BetaDiversity: A quick and dirty look

1
Beta-Diversity A quick and dirty look

• The richness in species of a particular stand or
  community, or a given stratum or group of
  organisms in a stand. Fishers (1943) alpha
  index is one means of measuring this, which may
  be designated as primary or alpha diversity.
• The extent of change in community composition,
  or degree of community differentiation, in
  relation to a complex gradient of environment, or
  a pattern of environments, which may be
  designated secondary or beta diversity.
• The species-diversity of a number of community
  samples, for some range of environments, which
  have been combined, so that the diversity value
  is a resultant of both alpha and beta diversities
  of these samples. The transect diversities in
  Table 18 are of this tertiary or gamma
  diversity type, as are many of those for animal
  collections to which diversity measurements have
  been applied.
• The same types of measurements may be applied to
  gamma as to alpha diversity beta diversity
  represents a different problem, to be discussed
  in the following section. (Whittaker 1960)

2
Whittaker (1960)
NON - GRADIENT
GRADIENT
ß?/a
Half changes Similarity v. distance
Harrison Wilson Schmida Cowling Willig
Sandlin Blackburn Gaston Oliver Young Pharo..
Cowling Rey Benayas Porembski Harrison Nekola
White Cody Syuzo Givnish..
3
Beta divided (gradient beta) Cody (1975, 1986,
1993) ß -diversity rate of species turnover
BETWEEN habitats function mainly of difference
between habitats, their areal extent, and their
contiguity ? - Diversity rate of species
turnover WITHIN a habitat type between different
sites a product fo overall speciation patterns
and generally a function of site separation and
of the intervening barriers to species
dispersal Nekola White (1992, 1999,
2002) Niche difference model Environmental
dissimilarity along a gradient, competitive
sorting of species Model of temporal and spatial
constraint Function of spatial arrangement and
histories of organisms and habitats, explained
largely by biogeographic history and dispersal
capability
4
(Koleff Gaston et al. 2003)
5
(Koleff Gaston et al. 2003)
6
Fig. 1. (a) The number of studies employing
different numbers of measures of beta diversity,
and (b) the number of times that each beta
diversity measure has been used, based on 60
publications that have employed at least one of
the measures in Table 1.
(Koleff Gaston et al. 2003)
7

• Velland (2001) Do commonly used indices of ß
  -diversity measure species turnover?
• Conclusions
• Different measures of ß -diversity reflect quite
  different properties of a given data set. ßw and
  its descendants measure the inverse average
  frequency of species. Mean dissimilarity
  represents the expected difference in species
  composition between a randomly chosen pair of
  plots.
• Whittakers half changes represent the magnitude
  of species turnover, and the slope of a
  similarity-distance graph gives the rate of
  species diversity per unit distance. Using the
  same term (ß -diversity) for all these measures
  is not advised, because it invites comparisons
  among studies that in fact are not comparable.
• 2. Because a and ß are meant to represent
  components of total (?) diversity, I feel that
  the term ß -diversity should be reserved for a
  value that can be related mathematically to a and
  ? diversity. However, neither ? / a nor (? - a)
  reflect the notion of species turnover, and the
  terms ß -diversity and species turnover
  should not be used interchangeably.

8
Velland (2001) Do commonly used indices of ß
-diversity measure species turnover? Uses for
ßw When underlying gradients are unknown, ßw
can be used to test the degree to which
heterogeneity in species composition varies among
functional groups, or among different regions for
which gradients are difficult to compare. If
measures of environmental characteristics cannot
be explicitly matched with vegetation plots, ßw
could also be used to test for relationships
between environmental heterogeneity and
compositional heterogeneity among different
regions. Simple indices of ß -diversity will
remain useful for asking how total species
diversity is partitioned within and among plots
when specific gradients are not of
interest. Uses for Species Turnover To
address hypotheses regarding compositional change
along gradients, measuring the rate and magnitude
of species turnover using similarity-distance
curves is appropriate and useful. Such questions
require explicit consideration of study-plot
position in physical and environmental space.
9
The Additive Partitioning of Diversity
? a ß
ß?/a
?
a4
a3
ß 3
ß 2
a2
a1
ß 1
(Wagner et al. 2003)
10
Advantages of Additive Partitioning (from Lande
1996, Loreau 2000, and Veech et al. 2002)
By additive partitioning, ß -diversity is simply
the average diversity within the complements
all plots pi. Therefore, both a -diversity
and ß -diversity are averages, which makes it
easier to compare to one another. (Veech et al.
2002)
ß -diversity as measured by additive
partitioning avoids the gradient-related
shortcomings of traditional metrics. (Veech et
al. 2002)
Continuum of scales At each scale, diversity
can then be partitioned using equation (1) ? a
ß such that total (or ?) diversity in a
spatial unit becomes within-unit (or a) diversity
at the next higher scale. The total diversity at
a scale is thus determined by diversity at the
next lower scale (a component) and the
between-unit diversity (ß component) (Loreau
2000)
Additive partition of diversity also suggests a
natural measure of similarity among multiple
communities, the proportion of the total
diversity found within communities. (Lande 1996)
11
Additive partition of diversity also suggests a
natural measure of similarity among multiple
communities, the proportion of the total
diversity found within communities. (Lande
1996) a good measure of community
dissimilarity is 1 ß/ ?. Defining ß -diversity
as the average amount of diversity not found in a
sample (as we did previously) does not explicitly
recognize differences among samples or
communities, which after all is the original
intent of ß -diversity . However, sample
similarity (measured by 1 ß/ ?) does directly
assess sample differentiation, and it can only be
derived from the additive relationship, ? a
ß. (Veech et al. 2002)
12
Species shared
a
aave 45 ? 100 ß 55 ? 0.45 Jave
0.29 Save 0.44
aave 29.25 ? 104 ß 74.75 ? 0.28 Jave
0.09 Save 0.16
aave 10.5 ? 29 ß 18.5 ? 0.36 Jave
0.18 Save 0.29
13
Uses of Additive Partitioning (from Veech et al.
2002)

