Paradise

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Community-Level Patterns Species Richness and
Diversity
Paradise From The Trilogy of the Earth
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Species Diversity Richness
S Species richness the number of species in a
collection of organisms
Sd Species density the number of species per
area
D Species diversity a simultaneous index of
both S and the evenness with which
individuals are distributed among species
(a.k.a. equitability)
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Diversity Indexes
Shannon-Weaver (a.k.a., Shannon-Weiner,
Shannon) Based on information theory H
S(pi ln pi)
Simpsons Based on the probability of
conspecific encounters D 1 S(pi2)
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Diversity Indexes
An empirical relative abundance distribution
portrays both S evenness, but it cannot be
described with a single variable
Unless that variable controls the mathematical
expression of an appropriate distribution function
Fishers alpha Based on the log series
distribution function S a ln (1 N/a)
Iterative procedures are used to solve for a,
given S and N
It is only as good as the shape of the log series
matches the empirical relative abundance
distribution
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Diversity at Different Scales
R. H. Whittaker (1972) proposed the following
measures of S and species turn-over
Sa Alpha diversity the number of species in
a local area (or habitat)
Sß Beta diversity the turn-over rate of
species from local area to local area
(e.g., from habitat to habitat)
S? Gamma diversity the number of species in
a region
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Global Patterns of BiodiversityAmphibians
Image from www.amphibiaweb.org
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Global Patterns of BiodiversityVascular plants
Image from staffwww.fullcoll.edu
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New World Alpha DiversityBirds
Hawkins et al. (2006)
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New World Alpha DiversityMammals
Willig et al. (2003)
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Biodiversity across the Isthmus of
PanamaFree-standing trees and shrubs
120 species / ha
70 species / ha
Image from biogeodb.stri.si.edu/bioinformatics/map
s
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Population-level range abundance
Community-level patterns are underpinned by the
processes that determine distributions and
abundances of species populations Sonoran
Desert distribution of Saguaro (Carnegiea
gigantea)
Temperature, moisture, and herbivory each play a
role Niering, Whittaker Lowe (1963) Science
Image from esp.cr.usgs.gov/data/atlas/little
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Major Determinants of Global Climate
1. Shape of the Earth causes unequal heating
(energy per area) with latitude
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Major Determinants of Global Climate
1. Shape of the Earth differential heating
cooling causes air masses to rise sink Ferrel
Hadley cells
Polar cell
Ferrel cell
Ferrel cell
Hadley cell
Ferrel cell
Ferrel cell
Image from NASA
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Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a
tilted axis
results in seasons as Ferrel Hadley cells
move latitudinally, tracking changes in the
position of the solar equator with a slight time
lag
Northern Hemisphere is tilted towards the Sun
Southern Hemisphere is tilted towards the Sun
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Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a
tilted axis
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Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a
tilted axis
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Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a
tilted axis
3. Rotation of the Earth on Earths axis creates
Coriolis forces (actually conservation of
momentum) Currents in air water are deflected
right in N. Hemisphere, left in S. Hemisphere
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Major Determinants of Global Climate
Polar cell
Ferrel cell
Ferrel cell
Hadley cell
Ferrel cell
Ferrel cell
Image from NASA
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Species Diversity Accumulation Rarefaction
Curves
E.g., estimating tree diversity within a large
study plot
Sample-based assessment Establish a set of
quadrats in the plot sum the total number of
species as each new quadrat is added
Individual-based assessment Choose trees at
random from the plot sum the number of species
as each new tree is added
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Species Diversity Accumulation Rarefaction
Curves
Sample-based species richness accumulates more
slowly than individual-based species richness.
Why?
Population-level spatial autocorrelation!
Figure from Gotelli Colwell (2001)
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Emerging from a sample-based approach, the
relationship between species number area is
asymptotically increasing
Botanist Olaf Arrhenius (1921) first formalized
the species-area curve
The Arrhenius equation is a power function S
cAz
log (S) log (c) z log (A)
Log (Number of species)
Two constants Intercept log (c) Slope
z
Number of species
Area
Log (Area)
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Species-Area Curves
Species-area curves from Rosenzweig (1995)
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Species-Area Curves
Species-area curves from Rosenzweig (1995)
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The power function S cAz typically works well
for islands E.g., Darlington (1957) proposed
that a ten-fold increase in island area results
in a two-fold increase in S
Land birds in the West Indies log (S) 0.94
0.11 log (A)
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How can we explain the island-area effect on
species richness?
