Landscape Ecology 15: 219­227, 2000.
 2000 Kluwer Academic Publishers. Printed in the Netherlands.
219
Additive partitioning of plant species diversity in an
agricultural mosaic landscape
Helene H. Wagner1,2, Otto Wildi1 & Klaus C. Ewald3
1Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), CH-8903 Birmensdorf, Switzerland;
2Geobotanical Institute, Swiss Federal Institute of Technology (ETH), CH-8092 Zürich, Switzerland; 3Nature and
Landscape Conservation, Swiss Federal Institute of Technology (ETH), CH-8092 Zürich, Switzerland
(author for correspondence)
Received 29 December 1998; Accepted 21 August 1999
Key words: heterogeneity, landscape, scale, species diversity
Abstract
In this paper, we quantify the effects of habitat variability and habitat heterogeneity based on the partitioning of
landscape species diversity into additive components and link them to patch-specific diversity. The approach is
illustrated with a case study from central Switzerland, where we recorded the presence of vascular plant species
in a stratified random sample of 1'280 quadrats of 1 m2 within a total area of 0.23 km2. We derived components
of within- and between-community diversity at four scale levels (quadrat, patch, habitat type, and landscape) for
three diversity measures (species richness, Shannon index, and Simpson diversity). The model implies that what
we measure as within-community diversity at a higher scale level is the combined effect of heterogeneity at various
lower levels. The results suggest that the proportions of the individual diversity components depend on the habitat
type and on the chosen diversity aspect. One habitat type may be more diverse than another at patch level, but
less diverse at the level of habitat type. Landscape composition apparently is a key factor for explaining landscape
species richness, but affects evenness only little. Before we can test the effect of landscape structure on landscape
species richness, several problems will have to be solved. These include the incorporation of neighbourhoodeffects,
the unbiased estimation of species richness components, and the quantification of the contribution of a landscape
element to landscape species richness.
Introduction
A natural habitat obtains its characteristics from environmental
factors such as climate, soil or topography,
from natural succession, and from the frequency
and type of natural disturbance. In agro-ecosystems,
human actors deliberately modify environmental conditions
through agricultural practices such as preparations
for crop and pasture seeding, crop management
(i.e. actions which directly benefit or protect the crop
such as fertilizer and pesticide application), harvesting
method and grazing management. In an agricultural
landscape, the habitat thus depends strongly on
the spatial and temporal pattern of disturbance by
agricultural practices.
Approaches that evaluate the biodiversity of a landscape
based on its structure often rely on the equilibrium
theory of island biogeography by MacArthur
and Wilson (1976). It predicts that the biodiversity of
an island is positively correlated with the area of that
island and negatively correlated with the distance to
the nearest continent. Applied to an agricultural landscape,
an evaluation of biodiversity would have to be
based on the surface area of each habitat island and
the distance to the nearest patch of the same habitat
type (Duelli 1997). In a review of empirical studies
of species richness and patch size in terrestrial landscapes,
Forman (1995) stated that in most cases, larger
patches have more species than smaller patches, and
area is more important than isolation, patch age, and
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many other variables in predicting species richness.
However, it was observed that while the area of patch
interior is positively related to the number of specialized
interior species (i.e., species primarily distant
from the perimeter), patch size can not explain the
number of edge species (i.e., species primarily near
the perimeter of a landscape element; Forman 1995).
If we assume that intensively cultivated land hosts only
few specialized interior species, the species richness
of an agricultural landscape without natural habitats
depends strongly on the edge species and can not be
predicted by patch size. According to Duelli (1997),
the factors most pertinent to predict and evaluate biodiversity
in an agricultural mosaic landscape are (1)
habitat variability, i.e., the number of biotope types
per unit area; (2) habitat heterogeneity, i.e., the number
of patches and the length of ecotones per unit area;
and (3) the surface proportions of natural, semi-natural
and intensively cultivated areas. Duelli (1992, 1997)
proposed the use of the mosaic concept as an alternative
approach to explain patch species richness in
cultural landscapes. The mosaic concept predicts that
the species diversity in an area increases with habitat
variability and with habitat heterogeneity.
