1. Advanced analytical approaches in ecological data analysis
The world comes in fragments 1

2. Species occurrences across a fragmented landscape
Biogeography
Species occurrences across a fragmented landscape
Islands
Lakes
River bed and irrigation systems
Mainlands continental distributions habitat islands mountain tops and valleys fragmented landscapes scattered distributed host plants
Cities and anthropogenic habitats
Routes of species invasion
Experimental plots (natural, macro-, meso-cosm experiments)

3. Galapagos Islands
The Darwin finches

4. The Darwin finches (Sanderson, Am. Scient. 2000)
Sanderson JG (2000) Testing ecological patterns. American Scientist 88:
A presence – absence matrix reflects the distribution of species across sites

5. The distribution of ground beetles across Mazuran lake islands
In presence – absence matrices zeros denote species absence, ones denote species presences.
Absences might be caused either by real absences of species or by incomplete detection.

6. Multivariate approaches to biodiversity
Traits
Sites
Interdepen-dence matrix X
Environmental variable matrix V
Variables
Variables
Why are species abundant or rare?
What determines community composition?
How does a community function in space and time?
Sites
Site GPS location matrix D L
Traits
Species
Sites
Species trait matrix T
Phylogenetic distance matrix P
Species abundance matrix M
Species
Species
Species

7. Species and environmental data in primary plant succession
Measured environmental data
WordClim, BioClim S
A1-2
C2-4
C3-1
D3-2
D3-4
CaCO3
0.27
1.17
0.06
1.04
Sand
82.54
76.71
88.56
79.02 pH
8.16
7.97
8.08
8.18
Plant species trait data from Bioflor and Leda
A1-2
C2-4
C3-1
D3-2
D3-4
Longitude
171.38
205.61
227.46
239.65
233.65
Latitude
295.09
275.55
293.74
271.88
GPS longitude and latitude data
Species
Leaf mass [mg]
Leaf size [mm2]
Life span
Achillea_pannonica
82.33
567.84 5
Agrostis_capillaris
Agrostis_stolonifera
Agrostis_vinealis
1.41
22.75
Ajuga_genevensis
17.99
365.5
Apera_spica-venti 1
Arctium_minus_agg. 2
Observed species abundances S
A1-2
C2-4
C3-1
D3-2
D3-4
Achillea_pannonica
Agrostis_capillaris
0.1
0.15
Agrostis_stolonifera
0.3
Agrostis_vinealis
0.9
0.2
Ajuga_genevensis
Apera_spica-venti
0.4 S
Achillea_pannonica
Agrostis_capillaris
Agrostis_stolonifera_agg.
Agrostis_vinealis
Ajuga_genevensis
Apera_spica_venti
0.0
179.0
117.0
2.5
6.7
Agrostis_stolonifera
Phylogenetic data from Genbank or own sequencing

11. Biogeographic matrices are static descriptions of colonization patterns.
Colonization and extinction are permanent processes. In reality presence – absence pattern change whole the time.
It makes therefore a difference if we use temporal point data to construct our matrices or a time series.
Time series data contain much more entries but might be ecologically unrealistic.

12. They do not give information on real species interactions Dispersion
Time axis
Time series matrices have too many entries and do not reflect real ecological patterns.
They do not give information on real species interactions
Dispersion
Extinction
For a proper assessment of ecological patterns we need point data.
The comparison of point and time series matrices gives information about dispersion rates.

13. The distribution of ground beetles across Mazuran lake islands
Abundance matrices contain additional information. Abundance matrices might be based on point or averaged time series data.

