢𝑠𝑡𝑒𝑟
𝑚𝑛(𝑚−1)(𝑛−1)
Niche conservatism is the tendency of closed related species to have
similar ecological requirements and life
history raits
Sites1 2 3 4 5 6 7 8
Species
A 0 1 0 0 0 0 1 1B 0 0 1 0 1 0 1 1C 0 0 0 1 1 0 0 0D 1 0 0 0 0 1 1 1E 0 1 0 0 0 0 1 1
EV -0.7 -0.6 0.3 2.4 1.4 -0.7 -0.4 -0.4
EV-0.50.262.16-0.6-0.5
Sites4 5 3 7 8 2 1 6
Species
C 1 1 0 0 0 0 0 0 2.16B 0 1 1 1 1 0 0 0 0.26A 0 0 0 1 1 1 0 0 -0.5E 0 0 0 1 1 1 0 0 -0.5D 0 0 0 1 1 0 1 1 -0.6
2.4 1.4 0.3 -0.4 -0.4 -0.6 -0.7 -0.7
Sort according to the dominant eigenvector of correspondence analysis
Spatial species turnover (b-diversity)
Sorting a presence-absence 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
1 2 3 4 5 6 7 812345
Squared correlation R2 of row and column ranks of species occurrrences.
R C Pearson1 1 0.751 22 2 R2
2 3 0.562 42 53 43 53 64 44 54 65 45 55 75 7
Sites1 2 3 4 5 6 7 8 Sum
Species
A 1 1 1 1 1 1 1 1 8B 1 1 1 1 1 0 0 0 5C 1 1 1 0 0 0 0 0 3D 1 1 0 0 0 0 0 0 2E 1 0 0 0 0 0 0 0 1
Sum 5 4 3 2 2 1 1 1
A nested subset pattern
Nestedness describes a situation where a species poorer site is a true subset of the next species richer site.
A presence – absence matrix ordered according to total species richness (marginal totals, degree distributions)
Sites1 2 3 4 5 6 7 8 Sum
Species
A 1 1 1 1 1 1 1 1 8B 1 0 1 1 1 0 0 0 4C 1 1 1 0 0 0 0 0 3D 1 1 0 0 0 1 0 0 3E 1 0 0 0 0 0 0 0 1
Sum 5 3 3 2 2 2 1 1
Unexpected absence
Unexpected presence
I A C M O P D F H K E B J N L G Sum1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 163 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 167 1 1 1 0 1 1 1 1 1 1 0 1 0 1 1 0 12
15 1 1 0 1 1 1 1 0 0 1 1 0 1 1 0 1 1120 1 1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 104 0 0 0 1 0 1 1 1 1 1 1 0 1 1 0 0 99 1 1 1 1 0 1 0 0 1 1 0 1 0 1 0 0 9
13 1 0 1 1 0 1 1 1 1 0 1 0 1 0 0 0 92 1 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 7
11 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 617 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 618 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 65 0 1 1 0 0 1 1 0 0 0 0 1 0 0 0 0 58 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 3
16 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 26 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1
10 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 112 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 114 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 119 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1
Sum 12 11 10 10 10 10 9 9 9 8 7 6 6 6 5 4
X;Y
13;J
20;Pd
d
D
D
The measurement of nestedness
The distance concept of nestedness.
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.