In order to test the predictions of the mosaic concept,
we need a quantitative description of landscape
species diversity that partitions overall diversity into
the contributions of habitat variability, habitat heterogeneity
and patch-specific diversity. Whittaker (1977)
proposed to link diversity components between ecological
scales by multiplication, so that landscape or
gamma diversity is the product of the mean alpha diversity
and beta diversity. In contrast to Whittaker's
(1977) multiplicative model, Allan (1975) applied an
additive linkage of diversity components to compare
the Shannon index measured at microsites, at different
sites and for the whole sample. Applied to Whittaker's
diversity components, gamma diversity is partitioned
into the sum of the average alpha diversity and the
beta diversity. Lande (1996) extended the approach
to species richness and to Simpson diversity and recommended
it as a unifying framework with which to
measure diversity at different levels of organization. In
contrast to the multiplicative model, all diversity components
are measured in the same way and expressed
in the same units so that they can directly be compared.
In most of the above approaches, diversity is
equated to species richness. In the present paper,
we use species diversity as a broad term encompassing
the two aspects of richness and evenness, while
we refer to their combination as mixed diversity. In
an empirical study on the diversity of invertebrates
and flowering plants in a cultivated landscape, Duelli
and Obrist (1998) found that for most taxonomic
groups, the mixed diversity measures Shannon index
and Simpson diversity were only weakly correlated
with patch-specific species richness. An interesting
question is therefore whether habitat variability and
habitat heterogeneity affect different aspects of species
diversity in a similar way.
In this paper, we quantify the effects of habitat
variability and habitat heterogeneity based on the partitioning
of landscape species diversity into additive
components and link them to patch-specific diversity
measurements. The approach is tested with data from
a case study in central Switzerland. Amongst the questions
we address are: (1) how is the partitioning of
diversity within the landscape affected by the measure
of diversity which is used?; (2) how does the
partitioning differ according to the type of land-use?;
and (3) how important are spatial effects such as the
differentiation between edge and patch interior?
Material and methods
Model approach
The landscape model we apply consists of a mosaic of
different habitat types. Each type can be fragmented
into patches, which we suppose to be internally homogeneous.
A habitat type corresponds to a type of
land-use with a typical set of agricultural practices,
and a patch to a management unit, e.g. a field. Linear
structural elements are treated as patches with a specific
width and a distinct border with each neighbouring
patch. This is the most parsimonious landscape
model that accounts for habitat variability and habitat
heterogeneity.
We define a new, consistent terminology of diversity
components (Figure 1). This is necessary
because compared to Whittaker (1977), we introduced
an intermediate level of habitat type between
patch and landscape and we imply an additive linkage
of diversity components. Whittaker (1977) equated
MacArthur's (1965) within- and between-habitat diversity
to alpha and beta diversity, though MacArthur
(1965) had not suggested any function to link these
components. MacArthur's (1965) concepts of withinand
between-habitat diversity can be generalized to
within-community and between-community diversity.
As Begon et al. (1996) noted, a community can be
221
Figure 1. The proposed hierarchical model of species diversity, where the scale-specific components of within- and between-community
diversity are linked additively to form the diversity at the next higher level. In italics the corresponding factors of the mosaic concept as defined
by Duelli (1992).
defined at any size, scale or level within a hierarchy
of habitats. Figure 1 shows the definitions of
the scale-specific components of within- and betweencommunity
diversity for the levels sampling quadrat,
patch, habitat type, and landscape.
As indicated in figure 1, habitat variability and
habitat heterogeneity defined by Duelli (1992) lead
to between-type diversity and between-patch diversity,
and patch-specific diversity corresponds to withinpatch
diversity.
Within-quadrat diversity equals Whittaker's (1977)
point diversity, within-patch diversity corresponds directly
to alpha diversity and within-landscape diversity
to gamma diversity. In a broader sense, betweenquadrat
and between-patch diversity are comparable to
Whittaker's (1977) point diversity and beta diversity.