14. Mutual interaction matrices
Food webs
Host – parasite networks
Plant – herbivore networks
Pollination networks
Predator – prey networks
Competition networks
Species impact networks
Food web example
Translation of a food web into a matrix. Ones denote direct links.
Typical terrestrial food web
Generalist predator
Specialist predator

15. A quantitative food web
Interaction strength is expressed by probabilities or by frequencies of interaction
A quantitative food web

16. Interaction matrices Pollination networks Plants Bees
Kratochwil A., Beil M., Schwabe A Complex structure of pollinator-plant interaction –webs: random, nested, with gradients or modules. Apodologie 40:
Ollerton, J., S. D. Johnson, L. Cranmer, and S. Kellie The pollination ecology of an assemblage of grassland asclepiads in South Africa. Annals of Botany 92:
Plants
From Ollerton et al. 2003
From Kratochwil et al. 2009
Bees

17. How to present a presence – absence matrix?
Unsorted raw data
Sorted according to marginal totals
Sorted to maximize species turnover
Correspondence analysis
Reciprocal averaging (seriation)

18. Spatial or ecological distance
Ecological gradients
Spatial or ecological distance
Sorting of matrix columns according to ecological gradients allows for an assessment of the importance of environmental variables.

19. Ordinated presence – absence matrix
Basic patterns
Species turnover
Species turnover or beta diversity is a special case of species segregation where there is an ordering change in species composition across the sites.
Raw matrix
Ordinated presence – absence matrix
Spatial distance between species
Unexpected occurrences
Ecological distance between sites

20. The data of our lecture
Small scale spatial variability in phylogenetic signals during early plant succession depends on soil properties
Werner Ulrich, Marcin Piwczyński, Markus Klemens Zaplata, Susanne Winter, Wolfgang Schaaf, Anton Fischer
Phylogenetic distance matrix according to the classification contained in APG III (Angiosperm Phylogeny Group 2009) S
Achillea_pannonica
Agrostis_capillaris
Agrostis_stolonifera_agg.
Agrostis_vinealis
Ajuga_genevensis
Apera_spica_venti
Arctium_minus_agg.
Arenaria_serpyllifolia_agg.
0.0
179.0
117.0
44.0
122.0
2.5
6.7
Artemisia_campestris_agg.
32.7
Artemisia_vulgaris_agg.
Berteroa_incana
127.0
Betula_pendula

21. Small scale spatial variability in phylogenetic signals during early plant succession depends on soil properties
Werner Ulrich, Marcin Piwczyński, Markus Klemens Zaplata, Susanne Winter, Wolfgang Schaaf, Anton Fischer
Database containing a total of 33 plant functional, genetic and morphological traits complied from the Leda (Kleyer et al. 2008) and BioFlor (Klotz et al. 2002) trait bases.
Species
Leaf mass [mg]
Leaf size [mm2]
Life span
Min releasing height [m]
Max releasing height [m]
Stem erect %
Stem ascending to prostrate %
Emergents attached to substrate
Terminal velocity m/s
Achillea_pannonica
82.33
567.84 5
0.2
0.8
100
Agrostis_capillaris
0.83 50
0.98
Agrostis_stolonifera_agg.
0.1
0.7 25
1.11
Agrostis_vinealis
1.41
22.75
0.4
1.59
Ajuga_genevensis
17.99
365.5
0.07
0.3 75
Apera_spica-venti 1
1.31

22. Literature
Zaplata M. K., Winter S., Fischer A., Kollmann J., Ulrich W Species-driven phases and increasing structure in early-successional plant communities. Am. Nat. 181: E17-E27.
Ulrich W., Gotelli N. J  Pattern Detection in Null Model Analysis. Oikos 122: 2-18.
Gotelli N. J., Ulrich W Statistical challenges in null model analysis. Oikos 121:
Ulrich W., Gotelli N. J A null model algorithm for presence – absence matrices based on proportional resampling. Ecol. Modell. 244:
Ulrich W., Piwczyński, M., Maestre F. T., Gotelli N. J Null model tests for niche conservatism, phylogenetic assortment and habitat filtering. Meth. Ecol. Evol. 3:
Ulrich W., Almeida-Neto M., Gotelli N. G A consumer’s guide to nestedness analysis. Oikos 118: 3-17.
Software
Niche – A Fortran program for meta-community analysis.
Turnover – A Fortran program for the analysis of species associations.
NODF – a Fortran program for nestedness analysis.
Past
Matrix Excel add in