-8-6-4-202468
0 50 100
Matrix size
Z-sc
ore
𝑇=100
0.041451𝑚𝑛 (∑1
𝑚
∑1
𝑛
( 𝑑𝑖𝑗
𝐷𝑖𝑗 )2
)
1 1
1 1
0 1
1 1
1 0
1 1
1 1
0 1
1 1
1 0
1 0
1 0
0 1
1 1
1 1
1 0
1 0
0 1
1 1
1 1
1 0
1 0
0 1
1 0
1 1
1 0
1 0
0 1
1 0
1 1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1 0
1 0
1 1
1 1
0 1
1 0
1 0
1 1
1 1
0 1
1 0
1 0
1 1
1 0
0 1
1 0
1 0
1 1
1 0
0 1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0 0
0 0
1 1
1 0
1 1
0 0
0 0
1 1
1 0
1 1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1 1 1 0
1 0 1 1
0
1
1 1 1 0
1 0 1 1
0
1
0 1 1 1
1 0 1 1
0
1
0 1 1 1
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
0
0 1 1 1
1 1 1 0
0
0
0 1 1 1
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
1 1 0 0
0
0
1 1 0 0
1 1 0 0
Nestedness among rowsN
este
dnes
s am
ong
colu
mns
c5c4c3c2c1
r5
r4
r3
r2
r1
0
0
0
0
1
1 1 0 0
1 1 0 0
0 1 1 1
1 1 1 0
1 0 1 1
c5c4c3c2c1
r5
r4
r3
r2
r1
0
0
0
0
1
1 1 0 0
1 1 0 0
0 1 1 1
1 1 1 0
1 0 1 1
c1 c2 c1 c3 c1 c4 c1 c5 c2 c3
c2 c4 c2 c5 c3 c4 c3 c5 c4 c5
Npaired=0 Npaired=67 Npaired=50 Npaired=100 Npaired=67
Npaired=50 Npaired=0 Npaired=100 Npaired=100 Npaired=100
r1
r2
r1
r3
r1
r4
r1
r5
r2
r3
r2
r4
r2
r5
r3
r4
r3
r5
r4
r5
Npaired=67
Npaired=67
Npaired=50
Npaired=50
Npaired=50
Npaired=50
Npaired=0
Npaired=0
Npaired=100
Npaired=100
Ncolumns = 63.4
Nrows = 53.4
NODF = 58.4
1 1
1 1
0 1
1 1
1 0
1 1
1 1
0 1
1 1
1 0
1 0
1 0
0 1
1 1
1 1
1 0
1 0
0 1
1 1
1 1
1 0
1 0
0 1
1 0
1 1
1 0
1 0
0 1
1 0
1 1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1 0
1 0
1 1
1 1
0 1
1 0
1 0
1 1
1 1
0 1
1 0
1 0
1 1
1 0
0 1
1 0
1 0
1 1
1 0
0 1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0 0
0 0
1 1
1 0
1 1
0 0
0 0
1 1
1 0
1 1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1 1 1 0
1 0 1 1
0
1
1 1 1 0
1 0 1 1
0
1
0 1 1 1
1 0 1 1
0
1
0 1 1 1
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
1
1 1 0 0
1 0 1 1
0
0
0 1 1 1
1 1 1 0
0
0
0 1 1 1
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
1 1 1 0
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
0 1 1 1
0
0
1 1 0 0
1 1 0 0
0
0
1 1 0 0
1 1 0 0
Nestedness among rowsN
este
dnes
s am
ong
colu
mns
c5c4c3c2c1
r5
r4
r3
r2
r1
0
0
0
0
1
1 1 0 0
1 1 0 0
0 1 1 1
1 1 1 0
1 0 1 1
c5c4c3c2c1
r5
r4
r3
r2
r1
0
0
0
0
1
1 1 0 0
1 1 0 0
0 1 1 1
1 1 1 0
1 0 1 1
c5c4c3c2c1
r5
r4
r3
r2
r1
0
0
0
0
1
1 1 0 0
1 1 0 0
0 1 1 1
1 1 1 0
1 0 1 1
c5c4c3c2c1
r5
r4
r3
r2
r1
0
0
0
0
1
1 1 0 0
1 1 0 0
0 1 1 1
1 1 1 0
1 0 1 1
c1 c2 c1 c3 c1 c4 c1 c5 c2 c3
c2 c4 c2 c5 c3 c4 c3 c5 c4 c5
Npaired=0 Npaired=67 Npaired=50 Npaired=100 Npaired=67
Npaired=50 Npaired=0 Npaired=100 Npaired=100 Npaired=100
r1
r2
r1
r3
r1
r4
r1
r5
r2
r3
r2
r4
r2
r5
r3
r4
r3
r5
r4
r5
Npaired=67
Npaired=67
Npaired=50
Npaired=50
Npaired=50
Npaired=50
Npaired=0
Npaired=0
Npaired=100
Npaired=100
Ncolumns = 63.4
Nrows = 53.4
NODF = 58.4
Nestedness based on Overlap and Decreasing Fill (NODF)
NODF is a gap based metric and more conservative than temperature.