So far, our diversity model does not assume any
specific diversity measure. If we accept richness and
evenness as distinct aspects of species diversity, the
question is no longer how to combine them into a single
measure, but how to compare them. An additive
partitioning of a pure evenness measure has not been
developed. Peet (1974) distinguished two groups of
mixed diversity measures. Type I measures are most
affected by rare species, while Type II measures are
most sensitive to changes in the abundance of the dominant
species. Magurran (1988) showed that various
measures correlate significantly within these groups
but not between the groups, and that Type I measures
stress richness while Type II measures stress evenness.
By comparing diversity patterns in a sequence from
pure species richness over a Type I measure to a Type
II measure, we will be moving along a gradient from
richness towards evenness.
Study site
The study area at Hohenrain (Swiss plateau) is situated
in a highly structured agricultural landscape with both
arable and grassland farming. We classified the study
area into 5 types of land-use. These included arable
fields, meadows, verges, hedgerows and ditches, and
roads (Figure 2). We combined hedgerows and ditches
to a single type, because they often occurred together
within the same management unit. The agricultural
landscape of the region contained two other frequent
types of land-use, forests and farm yards, which were
not represented in the study area.
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Figure 2. The management units included in the sample and of the surrounding area near Hohenrain (Switzerland) are classified into 7 types of
land-use, namely arable fields, meadows, verges, roads, hedgerows and ditches, farm yards and forests. For one meadow, the subdivision into a
3-m wide edge and a core area is indicated together with the random sample of 20 quadrats within each stratum.
223
Data collection
Within an area of 0.23 km2, we recorded the presence
of vascular plants for a stratified random sample
of 1'280 quadrats of 1 m2 size (Figure 2). For this
purpose, we mapped the management units from a rectified
aerial photograph and classified them according
to present (i.e., summer 1997) land-use. To check for
spatial interactions, we subdivided the meadows and
arable fields into a 3-m wide boundary strip (edge) and
the rest of the field (core). Within every patch or subdivision,
we sampled 20 quadrats of 1 m2 randomly
from a 1-m grid. We kept a minimum distance of 5 m
between quadrats of the same patch in order to prevent
spatial dependence. To achieve an even representation
of ecotones, we subdivided patches with a width up
to 10 m into 1-m wide strips and required an even
distribution of the 20 quadrats over the strips. In summer
1997, we recorded the presence of vascular plant
species for each quadrat between the last herbicide
application and harvesting. For the grass verges, the
main period of observation lay in June, for the arable
fields in July, for the meadows in August, and for
the hedgerows and the roads between mid-August and
mid-September. Three ecotone patches shorter than
100 m were sampled with 10 quadrats only, and two
patches were plowed before they could be sampled.
Data processing and statistics
We divided the total species diversity observed in
the stratified sample of 1'280 quadrats according to
the model in Figure 1. For each of the three diversity
measures species number, Shannon index and
Simpson diversity, we derived separate diversity components
for the total area and for each type of land-use
applying the formulae in Lande (1996).
The observed number of species S is a pure richness
measure. Let w and b denote components of
within- and between-community diversity. Withinquadrat
species richness SWq is the number of species
found in quadrat q, and SWp, SWt and SWl are the
numbers of species found in the pooled quadrats of
patch p, type t and the total landscape l respectively.
Let SWq denote the arithmetic mean of the number of
species SWq of all quadrats q, so that between-quadrat
diversity SBq is derived as:
SBq = SWp - SWq. (1)
Similarly, between-patch species richness SBp is
the difference between SWt and SWp, and betweentype
species richness SBt is the difference between
SWl and SWt.
