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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.

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Community assembly
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 assembly1
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
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
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’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 rules1
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 rules2
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 rules3
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 rules4
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 rules5
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 rules6
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 rules7
Diamond’s Assembly Rules

  • Checkerboard distribution of two Macropygia cuckoo-dove species in the Bismarck Archipelago

Diamond s assembly rules8
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
Null Assembly ModelsR-mode analyses

  • They constrained the observed presence-absence 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
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 models1
    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 models2
    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 ModelsConnor and Simberloff

    Null assembly models matthews
    Null Assembly ModelsMatthews

    • Matthews (1982) analyzed the occurrence of 13 minnow species distribution in six streams of the Ozark watershed

    • Although some species pairs that never co-occurred 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
    Null Assembly ModelsCriticisms

    • 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 models3
    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

    Null assembly models criticisms1
    Null Assembly ModelsCriticisms

    • 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 criticisms2
    Null Assembly ModelsCriticisms

    • 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 criticisms3
    Null Assembly ModelsCriticisms

    • 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 criticisms4
    Null Assembly ModelsCriticisms

    • 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 criticisms5
    Null Assembly ModelsCriticisms

    • 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
    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
    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
    Analyzing +/- Matrix

    • Two modes of analysis Q-mode and R-mode

    • 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
    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
    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
    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
    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 limitation1
    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
    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 ii1
    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
    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
    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

    • 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 diamond1
    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 diamond2
    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 diamond3
    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 expectedvalues, not absolute constraints

    Gilpin and diamond4
    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
    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 analysis1
    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 analysis2
    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 analysis3
    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 analysis4
    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 analysis5
    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 analysis6
    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 analysis7
    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
    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 options1
    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 options2
    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
    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
    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 functions1
    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 functions2
    Incidence Functions

    • “High-S” species occurred mostly on large, species-rich islands, whereas the much less common “supertramp” species showed the opposite pattern

    Incidence functions3
    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 functions4
    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 functions5
    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

    Incidence functions6
    Incidence Functions

    • They found examples of both high-S species (CM) as well as supertramps (GWG)

    Frequency of Occurrence

    Species Richness

    Incidence functions other implications
    Incidence Functionsother 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 functions7
    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)


    • 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
    Occurrence Sequence

    • Lizards are perfectly ordered

    • Resident birds are highly structured

    • Migrant birds are more haphazard


    • 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


    • 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