Download Assembly Rules

Community Assembly
• A pervasive theme in community ecology
is that the species composition of a
community is governed by deterministic
“assembly rules”
• Typically these rules emphasize the
importance of interspecific interactions
(e.g. niche overlap, body size distributions)
Community Assembly
• In this section we will focus on assembly
rules that predict the presence or absence
of particular species combinations
Community Assembly:
laboratory evidence?
• The best evidence: laboratory studies
• Gilpin et al. (1986) examined the structure of
Drosophia communties.
• When communities were established with 10 (of
28 considered) species, the subsequent stable
community was always fewer than four species
• 210=1024 initial combos,
<12 persist
Community Assembly:
field studies
• Ant communities in
Florida mangroves
• Two ‘primary’ species,
limited by island size;
formed a
checkerboard pattern
• Two ‘secondary’
species, limited by
presence of ‘primary’
species
Diamond’s Assembly Rules
• Diamond (1975)
popularized the study
of community
assembly in a
detailed account of
the distribution of 141
land-bird species on
New Guinea and its
satellite islands in the
Bismark Archipeloago
Diamond’s Assembly Rules
• 1) ‘if one considers all the combinations
that can be formed from a group of related
species, only certain ones of these
combinations exist in nature’
• 2) ‘these permissible combinations resist
invaders that would transform them into
forbidden combination’
Diamond’s Assembly Rules
• 3) ‘a combination that is stable on a large
or species-rich island may be unstable on
a small or species-poor island’
• 4) ‘on a small or species-poor island a
combination may resist invaders that
would be incorporated on a larger or more
species-rich island’
Diamond’s Assembly Rules
• 5) ‘some pairs of species never coexist,
either by themselves or as part of a larger
combination’
• 6) some pairs of species that form an
unstable combination by themselves may
form part of a stable larger combination’
• 7) ‘some combination that are composed
entirely of stable sub-combinations are
themselves unstable’
Diamond’s Assembly Rules
• Although not explicitly stated, the rules
infer competition (forbidden combinations)
• Some of the rules are so general it has
been very difficult to make them
operational
Diamond’s Assembly Rules
• In 1979, Conner and Simberloff attacked
Diamond’s study suggesting Rules 2,3,4,6,
and 7 were either tautologies or
restatements or other rules
• Rules 1 and 5 are identical, just differing
on ‘related species’
Diamond’s Assembly Rules
• Rule 5 describes a chekerboard pattern of
species occurrences, which is perhaps the
simplest of Diamond’s assembly rules.
• The rule for a ‘complete’ checkerboard
pattern is very stringent: two species may
never co-occur (99 of 100)
Diamond’s Assembly Rules
• Checkerboard
distribution of
two Macropygia
cuckoo-dove
species in the
Bismarck
Archipelago
Diamond’s Assembly Rules
• But, is it really that surprising?
• With (2141) =9,870 possible species pairs,
7 pairs showing exclusive distributions
may not be surprising…
• Because Diamond did not publish original
data, Conner and Simberloff used other
data
Null Assembly Models
R-mode analyses
• They constrained the observed presenceabsence matrix subject to the following
three constraints:
– 1) row totals of RMatrix were maintained
– Constraint: maintains the differences
between species in their frequency of
occurrence
Null Assembly Models
– 2) column totals of the RMatrix were
maintained
• Constraint: maintained differences among
islands in the number of species they
contained
Null Assembly Models
– 3) for each row, species occurrences
were restricted to those islands for
which total species richness fell within
the range occupied by the species
• Constraint: maintained the observed
incidence function for each species (it
could not occur in assemblages larger or
smaller than those observed)
Null Assembly Models
• Although the constraints were too much
for matrices with a large number of
widespread species, recent advances in
randomization algorithms have overcome
this shortcoming
Null Assembly Models
Connor and Simberloff
Null Assembly Models
Matthews
• Matthews (1982) analyzed the occurrence of 13
minnow species distribution in six streams of the
Ozark watershed
• Although some species pairs that never cooccurred in watershed were morphologically and
ecologically similar, the observed number of
checkerboard pairs matched the predictions of
the null model (although assumed binominal
distribution)
Null Assembly Models
Criticisms
• The dilution effect: because C&S analyzed
confamilial groups or entire avifaunas,
competitive effects were no apparent
• Diamond’s choice of examples suggested
that the ecological guild was the correct
unit of measure (although guild
identification is not always easy or
apparent)
Null Assembly Models
• For example, Graves and Gotelli (1993)
tested the significance of checkerboard
distributions in mixed-species flocks of
Amazonian forest birds
• Results: No difference for the entire
assemblage of flocking or for guilds
• Only a difference when analysis was
restricted to congeneric species within
feeding guilds
Table 7.3
Null Assembly Models
Criticisms
• Effects of randomization constraints: the 3
constraints of C&S were severe and made
it less likely that the null hypothesis would
be rejected
• For example, relaxing the ‘incidence
function’ constraint, the New Hebrides
matrix revealed a significant negative
association
Null Assembly Models
Criticisms
• Also, does the assumptions of C&S have
their flaws? What if the incidence
frequency is actually influenced by
competition? (or some other force)
• How would you test this?
