Number of species (S)

Comments

Transcription

Number of species (S)
Community-Level Patterns: Species Richness & Diversity
“Paradise” by Suzanne Duranceau
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)
Diversity Indexes
Shannon’s (a.k.a. Shannon-Wiener)
Based on information theory / entropy
H’ = – Σ(pi * ln pi)
Diversity Indexes
Simpson’s
Based on the probability of conspecific encounters in
an infinitely large collection:
D = Σ(pi2)
For a finite community, use:
D = Σ((ni (ni-1))/(N(N-1)))
The index is generally expressed as the probability that
two individuals differ:
DSimpson = 1 - D
or
DSimpson = 1 / D
Diversity at Different Scales
R. H. Whittaker (1972) proposed the following measures
of S and species turn-over:
Sα = Alpha “diversity” – the number of species in a local area
(or habitat)
Sβ = Beta “diversity” – the turn-over rate of species from local
area to local area (e.g., from habitat to habitat)
Sγ = Gamma “diversity” – the number of species in a region
New World Alpha Diversity
Birds
C. Jenkins: http://biodiversitymapping.org/index.htm
New World Alpha Diversity
Mammals
C. Jenkins: http://biodiversitymapping.org/index.htm
New World
Alpha Diversity
Birds
Hawkins et al. (2006)
New World
Alpha Diversity
Mammals
Willig et al. (2003)
Biodiversity across the Isthmus of Panama
Free-Standing Trees & Shrubs
~ 120 species / ha
~ 70 species / ha
Image from biogeodb.stri.si.edu…
Major Determinants of Global Climate
1. Shape of the Earth – causes unequal heating
(energy per area) with latitude
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
Image from NASA
Ferrel cell
Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a tilted axis
– Ferrel & Hadley cells move latitudinally, tracking seasonal changes
in the position of the solar equator, with a slight time lag
Southern Hemisphere
is tilted towards the
Sun
Northern Hemisphere
is tilted towards the
Sun
Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a tilted axis
Major Determinants of Global Climate
1. Shape of the Earth
2. Revolution of the Earth around the Sun on a tilted axis
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 Earth’s axis creates
Coriolis forces (actually conservation of momentum)
Currents in air & water are deflected;
right in N. Hemisphere, left in S. Hemisphere
Major Determinants of Global Climate
Polar cell
Ferrel
cell
Ferrel cell
Hadley cell
Ferrel
cell
Image from NASA
Ferrel cell
Species Diversity –
Accumulation & Rarefaction Curves
E.g., estimating tree diversity within a large study plot:
Individual-based assessment: Choose trees at random from
the plot; sum the number of species as each new tree is added
Sample-based assessment: Establish a set of quadrats in the
plot; sum the total number of species as each new quadrat is added
(or higher taxa)
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)
Species-Area Relationships
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
Number of species
Log (Number of species)
log (S) = log (c) + z * log (A)
Area
Two constants:
Intercept = log (c)
Slope = z
Log (Area)
Species-Area Relationships
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)
Map of Caribbean islands from Wikimedia Commons
Species-Distance Relationships
Diamond (1972) compared species
richness on islands with that expected
for an island “near” (< 500 km) a
“mainland” source
“Mainland” = New Guinea
Islands = Bismark Archipelago
Map of Oceania from Wikimedia Commons
Theory of Island Biogeography
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)
Photos of MacArthur & Wilson from Wikimedia Commons
Theory of Island Biogeography
s = (-I / P) * S + I
Immigration rate (s)
(e.g., new species
per yr)
I
P
Number of species (S)
Theory of Island Biogeography
µS = (E / P) * S
E
Extinction rate (µS)
(e.g., number of
species per yr)
P
Number of species (S)
Theory of Island Biogeography
dS/dt = (immigration rate) – (extinction rate) = (-I/ P)S + I - (E/P)S
Equilibrium S when dS/dt = 0  S* = IP/(I+E)
Immigration rate (s)
(e.g., new species
per yr)
I
E
Equil. turn-over rate (T*)
Extinction rate (µS)
(e.g., number of
species per yr)
S*
P
Number of species (S)
Theory of Island Biogeography
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 doesn’t (so far) “explain” the
species-area relationship
