Variability in Species Richness
• Why is the distribution of species richness
so variable across the landscape?
• One of the most basic correlates is area
• For example, in oceanic archipelagoes,
species number approximately doubles for
every tenfold increase in island area
(Darlington 1957)
Species-area Relationship
• The pattern is
extremely well
documented
Species-area Relationship
• Four general patterns have emerged:
• 1) S-A curves among tiny pieces of a
single biota
• 2) S-A curves among larger pieces of
larger biota
• 3) S-A curves among islands of one
archipelago
• 4) S-A curves among areas that have had
separate evolutionary histories
Species-area Relationship
• 1) S-A curves among tiny pieces of a
single biota
• Plant ecologists typically census their
subjects at relatively small scales (0.1 ha)
• Nested within a 1000m2 plot are subplots
(e.g. 100m2, 25m2, 4m2, or 1m2)
• This results in a convex curve that is too
steep
Species-area Relationship
Species-area Relationship
• 2) S-A curves
among larger pieces
of larger biota
• If you take relatively
large subsets of large
biotas, you generate
a ‘traditional’ species
area curve
Species-area Relationship
• 3) S-A curves
among islands of
one archipelago
• Curves may differ
among taxa and
among island groups
Species-area Relationship
• 4) S-A curves
among areas that
have had separate
evolutionary
histories
• The slopes of similar
may or may not
converge
Species-area Relationship
• 4) S-A curves
among areas that
have had separate
evolutionary
histories
• Among areas, the
slope is quite steep
Species-area Relationship
• What are the mechanisms that generate a
species-area curve?
• 1) Disturbance hypothesis
• 2) Habitat diversity hypothesis
• 3) Equilibrium hypothesis
• 4) Passive sampling hypothesis
Species-area Relationship
mechanisms
• Disturbance Hypothesis: disturbances
that reduce species diversity are more
common on small islands than on large
islands (McGuinness 1984; Biological
Reviews)
• This is a result of smaller islands being
more vulnerable to chronic disturbances
that remove species
Species-area Relationship
mechanisms
• Disturbance Hypothesis
• Similar to MacArthur-Wilson, model
predicts high species turnover
• It is different in that it predicts synchronous
turnover (extinctions) and small islands in
relatively continuous disequilibrium
Species-area Relationship
mechanisms
• Habitat Diversity Hypothesis
• Assumes that species diversity is
controlled by the availability of different
habitat types
• Habitat diversity will increase with area
and species richness increases with
habitat diversity
• Area per se has a minor role and is just a
surrogate for habitat diversity
Species-area Relationship
mechanisms
• Habitat &
diversity
Species-area Relationship
mechanisms
• If unique habitat types are found only on
large islands or areas, then species
richness will inevitably increase with area
• For example, there are many habitat
specialists that only occur on rare habitat
and that habitat is more likely to occur on
larger islands
Species-area Relationship
mechanisms
• How to test for area effect?
• Multiple regression has been used, but
may there be a problem?
Species-area Relationship
mechanisms
• If the habitat diversity hypothesis is
correct, then species will be nonrandomly
distributed with respect to different
habitats within a single island
• If the HDH is correct, relative areas of
different habitats should be a better
predictor of species richness than total
island area (habitat unit model)
Species-area Relationship
mechanisms
• Equilibrium Hypothesis
• Developed by MacArthur and Wilson
(1967) the equilibrium theory envisions
island species richness as a balance
between rates of colonization from a
mainland source pool of P species and
island extinctions of established
populations
Species-area Relationship
mechanisms
• Equilibrium Hypothesis
• Four population-level assumptions:
– 1) the mainland source pool is a canonical log normal
(not necessary, but allows for quantitative predictions
about the form and slope of the S-A relationship
– 2) the summed abundance is proportional to island
size
– 3) probability of population extinction is inversely
proportional to island population size
– 4) probability of colonization is inversely proportional
to island isolation or distance from source pool
Species-area Relationship
mechanisms
• Equilibrium Hypothesis
• Two main community-level assumptions of
the model:
– 1) the immigration rate decreases with
increasing species number on the island and
decreases with increasing isolation of the
island
– 2) extinction rate increases with increasing sp
number and decreases with increasing island
size
Species-area Relationship
predictions
• 1) there should be substantial turnover in species
composition through time
• 2) the S-A curve should be best fit by a power function
(S = CAz)
• 3) the slope of the curve on a log-log plot (z) should
approximate 0.26 for isolated archipelago and should be
shallower with decreasing isolation
• 4) species number on an island should be relatively
constant through time (variability in S is due to stochastic
nature of E & I)
• 5) intercept of regression should be higher for similar
sized areas of mainland habitat
Equilibrium Theory
tests of the assumptions
• Do E & I rates vary with species numbers?
