CommunityLevel Patterns Species Richness Diversity Paradise by Suzanne

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(pi 2) 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 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 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 = c. Az 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 = c. Az 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; Mac. Arthur & Wilson 1963, 1967; for a good description see Gotelli 2001, chapter 7) Photos of Mac. Arthur & 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 d. S/dt = (immigration rate) – (extinction rate) = (-I/ P)S + I - (E/P)S Equilibrium S when d. S/dt = 0 S* = IP/(I+E) Immigration rate ( s) (e. g. , new species per yr) E I 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 Extinction rate (µS) (e. g. , number of species per yr) TLarge 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 Extinction rate (µS) (e. g. , number of species per yr) Far island TFar 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 km 2 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 1970 s 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, 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