Best estimates of biodiversity
value:
using genealogy to predict
genetic or character richness
Principles
Biologists needing to estimate richness in a particularly valued currency
of different genes or characters are usually unable to measure this directly,
or at best are only able to study small samples of genes or characters.
However, because genes and characters are inherited, biologists have been
able to respond by proposing phylogenetic
or taxonomic measures
of diversity. These measures predict the biodiversity value of different
biotas, using knowledge of the genealogical (or hierarchical) relationships
among organisms in combination with models of gene or character evolution
(ref 2, ref
3).
To illustrate how classifications may be used to predict diversity value
by estimating richness at the level of the genes or characters, the example
below shows a classification for some African species of milkweed butterflies
(family Nymphalidae). The branching pattern of the classification is derived
by analysis of 217 morphological and chemical characters, and the branch
lengths are scaled by the number of character changes found within this
sample (shown as vertical ticks). Considering all combinations of three
species, the most diverse set of three species is niavius, echeria
and damocles, because these three have the longest total branch
lengths with the largest numbers of character differences between them
(shown in black) (below):
To illustrate how using this approach can effect the relative values
of different faunas or floras, consider first one of the most popular
measures of diversity, species richness. The example below shows counts
of the numbers of species of sibiricus-group bumble bees among
equal-area grid cells (below):
(31 Kb image)
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Link to image showing results of species richness measure. ; |
For these bumble bees, a large representative sample of character-difference
data is not yet available, only a genealogical classification. Nonetheless,
a simple evolutionary model can still be used to estimate the way changes
in characters for these bees are likely to have accumulated, given this
classification tree. When combined with a measure of tree length to count
the relative expected number of character differences within each fauna,
the next example shows an improved prediction of relative diversity value
for the same bee faunas, to take into account the expected numbers of gene
or character differences (below):
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(31 Kb image)
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Link to image showing results of phylogenetic diversity
measure. |
Phylogenetic
& taxonomic measures
In the absence of complete knowledge of the valued genetic or character
differences among organisms, the most direct approach to estimating relative
value is to use phylogenetic measures. This is used to scale the branch
lengths on the tree for use by the measure in the third step. It can use
sample data for gene or character variation, or it can be based on just
a taxonomic classification, if that is all that is available and if it
is believed to represent genealogical relationships. These require three
components (ref 2):
1. Cladograms
The phylogenetic approach is based on the general evolutionary model
of descent with modification: that genes and characters are inherited,
with rare alterations or changes. Some of these changes are reversals,
so that data often conflict with any one tree (homoplasy), although
such conflicts are minimised in the construction of cladograms. If the
resulting trees are good estimates of genealogical relationships, then
they should be more reliably predictive of the unsampled genetic or character
variation, which always remains the great majority.
2. Models of gene/character evolution
Next, an explicit choice has to be made of a special evolutionary model
for linking the branching pattern of the tree with the way genes or characters
change along the tree (ref 2). Three
extreme options for this model are envisaged (below):
The clock
(anagenetic) model
assumes that changes occur at random and are subject
to little constraint by selection. Consequently, in effect, changes accumulate
more or less in proportion to the time elapsed along the branches.
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Result:
if sample data are unavailable or are expected to be
biased and unrepresentative,
all lineages are scaled to a common length. |
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The sample
(empirical) model
assumes that the distribution of changes in a small sample
of variation is representative of the great majority of unsampled variation.
The pattern of changes is usually expected to be intermediate between those
from the other two models.
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Result:
if sample data are available and are expected to be representative,
all branches are scaled in proportion to sample changes. |
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The saltatory
(cladogenetic) model
assumes that most changes are associated with speciation
or divergence events, for example if strong selection constraints are relaxed
at these times. Although the numbers of changes associated with each branching
event may differ, in effect changes accumulate more or less in proportion
to the number of branching events (including those to extinct branches).
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Result:
if sample data are unavailable or are expected to be
biased and unrepresentative,
all branches are scaled to unit length.
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3. Measure of gene/character richness
Third, a measure of relative richness in different genes or characters
is needed, which sums the relative degree of change along the tree using
the branch lengths scaled by the chosen special evolutionary model. There
is now broad agreement on the form of this measure, as a measure of the
length of the subtree that spans any given set of species of interest on
the tree. A simple case of this measure is illustrated graphically, for
calculating the increase in diversity (or complementary diversity) when
a species C is added to a tree for two species A and B from the pairwise
differences between species, AB AC and CB (below):
For the example of the butterfly cladogram shown at the top of the
page, branch lengths can be scaled on the horizontal axis (the vertical
components should be ignored) using the three evolutionary models described
above. For each model, the set of three species that is estimated to have
the greatest genetic or character richness is sought. For this tree, only
with the sample model is there a unique solution. With the other models,
there are at least two equivalent choices for each species, as shown by
the vertical tie bars (below):
Most disagreement is now centred on the choice of special evolutionary
model (ref 2). The sample model is the
easiest to use, and its consequences in this example show that it may given
less equivocal answers concerning which species represent the greatest
relative diversity.
However, the apparent advantages of the sample model are only real
if the sample truly represents the overall pattern of variation. For example,
if a sample of unconstrained genetic data were available that behaved as
though following the clock model, whereas the value being sought for expressed
characters was under strong stabilising selection and distributed as though
it followed the saltatory model, then using the sample model could introduce
a severe bias into the measure. Consequently, any apparent increase in
resolution arising from using information from the sample in this way could
actually be misleading.
Lack of
phylogenetic information
In practice, detailed and reliable phylogenetic (genealogical and difference)
information is often unavailable. Nevertheless, arguments for measuring
biodiversity value as gene or character richness do at least provide a
philosophically and economically defensible starting point, as one possible
answer to the problem of what is valued in diversity. Accepting that phylogenetic
or taxonomic diversity measures can use genealogical pattern as a predictor
of value also provides a possible key to the problem of finding more practical
measures (ref 4).