• If species extinctions are independent (a
noninteractive community) and species
immigrations are equiprobable, the curves
are strictly linear
• In an interactive will give concave
immigration and extinction curves
Equilibrium Theory
tests of the assumptions
• Although these data are important, long-term
datasets with I & E curves are relatively rare
Equilibrium Theory
tests of the assumptions
• Although these data are important, longterm datasets with I & E curves are
relatively rare
Equilibrium Theory
tests of the assumptions
• Skokholm Island
birds, E was
correlated with S, but
I was not (and was
positive)
• For a 26 dataset, I
declined significantly
with S, but extinction
did not
Equilibrium Theory
tests of the assumptions
• Is there substantial turnover in species
composition?
• Turnover is an important feature of the
M-W model and distinguishes it from other
models of insular community assembly
• Again, this is a particularly difficult metric
to accurately assess (i.e. sampling effort,
sampling error, census interval, habitat
changes, establishment of an equilibrium)
Equilibrium Theory
tests of the assumptions
• Is the S-A curve best fit by a power
function?
• the log normal provides theoretical
justification for using the power function in
a species-area studies (Preston 1962)
• Connor and McCoy (1979; Am. Nat.) fit
regression models to a heterogeneous
collection of 100 species-area curves
Equilibrium Theory
tests of the assumptions
• Although the power function (log-log
model) fit ¾ of the data sets, it was only
the best fit in only 43 cases
Equilibrium Theory
tests of the assumptions
• What is the observed value of z and
what is its significance?
• The significance of using a log-log
transformation may have little biological
significance; however, interpreting the
slope has a long history
• Range varies (Preston 0.17-0.33, M-W
0.20-0.35, May 0.15-0.39)
Equilibrium Theory
tests of the assumptions
• Within the equilibrium framework, speciesarea slopes were thought to reflect the
degree of isolation of an archipelago
(which only affects immigration rates)
• Consequently, distant islands have a lower
S and distant archipelagos have a steeper
slope
Equilibrium Theory
tests of the assumptions
• Effects of isolation;
slopes were steeper
for more isolated
archipelagos
Equilibrium Theory
tests of the assumptions
• Slopes of S-A curves have also been used
to compare taxa within an archipelago
• A shallow S-A curve has been interpreted
as an indicator of good colonization
potential (all islands are a little more rich)
• As a result, comparisons among different
taxonomic groups is problematic
Equilibrium Theory
tests of the assumptions
• Since colonization is correlated with
several life-history characteristics,
differences may exist between
phylogenetic groupings
Equilibrium Theory
tests of the assumptions
Equilibrium Theory
tests of the assumptions
• Other factors (as discussed earlier as
alternative hypothesis to S-A relationships,
can also influence the slope [i.e. habitat
heterogeneity])
Equilibrium Theory
tests of the assumptions
• There is much discussion
in the biological value of
slopes, especially as the
statistical concerns are
many
• There are certain
conditions where we can
apply biological meaning
to slopes, but this should
be done cautiously
Equilibrium Theory
tests of the assumptions
• Does the intercept provide biological
insight?
• It can; if two slopes are similar, the
differences in the intercepts informs us
that one group is consistently more
diverse, irrespective of island size
Equilibrium Theory
tests of the assumptions
• Is species number constant through
time?
• Although the M-W model suggests
‘equilibrium’ is a dominant feature, it does
not predict a constant S through time
• So how much variability is acceptable?
• Through computer simulations of different
sampling distributions, 10% suggested
Equilibrium Theory
tests of the assumptions
• Since equilibrium is based upon correct
estimations of I & E, some of the same
caveats in estimating those parameters
exist as previously discussed
Equilibrium Theory
tests of the assumptions
• Simberloff (1983; Science) used a Markov model
of species colonization and extinction to contrast
the M-W equilibrium model
• The Markov model assumes a constant
probability of successful immigration and
constant probability of extinction
• If M-W equilibrium is occurring, variance in S
should be smaller than the null hypothesis of the
Markov model
Equilibrium Theory
tests of the assumptions
• Contrast of
expected S
in the M-W
equilibrium
model and
the Markov
model
T
Equilibrium Theory
tests of the assumptions
• Simberloff applied this null model to
Skokholm and Farne Island data sets, and
the forested plot of Eastern Wood
Equilibrium Theory
tests of the assumptions
• Results suggest
variance was not
greater than
expected by
chance
• However, both I &
E increased with
increasing S
(which was very
variable)
Equilibrium Theory
tests of the assumptions
• Do population sizes vary with island size?
