Download This talk will be about patterns of species diversity

Comparing Communities: Using β-diversity and
similarity/dissimilarity indices to measure diversity across
sites, communities, and landscapes
J.Jacobs
Introduction to Diversity
There are many different ways to measure biological diversity, and at different spatial
scales.
Biological diversity, within an ecological context, is the different type of species and
their abundances at a given scale. However, many investigators are not able to gather
information on species’ abundances and they are only able to obtain presence/absence
(incidence) data. The number of species, without knowing the abundances of those
species, is usually referred to as species richness.
This webpage is about how to compare species diversity (using only species richness or
species richness and abundance) among sites/habitats/communities. Some people call this
beta diversity and others call it complementarity, turnover, similarity, dissimilarity, etc.
Often, these terms are used interchangeably and at a variety of spatial scales. Methods
for making these comparisons are used in other fields of science but we will only address
ecology-based methods here.
Alpha, beta, gamma diversity- α, β, and γ diversity
Many researchers use these terms and they are part of the ecological vocabulary.
Alpha diversity is usually thought of as biological diversity at one site or sampling
location. γ diversity is often thought of as regional/landscape diversity, or the entire
diversity of the area in which one is sampling multiple α diversities. β diversity is
generally thought of as the change in diversity among various α diversities. Historically,
and often today, these terms only applied to measures of species richness. β diversity was
originally introduced by Whittaker to describe changes in species composition and
abundance across environmental continua such as gradients, elevation and moisture
(1956). According to Whittaker, each plant species exhibited an individualistic response
to environmental conditions. β diversity was then thought of as the change in the number
of species from one place to another place along a gradient (1956, 1960), and later
defined as “species turnover” or changes in specie composition from one community to
another (1972). β diversity was incorporated into the ecological language to mean a
change in species composition/abundance along a gradient and across different sites.
1
These categories of diversity are related to each other in this way:
(Magurran 2004)
2
In general, the larger the scale of the inventory/study, the less easy it is to measure
species abundance and the more likely it is to only use species richness or higher taxon
diversity. Investigators define their levels of diversity in different ways. Some treat α
diversity as one sample whereas others treat α diversity as a 100m x 100m plot. Also, it’s
difficult to transfer terrestrial terminology to marine systems.
Leaving behind estimates of α diversity
There are many ways to measure α diversity and that topic needs another webpage.
Some of the classic ways to measure α diversity are; species richness, Simpson Index,
Shannon entropy, and a variety of parametric and non-parametric estimators (see papers
by Chao and Jost for more detail). Here, we will focus on how to compare multiple α
diversities. From now on we will just use the term α diversity, and assume it was
measured correctly, but not define how we measured it.
3
For every organism and every study, the scale can be different, both in terms of the
distributions of the organism and the geographical range of the study. In addition, habitat
complexity can affect your ability to compare diversity across sites/habitats/communities.
According to Magurran (2004), there are 3 general categories for
measuring β diversity. Most of these are based on presence/absence
data.
1. Methods that examine the extent of the difference between two or more areas of α
diversity relative to γ diversity, where γ diversity is measured as total species
richness. These measures were originally and explicitly proposed as the measures of
β diversity.
Alpha diversity is averaged across all sites/habitats/communities and the average α
is used to compute β diversity.
i.e. Whittaker (1960) and Lande (1996)
Whittaker suggested a variety of metrics to describe β diversity, but the one that seemed
to stick the most, and was not related to his gradient-definition of β diversity, was what
became most commonly used.
Whitaker: βw = S/ a
where S = the total number of species recorded in the system (i.e. γ diversity); α = the
average sample diversity, where each sample is a standard size and diversity is measured
as species richness. He arrived at this equation by reasoning that if you know the average
diversity within a set of communities or samples (α diversity), you could find the total
diversity represented by all samples by multiplying the average diversity by the number
of communities or samples. γ = α x β. In this way, he recognized the number of
communities as a measure of β diversity. However this overestimated γ diversity when
communities or samples shared species. Investigators using this equation often had
estimates of the α and γ diversity and they just rearranged the equation to solve for β
diversity. Interestingly, Whittaker and other ecologists more often used different metrics
to look at species turnover but this equation stuck with the ecology discipline.