Shannon index H and Simpson diversity D are
both functions of the proportional abundance i of
species i. We derived the proportional abundances ip
of species i in patch p by dividing the number fip of
quadrats in p that contained i by their sum f.p:
ip =
fip
fp
. (2)
We calculated the pooled proportional abundances
it of i in type t and il in landscape l as the weighted
sums of the ip's (cf., Formulae 3a and 3b). On type
level, we defined the weight of patch p in type t as the
area apt of p in t divided by the total area a.t of all
patches in t . For the total area, the weight of patch p
in landscape l equaled the area apl of p in l divided by
the total area a.l of l:
it =
p
apt
at
 ip, (3a)
il =
p
apl
al
 ip. (3b)
The Shannon index H is a Type I measure of mixed
diversity:
H = -
i
i  ln i. (4)
The Type II measure Simpson diversity D is a function
of the dominance . Two different functions are
used in the literature. The reciprocal form (D = 1/)
cannot be divided into additive components (Lande
1996). Therefore we applied the form that is also
known as the Gini Index:
D = 1 -  = 1 -
i
2
i (5)
Let within-patch Shannon index HWp be the Shannon
index calculated from the ip's, HWt and HWl
the Shannon index based on the pooled proportional
abundances it and il. HWp is the weighted mean of
the HWp of all patches p (with weigths proportional
to area), so that between-patch Shannon index HBp is
derived as:
HBp = HWt - HWp (6)
Similarly, between-type Shannon index HBt is the
difference between HWl and HWt . The components of
Simpson diversity D were derived in the same way as
for H, applying formula (5) instead of (4).
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Figure 3. Each bar shows the species number S (top), Shannon index H (middle) or Simpson diversity D (bottom) for a particular type of
land-use and for the study area as a whole, partitioned into the mean S, H or D per quadrat, the mean S, H or D per patch, for every type of
land-use the total S, H or D observed in the type, and for the whole study area the mean S, H or D per type and the total S, H or D observed in
the entire sample.
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Results
Figure 3 shows the additive components of the observed
plant species diversity for species number S,
Shannon index H and Simpson diversity D. For species
number S, the total of 179 species that were observed
(SWl) can be divided into a mean within-type richness
SWt of 80 and the between-type richness SBt of 99
species. SWt consists again of a mean within-patch
richness SWp of 29 and the between-patch richness
SBp of 51 species. SWp consists of a mean withinquadrat
richness SWq of 9 and the between-quadrat
richness SBq of 20 species.
For the Type I measure Shannon index H, the
within-landscape HWl of 3.5 is composed of the
between-type HBt of 0.4 and a mean within-type component
HWt of 3.1. The latter again is the sum of a
mean within-patch HWp of 2.5 and the between-patch
HBp of 0.6. For the Type II measure Simpson diversity
D, the within-landscape DWl of 0.96 is composed
of the between-type DBt of 0.02 and a mean withintype
DWt of 0.94. The latter is the sum of a mean
within-patch DWp of 0.89 and the between-patch DBp
of 0.5.
The percentages of the total landscape diversity
attributed to patch-specific diversity, habitat heterogeneity
and habitat variability are therefore 12:27:61
for S , 71:18:11 for H and 93:5:2 for D. For D, and to
a lesser degree for H, the components become smaller
with higher scale levels. The opposite is the case for S,
where diversity components increase with higher scale
levels. This reversed diversity pattern for S as compared
to the mixed diversity measures occurs within
all types.
The proportions of diversity components vary between
the different types of land-use. For example,
while the verges have a much higher within-quadrat
SWq than the hedges, their between-quadrat SBq is
considerably lower. The core areas of arable fields and
meadows give another example of how the comparison
of different types depends on the scale level. The
meadows show higher within-patch HWp and Dwp, but
considerably lower between-patch HBp and DBp than
the arable fields. Thus, while the average meadow appears
to be more diverse than the average arable field,
this relation is reversed at the type level. Also for
species richness, the meadows have a higher withinquadrat
SWq, but smaller between-quadrat SBq and
between-patch SBp than the arable fields, which results
in a lower within-type SWt.
There is a marked difference in diversity between
the edge and the core area both of meadows and arable
fields. This difference is rather large compared to the
overall difference between meadows and arable fields.
The edges are generally more diverse, with higher
within-quadrat, within-patch and within-type components
for all three diversity measures. But they have
a smaller between-patch HBp and DBp than the core
areas, which means that the edges are more similar to
each other. As to the number of interior species, only
12 species were restricted to the 460 quadrats from the
core area of meadows and arable fields.