• Evaluating the statistical significance of
  diversity components

(Summerville et al. 2003)
(Summerville et al. 2003)
(Summerville et al. 2003)
14
BUT, keep in mind study design SCALE GRAIN EXTENT
15
Uses of Additive Partitioning (from Veech et al.
2002)

• Survey design
• Nature reserve placement and design

(Gering et al. 2003)
(Gering et al. 2003)
16
Uses of Additive Partitioning (from Veech et al.
2002)

• Comparative analysis of the diversity within a
  set of samples and that among samples
• Relationship between local and regional species
  diversity

Schematic illustration of the relationship
between local and regional diversity and the
partitioning of regional diversity into its alpha
and beta components. (Gering Crist 2002)
(ac) Scenarios where alpha is the dominant
contributor (alpha-dominant systems) to
regional diversity. (df) Scenarios where beta
is the dominant contributor (beta-dominant
systems) to regional diversity. Scale
independence (a, d) will occur when alpha and
beta contribute in a consistent manner to
regional richness across the range of spatial
scales. Constant scale dependence (b, e) will
occur if alpha and beta increase in a predictable
manner across the range of scales, whereas
irregular scale dependence (c, f) will be evident
if alpha and beta contribute to regional richness
in a nonlinear manner across the range of scales.
(Gering Crist 2002)
17
Figure 5 Graph showing the relative contributions
of alpha (solid lines) and beta (stippled lines)
richness to regional richness. As in the
preceding figures, the hashed line represents the
points on the graph where the sum of alpha and
beta diversity equal the regional diversity,
whereas the light grey line represents the plane
at which alpha and beta each account for half of
the regional diversity. Note the switch in
dominance from beta to alpha at the broadest
spatial scale. (Gering Crist 2002)
18
last words Additive partitioning of diversity
can be useful in analyzing components of
diversity over multiple scales and a helpful
addition to the suite of tools used for
conservation planning. HOWEVER it is NOT a
substitute for measures of species turnover along
environmental and geographic gradients NOR for a
measure of similarity. While additive
partitioning may give insight into the importance
of the components at different scales, it says
nothing about variation within the same
scale. CLEAN UP THE LEXICON!! The ß -diversity of
? a ß is NOT THE SAME as the ß -diversity of
species turnover. The ? diversity used by Cody,
Cowling, Ferrier and a few others is not the same
as the ? referred to by everyone else.
19
SCI Cited Reference search on Lande 1996 84
hits SCI BIOSIS General Search on additive and
partitio diversity 18 hits (6 not applicable)
Gering JC, Crist TO. 2002. The Alpha-Beta-Regional
Relationship Providing New Insights Into
Local-Regional Patterns of Species Richness and
Scale Dependence of Diversity Components. Ecology
Letters 5(3)433-44. Gering JC, Crist TO, Veech
JA. 2003. Additive Partitioning of Species
Diversity Across Multiple Spatial Scales
Implications for Regional Conservation of
Biodiversity. Conservation Biology
17(2)488-99. Koleff P, Gaston KJ, Lennon JJ.
2003. Measuring Beta Diversity for
Presence-Absence Data. Journal of Animal Ecology
72(3)367-82. Lande R. 1996. Statistics and
Partitioning of Species Diversity, and Similarity
Among Multiple Communities. Oikos
76(1)5-13. Loreau M. 2000. Are Communities
Saturated? On the Relationship Between Alpha,
Beta and Gamma Diversity. Ecology Letters
3(2)73-6. Summerville KS, Boulware MJ, Veech JA,
Crist TO. 2003. Spatial Variation in Species
Diversity and Composition of Forest Lepidoptera
in Eastern Deciduous Forests of North America.
Conservation Biology 17(4)1045-57. Veech JA,
Summerville KS, Crist TO, Gering JC. 2002. The
Additive Partitioning of Species Diversity
Recent Revival of an Old Idea. Oikos
99(1)3-9. Vellend M. 2001. Do Commonly Used
Indices of Beta-Diversity Measure Species
Turnover? Journal of Vegetation Science
12(4)545-52. Wagner HH, Wildi O, Ewald KC. 2000.
Additive Partitioning of Plant Species Diversity
in an Agricultural Mosaic Landscape. Landscape
Ecology 15(3)219-27. Whittaker, RH. 1960.
Vegetation of the Siskiyou Mountains, Oregon and
California. Ecological Monographs 30(3)279-338.