A number of other corrections and modifications to Whittaker’s multiplicative measure
of β-diversity were made. Some of these modifications incorporate species loss and gain
along a transect. See Magurran (2004) and Jost (2007) for these modifications.
Around the same time as Whittaker’s definition of β diversity took hold, in the early
1960’s, McArthur and then Levins formulated an additive partitioning of diversity. But it
wasn’t officially taken up by ecologists because they didn’t express their diversity in
terms of α, β, and γ and their measures weren’t developed analytically. A few other
researchers used the additive partitioning of diversity but it went relatively unnoticed.
4
Lande, in 1996, appears to be the first person to place the additive partitioning of species
idea into the context of α, β, and γ diversity.
Dβ = D α + Dβ
When species richness is used to measure α and γ, β diversity can be estimated as
follows:
Dβ = S T − S j = ∑ q j ( S T − S j )
j
Where ST = the richness of the landscape (γ diversity); Sj = the richness of assemblage j;
and qj = the proportional weight of assemblage j based on its sample size or importance.
This method can also be adapted for the Shannon and Simpson diversity measures. See
Lande (1996).
Lande’s approach contrasts with that of Whittaker because α and β are added to produce γ
diversity, as opposed to multiplied.
Lande’s additive partitioning treats α diversity as the average within-sample diversity,
regardless of how diversity is measured (i.e. species richness, Shannon or Simpson
indices). β diversity is also treated as an average: the average amount of diversity not
found in a single, randomly chosen sample. β diversity is the average diversity within the
complements. Both α and β diversity are averages, using the same units of measure,
which makes them possible to compare. Lande’s additive partitioning can also be applied
across different scales if standardized sampling is used.
Many small sampling units will yield low values of α diversity and high values of β
diversity, while larger, and fewer samples will yield the opposite; higher α diversity and
lower β diversity. β diversity will increase in heterogeneous landscapes where few
species are shared in samples. β diversity will decrease in homogeneous landscapes
where species’ composition in sampling units approaches complete identity.
5
(Magurran 2004)
6
Since Lande, other ecologists have been using various versions of his classic formula to
calculate β diversity with additive partitioning. See Magurran (2004) and Jost (2007)
2. Methods that examine the differences in species composition and/or diversity
among areas of α diversity. These methods are formulated as measures of
similarity/dissimilarity and/or complementarity. These measures evaluate the
distinctness of assemblages and are used in applied contexts. (We will refer to all of
these as similarity measures or indices)
Pairwise comparisons of alpha diversities are made between all pairs of
sites/habitats/communities in the study area.
(Magurran 2004)
Some people, including Magurran, say that complementarity (dissimilarity) is another
way of saying β diversity-the more complementary two sites are, the higher their β
diversity. Other investigators don’t like to apply the term “β diversity” to these other
measures.
Most similarity measures combine 3 variables. For the purpose of examples, lets use: a,
the total number of species present in both samples; b, the number of species present only
in sample 1; and c, the number of species present only in sample 2. (Of course, any
coefficients can be substituted into the equations). One of the easiest and most intuitive
methods to describe similarity between pairs of sites is to use a similarity/dissimilarity
coefficient. A large number of measures exist and only the most common ones are shown
here:
a
and the Marczewski-Steinhaus (MS)
a+b+c
a
= 1−
a+b+c
Jaccard (1908): C J =
distance C MS
7
The MS dissimilarity measure (1-similairty) is know as a metric (as opposed to a nonmetric) measure. This means that is satisfies certain geometric requirements and it can be
treated as a distance measure which can be used in ordination.
Another popular measure is the Sorenson similarity measure. Sorenson’s measure is
regarded as one of the most effective presence/absence similarity measures. It is identical
to the Bray-Curtis presence/absence coefficient.