𝑁𝑂𝐷𝐹=2∑𝑁 𝑝𝑎𝑖𝑟𝑒𝑑
𝑚 (𝑚−1 )+𝑛(𝑛−1)
Back to the HuehnerwasserHow does species co-occurrence change during early succession?
00.0020.0040.0060.008
0.010.012
2005 2006 2007 2008 2009 2010 2011
C-sc
ore
Study year
00.10.20.30.40.50.6
2005 2006 2007 2008 2009 2010 2011
NO
DF
Study year
0
0.2
0.4
0.6
0.8
1
2005 2006 2007 2008 2009 2010 2011
R2
Study year
The number of reciprocal species co-occurrences increases in time The degree of nestedness
is at an average level (neithert nested nor anti-nested)
The degree of species spatial turnover decreases in time
But are raw scores reliable?
What do we expect if colonisation were a simple random process?
Statistical inference using null models
What is random in ecology?
Sites1 2 3 4 5 6 7 8 Sum
Species
A 0 0 0 0 0 0 0 0 8B 0 0 0 0 0 0 0 0 5C 0 0 0 0 0 0 0 0 3D 0 0 0 0 0 0 0 0 2E 0 0 0 0 0 0 0 0 1
Sum 5 4 3 2 2 1 1 1
11
1 1
11
1 Fill the matrix at random but proportional to observed
marginal (row/column) totals until the observed total
number of occurrences is reached
The proportional- proportional null model
Fill the matrix at random until for each row and each column the observed total number of
occurrences is reached
The fixed - fixed null modelSites1 2 3 4 5 6 7 8 Sum
Species
A 1 1 1 1 0 1 0 1 6B 1 1 1 1 1 0 0 0 5C 1 1 0 0 1 0 1 0 3D 1 1 1 0 0 0 0 0 3E 1 0 0 0 0 0 0 0 1
Sum 5 4 3 2 2 1 1 1
Take a checkerboard pair and swap. Do this 100000 times to
randomize the matrix.
0.000.050.100.150.200.250.30
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Freq
uenc
y
Score class
020406080
100120
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Freq
uenc
y
Score class
Statistical inference using null models
Observed score
400 randomized matrices
For each randomized matrix we calculate the respective metric (C-score, NODF, R2).
𝑆𝐸𝑆=(𝑂𝑏𝑠−𝐸𝑥𝑝)
𝑆𝑡𝐷𝑒𝑣Standardized effect sizes (SES) are Z-transformed scores and can be linked to a normal distribution.