• Compare archipelagoes with varying
numbers of competitors and see if their
occurrence frequency varies
Null Assembly Models
Criticisms
• Also, some have claimed that is circular to
constrain marginal totals, because the
marginals also reflect interspecific
competition
• If true, a separate analysis for determining
the total number of island occurrences is a
separate hypothesis and requires a separate
null model (however, competition may not be
only factor in island distribution)
Null Assembly Models
Criticisms
• Should marginal constrains be
incorporated into null model at all?
• View 1: co-occurrence patterns are
nonrandom, given the observed ‘sample’
of species and islands (appropriate)
• View 2: the randomization is viewed as a
model of community colonization in the
absence of competition (not appropriate)
Null Assembly Models
Criticisms
• Significance tests: C&S compared the
observed and expected distributions with a
chi-squared test
• May not be appropriate due to constraints
of marginal totals (non-linear)
Other Null Models
• Wright and Biehl (1982) suggested a
“shared-island” test for detecting unusual
species co-occurrences
• For each species pair, they calculated the
tail probability of finding the observed
number of co-occurrences, but with R&C
transposed
Wright and Biehl (1982)
• Advantage: directly pinpoints particular
species pairs that show aggregated or
segregated distributions (however a few
pairs can unduly influence statistics)
• Problem: assumes all sites are equivalent,
thus confounds species-site associations
with the effects of species interactions
Analyzing +/- Matrix
• Two modes of analysis Q-mode and Rmode
• Q-mode analysis assesses the similarity
of different columns, indicating how similar
sites are in the species they contain
• R-mode compares the rows of the matrix
and indicates how similar species are in
the set of islands they occupy
Q-mode: biogeograpy
• How to quantify the degree of similarity
between ≥2 islands?
• Biogeographers have developed such
tools as Jaccard’s Index (0-1)
J = Nc / (N1 + N2 –Nc)
But it lacks a statistical distribution. So
what?
What would your null model be?
A simple colonization model (0)
• Johnson (unpublished 1974 presentation)
used the number of shared species as a
simple index of similarity between sites
and then asked what should be the
number of shared species under the
simplest colonization model (Null 0)
Ess = mn / P
• (Two islands with m & n species, P # in the
equiprobable source pool)
Small-island Limitation (Null 1)
• Habitat availability might be responsible
for the fact that most sites shared more
species than expected compared with Null
Hypothesis 0
• In particular, species may be missing from
small islands (lacking appropriate habitat)
Ess = mn / Pn (where Pn is # of sp. in
pool of larger island (m≤n)
Island Limitation
• There could also be a size restriction, but
from the other direction
• Islands could be too big, not allowing for
‘’supertramp’ species to persist
• To incorporate this constraint, you could
limit your source pool to only those
species which occur on islands of a
particular size or larger
Island Limitation
• The probability of occurrence is influenced
by community size, island area, or
attributes (e.g. distance) and can be
incorporated as an ‘incidence function’
Nonrandom Dispersal (Null II)
• Null 0 assumes colonization is identical
• If colonization is stochastic, species still
would be expected to occur at different
frequencies on islands because they differ
in their abilities to disperse and persist
• However, the attributes related to disperal
and persistence (body size, population
size, geographic range size) are difficult to
assess
Nonrandom Dispersal (Null II)
• What to do?