CS =
2a
Sorensen’s similarity measure (1948)
b+c
C BC = 1 −
2a
Bray-Curtis Distance or dissimilarity (1957)
b+c
Lennon et al. (2001) noted that if samples differ greatly in terms of their species richness,
Sorenson measures will always be large. Their measure works better for largely varying
values in species richness:
⎛
⎞
a
⎟⎟
Bsim = 1- ⎜⎜
⎝ a + min(b, c) ⎠
using the smallest values of b and c in the denominator to reduce the impact of
imbalances in species richness.
These similarity measures mentioned above are great because they are simple. However,
they don’t take into account the relative abundance of species. A species that dominates
an assemblage doesn’t carry more weight in a presence/absence similarity measure than
one species represented by only one individual. Due to this problem, people have been
developing similarity measures with quantitative diversity data.
A modified of version (Bray-Curtis 1957) of the Sorenson’s measure, which is sometimes
called the Sorenson’s quantitative index or the Bray-Curtis index (Magurran 1988)
CN =
2 jN
(N a + N b )
Where Na = the total number of individuals in site A; Nb = the total number of individuals
in site B; and 2jN = the sum of the lower of the two abundances for species found in both
sites.
If 12 individuals of a species were found in site A, and 29 individuals of the same species
were found in site B, the value 12 would be included in the summation to produce jN.
This index has been considered to be very satisfactory (Clarke and Worwick 2001a)
8
Wolda (1981) investigated a range of quantitative similarity indices and found that only
one, the Morisita-Horn index, was not strongly influenced by species richness and sample
size. However, the M-H index is sensitive to the abundance of the most abundant species.
S
C mh =
2∑ [(ani )(bni )]
i =1
(da + db )(aN )(bN )
S = total number of species at both sites
aN = total number of individuals of all species collected at site A
bN = total number of individuals of all species collected at site B
ani = number of individuals of the ith species collected at site A
bni =number of individuals of the ith species collected at site B
-the denominator terms are:
S
da =
∑ an
i =1
aN 2
2
i
S
and db =
∑ bn
i =1
2
i
bN 2
Wolda then made modifications of the M-H measure to reduce the bias of the most
abundant species.
CMH =
2∑ (ai • bi )
(d a + d b ) ∗ (N a ∗ N b )
Where Na = the total number of individuals at site A; Nb = the total number of individuals
at site B; ai = the number of individuals in the ith species in A; bi = the number of
inviduals in the ith species in B; and
da =
∑a
2
i
N a2
The M-H measure is widely used.
Another simple measure is percentage similarity (Southwood & Henderson 2000; after
Whittaker 1952).
9
s
P = 100-0.5 ∑ Pai − Pbi
i =1
Where Pai and Pbi = the percentage abundances of species I in samples a and b,
respectively; and S = the total number of species.
A large review and evaluation was carried out (Smith 1986) and both qualitative and
quantitative similarity measures were used. The best proved to be the Sorensen
quantitative index and all of the presence/absence (qualitative) measures proved
unsatisfactory. However, Smith advised that the choice of index for any particular study
depends on the goals of the investigator and the form of the data. She also concluded that
Wolda’s version of the M-H was also very good (Magurran 2004).
Clarke and Warwick (2001a) point out that quantitative measures can be very influenced
by the abundance of the most dominant species and they recommend to transform the raw
data. But too much transformation can lead you back to only presence/absence data.
Many qualitative and quantitative similarity/dissimilarity measures exist and only the
most commonly used measures are described here. Please see the bibliography for more
details on these measures.
3. The Third group of measures exploit the species-area relationship and measures
turnover related to species accumulation with area.
The slope in the relationship between species richness and area can also be considered as
a measure of turnover in areas that are nested subsets. I don’t have as much information
on this type of measure for β diversity because it is not commonly used in the current
ecological literature and many people don’t have data that would allow them to use these
types of analyses. See Harte et al. (1999b), Lennon et al.(2001), Ricotta et al. (2002),
Connor and McCoy (1979).
Problems with above measures
The measures listed above make the assumption that the sites being compared have been
completely inventoried, which is most often NOT the case.
