Transcript Fundamental relationships in macroecology

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
Single island
Theory of Island biogeography
Immigration
Rate
Extinction
Robert MacArthur
(1930-1972)
Equilibrium species richness
Edward O. Wilson
(1929-)
Species richness
tries to understand diversity from
stochastic colonization of islands.
Two islands
Immigration
Extinction
Colonization rates depend on
island area and isolation
Near by
Rate
Extinction rates depend on island
area
Small
Large
Isolated
The model is species based
Equilibrium species richness
Species richness
Theory of Island biogeography
S = S0e-kI
Isolation
Species richness
Species richness
Galapagos
islands
S = S0f(A)
Area
Patterns related to the spatial scale
The species – area relationship
Number of species
Species accumulation on seamounts
in the pacific west of Australia
300
250
200
150
100
50
0
1. The number of species raises with the area
under study
2. This relation often follows a power function
0.85
y =25.5x
R = 0.77
0 20 40 60 80 100
Number of seamounts
S=
S0Az
+e
log S = log S0 + z logA + e
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
3.2. Species area
relations (SPARs)
and slope reported
values from various
Slopes ofTab.species
– area
relations
bystudies.
various researchers
Reference
Sampling a community
Ulrich 1998a
Ulrich 1998a
Ulrich 1998a
Ulrich 1998a
Ulrich 1998a
Ulrich 1998a
Ulrich 1998a
Lawrey 1992
Lawrey 1992
Communities
SPAR
Parasitoids of Lepidoptera
Parasitoids of Diptera
Parasitoids of Coleoptera
Hyperparasitoids
Parasitoids of Aphidina
Parasitoids of Cicadina
All hymenopteran parasitoids
Lichen communites in Maryland
Lichen communites in Virginia
power function
power function
power function
power function
power function
power function
power function
power function
power function
0.44
0.46
0.37
0.67
0.43
0.3
0.43
0.28
0.16
Sampling different communities of the same structure
Blake and Karr 1987
Birds of Central Illinois woodlots
Baldi and Kisbenedek 1999
Orthoptera in small steppe patches
Coleman et al. 1982
Birds of a lake island in Ohio
Nilsson et al.. 1988
Birds of islands in a Swedish lake
Wright 1988
Birds of islands in a Panamanian lake
logarithmic
logarithmic
power function
power function
power function
5.2
3.22
0.6
0.62
0.27
Sampling oceanic islands
Wilson and Taylor 1967
Wilson and Taylor 1967
MacArthur and Wilson 1963
Harris 1973
Preston 1962
Terborgh 1973
MacArthur and Wilson 1967
Ricklefs and Lovette 1999
Ricklefs and Lovette 1999
Ricklefs and Lovette 1999
Ricklefs and Lovette 1999
Baroni Urbani 1971
MacArthur and Wilson 1963
MacArthur and Wilson 1963
MacArthur and Wilson 1963
Johnson et al. 1968
Brown 1978
power function
power function
power function
logarithmic
power function
logarithmic
power function
power function
power function
power function
power function
power function
power function
power function
power function
power function
power function
0.22
0.14
0.4
1.98
0.32
2.2
0.3
0.232
0.207
0.265
0.167
0.19
0.3
0.5
0.5
0.4
0.33
Polynesean ants
Solomon islands
Birds of Solomon islands
Birds of Galapagos
Land plants of galapagos
Birds of West Indies
Herpetofauna of West Indies
Bats of Lesser Antilles
Birds of Lesser Antilles
Butterflies of Lesser Antilles
Herpetofauna of Lesser Antilles
Ants of tuscan archipelago
Carabidae of Greater Antilles
Ponerine ants of Melanesia
Birds of Indonesia
Vascular plants of california Islands
Boreal mammals
Slope
Slopes of species – area relations reported by various researchers
Sampling habitat islands
Whitehead and Jones 1968
Rosenzweig and Sandlin 1997
Galli et al. 1976
Martin 1980
Rusterholz and Howe 1979
Nilsson et al. 1988
Nilsson et al. 1988
Nilsson et al. 1988
Sampling mainland areas
Williams 1964
Williams 1964
Begon et al. 1986
Reichholf 1980
Preston 1960
Preston 1960
Harner and Harper 1976
Judas 1988
Ulrich 1999c
Kapaminga atoll
Tropical freshwater fishes
Birds in small woods in New Jersey
Great Plain birds
Birds from Minesota lakes
Carabidae of islands in a Swedish lake
Woody plants of islands in a Swedish lake
Land snails of islands in a Swedish lake
power function
power function
power function
power function
power function
power function
power function
power function
0.1
1.36
0.39
0.41
0.44
0.36
0.1
0.15
Flowering plants Great Britain
Land plants Great Britain
Mediterranean birds
Middle european birds
Nearctic birds
Neotropical birds
Vascular plant species of Utah and new
Mexico
European Lumbricidae
European Hymenoptera
power function
power function
power function
power function
power function
power function
0.1
0.16
0.13
0.14
0.12
0.16
power function
0.19
power function
power function
0.09
0.11
Empirical conclusions
•
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
How to explain SARs?
•Passive sampling
•Habitat diversity
•Area per se
•Fractal geometry
Passive sampling

206
91
1895
3450

102
342
505

102
342
505
55
829
89
1410
55
829
89
1410
160
149
325
1704
160
149
325
1704
206
91
1895
3450
206
91
1895
3450
Assume a number of sites randomly colonized (occupied) by individuals of a number of species.
102
342
505
102
342
05


