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

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.

Euryoecious organisms tolerate a wider range of habitat conditions. The law of the minimum Limiting factors: Light Water Space Nutrients Justus von Liebig (1803-1873) 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

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) + 11.5 R 2 = 0.96 10 20 30 40 50 60 Number of species Total plant cover (%) y = 28.6Ln(x) - 10.7 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. 1999 - The ecological consequences of changes in biodiversity: a search for general principles - Ecology 80: 1455-1474.] 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. 1996 - Productivity and sustainability influenced by biodiversity in grassland ecosystems - Nature 379: 718-720.] Tilman 1999, Ecology 80: 1455-1474

Results of the BIODEPTH experiment Source of variation SS % SS F p Locality 12.4 28.3% 24.7 < 0.00001 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, 1123-1127 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. 1999 - Plant diversity and productivity experiments in European grasslands - Science 286: 1123-1127.] Grassland productivity declines as the number of functional groups decreases.

Biodiversity and bacterial activity Day 0-7 Day 7-14 28 days experimental time Day 14-28 Bell et al. 2005, Nature 436: 1157-1160 Bell T., Newman J. A., Silverman B. W., Turner S. L. and Lilley A. K. 2005. The contribution of species richness and composition to bacterial services. Nature 436: 1157-1160. 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

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

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. 1993 - The maintenance of species richness in plant communities (In: Species Diversity in Ecological Communities, Eds.: R. E. Ricklefs, D. Schluter) - Univ. Press, Chicago, pp. 13-25.;, Rosenzweig M. L., Abramsky Z. 1993 - How are diversity and productivity related? (In: Species Diversity in Ecological Communities, Eds.: R. E. Ricklefs, D. Schluter) - Univ. Press, Chicago, pp. 52-65.] Species richness peaks often at intermediate productivity

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: 3105-3117 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. 2003. Energy, water, and broad-scale geographic patterns of species richness. Ecology 84: 3105-3117]

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. 2003. Productivity and history as predictors of the latitudinal gradient of terrestrial birds. Wcology 84:1608-1623. Hawkins et al. 2003, Ecology 84: 3105-3117 Bird species numbers are correlated with annual evapotranspiration and temperature.

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. 2006. The influence of productivity on the species richness of plants: a critical assessment. Ecology 87: 1234-1243. Gillman, Wright, 2006, Ecology 87: 1234-1243

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

Lake volume is of minor importance 20 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. 2006. 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

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. 2006. 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.

Productivity and stability Are tropical populations more stable than populations in temperate or arctic regions? Vazquez D. P., Stevens R. D. 2004. 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