• So one option is to use the “occurrence
distribution” to weight species (circular?)
• However, marginal constraints do not
determine the occurrence pattern itself
• Constraints can be absolute or
probabilistic (more later…)
Problems with Q-mode
• Competition may not be being assessed as
pairwise island comparisons because many are
between islands that have the same species
sets. Consequently, it would fail to detect a
significant ‘checkerboard effect’
• Second, because the pairs of islands are not
independent, it is not appropriate to ask whether
more than 5% of the pairs are significantly
different from expectation
Summary of Q- and R-mode
• Q-mode appears strong to test for
biogeographic grouping (similarities)
• R-mode is better to assess species
interactions (i.e. competition) at sites
shared in common
Gilpin and Diamond
• Gilpin and Diamond (1982) developed
their own ‘R-mode’ analysis
• For species i on island j, they calculated
the probability of occurrence as
Pij = RiCj / N
• Where R is the row total for species i and
C is the column total for island j and N is
the grand total
Gilpin and Diamond
• Next, they calculated the expected overlap
for each species pair by summing the
product of these probability across all
islands
• Observed and expected overlaps for each
species pair were standardized and then
compared with a chi-squared test
Gilpin and Diamond
• If the null hypothesis of independent
placement were true, the histogram of
normalized deviates would follow a normal
distribution with unusual aggregation at
the right and unusual segregation at the
left
• Upon re-testing the New Hebridean birds,
no new differences were found
Gilpin and Diamond
• However, the original Bismarck data, they
found a strong excess of positive
association and a weak excess of negative
associations (but overall placed less
emphasis on competitive interactions
dictating community structure)
• Importance: introduced idea that marginal
totals (min & max) were expected values,
not absolute constraints
Gilpin and Diamond
• How? In different runs of a stochastic model, we
would not expect each island to support
precisely the observed number of species, or
each species, to always occur with its observed
frequency.
• In fact, putting a cap on species numbers could
be interpreted as a competitive ‘cap’ or limit
• Instead, islands are treated as ‘targets’
independently by species with some variance
about the expected species number in the null
model
Summary of R-mode Analysis
• The controversy over R-mode analysis
reduces to four issues:
• 1) Which species and which islands
should be analyzed?
• Issues such as source pools, colonizations
potential, habitat availability should be
considered before any analysis is
conducted
Summary of R-mode Analysis
• 2) Which metric should be used?
• What is the proper way to quantify
nonrandomness and species associations
in the +/- matrix
• Since there are many different kinds of
‘structure’ in a +/- matrix, we will utilize five
different metrics
Summary of R-mode Analysis
• 2) Which metric should be used?
• A) the number of species combinations
– If assembly rules are operative, there should be
fewer species combinations than expected
• B) the number of checkerboard distributions
– Is the most testable of the ‘Diamond Rules’ and
represent the strongest form of species
competition (complete species repulsion)
Summary of R-mode Analysis
• 2) Which metric should be used?
• C) the “checkerboardness” index of Stone and
Roberts (1990)
– Measures the overall tendency for species pairs to
co-occur. May reveal competitive pairs, but not
occuring in a perfect checkerboard
• D) the “togetherness” index of Stone and
Roberts (1992)
– Measures overall tendency of species to co-occur
(although both positive and negative are possible)
Summary of R-mode Analysis
• 2) Which metric should be used?
• E) Schulter’s Variance Ratio (1984)
– A modified version of checkerboardedness;
this measure does not constrain column totals
– Different patterns of negative covariation may
be revealed by comparing the variance ratio
to null model predictions
Summary of R-mode Analysis
• 3) Which simulation procedure should be
used?
– If we accept that C&S were correct in that
neither islands nor species are equiprobable,
this should be reflected in the null model
– Connor and Simberloff (RxC too constrained)
– Gilpin and Diamond (RxC expectations)
Summary of R-mode Analysis
• 3) Which simulation procedure should be
used? Two alternatives:
– Gotelli and Graves (R total fixed, C totals
probabilistic)
• Observed frequency of each species is fixed and
sites are treated as ‘targets’; the probability of
occurrence of each sp. at each site is
proportional to the total number of species at that
site. Thus S will vary, but will on average, be
arranged similarly to observed rankings
Summary of R-mode Analysis
• 3) Which simulation procedure should be used?