Scale and habitat heterogeneity affect estimates of β diversity, complementarity, and
similarity/dissimilarity
Most sites have not been thoroughly sampled, and similarity/dissimilarity, do to statistical
properties (Colwell and Coddington 1994), is more likely to be overestimated between
rich samples than between species-poor samples unless sampling effort is sufficientlylarge throughout or has been proportionally increased for species-rich sites (Magurran
2004).
10
Quantitative measures that do include species abundance data are often biased by species
that are dominant in the samples or have disproportionately high abundances compared to
that of other species in the samples.
Even though we are not discussing measurements of alpha diversity here, it’s very
important to note that “coefficients of community similarity inherit the statistical
sampling properties of the diversity measures on which they are based” (Lande 1996)
Many of these alpha diversity measures are biased, thus directly affecting one’s ability to
accurately compare diversity across sites/habitats/communities.
New measures to compare diversity among site/communities/landscapes
Anne Chao and colleagues are developing new techniques to estimate the number of
species that two communities have in common, for both presence/absence and abundance
data. Her techniques make estimates based on the number of rare species to predict the
number of unobserved shared species. The number of abundant species is then added to
this. These similarity measures are new and include probabilistic methods, and will
hopefully prove more accurate and useful in future studies. See Chao et al. (2005), Chao
et al. (2000), Chao et al. (2006), Chao et al. (2008).
Lou Jost, who has also been working with Anne Chao on this topic, has recently
published a paper, “Partitioning diversity into independent alpha and beta components”
(2007). He presents a new definition of beta diversity and says that Shannon measures of
diversity are the only standard diversity measures that can be decomposed into logical
and independent alpha and beta components. See this paper and his webpage for more
details (http://www.loujost.com) Lou Jost and Anne Chao are writing a book, Diversity
Analysis, that will be published in fall 2008, addressing all issues of measuring diversity
and comparing communities.
Recommendations
Though all of the similarity/dissimilarity measures mentioned above (including those not
mentioned here) have biases, they can be useful when attempting to compare species
diversity (richness and/or abundance) among sites/communities. Regarding the selection
of one particular similarity index over another, it depends on the question and the data.
Below, are some suggestions regarding which similarity indices to use and when
following Chao et al. (2005), Chao et al. (2006), and Magurran (2004). Please consult
these references for more details.
For exhaustive sampling, with only presence/absence data, the classic Jaccard and
Sorensen provide simple overlap measures to compare two species list. Chao provides
bias-corrected formulas for these measures when sample sizes are unequal or insufficient,
but abundance data is necessary for Chao’s corrected measures.
11
For abundance data, the Bray-Curtis (or quantitative Sorensen index) and the Morisita or
Morisita-Horn indices are seen frequently in the ecological literature. However, Chao et
al. state that the Bray-Curtis measure only works well when sampling fractions are know
to be equal (species assemblages must be assumed to have the same total number of
individuals susceptible to sampling) and this is difficult to establish for field conditions
(2006). The authors state that his index only works “satisfactorily” with equal and
sufficient sampling. Chao et al. acknowledge that the Morisita-Horn index is not strongly
sensitive to sampling sizes and species richness, but it is highly sensitive to the most
abundant species (2006). Chao et al. have created new probability-based indices that
reduce undersampling bias by estimating and compensating for the effects of unseen,
shared species. They show their indices to consistently reduce undersampling bias (2005,
2006).
An important thing to remember is that the classic abundance-based indices, for example,
the Bray-Curtis and Morisita-Horn indices, match abundances species-by-species. These
two indices primarily measure similarity in the composition of dominant species so they
are affected by dominant species and may ignore the effect of rare species. The new
indices created by Chao et al. assess the probability that individuals belong to shared vs.
unshared species, without regard to which species they belong to. These indices are
formulated by pooling shared abundances but detailed species by species composition is
not taken into account. However, Chao et al. suggest that researchers consider carefully
the aim of their study and questions, regarding the meaning of “similarity” or
“overlap”and taking into account the limitations of their data. The authors recommend
their new similarity indices for any application in which species matching and similarity
of relative abundance are in question (2005).
Comparing Communities
Let’s make the assumption that the correct number of shared species has been estimated
and scaling issues and species richness differences among communities have been
accounted for. How do you make comparisons between communities using β diversity
and/or similarity/complementarity measures that were reviewed above?
