1. Statistical averaging
Function and diversity
The Portfoilio effect
Statistical averaging
David Tilman (1949-
Michel Loreau
𝐶𝑉∝ 1 𝑆
If species act independent the coefficient of variation of aggregate ecosystem properties is expected to decrease to the root of species richness.
Aggregate properties are particularly:
Biomass
Total abundance
Productivity
Assimilation

2. The law of the minimum and ecosystem functioning
Average performance without limiting effects
Performance with limiting effects
Species at minimum limit the functioning of ecosystem properties
𝐶𝑉∝ 1 𝑆
Ecosystem functioning increases non-lineary with species richness.
Point of fast change
Point of fast change
This model works if species form functional guilds whose members have equivalent properties.

3. Euryoecious organisms tolerate a wider range of habitat conditions.
The law of the minimum
Limiting factors:
Light
Water
Space
Nutrients
Justus von Liebig ( )
Water is the limiting factor for photosynthetic rates with respect to temperature
Euryoecious organisms tolerate a wider range of habitat conditions.
Stenoecious organisms have limited tolerance.
Photosynthetic activity
Precipitation
Temperature

4. LTER – Long term ecological research at Cedar Creek, Minnesota
Variance and covariance of native savannah plants at Cedar Creek in relation to species diversity.
LTER – Long term ecological research at Cedar Creek, Minnesota
147 experimental plots at Cedar Creek in Minnesota
120 samples from undisturbed native Minnesota grasslands.
y = 12.8Ln(x) R 2
= 0.96 10 20 30 40 50 60
Number of species
Total plant cover (%)
y = 28.6Ln(x) R 2
= 0.77 20 40 60 80
100 10
Number of species
Total plant cover (%)
Above: Variance and covariance of native savannah plants at Cedar Creek in relation to species diversity. As predicted by theory total variance in density decreases and covariances increases with diversity. Modified from Tilman (1999). [Tilman D The ecological consequences of changes in biodiversity: a search for general principles - Ecology 80: ]
Below: Total plant cover increases with the number of plant species. Results of 147 experimental plots at Cedar Creek in Minnesota (A) and of 120 samples from undisturbed native Minnesota grasslands. Redrawn and modified from Tilman et al. (1996).[Tilman D., Wedin D., Knops J Productivity and sustainability influenced by biodiversity in grassland ecosystems - Nature 379: ]
Tilman 1999, Ecology 80:

6. Results of the BIODEPTH experiment
Source of variation SS
% SS F p
Locality
12.4
28.3%
24.7
<
Species richness
6.6
15.1%
7.15
Functional group richness
1.17
2.7%
6.34
0.002
Assemblage
17.1
39.0%
1.29
0.2
Locality x Assemblage
2.08
4.7%
3.77
Residual
4.46
10.2%
Total
43.81
Grassland aboveground biomass depends on several factors among which locality, diversity and functional diversity are of major importance.
Hector et al. 1999, Science 286,
Grassland productivity declines as the number of functional groups decreases. Results of a biodiversity experiment combining data from 8 European countries. The numbers refer to the total species number involved. Modified from Hector et al. (1999). [Hector A. et al Plant diversity and productivity experiments in European grasslands - Science 286: ]
Grassland productivity declines as the number of functional groups decreases.

7. Biodiversity and bacterial activity
Day 0-7
Day 7-14
28 days experimental time
Day 14-28
Bell et al. 2005, Nature 436:
Bell T., Newman J. A., Silverman B. W., Turner S. L. and Lilley A. K The contribution of species richness and composition to bacterial services. Nature 436:
Bacterial species richness influences respiration of soils from beech stands.
Respiration is not a linear function of bacterial richness
This points to the existence of redundant species

8. The current state of art:
Ecosystem functioning depends not such much on species richness but on richness of functional groups (ecologigal guilds)
Productivity increases with plant functional group richness
Stability increases with plant functional group richness
Drought restistance increase with plant functional group richness
Bacterial species richness promotes efficiency of bacterial services like breakdown of pollutants
Decomposition increases with eukaryotic species richness
Total bacterial activity increases with bacterial foodweb complexity
Stability decreases with dispersal among patches
Habitat fragmentation and species richness act synergistically and decrease stability