Two alternatives:
• Gotelli and Graves (RxC totally probabilistic)
– Less constrained, allows R and C to be probabilistic).
The placement is not simulated, but rather N species
occurrences across the entire matrix
– Specifically, it the cell probability that a species (Ri/N)
and selecting the site (Cj/N) will occur simultaneously;
thus the cell probability is (RiCj / N2), hence the most
likely occurrence will be the most common species on
the most species-rich island and vice-versa
Grouping Options
• In EcoSim, you can group by Guild (row)
• This analysis expects a data matrix in
which each species is classified into a
single guild
• Guild designations are in the second
column
• The simulation reshuffles the guild labels
to different species (e.g. reorganizes
guilds)
Grouping Options
• You can also group by Region (columns)
• Region designations are given in the
second row of the matrix
• The simulation does not alter the structure
of the matrix, but reshuffles the region
labels among the different sites
Grouping Options
• Another option in the ‘Guild Analysis’ for
EcoSim is that of ‘favored states’.
• This approach tests the hypothesis of Fox
that species are added sequentially to a
community so that different ‘functional
groups’ or guilds are represented as
evenly as possible
Favored States
• Communities are classified as ‘favored’ or
‘unfavored’.
• EcoSim reshuffles the guild labels then
examines each column of the matrix and
designates it as favored or unfavored
Incidence Functions
• Concept introduced by Diamond (1975) to
describe the probability of occurrence of a
species with respect to ordered site
characteristics, such as species number
Incidence Functions
• The x-axis is the number of species on the
island and the y axis is the proportion of
islands in a given size class that were
occupied by the species
Incidence Functions
• “High-S” species
occurred mostly on
large, species-rich
islands, whereas the
much less common
“supertramp”
species showed the
opposite pattern
Incidence Functions
• Gilpin and Diamond (1981) explored the
connection between the incidence function and
the equilibrium theory of island biogeography
• The IF represents the time that a species
occupies islands of a particular size class (early
succession species occur briefly…)
• Paradigm was a lack of competition with each
species having a species-specific colonization
and extinction rates
Incidence Functions
• The IF may also simply reflect the
distribution of habitat types among islands
• For example, high-S species may be
habitat specialists and those ‘specialized’
habitat may only exist on larger islands
Incidence Functions
• We can use null models to clarify what the
proper interpretations of the IF should be
• Whittam and Siegel-Causey (1981)
examined Alaskan seabird colonies using
IF
• They found examples
of both high-S
species (CM) as well
as supertramps
(GWG)
Frequency of Occurrence
Incidence Functions
Species Richness
Incidence Functions
other implications
• IF analysis can be used to identify unusual
minimum area requirements for particular
species
• Just looking at the charts may not be
enough as small islands may be missing
certain species due to the small likelihood
of random settlement
Incidence Functions
• Schoener and Schoener (1983) expanded
Diamond’s IF idea to go beyond island
area or species richness.
• One can order sites by any number of
criteria, and then the occurrence of
species tested against this ordering (i.e.
Mann-Whitney U test; a measure of the
strength of ordering)
Example
• Schoener and Schoener examined 76
species of birds on 521 small islands in
the Bahamas (as well as other vertebrate
groups)
• They also measured area, isolation,
habitat availability and vegetation structure
Occurrence Sequence
• Lizards are
perfectly ordered
• Resident birds are
highly structured
• Migrant birds are
more haphazard
Results
• Species occurrences were predictable,
although different groups followed different
assembly rule
• Lizards and resident birds were ordered
with respect to island area, migrant birds
were more related to island isolation
• The occurrence of both lizards and birds
cold be predicted by vegetation and
habitat structure
Implications
• Some checkerboards will only be detected
when habitat differences among sites are
measured and incorporated into the
analysis
• When distributions of species are with
respect to site characteristics, the less the
patterns will conform to a simple
checkerboard pattern
• An alternative is ‘nested’ species patterns