12
A classic representation of a similarity matrix
(Azevedo-Ramos & Galatti 2002)
Correlations: Correlations between the amount of similarity/dissimilarity in diversity
among sites correlated with distance among sites.
(Novotny et al. 2008)
13
Ordination: Ordination is often used to describe the relationship between a set of
samples or localities based on their attributes (i.e. presence or abundance of species found
at different sites). PCA and nonmetric multidimensional scaling are widely used
ordination techniques (Clarke and Warwick 2001a and Southwood and Henderson 2000).
(Cleary & Mooers 2004)
Cluster Analysis: Similarity or dissimilarity/distance measures are used to measure the
distance (based on species composition) between all pairs of sites. Presence/absence or
abundance data can be used. The two most similar sites are formed into one cluster and
the analysis proceeds by successively clustering similar sites until a single dendrogram is
formed. There are many techniques for deciding how sites should be joined into clusters
and how clusters show be combined with each other. Depending on the method, the
distance between nodes on the dendrogram may represent β diversity. Bootstrap values
can be added to dendrograms to indicate robustness of analysis. Bootstrap values inform
you of the percentage of times a tree reconstructed using a resampling algorithm would
exhibit the same pattern.
14
Analysis of Similarity, ANOSIM: This is a nonparametric test applied to the rank
similarity matrix. It is somewhat analogous to a standard univariate ANOVA, and tests a
priori-defined groups against random groups in ordinate space. The analysis uses a
permutation procedure and tests the null hypothesis that there is no difference in
community composition among sites. Significance levels are generated using a
randomization approach. See Clarke & Gorley (2001).
Mantel Test: This is a mulivariate measure that evaluates the null hypothesis of no
relationship between two similarity matrices.
15
(Su et al. 2004)
Comparing distributions of pairwise similarity measures:
16
For example, investigators examined patterns of β diversity of pollution in freshwater fish
assemblages in Trinidad (Magurran and Phillip, unpub. data in Magurran 2004). They
observed that the loss of β diversity is not only a consequence of compositional change,
but that β diversity also declines if species found in polluted sites are consistently ranked
in order of abundance; if the same species tend to dominate polluted assemblages and
other species occur at moderate to low levels. (These fish species can probably deal with
impacts better than others). They divided sites into 3 categories: severely impacted by oil
pollution, moderately impacted, and unpolluted. Then they calculated pairwise estimates
of the M-H index, (they needed a quantitative measure because their study deals with
abundance rankings). The median value of β diversity was much lower for polluted sites
and a Kolmorogov-Smirnov test confirmed that the two distributions were significantly
different. In this case, patterns of species richness were generally similar so local species
richness was not heavily impacting β diversity, but rather the difference in environments.
(Magurran 2004)
17
Visual representation (GIS): Here, the authors show that measures of similarity, using
their newly defined similarity measure “compositional representativeness”, based on the
Bray-Curtis measure of similarity, do not equal species richness. They are indicating the
need to include compositional data when using similarity measures, especially when
applied to conservation.
(Jennings et al. 2008)
Turnover in time
Some investigators also use the α, β, γ diversity definitions to measuring species diversity
through time. For additional details on this application, see Preston (1960), McArthur and
Wilson (1967), Brown and Kodric-Brown (1977), Diamond and May (1977), Sepkoski
(1988), Russell et al. (1995), Nichols et al. (1998), Lekve et al. (2002).
Software Links:
Here is a limited list of software that perform different types of
similarity/dissimilarity/complementarity analyses and allow you to compare communities
with a variety of methods
PRIMER: http://www.primer-e.com/
PAST: http://folk.uio.no/ohammer/past/ (free)
EstimateS: http://viceroy.eeb.uconn.edu/estimates (free)
SPADE: http://chao.stat.nthu.edu.tw/indexE.html (free)
EcoSim: http://www.garyentsminger.com/ecosim/index.htm (free)
18
PC-ORD: http://home.centurytel.net/~mjm/pcordwin.htm
R: http://www.r-project.org/ (free)
Summary
All metrics for determining β diversity and measuring
similarity/dissimilarity/complementarity have biases and issues. In general, the classic
equations of Whittaker and Lande for determining β diversity are used theoretically and
rarely seen in applied contexts. The most common presence/absence and abundancebased similarity metrics are used in applied contexts and are often called β diversity
metrics, though they are not in the “classic sense”. There are numerous
similarity/dissimilarity measures and there is no measure that is superior above all others.