9. How do diversity and stability depend on productivity?
Five examples of the relation between plant species diversity and productivity at a continental scale. Note that in every case right skewed unimodal pattern appears. Data from Shmida et al. (1986) and Tilman and Pacala (1993)(A), Puerto et al. (1990)(B); Beadle (1966) (C); Dix and Smeins (1967)(D); Al-Mufti et al. (1977)(E). Redrawn and modified from Tilman and Pacala (1993) and Rosenzweig and Abramsky (1993). [Tilman D., Pacala St The maintenance of species richness in plant communities (In: Species Diversity in Ecological Communities, Eds.: R. E. Ricklefs, D. Schluter) - Univ. Press, Chicago, pp ;, Rosenzweig M. L., Abramsky Z How are diversity and productivity related? (In: Species Diversity in Ecological Communities, Eds.: R. E. Ricklefs, D. Schluter) - Univ. Press, Chicago, pp ]
Species richness peaks often at intermediate productivity

10. It is a measure of total energy input.50
100
150
200
250
500
1000
1500
Evapotranspiration S
Palearctic birds
Evapotranspiration is the sum of evaporation and transpiration, hence the total amount of water going from living organismas and the soil into the atmosphere.
It is a measure of total energy input.
Hawkins et al. 2003, Ecology 84: 50
100
150
200
250
500
1000
1500
Evapotranspiration S
Palearctic butterflies
Species richness often peaks at intermediate degrees of evapotransiration.
Potential evapotranspiration as a measure of available energy is related to species diversity. Species diversity peaks a intermediate levels of evapotransiration. Data for palearctic birds and butterflies from Hawkins et al.. (2003). [Hawkins B. A Energy, water, and broad-scale geographic patterns of species richness. Ecology 84: ]

11. Data from Hawkins B. A. , Porter E. E. , Diniz J. A. F. 2003
Data from Hawkins B. A., Porter E. E., Diniz J. A. F Productivity and history as predictors of the latitudinal gradient of terrestrial birds. Wcology 84:
Hawkins et al. 2003, Ecology 84:
Bird species numbers are correlated with annual evapotranspiration and temperature.

12. The influence of productivity on the species richness of plants
Meta-analysis found very variable patterns of the productivity species richness relationship at local scales.
Above the local scale plant species richness increases with productivity.
Gillman L. N., Wright S. D The influence of productivity on the species richness of plants: a critical assessment. Ecology 87:
Gillman, Wright, 2006, Ecology 87:

13. Patterns of fish species richness in China’s lakes
Zhao S., Fang J., Peng. C., Tang Z., Piao S Patterns of fish species richness in China’s lakes. Global Ecol. Biogeogr. 15:.
Zhao et al. 2006, Gl. Ecol. Biogeogr.

14. Lake volume is of minor importance20 40 60 80
100
120
140 1 10
1000
10000
Altitude [m] S R 2
= 0.75
Maximum depth [m]
= 0.34
0.001
0.1
Lake volume [10 8 m 3 ]
100000
Lake area [km
Zhao S., Fang J., Peng. C., Tang Z., Piao S Patterns of fish species richness in China’s lakes. Global Ecol. Biogeogr. 15: in press.
Fish species richness scales significantly with altitude and maximum depth of a lake
Lake volume is of minor importance

15. 1 10
100
1000
-10 20 30
Mean annual temperature S R 2
= 0.43
500
1500
Annual potential
evapotranspiration [mm]
= 0.57
Annual actual
= 0.53
2000
Annual precipitation [mm]
= 0.40
Zhao S., Fang J., Peng. C., Tang Z., Piao S Patterns of fish species richness in China’s lakes. Global Ecol. Biogeogr. 15: in press.
Main determinants of fish species richness were annual PET, altitude, and lake area.

16. Productivity and stability
Are tropical populations more stable than populations in temperate or arctic regions?
Vazquez D. P., Stevens R. D The latitudinal gradient in niche breath: concepts and evidence. Am. Nat. 164: E1-E19.
There is no general latitudinal trend in population variability
Vazquez, Stevens, 2004, Am. Nat 164: E1-E19