Discussion
We propose a model that provides a quantitative description
of the diversity within and between landscape
elements at various scales. The model makes no
assumption about the processes that determine these
patterns, but provides a useful basis for investigating
and understanding them. The contributions of
habitat variability, habitat heterogeneity and patchspecific
diversity to landscape diversity are quantified
and can directly be compared, since all components
are measured in the same units.
The question arises why Allan's (1975) additive
model of diversity has been generally neglected and
Whittaker's (1977) multiplicative model has been
largely reduced to the individual diversity components
over the last twenty years. Whittaker's (1977) model
implies that alpha-type and beta-type diversity cannot
be expressed in the same units and are therefore not
comparable. While alpha, beta and gamma diversity
are often quantified individually, their multiplicative
linkage is generally not interpreted as a mathematical
operation but as a sign of their independence.
As Gaston (1996) noted, the distinctions between genetic,
species and ecosystem diversity are becoming
increasingly conventional. Although genes correlate
with species and species with ecosystems, they are often
treated as discrete ecological scales in the sense of
hierarchy theory (Allen and Starr 1982; O'Neill et al.
1986). This theory predicts that for a hierarchically
structured landscape, patterns are unrelated between
domains of scales as they are caused by processes
isolated at discrete scales (O'Neill et al. 1991).
Our model implies that what we measure as withincommunity
diversity at a higher scale level is the
combined effect of heterogeneity at various lower levels.
The case study suggests that these are not equally
226
important for all types of habitat. For a given measure
of diversity, the type-specific sizes of the diversity
components were not proportional, but varied considerably.
The question which habitat type is the most
diverse will depend on the level ofcomparison. While
one might identify an appropriate scale for studying
a specific phenomenon in a specific habitat, we recommend
using several scale levels simultaneously for
comparing different habitats.
The case study indicates that the way in which
the total diversity is divided strongly depends on
the chosen diversity aspect. Landscape composition
apparently is a key factor for explaining landscape
species richness, but has little effect on evenness. Both
measures of mixed diversity were little affected by
habitat variability and habitat heterogeneity, with the
exception of arable fields. The dominance of the crop
species caused low within-patch diversity, whereas
crop variability induced a large between-patch diversity
component. This effect might even be stronger
if the abundance is measured in terms of biomass or
cover. As expected, the Type II measure of mixed
diversity, Simpson diversity, was more affected by
a change of the dominant species than the Type I
measure Shannon index.
Before we can test the effect of landscape structure
on landscape species richness, several problems must
be solved: (1) the incorporation of neighbourhood effects;
(2) the unbiased estimation of species richness
components; and (3) the quantification of the contribution
of a landscape element to landscape species
richness.
(1) The proposed model links species diversity to
landscape composition, but does not account for the
spatial arrangement of landscape elements. A marked
difference in diversity patterns was observed between
the edge and the core area for arable fields and meadows,
with the edge being generally more diverse than
the core. This effect can probably best be explained
in the context of spatial vicinism. That is, the diversity
within a patch depends not only on the conditions
within the patch, but a neighbouring patch can provide
a source of rhizomes and diaspores over a short
distance (Zonneveld 1995). In order to account for
such effects, a modified landscape model is needed
which contains information on the spatial arrangement
of landscape elements, and the diversity model should
be extended to include neighborhood effects.
(2) If we want to proceed from a surrogate approach,
i.e. an intuitive estimate based on theories,
models or concepts, to a truly correlative approach,
i.e. a statistically testable estimate (Duelli 1997) of
the species diversity of a landscape, we need unbiased
estimates of the true size of diversity components. In
the case study, which served for explorative purposes
only, we approximated the true species diversity by
the observed diversity of the sample. For a given diversity
measure, we assumed that comparability was
granted by the sampling design. Of the three measures,
species number is the most sensitive to sample
size, followed by Shannon index (Magurran 1988).