• Population size is critical to extinction and the
equilibrium theory; however, few studies
examine the relationship between island size
and population size
• Populations could simply vary with island size or
could also be influenced by S
• Either way, should increase with island size
Equilibrium Theory
tests of the assumptions
• Support: For lizards on islands in the Gulf
of California, the highest densities were
found on the smallest islands
• In contrast to the M-W model, lizard
density declined with increasing species
richness and island area
Equilibrium Theory
tests of the assumptions
• Evidence is not
particularly strong
that population size
varies with island size
• Drosophila densities
was constant for
large island and
mainland areas, but
considerable lower
for small islands
Equilibrium Theory
tests of the assumptions
• Does species richness increase in equal-sized
quadrates?
• A prediction of Preston (1962; Ecology) was that
not only will species richness be greater on the
mainland compared to islands, but so will species
richness in equal-sized quadrates
• These species are from the tail of the log normal
distribution and unlikely to occur on islands
Equilibrium Theory
tests of the assumptions
• This prediction has been tested
• Westman (1983; J Biogeo) examined xeric
shrublands of the California Channel
Islands (Not Significant)
• Kelly et al. (1989; J of Ecology) found a
weak correlation (17%)
• Stevens (1986; Am. Nat.) examined woodboring insects; no relationship found
Equilibrium Theory
tests of the assumptions
• Is there substantial turnover in species
composition?
• Turnover is an important component of the
M-W equilibrium model
• Difficult to establish (e.g. consistent effort
in censuses, length of census interval,
sampling error, habitat change during
period, the presence of ‘equilibrium’ itself,
who is included in the definition)
Equilibrium Theory
tests of the assumptions
• For example, Simberloff and Wilson
(1969) calculated turnover rates at 0.67
per day
• However, later (Simberloff 1976) he
reanalyzed his data and when ‘transients’
and wide-ranging dispersers who were
unlikely to stay and colonize were
excluded, colonization reduced to…
1.5 sp/yr!!
Equilibrium Theory
tests of the assumptions
• Turnover of individuals can also be
interesting (not just populations)
• Consider how age-structured populations
may change by a surge of juveniles into it
• Individual ‘turnover’ can also be very
important for isolated populations as it
may represent a very important source of
genetic variation
M-W Equlibrium Theory
• Let’s look at the model graphically and
consider a few special cases
Effect of island area, distance held constant
Effect of island distance (isolation), area held
constant
Final pattern: Isolation effect, shown by fewer species on
isolated islands, in species-area curve for birds of warm
ocean regions: red triangles represent isolated islands
(>300 km from next largest land mass) (from Paul Slud)
Cocos Island, Costa Rica
Both isolation
(distance) effects on
immigration, and
island size (area)
effects on extinction,
combined into one
model--showing
different predicted
equilibrium species
richness values
Target Effect of island area, distance held
constant
L
Is
Rescue Effect of island distance (isolation),
area held constant
S
EL
Species Area
• Are there a possible ‘null’ model to how
species are accumulated on an island?
Passive Sampling Hypothesis
• Although many biological processes (e.g.
local extinction, disturbance, habitat
heterogeneity) have provided competing
explanations for the S-A relationship, it
could also simply be the result of sampling
• Connor and McCoy (1979) describe island
as targets and species as darts and larger
targets will accumulate more species,
even if simply by chance
Passive Sampling Hypothesis
• Although developed in 1921, it was largely
ignored until Coleman (1981; Am. Nat)
developed the theory
• Two assumptions of the model
– 1) the probability that an individual or a
species occurs on an island is proportional to
island area
– 2) islands sample individuals randomly and
independently (no inter- or intraspecific forces)
Passive Sampling Hypothesis
• Expected species richness is simply:
E(Sj) = ∑ 1-(1- [aj/Ar])ni
• Where aj is the area of the jth island, Ar is
the summed area of all islands and ni is
the abundance of species i summed over
all islands
• The ( ) term is the probability sp i occurs
on the island, given ni dart tosses
Passive Sampling Hypothesis
• This model makes no demographic
assumptions (e.g. extinction more likely
with small population size)
• Appears ‘target area’ is a biologically
justifiable position
Passive Sampling Hypothesis
• Although many biological processes (e.g.
local extinction, disturbance, habitat
heterogeneity) have provided competing
explanations for the S-A relationship, it
could also simply be the result of sampling
• Connor and McCoy (1979) describe island
as targets and species as darts and larger
targets will accumulate more species,
even if simply by chance