What do we need?
Theory of Island Biogeography
Why does the probability of extinction for each
species vary with island size?
Small island
Immigration rate (s)
(e.g., new species
per yr)
Large island
TSmall
TLarge
Extinction rate (µS)
(e.g., number of
species per yr)
SSmall SLarge
Number of species (S)
Theory of Island Biogeography
Why does the probability of immigration for each
species vary with island isolation?
Near island
Immigration rate (s)
(e.g., new species
per yr)
TNear
Far island
TFar
Extinction rate (µS)
(e.g., number of
species per yr)
SFar SNear
Number of species (S)
Theory of Island Biogeography
Some of the simplifying assumptions:
- Fixed source pool of species from which colonists are drawn
- Source pool species have the same colonization & extinction probabilities
- Population sizes scale with island size
- Immigration rate is inversely proportional to distance
- The probability of extinction is inversely proportional to population size
- The probability of immigration & extinction is independent of species
composition on the island (i.e., no effects of species interactions)
- Habitat heterogeneity is constant relative to island size
There is no species-specific biology in this theory!
The radical idea is that species are identical!
Some of these assumptions do not significantly
alter the model’s predictions…
Theory of Island Biogeography
Predictions are fairly robust to non-linear
extinction and immigration functions
Figure modified from Gotelli (2001)
Theory of Island Biogeography
Predictions are fairly robust to non-linear
extinction and immigration functions
Small
ELarge
Figure modified from Gotelli (2001)
Theory of Island Biogeography
Predictions are fairly robust to non-linear
extinction and immigration functions
Near
IFar
Figure modified from Gotelli (2001)
Theory of Island Biogeography
Target effect: Larger islands present larger immigration targets
(Gilpin & Diamond 1976)
Recall that without
target effect
I Small = I Large
Notice the influence
on T*
Figure modified from Gotelli (2001)
Theory of Island Biogeography
Rescue effect: Higher rates of continued immigration to near vs. far islands
results in larger N (or more patches of populations) & potentially greater
genetic diversity (Brown & Kodric-Brown 1977)
Recall that without
rescue effect
E Near = E Far
Notice the influence
on T*
Figure modified from Gotelli (2001)
Island Biogeography in the Real World
Floral & 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 & isolation?
What are the best strategies within the SLOSS debate?
Island Biogeography in the Real World
Floral & Faunal Relaxation in Habitat Fragments
Leigh et al. (1993)
sampled species
composition on small
islands (< 2 ha) in
Lake Gatun ~ 80 yr
after construction of
the Panama Canal
Tree diversity on small islands < equivalent sized areas of mainland
or large islands like Barro Colorado Island
A subset of tree species is favored on small islands
Island Biogeography in the Real World
Floral & Faunal Relaxation in Habitat Fragments
Terborgh et al. (2001) 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
Island Biogeography in the Real World
Floral & 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
Island Biogeography in the Real World
Floral & Faunal Relaxation in Habitat Fragments
The Biological Dynamics of Forest
Fragments Project isolated 1, 10, 100
&1000 ha fragments and continues to
compare 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)
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.
Spatial & Temporal Scale in Ecology
Spatial & 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)
Spatial & Temporal Scale in Ecology
Processes that impact organisms, populations & communities
act on a variety of spatial & temporal scales
Processes occurring at any given scale differentially determine
patterns at increasing – or decreasing – scales
Spatial & temporal patterns change
with the scale of measurement
Spatial & 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)
Scale in Ecology
We seek mechanistic links among patterns and processes across scales
E.g., how can we extrapolate from one scale to another
(e.g., leaf-level gas exchange and photosynthesis 
forest productivity  global climate change)?
Photos from Wikimedia Commons

Similar documents