In addition, there are numerous applications of these indices when attempting to compare
communities. The selection of particular similarity measures and then methods by which
to compare these measures across sites, habitats, and communities, depends on the type
of data, type of questions, and ability to access various software packages. A popular and
recent use of similarity measures has been in the context of conservation-especially when
attempting to choose habitats/communities/ecoregions as future preserves. However, it is
somewhat unclear as to how all of these similarity metrics truly aid in the process of
selecting protected areas, largely due to their inherent biases, difficulty in interpreting the
results in a biologically meaningful manner, and the fact that there are no “standard”
measures that are commonly used across the board.
In addition to references cited throughout the body of this webpage,
here are more references…
Classic papers and annotated bibliographies:
http://userwww.sfsu.edu/~efc/classes/biol862-comm/fenter&lindzey.pdf
http://userwww.sfsu.edu/~efc/classes/biol862-comm/jacobs.pdf
Texts:
Legendre, P. & L. Legendre. 1998. Numerical Ecology, 2nd English Edition. Elsevier
Scientific Publishing Company, Amsterdam.
Magurran, Anne E. 2004. Measuring Biological Diversity. Blackwell Publishing.
Malden, MA.
Pielou, E.C. 1984. The Interpretation of Ecological Data: A Primer on Classification and
Ordination. Wiley, New York.
Selected theoretical studies on measures of β-diversity and similarity
19
Harte, J., McCarthy, S., Taylor, K., Kinszig, A., & M. Fischer. 1999. Estimating speciesarea relationships from plot to landscape scale using species spatial-turnover data.
Oikos 86: 45-54.
Chao, A., Hwang, W., Chen, Y. & C-Y Kuo. 2000. Estimating the number of shared
species in two communities. Statistica Sinica 10: 227-246.
Chao, A., Chazdon, R.L., Colwell, R.K., & T. Shen. 2005. A new statistical approach for
assessing similarity of species composition with incidence and abundance data.
Ecology Letters 8: 148-159.
Chao, A., Chazdon, R. L., Colwell, R.K., & T. Shen. 2006. Abundance-based similarity
indices and their estimations when there are unseen species in samples.
Biometrics 62: 361-371.
Chao, A., Jost, L., Chiang, S.C., Jiang, Y.H., & R. Chazdon. 2008. A two-stage
probabilistic approach to multiple-community similarity indices. Biometrics.
March 19th. Electronic publication.
Diserud, O., & F. Ødegaard. 2007. A multiple-site similarity measure. Biology letters 3:
20-22.
Jost, L. 2006. Entropy and diversity. Oikos 113: 363-375.
Jost, L. 2007. Partitioning diversity into independent alpha and beta components.
Ecology 88: 2427-2439.
Lande, R. 1996. Statistics and partitioning of species diversity, and similarity among
multiple communities. Oikos 76: 5-13.
Pelissier, R., & P. Couteron. 2007. An operational, additive framework for species
diversity partitioning and beta-diversity analysis. Journal of Ecology 95: 294-300.
Plotkin, J., & H.C. Muller-Landau. 2002. Sampling the species composition of a
landscape. Ecology 83: 3344-3356.
Wilson, M.V. & A. Shmida. 1984. Measuring beta diversity with presence-absence data.
Journal of Ecology 72: 1055-1064.
Wolda, H. 1981. Similarity indices, sample size, and diversity. Oecologia 50: 296-302.
Veech, J.A., Summerville, K.S., Crist, T.O., & J.C. Gering. 2002. The additive
partitioning of species diversity: Recent revival of an old idea. Oikos 99: 3-9.
Velland, M. 2001. Do commonly used indices of β-diversity measure species turnover?
