1. Fundamental patterns of macroecology Patterns related to the spatial scale Patterns related to the temporal scale Patterns related to biodiversity

2. Patterns related to the spatial scale Theory of Island biogeography tries to understand diversity from stochastic colonization of islands. Colonization rates depend on island area and isolation Extinction rates depend on island area The model is species based Robert MacArthur (1930-1972) Edward O. Wilson (1929-) Species richness Rate Immigration Extinction Equilibrium species richness Single island Species richness Rate ImmigrationExtinction Equilibrium species richness Isolated Near by Large Small Two islands

3. Theory of Island biogeography Isolation Species richness S = S 0 e -kI Area Species richness S = S 0 f(A) Galapagos islands

4. Patterns related to the spatial scale The species – area relationship Species accumulation on seamounts in the pacific west of Australia y = 5.5x 0.85 R 2 = 0.77 0 50 100 150 200 250 300 020406080100 Number of seamounts Number of species 1.The number of species raises with the area under study 2.This relation often follows a power function 3.The slope z of this function measures how fast species richness increases with increasing area. It is therefore a measure of spatial species turnrover or beta diversity 4.The intercept S 0 is a measure of the expected number of species per unit of area. It is therefore a measure of alpha diversity 5.Outliners from this pattern mark ecologcal hotspots or cold spots 6.Changes in slope through time point to disturbances like habitat fragmentation or destruction S = S 0 A z + e log S = log S 0 + z logA + e

5. Slopes of species – area relations reported by various researchers

7. Most regional SARs are best described by a power function model Island slopes z of the power function are mostly higher than mainland slopes Island slopes are in the order of 0.2 to 0.6 Mainland slopes are in the order of 0.1 to 0.3 Slopes of local SARs are higher than those of regional SARs Empirical conclusions How to explain SARs? Passive sampling Habitat diversity Area per se Fractal geometry

8. Passive sampling Assume a number of sites randomly colonized (occupied) by individuals of a number of species. The abundances of the colonizing metacommunity need not to differ in abundances but most often they do. The probability tha a species i is not found in the k- th patch is (a k is the relative area of a patch k, n i is the number of individuaks of species i. The probability to find a member of i and therefore this species is then The rise of species richness S(a) with area is a then given by (Coleman et al. 1982) Passive sampling predicts an increase of species richness with area. The slope of this increase is lower than observed in nature.

9. Area per se and habitat diversity Stepwise multiple regression shows how various factors influence species numbers of mammals in South America (Ruggiero 1999) Faunal groups of the Lesser Antillean (Ricklefs and Lovette 1999)

10. How to assess diversity patterns? Grid approach Species richness within each grid is assessed from Museum collections. Environmental data come from Satellite images. An important variable is the distance between grid cells: Spatial autocorrelation

11. How to infer large scale patterns? Species richness of European bats for 58 European countries and larger islands (Ulrich et al. 2007) Formulating a linear regression model Vespertilio murinus

12. SARs and fractal geometry In 1999 John Harte and co-workers asked whether thre is a common theme behind the spatial distribution of all plant and animals species. They argued that fractal geometry might explain observed patterns in the abundance and distribution of species Graphic: Jean-Francois Colonna Using a probabilistic argument they showed that SAR EAR, Endemics – area relationship Subsequent studied showed that this holds only approximately, but reasonably well Cerro Grande Wildfire / Weed Map Important: Spatial distribution of single species is self similar The fractal dimension of each species can be used as a species fingerprint.

13. How to use SARs? 0 1 2 3 4 5 6 46810121416 ln Area [km 2 ] ln end. species FL L MAZ CAN B IRLN 0 1 2 3 4 5 6 7 8 46810121416 ln Area [km 2 ] ln S FL AND MAD AZO IRL A TRA RUS MAZSLOALCH SARs are used to estimate species numbers and to detect ecological hot- and cold spots 0 1 2 3 4 5 6 7 8 0246810 ln Area ln S +  -  ln(S 0 )-CL 0.95 ln(S 0 )+CL 0.95 Estimating species numbers The mean number of bird species in Poland [312685 km 2 ] is about 350, the total European [10500000 km 2 ] species number is about 500. How many species do you expect for the Czech Republic [78866 km 2 ]? We extrapolated outside the range for which the SAR was defind by our data. The estimate of the European number is very imprecise. The true number is about 380. What causes the higher number of birds in the Czech Republic?

14. Species - area relationship of the world birds at different scales 1 10 100 1000 10000 1.0E-011.0E+011.0E+031.0E+051.0E+071.0E+091.0E+111.0E+13 Area [Acres] Number of species small areas: z = 0.43 within a regional pool: z = 0.09 between biotas: z = 0.53

15. The species – area relationship of plants follows a three step pattern as in birds 1 10 100 1000 10000 100000 1000000 1.E-041.E-021.E+001.E+021.E+041.E+061.E+081.E+101.E+12 Area [km 2 ] Number of species Local scale: z = 0.25 Regional scale: z = 0.14 Intercontinental scale: z = 0.5

16. Today’s reading SAR: http://math.hws.edu/~mitchell/SpeciesArea/speciesAreaText.htmlhttp://math.hws.edu/~mitchell/SpeciesArea/speciesAreaText.html Theory of Island biogeography: http://books.google.pl/books?id=yRr4yPSyPvMC&dq=Theory+Island+biogeogr aphy&printsec=frontcover&source=bn&hl=de&ei=HsibSbSJEdSujAfZ7qS9BQ& sa=X&oi=book_result&resnum=4&ct=result#PPA4,M1 Ulrich W., Buszko J. 2005. Detecting biodiversity hotspots using species - area and endemics - area relationships: The case of butterflies. Biodiv. Conserv. 14: 1977-1988 pdfpdf Ulrich W., Buszko J. 2003b. Species - area relationships of butterflies in Europe and species richness forecasting. Ecography 26: 365-374. pdfpdf