Perhaps it results from greater habitat diversity
on larger islands
Large West Indian islands (Cuba, Hispaniola,
Jamaica) have substantial mountains, consequently
windward (wet) and leeward (dry)
slopes Intermediate-sized islands are volcanic
plugs that lack some of the large-island habitats
(e.g., swamp, karst) Small islands are coral
atolls with simple vegetation structure
The habitat diversity hypothesis fails to
explain lower species richness of same-sized
islands that vary in their degree of isolation
from the mainland...
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Distance effect
Diamond (1972) compared species richness on
islands with that expected for an island near
(lt 500 km) a mainland source Mainland New
Guinea Islands Bismark Archipelago
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Joint consideration of area and distance led to
the Equilibrium Theory of Island Biogeography
(Munroe 1948 MacArthur Wilson 1963, 1967
for a good description see Gotelli 2001, chapter
7)
S represents the equilibrium balance between
immigration and extinction
A key assumption of the model is that there is a
permanent mainland source pool of species from
which colonists are drawn
Photos of MacArthur Wilson from Wikipedia
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Determinants of the immigration rate Maximum
immigration rate (I ) occurs when S 0, and
decreases as more species are added When S P
(size of the mainland source pool), the
immigation rate must equal 0
Immigration rate, ?s intercept
slope S I (-I / P) S
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Determinants of the extinction rate Should
increase with S, since the more species there
are, the fewer individuals there are per species
(N) Maximum extinction rate (E) occurs when S
P, and must be zero when no species are present
Extinction rate, µS 0 slope S
(E / P) S
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Now dS/dt (immigration rate) (extinction
rate) I-(I/P)S - (E/P)S We can then solve for
the equilibrium species richness of a given
area S IP/(IE), which is determined by the
size of the source pool and the maximum
immigration and extinction rates...
S is the point at which the rate of arrival of
species is exactly balanced by the rate of
extinction
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Now dS/dt (immigration rate) (extinction
rate) I-(I/P)S - (E/P)S We can then solve for
the equilibrium species richness of a given
area S IP/(IE), which is determined by the
size of the source pool and the maximum
immigration and extinction rates...
S is the point at which the rate of arrival of
species is exactly balanced by the rate of
extinction S has a characteristic T, i.e., the
rate of turnover of species per unit time at
equilibrium
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Turnover is a key feature of this model because
there is no fixed stable composition of species
even though S is constant Therefore, the model
is simultaneously both equilibrial (species
number) and non-equilibrial (species composition)
Notice that the model doesnt (so far) explain
the species-area relationship What do we need?
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Two more assumptions - Larger islands support
larger N - The probability of extinction
decreases with increasing N
Consider two islands equally distant from the
mainland source pool
Es gt El (max. extinction rate on a small island
gt max. extinction rate on a large island)
Notice the difference in T
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Another assumption - Distance to the source
pool (isolation) alters the immigration rate
In gt If
Notice the difference in T
There is no species-specific biology in this
theory! The radical idea is that species are
identical!
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Additional assumptions of Island Biogeography
Theory - The source pool species have the same
colonization and extinction rates - Population
sizes scale with island size (e.g., no effect of
species richness on population size via
competition) - Immigration rate is inversely
proportional to distance - The probability of
extinction is inversely proportional to
population size - The probability of immigration
and extinction is independent of species
composition on the island (i.e., no effects of
species interactions) - Habitat heterogeneity is
constant relative to island size
Some of these assumptions do not significantly
alter the models predictions
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Predictions are fairly robust to non-linear
extinction and immigration functions
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Predictions are fairly robust to non-linear
extinction and immigration functions
s
El
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Predictions are fairly robust to non-linear
extinction and immigration functions
n
If
A more problematic assumption Distance
(isolation) only affects the immigration
rate One might also imagine that isolation could
influence the extinction rate
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Rescue effect Higher rates of continued
immigration of individuals to near vs. far
islands will result in larger N (or more patches
of populations) and potentially greater genetic
diversity (Brown Kodric-Brown 1977)
Extinction rate without rescue effect on far
island
Lower extinction rate for near island
Notice the difference in T now!