Simpson diversity is not only the most robust of the
three, but also the only one for which an unbiased estimator
exists (Lande 1996). Colwell and Coddington
(1994) reviewed extrapolation methods for the species
richness of a simple random sample. The approaches
should be extended to stratified samples and should
not rely on unrealistic assumptions about the spatial
distribution and abundance of species. Once the
methodological problems are solved, we can estimate
landscape species richness from a standardized sample
representing the pattern of land-use, which can be
derived from remote sensing.
(3) So far, we have not discriminated between
species. The model facilitates the comparison of diversity
components between habitat types and scale
levels, but it does not tell us which landscape elements
contribute most to landscape species diversity.
Species richness components are inflated by generalist
species that occur in most of the habitat types, whereas
specialist species that are restricted to a single type
receive little weight. An appropriate weighting to adjust
for specificity could help us proceed from mere
counting to assessing conservation value and deriving
strategies for biodiversity management.
Acknowledgements
This project has partly been financed by the Swiss
Agency of the Environment, Forests and Landscape
(BUWAL). We profited from suggestions by Peter J.
Edwards, Geobotanical Institute, Swiss Federal Institute
of Technology Zürich (ETH Zürich), Zürich,
by Thomas Wohlgemuth, Swiss Federal Institute for
Forest, Snow and Landscape Research (WSL), Birmensdorf,
and by two anonymous reviewers.
References
Allan, J.D. 1975. Components of Diversity. Oecologia 18: 359­367.
227
Allen, T.F.H. and Starr, T.B. 1982. Hierarchy: perspectives for ecological
complexity. The University of Chicago Press, Chicago.
Begon, M., Harper, J.L. and Townsend, C.R. 1996. Ecology.
Oxford, Blackwell Science Ltd.
Colwell, R.K. and Coddington, J.A. 1994. Estimating terrestrial biodiversity
through extrapolation. Phil. Trans. Roy. Soc. London B
Biol. Sci. 345(1311): 101­118.
Duelli, P. 1992. Mosaikkonzept und Inseltheorie in der Kulturlandschaft.
Verh. Ges. für Oekologie (Berlin 1991) 21: 379­384.
Duelli, P. 1997. Biodiversity evaluation in agricultural landscapes.
An approach at two different scales. Agr. Ecosys. Env. 62: 81­91.
Duelli, P. and Obrist, M.K. 1998. In search of the best correlates for
local biodiversity in cultivated areas. Biodiv. Cons. 7(3): 297­
309.
Forman, R.T.T. 1995. Land mosaics: the ecology of landscapes and
regions. Cambridge University Press, Cambridge.
Gaston, K.J. 1996. What is biodiversity? In Biodiversity: a Biology
of Numbers and Difference. pp. 1­9. Edited by K.J. Gaston.
Blackwell Science, Oxford.
Lande, R. 1996. Statistics and partitioning of species diversity, and
similarity among multiple communities. Oikos 76(1): 5­13.
MacArthur, R.H. 1965. Patterns of species diversity. Biol. Rev. 40:
510­533.
MacArthur, R.H. and Wilson, E.O. 1976. The theory of island
biogeography. Princeton University Press, Princeton.
Magurran, A.E. 1988. Ecological Diversity and Its Measurement.
Chapman and Hall, London.
O'Neill, R.V., De Angelis, D.L. and Allen, T.F.H. 1986. A Hierarchical
Concept of Ecosystems. Princeton University Press,
Princeton.
O'Neill, R.V., Gardner, R.H., Milne, B.T., Turner, M.G. and
Jackson, B. 1991. Heterogeneity and spatial hierarchies. In Ecological
Heterogeneity. Vol. 86. pp. 85­96. Edited by J. Kolasa
and S.T.A. Pickett. Springer-Verlag, New York.
Peet, R.K. 1974. The measurement of species diversity. Ann. Rev.
Ecol. Syst. 5: 285­307.
Whittaker, R.H. 1977. Evolution of species diversity in land communities.
In Evolutionary Biology. Vol. 10 pp. 1­67. Edited by
M.K. Hecht and B.W.N.C. Steere. Plenum Press, New York.
Zonneveld, I.S. 1995. Vicinism and mass effect. J. Veg. Sci. 5: 441­
444.