Fundamental patterns of macroecology

Patterns related to the spatial scale

Patterns related to the temporal scale

Patterns related to biodiversity

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

Rat

e

Immigration

Extinction

Equilibrium species richness

Single island

Species richness

Rat

e

Immigration Extinction

Equilibrium species richness

Isolated

Near by

Large

Small

Two islands

Theory of Island biogeography

Isolation

Spe

cies

rich

ness S = S0e-kI

Area

Spe

cies

rich

ness S = S0f(A)

Galapagos islands

Patterns related to the spatial scale

The species – area relationship

Species accumulation on seamounts in the pacific west of Australia

y = 5.5x0.85

R2 = 0.77050

100150200250300

0 20 40 60 80 100Number of seamounts

Num

ber o

f spe

cies

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 S0 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 = S0Az + e

log S = log S0 + z logA + e

Tab. 3.2. Species area relations (SPARs) and slope values from various studies.

Reference Communities SPAR SlopeSampling a communityUlrich 1998a Parasitoids of Lepidoptera power function 0.44Ulrich 1998a Parasitoids of Diptera power function 0.46Ulrich 1998a Parasitoids of Coleoptera power function 0.37Ulrich 1998a Hyperparasitoids power function 0.67Ulrich 1998a Parasitoids of Aphidina power function 0.43Ulrich 1998a Parasitoids of Cicadina power function 0.3Ulrich 1998a All hymenopteran parasitoids power function 0.43Lawrey 1992 Lichen communites in Maryland power function 0.28Lawrey 1992 Lichen communites in Virginia power function 0.16

Sampling different communities of the same structureBlake and Karr 1987 Birds of Central Illinois woodlots logarithmic 5.2Baldi and Kisbenedek 1999 Orthoptera in small steppe patches logarithmic 3.22Coleman et al. 1982 Birds of a lake island in Ohio power function 0.6Nilsson et al.. 1988 Birds of islands in a Swedish lake power function 0.62Wright 1988 Birds of islands in a Panamanian lake power function 0.27

Sampling oceanic islandsWilson and Taylor 1967 Polynesean ants power function 0.22Wilson and Taylor 1967 Solomon islands power function 0.14MacArthur and Wilson 1963 Birds of Solomon islands power function 0.4Harris 1973 Birds of Galapagos logarithmic 1.98Preston 1962 Land plants of galapagos power function 0.32Terborgh 1973 Birds of West Indies logarithmic 2.2MacArthur and Wilson 1967 Herpetofauna of West Indies power function 0.3Ricklefs and Lovette 1999 Bats of Lesser Antilles power function 0.232Ricklefs and Lovette 1999 Birds of Lesser Antilles power function 0.207Ricklefs and Lovette 1999 Butterflies of Lesser Antilles power function 0.265Ricklefs and Lovette 1999 Herpetofauna of Lesser Antilles power function 0.167Baroni Urbani 1971 Ants of tuscan archipelago power function 0.19MacArthur and Wilson 1963 Carabidae of Greater Antilles power function 0.3MacArthur and Wilson 1963 Ponerine ants of Melanesia power function 0.5MacArthur and Wilson 1963 Birds of Indonesia power function 0.5Johnson et al. 1968 Vascular plants of california Islands power function 0.4Brown 1978 Boreal mammals power function 0.33

Slopes of species – area relations reported by various researchers

Sampling habitat islandsWhitehead and Jones 1968 Kapaminga atoll power function 0.1Rosenzweig and Sandlin 1997 Tropical freshwater fishes power function 1.36Galli et al. 1976 Birds in small woods in New Jersey power function 0.39Martin 1980 Great Plain birds power function 0.41Rusterholz and Howe 1979 Birds from Minesota lakes power function 0.44Nilsson et al. 1988 Carabidae of islands in a Swedish lake power function 0.36Nilsson et al. 1988 Woody plants of islands in a Swedish lake power function 0.1Nilsson et al. 1988 Land snails of islands in a Swedish lake power function 0.15

Sampling mainland areasWilliams 1964 Flowering plants Great Britain power function 0.1Williams 1964 Land plants Great Britain power function 0.16Begon et al. 1986 Mediterranean birds power function 0.13Reichholf 1980 Middle european birds power function 0.14Preston 1960 Nearctic birds power function 0.12Preston 1960 Neotropical birds power function 0.16

Harner and Harper 1976 Vascular plant species of Utah and new Mexico power function 0.19

Judas 1988 European Lumbricidae power function 0.09Ulrich 1999c European Hymenoptera power function 0.11