Journal of Vegetation Science 12: 545-552.
Selected empirical studies using measures of similarity and β-diversity
Benedick, S., Hill, J.K., Mustaffa, N., Chey, V.K., Maryati, M., Searle, J.B.,
Schilthusizen, M., & K.C. Hamers. Impacts of rain forest fragmentation on
butterflies in northern Borneo: Species richness, turnover, and the value of small
fragments. Journal of Applied Ecology 43: 967-977.
Clarke, K.R. & Warwick, R.M. 2001a. Change in marine communities: an approach to
statistical analysis and interpretation, 2nd edn. Plymouth Marin Laboratory, UK:
PRIMER-E Ltd.
Cleary, D.F., & A.Ø. Mooers. 2004. Butterfly species richness and community
composition in forests affected by ENSO-induced burning and habitat isolation in
Borneo. Journal of Tropical Ecology 20: 359-367.
20
Clough, Y., Holzchuh, A., Gabriel, D., Purtauf, T., Kleijn, D., Krusess, A., SteffanDewenter, I., & T. Tscharntke. 2007. Alpha and beta diversity of arthropods and
plants in organically and conventionally managed wheat fields. Journal of
Applied Ecology 44: 804-812.
Cornell, H.V., Karlson, R.H. & T.P. Hughes. 2007. Scale-dependent variation in coral
community similarity across sites, islands, and island-groups. Ecology 88: 17071715.
Correa, S.B., Cramption, W.G.R., Chapman, L.J. & J.S. Albert. 2008. A comparison of
flooded forest and floating meadow fish assemblages in an upper Amazonian
floodplain. Journal of Fish Biology 72: 629-644.
Davis, A.L. & C.H. Scholtz. 2004. Local and regional species ranges of a dung beetle
assemblage from the semi-arid Karoo/Kalahari margins, South Africa. Journal of
Arid Environments 57: 61-85.
Ghazoul, J. 2002. Impact of logging on the richness and diversity of forest butterflies in a
tropical dry forest in Thailand. Biodiversity and Conservation 11: 521-541.
Grimbacher, P.S., Catterall, J.K., & H.C. Proctor. 2007. Response of ground-active beetle
assemblages to different styles of reforestation on cleared rainforest land.
Biodiversity Conservation 16: 2167-2184.
Hardy, O.J., & B. Senterre. 2007. Characterizing the phylogenetic structure of
communities by an additive partitioning of phylogenetic diversity. Journal of
Ecology 95: 493-506.
Jennings, M.D., Hoekstra J., Higgins, J., & T. Boucher. 2008. A comparative measure of
biodiversity based on species composition. Biodiversity Conservation 17: 833840.
Jobe, R.T. 2008. Estimating landscape-scale species richness: Reconciling frequency-and
turnover-based approaches. Ecology 89: 174-182.
La Sorte, F.A., McKinney, M.L., Pysek, P., Klostz, S., Rapson, G.L., Celesti-Grapow, L.,
& K.Thompson. 2008. Distance decay of similarity among European urban floras:
the impact of anthropogenic activities on β diversity. Global Ecology and
Biogeography 17: 363-371.
Novotny, V., Miller, S.E., Hulcr, J., Drew, R.A.I., Basset, Y., Janda, M., Setliff, G.P.,
Darrow, K. Stewart, A.J.A., Auga, J., Isua, B., Molem, K., Manumbor, M.,
Tamtiati, E., Mogia, M., & G.D. Weiblen. 2007. Low beta diversity of
herbivorous insects in tropical forests. Nature 448: 692-695
Su, J.C., Debinski, D.M., Jakubauskaus, M.E., & K. Kindscher. 2004. Beyond species
richness: Community Similarity as a measure of cross-taxon congruence for
course-filter conservation. Conservation Biology 18: 167-173.
Wolda, H. 1983. Diversity, diversity indices and tropical cockroaches. Oecologica 58:
290-298.
Yanoviak, S.P., Fisher, B.L, & A. Alonso. 2007. Arboreal ant diversity (Hymenoptera:
Formicidae) in a central African forest. African Journal of Ecology 46: 60-66
21