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Target effect Larger islands present larger
targets to which immigration can successfully
occur
Immigration rate with target effect
Immigration rate without target effect
Once again, notice the difference in T
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Island Biogeography in the Real WorldFloral
Faunal Relaxation in Habitat Fragments
Departures from predictions of the null model
may be the most important contribution of this
theory to modern ecology and management How do
newly created islands respond to fragmentation
and isolation? What are the best strategies
within the SLOSS debate?
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Island Biogeography in the Real WorldFloral
Faunal Relaxation in Habitat Fragments
Leigh et al. (1993) sampled species composition
on small islands (lt 2 ha) in Lake Gatun 80 yr
after construction of the Panama Canal
Tree diversity on small islands lt equivalent
sized areas of mainland or large islands like
Barro Colorado Island
A subset of tree species is favored on small
islands
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Island Biogeography in the Real WorldFloral
Faunal Relaxation in Habitat Fragments
John Terborgh and colleagues studied
forest-savanna ecosystems on islands within Lago
Guri, a 4300 km2 hydroelectric lake in Venezuela,
formed by damming the Caroní Rio in 1986
Species loss has been rapid, but the loss of
species through local extinction has not been
random
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Island Biogeography in the Real WorldFloral
Faunal Relaxation in Habitat Fragments
The Brazilian government mandated in the 1970s
that a fraction of each Amazonian cattle ranch
had to be retained as forest
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Island Biogeography in the Real WorldFloral
Faunal Relaxation in Habitat Fragments
The Biological Dynamics of Forest Fragments
Project isolated 1, 10, 100, and 1000 ha
fragments and continues to compares them to
forested control plots on ranches north of
Manaus, Brazil
Tom Lovejoy, Bill Laurance, Robb Bierregaard,
Phil Stouffer, Bruce Williamson, etc. have
demonstrated dramatic changes, especially in the
smallest fragments, as a function of size,
degree of isolation, and type of intervening
matrix
A paradigm like IBT that considers only changes
in fragment size and isolation while ignoring
other anthropogenic effects is dangerously
inadequate for conservation purposes (Laurance
2008, pg. 1739)
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Spatial Temporal Scale in Ecology
It is argued that the problem of pattern and
scale is the central problem in ecology, unifying
population biology and ecosystems science, and
marrying basic and applied ecology S. Levin
(1992)
Photo from Princeton U.
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Spatial Temporal Scale in Ecology
Spatial and temporal patterns change with the
scale of measurement
For example, the slope of the species-area curve
changes across scales
Focus
Extent
See Willig et al. (2003, pg. 275)
Figure from Hubbell (2001, pg. 158)
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Spatial Temporal Scale in Ecology
Spatial and temporal variability change with the
scale of measurement
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Spatial Temporal Scale in Ecology
Spatial and temporal variability change with the
scale of measurement
Correlogram for spatial or temporal
autocorrelation
A measure of autocorrelation, e.g., Morans I
Envelope indicating no significant difference
from zero
0
Distance (d) or time (t)
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Spatial Temporal Scale in Ecology
Processes that impact organisms, populations, and
communities act on a variety of spatial and
temporal scales
Figure from Levin (1992)
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Spatial Temporal Scale in Ecology
Processes that impact organisms, populations, and
communities act on a variety of spatial and
temporal scales
Processes occurring at any given scale
differentially determine patterns at increasing
or decreasing scales
Spatial and temporal patterns change with the
scale of measurement
Spatial and temporal variability change with the
scale of measurement
How can we meaningfully extrapolate ecological
information across spatial scales? This is one
of the central issues in ecology P. Turchin
(1996)