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%
The Fisherian significance levels
SES- SES
Year Score Average null distribution score
Standard deviation
Z-score (SES)FF null model P(Z)
C-score2005 0.01087 0.01085 0.00009 0.193 0.8471842006 0.00106 0.00104 0.00002 1.106 0.268572007 0.00132 0.0013 0.00001 3.036 0.0023192008 0.00355 0.00349 0.00001 4.995 6E-072009 0.00492 0.00487 0.00001 4.454 7.9E-062010 0.00756 0.00747 0.00001 7.273 02011 0.00813 0.008 0.00001 10.273 0
NODF2005 0.05931 0.05999 0.00575 -0.12 0.9048512006 0.48707 0.48834 0.00116 -1.095 0.273622007 0.53815 0.53838 0.00171 -0.138 0.8900532008 0.46488 0.4686 0.00274 -1.358 0.1742242009 0.49842 0.49832 0.00122 0.083 0.9339612010 0.52119 0.52159 0.00081 -0.498 0.6186282011 0.49632 0.49627 0.00089 0.053 0.95803
R2
2005 0.91608 0.92746 0.02176 -0.523 0.6010392006 0.27526 0.28248 0.04284 -0.168 0.8662522007 0.20723 0.17799 0.02361 1.238 0.2154092008 0.12074 0.05448 0.011 6.025 02009 0.06106 0.02695 0.00509 6.705 02010 0.04678 0.01907 0.00507 5.463 1E-072011 0.02964 0.01728 0.00497 2.488 0.012634
0
2
4
6
8
10
12
2005 2006 2007 2008 2009 2010 2011
SES
C-sc
ore
Study year
SES scores (FF mull model)The degree of reciprocal species segregation constantly increases during early succession
Local plant communities are not significantly
nested during succession
Species spatial turnover peaks at intermediate stages of succession
In ecological research raw metrics are most often meaningless!!-1
012345678
2005 2006 2007 2008 2009 2010 2011
SES
R2
Study year
-1.6-1.4-1.2
-1-0.8-0.6-0.4-0.2
00.2
2005 2006 2007 2008 2009 2010 2011
SES
NO
DF
Study year
Different null assumptions give different answers
FF
PP
FF PP
-1.6-1.4-1.2
-1-0.8-0.6-0.4-0.2
00.2
2005 2006 2007 2008 2009 2010 2011
SES
NO
DF
Study year
-2
-1
0
1
2
3
4
2005 2006 2007 2008 2009 2010 2011
SES
NO
DF
Study year
-2
-1.5
-1
-0.5
0
0.5
1
2005 2006 2007 2008 2009 2010 2011
SES
C-sc
ore
Study year
0
2
4
6
8
10
12
2005 2006 2007 2008 2009 2010 2011
SES
C-sc
ore
Study year
FF PP
The FF null model assumes that sites are filled with species and that each species occupies the
maximal number of sites.
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.
-2-1012345
2005 2006 2007 2008 2009 2010 2011
SES
R2
Study year
-1012345678
2005 2006 2007 2008 2009 2010 2011
SES
R2
Study year
Idiosyncratic species are those that deviate in their patterns of occurrences
Species 2005 TotalOcc NODF ExpNODF SpResult Z-SpResu DeltaSpC
Cirsium_arvense 11 56.618 63.431 6.087 0.864 -2.229Chenopodium_album_agg. 7 69.118 69.402 5.975 1.049 -1.146Agrostis_stolonifera_agg. 6 75 74.615 5.409 -0.529 -1.452Crepis_tectorum 6 91.176 79.348 5.365 -0.607 -1.382Echium_vulgare 6 66.912 80.944 6.245 3.091 -0.536Rumex_acetosella_var._tenuifoliu 3 86.029 86.852 5.919 1.163 -0.05
Calamagrostis_epigejos 3 94.118 85.908 5.311 -1.004 -0.841Arenaria_serpyllifolia_agg. 2 92.647 90.293 5.859 1.341 -0.008Festuca_rubra_agg. 2 85.294 90.795 5.97 1.683 0.075Daucus_carota 2 92.647 92.899 5.505 -0.527 -0.383Agrostis_capillaris 2 92.647 91.203 5.831 1.133 -0.092Carex_ericetorum 2 98.529 91.166 5.792 1.035 -0.133Bromus_tectorum 2 92.647 91.345 5.822 0.806 -0.092Robinia_pseudoacacia 1 92.647 96.805 5.838 1.672 0.075Lupinus_luteus 1 92.647 96.949 5.789 1.126 0.075Poa_palustris 1 92.647 94.787 5.816 1.269 0.075Rubus_fruticosus_agg. 0 100 100 5.629 0 0.075
Sites1 2 3 4 5 6 7 8
Species
A 1 1 1 1 1 1 1 1B 1 1 1 1 1 0 0 0C 1 1 1 1 0 0 0 0D 1 1 0 0 0 1 1 0E 1 0 0 0 0 0 0 1
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.