The abundances
of
the 5colonizing
metacommunity
need not to differ in abundances but most
often 8they
do.
55
29
89
1410
55
829
89
1410
The probability tha a species i is not found in the k120
160
1 4 9 n is3 2 5
1704
th patch
area of a patch
k,
1 6 0 is (a
1 4k9 is the
3 2 5 relative
1704
i
100
the number of individuaks of species i.
p  i (k )  (1  a k )
91
1895
3450
206
ni
91
The probability to find a member of i and
102
342
505

therefore this species is then
55
29
1410
p i8(k
) 8 91  (1
 ak)
ni
The rise
of1 4species
richness
S(a) with area is
160
9
325
1704
a then given by (Coleman et al. 1982)
206
91
1895
S
3450
S(a )  S total   (1  a k )
i 1
1895
S
206
ni
80
3450
60
40
20
0
0.01
y = 81x0.05
0.1
1
10
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
diversity.
habitat per
on island area and Area
se and habitat diversity
Faunal groups of the Lesser Antillean (Ricklefs and Lovette 1999)
Habitat
Significance
Significance
Area
Number of
diversity
Faunal group
value
value
slope
samples
slope
0.074 < 0.05
0.126 < 0.05
19
Birds
0.087 > 0.05
0.375 < 0.05
17
Bats
0.128 <0.0001
0.026 > 0.05
19
Herpetofauna
0.116 < 0.05
0.139 > 0.05
15
Butterflies
31.73333333 28.73333 60.46667
Stepwise multiple regression shows how various factors influence species numbers of
mammals in South America (Ruggiero 1999)
F actor
b
A rea
0.94
N et prim ary productiv ity
0.01
Latitude
0.73
S um m er precipitation
0.2
W inter precipitation
-0.35
S um m er tem perature
0.71
W inter tem perature
0.7
R ichness of v egetation
0.74
V ariability in sum m er precipitation
-0.41
V ariability in w inter precipitation-0.48
V ariability in sum m er tem perature
0.21
V ariability in sum m er tem perature
0.22
R
2
0.86
0.46
0.42
0.4
0.46
p
0.0006
0.99
0.04
0.64
0.39
0.05
0.05
0.04
0.31
0.23
0.62
0.59
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
How to infer large scale patterns?
Species richness of European bats
for 58 European countries and larger
islands (Ulrich et al. 2007)
S
100
10
Formulating a linear regression model
S V  A  b1  L  b 2 D  b3 H  b 4  T  b 5 N T  0
z
SV  A
0.20  0.01
 (0.63  0.11)  L  (0.64  0.08)  T
SV  A
0.19  0.01
 (0.52  0.09)  L  (0.30  0.08)  T
A
Azores
0.19
(  0.16  0.07 )
L
Iceland
Cyclades
1
1
100
10000
1000000
Area
25
Croatia
20
S
15
10
5
0
-5
-10
20
30
40
50
Latitude
60
70
80
Vespertilio murinus
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
Using a probabilistic argument they showed that
S  S0A
z
E  E 0A
Graphic: Jean-Francois Colonna
SAR
1 y
EAR, Endemics – area relationship
Subsequent studied showed that this holds
only approximately, but reasonably well
Important:
Spatial distribution of single species is self similar
The fractal dimension of each species can be used
as a species fingerprint.
Cerro Grande Wildfire / Weed Map
How to use SARs?
SARs are used to estimate species
Estimating species numbers
numbers and to detect ecological hotand cold spots
The mean number of bird species in Poland [312685 km2]
8
7
6
ln(S0)+CL0.95
5
ln S
is about 350, the total European [10500000 km2] species
number is about 500. How many species do you expect
for the Czech Republic [78866 km2]?
+a
4
-a
3
S  S0A 
z
2
ln(S0)-CL0.95
1
0
0
2
4
6
8
10
ln S
ln Area
8
7
6
5
4
3
2
1
0
SLO MAZ AL CH
A
FL
6
SC 
8
10
12
14
16
2
ln Area [km ]
ln end. species
B
MAZ
4
L
3
FL
CAN
0
4
6
8
SC
SA
z
 SC 
ln(440)  ln(800)
ln(312685)  ln(10500000)
 0.17
z
440
(312685 / 78688)
0.17
 348
The true number is about 380.
We extrapolated outside the range for which the
SAR was defind by our data.
2
1
 z
A 
 A 
 AC 
SA
(A A / A C )
z
What causes the higher number of birds in the
Czech Republic?
6
5
ln(A A )  ln(A B )
RUS
AZO
A 
 A 
 AB 
ln(S A )  ln(S B )
z
IRL
4
SB
S  S0A 
TRA
AND
MAD
z
SA
IRL
N
10
12
2
ln Area [km ]
14
16
The estimate of the European number is very
imprecise.
Species - area relationship of the world birds at different scales
10000
Number of species
between biotas: z = 0.53
1000
100
within a regional pool: z = 0.09
10
small areas: z = 0.43
1
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]
The species – area relationship of plants follows a three step pattern as in birds
Number of species
1000000
100000
Intercontinental scale: z = 0.5
10000
1000
100
10
Regional scale: z = 0.14
Local scale: z = 0.25
1
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
2
Area [km ]
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+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 pdf
Ulrich W., Buszko J. 2003b. Species - area relationships of butterflies in Europe
and species richness forecasting. Ecography 26: 365-374. pdf