Slopes of species – area relations reported by various researchers

• 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

Passive sampling

102 342 505

55

206

325

91

160 149 1704

1895

829 89 1410

3450

102 342 505

55

206

325

91

160 149 1704

1895

829 89 1410

3450

102 342 505

55

206

325

91

160 149 1704

1895

829 89 1410

3450

102 342 505

55

206

325

91

160 149 1704

1895

829 89 1410

3450

102 342 505

55

206

325

91

160 149 1704

1895

829 89 1410

3450

102 342 505

55

206

325

91

160 149 1704

1895

829 89 1410

3450

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 (ak is the relative area of a patch k, ni is

the number of individuaks of species i. in

i kp (k) (1 a )

ini kp (k) 1 (1 a )

The probability to find a member of i and therefore this species is then

i

Sn

total ki 1

S(a) S (1 a )

The rise of species richness S(a) with area is a then given by (Coleman et al. 1982)

y = 81x0.05

0

20

40

60

80

100

120

0.01 0.1 1 10

S

Area

Passive sampling predicts an increase of species richness with area. The slope of this increase is lower than observed in nature.

Tab. 3.3 Results of multiple regression of the logarithm of species richness on island area and habitat diversity.

Faunal group Number of samples

Area slope

Significance value

Habitat diversity

slope

Significance value

Birds 19 0.126 < 0.05 0.074 < 0.05Bats 17 0.375 < 0.05 0.087 > 0.05Herpetofauna 19 0.026 > 0.05 0.128 <0.0001Butterflies 15 0.139 > 0.05 0.116 < 0.05

31.73333333 28.73333 60.46667

Factor b R2 pArea 0.94 0.86 0.0006Net primary productivity 0.01 0.99Latitude 0.73 0.46 0.04Summer precipitation 0.2 0.64Winter precipitation -0.35 0.39Summer temperature 0.71 0.42 0.05Winter temperature 0.7 0.4 0.05Richness of vegetation 0.74 0.46 0.04Variability in summer precipitation-0.41 0.31Variability in winter precipitation-0.48 0.23Variability in summer temperature0.21 0.62Variability in summer temperature0.22 0.59

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)

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

1

10

100

1 100 10000 1000000

S

Area

AzoresCyclades Iceland

-10

-5

0

5

10

15

20

25

20 30 40 50 60 70 80

S

Latitude

Croatia

How to infer large scale patterns?

Species richness of European bats for 58 European countries and larger islands (Ulrich et al. 2007)

054321 Tz

V NbTbHbDbLbAS

0.20 0.01VS A (0.63 0.11) L (0.64 0.08) T

0.19 0.01V

0.19 ( 0.16 0.07)

S A (0.52 0.09) L (0.30 0.08) T

A L

Formulating a linear regression model

Vespertilio murinus

SARs and fractal geometryIn 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

z0S S A

1 y0E E A

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.

How to use SARs?

0

1

2

3

4

5

6

4 6 8 10 12 14 16 ln Area [km2]

ln e

nd. s

peci

es

FLL

MAZ

CAN

B

IRL N

012345678

4 6 8 10 12 14 16 ln Area [km2]

ln S

FL AND

MADAZO

IRL

A

TRARUS

MAZSLO AL CH

SARs are used to estimate species numbers and to detect ecological hot-

and cold spots

012345678

0 2 4 6 8 10

ln Area

ln S

+a

-a

ln(S0)-CL0.95

ln(S0)+CL0.95

Estimating species numbers

The mean number of bird species in Poland [312685 km2]is about 350, the total European [10500000 km2] speciesnumber is about 500. How many species do you expect

for the Czech Republic [78866 km2]?

z

z A A0

C C

AC Cz 0.17

A C

S AS S AS A

S 440S S 348(A / A ) (312685 / 78688)

zz A A

0B B

A B

A B

S AS S AS A

ln(S ) ln(S ) ln(440) ln(800)z z 0.17ln(A ) ln(A ) ln(312685) ln(10500000)

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?

Species - area relationship of the world birds at different scales

1

10

100

1000

10000

1.0E-01 1.0E+01 1.0E+03 1.0E+05 1.0E+07 1.0E+09 1.0E+11 1.0E+13

Area [Acres]

Num

ber o

f spe

cies

small areas: z = 0.43

within a regional pool: z = 0.09

between biotas: z = 0.53

The species – area relationship of plants follows a three step pattern as in birds

1

10

100

1000

10000

100000

1000000

1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 1.E+12

Area [km2]

Num

ber o

f spe

cies

Local scale: z = 0.25

Regional scale: z = 0.14

Intercontinental scale: z = 0.5

Today’s reading

SAR: http://math.hws.edu/~mitchell/SpeciesArea/speciesAreaText.html Theory of Island biogeography:http://books.google.pl/books?id=yRr4yPSyPvMC&dq=Theory+Island+biogeography&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 pdf Ulrich W., Buszko J. 2003b. Species - area relationships of butterflies in Europe and species richness forecasting. Ecography 26: 365-374. pdf