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Natural history museums can do better:
Simple analyses and visualizations of
collection data to attract more
researchers
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Claudio Bozzuto
Wildlife Analysis GmbH
Hannes Geisser
Natural History Museum Thurgau
Zurich, June 2022!
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Natural history museums can do better: simple analyses and
visualizations of collection data to attract more researchers
Technical report
Authors
Claudio Bozzuto Hannes Geisser
Wildlife Analysis GmbH Natural History Museum Thurgau
Oetlisbergstrasse 38 Freie Strasse 24
8053 Zurich 8510 Frauenfeld
Switzerland Switzerland
bozzuto@wildlifeanalysis.ch hannes.geisser@tg.ch
Date published | June 6, 2022.!
How to cite this document | Bozzuto, C., Geisser, H. (2022): «Natural history museums can
do better: simple analyses and visualizations of collection data
to attract more researchers». Technical report.
Wildlife Analysis GmbH, Zurich, Switzerland.
DOI: 10.13140/RG.2.2.35625.06243!
Copyright notice | The authors are the copyright holders, license CC-BY-NC-ND 4.0.
Drawings | Desktop (front page): Andrea Klaiber, Doppelkopf Grafik & Illustration,
Schaffhausen, Switzerland; © Wildlife Analysis GmbH. Butterflies: Eliane Huber,
Naturmuseum Thurgau, Frauenfeld, Switzerland; © E. Huber.
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Keywords | Biodiversity; Delaunay triangulation; diversity index; hierarchical clustering; !
Hill numbers; natural history collection; population genetics; Voronoi tessellation.
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Conflicts of interest | The authors declare no conflicts of interest.!
Author contributions | CB and HG conceived the study. CB contributed methods and
results; HG provided NHC data. CB wrote the manuscript
with input from HG.!
Acknowledgements | We thank Iris Biebach (University of Zurich), Holger Frick (Natural
history museum Basel), and Ana Petrus (University of Applied
Sciences of the Grisons) for insightful comments and discussions.
This study has been made possible thanks to the financial
support of:
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Lottery fund of the Swiss canton of Thurgau.!
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Natural History Museum of the Swiss canton of Thurgau.!
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Wildlife Analysis GmbH Phone +41 44 550 40 30 !
Oetlisbergstrasse 38 hello@wildlifeanalysis.ch!
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Contents
Abstract ………………….………………….………………….………………….……………
4
Introduction ...……….………………….………………….………………….……………….
5
Materials and methods ...……….………………….………………….……………………..
10
Data requirements .…………………………………………….……………..………….
10
A collection’s diversity ….…….………………………………………………..………...
11
Temporal data …………..…….………………………………………………..………...
12
Spatial data …………..…….…………………….……………………………..………...
14
Combination of different methods ………….….……………………………..………...
16
An example collection ……………………….….……………………………..………...
17
Results ...……….………………….………………….………………….……………………..
18
A collection’s diversity ….…….………………………………………………..………...
18
(Dis-)Similarity ……………………………………………..…….……………..………...
21
Spatio-temporal analyses ……………………………………………………..………...
22
Comparison of several NHCs ……………………………………………………..…….
27
Discussion ...……….………………….………………….………………….………………...
29
References …………….………………….………………….………………….……………..
32
Supplementary material …………….……………….....………………….…………………
35
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Abstract!
Over the last two decades, many studies have emphasized the value of natural history
collections (NHCs) for ecological and evolutionary research. Furthermore, with the current
biodiversity crisis worsening by the day, these specimens offer invaluable insights into past
changes, directly helping researchers to understand the current status and to propose apt
measures to halt the decline of species and communities. In parallel, the digitization of
collections continues being an on-going and pressing endeavor at the global scale. Several
achievements are already impressive, with global databases meanwhile offering online
access to many millions of specimen data. Unfortunately, especially the use of regional data
for regional-scale studies is partly hampered by small- to medium-size natural history
museums (NHMs) still awaiting digitalization. But even with completed digitization, many NHC
data continue being only available by request. As an incentive for NHMs to more actively and
rapidly share their data, in this study we present simple spatio-temporal analyses and
visualizations helpful to display NHC data in a research-oriented way. The aim is to allow
researchers a rapid online assessment of NHC data for their purposes. To this end, we
propose the use – alone and combined – of (i) well-known indices from biodiversity research,
(ii) cumulative and/or parametric representations of temporal data, and (iii) Voronoi
tessellations and Delaunay triangulations for spatial data. As an illustrative example, we
analyze butterfly collection data from a Swiss NHM. With today’s possibilities to quickly set up
web applications and with the modest attribute requirements per specimen for our methods,
we believe the implementation of these ideas will be affordable and quickly realizable, all the
more – to the benefit of research – if NHMs share forces. The ideas and methods will also
appeal to global initiatives ultimately aiming at offering access to the majority of NHCs. For
the time being, our study may serve as a regional incentive encouraging NHMs to aid
researchers generating much-needed knowledge on a rapidly changing natural world.! !
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Introduction!
« We argue that, whereas natural history collections !
and museums began with a focus on describing the !
diversity and peculiarities of species on Earth, they!
are now increasingly leveraged in new ways that!
significantly expand their impact and relevance. »!
(Bakker et al., 2020:1)!
The widespread advent of the internet in the 1990s, and with it the (potential) online access
for researchers and laymen to a vast number of natural history institutions, spurred an
unparalleled development in digitizing, sharing, and analyzing natural history collection (NHC)
data (Bakker et al., 2020; Graham et al., 2004; Nelson & Ellis, 2019). Researchers in
conservation biology, ecology, evolutionary biology, and global change biology, among other
fields, gained new and unprecedented opportunities to study natural phenomena in space
and time (e.g. Meineke et al., 2019, and references therein). The vast amount of data made
accessible was especially a treasure trove for the study of environmental changes affecting
biodiversity on Earth. One reason is that NHCs offer the unique opportunity to study long
periods of time, e.g. a century or more, thus potentially allowing to study phenomena before
massive anthropogenic effects started taking a considerable toll on nature (e.g. Bakker et al.,
2020; Bozzuto, 2020; Laussmann et al., 2021; Lister, 2011; Shaffer et al., 1998; Theng et al.,
2020).!
The role of natural history museums (NHMs) «to deploy their vast research collections,
systematics expertise, and knowledge of the planet's biodiversity to inform the stewardship of
life on Earth» (Krishtalka & Humphrey, 2000:611), however, had to be reinforced repeatedly
(e.g. Alberch, 1993; Krishtalka & Humphrey, 2000; Meineke & Daru, 2021). This is especially
true for the digitization process: despite already starting in the 1970s and reaching 5-10% of
specimens housed in NHMs worldwide two decades ago (Graham et al., 2004, and
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references therein), today for example in Switzerland approximately 17% of all specimens
housed in NHMs are digitized (Fig. 1), leaving – trivially – 83% not digitized (Swiss
Academies of Arts and Sciences, 2019).!
Figure 1 | Characteristics of Swiss natural history collections. Shown are the distribution (three histograms) of
the number of objects, the proportion of objects digitized (in percent), and the proportion of objects collected in
Switzerland (in percent), respectively, of natural history collections housed in 56 Swiss natural history institutions.
Furthermore, the two scatter plots show how the proportion of objects digitized and the proportion of objects
collected in Switzerland depend on the number of objects in the collections, respectively; for better readability, in
both scatter plots the axes have been inverted, with the number of objects shown on the y-axis. Source raw data:
Swiss Academies of Arts and Sciences (2019: Appendix I).!
While in the age of big data it might be tempting to think ‘the bigger the merrier’, several
recent studies suggest a more nuanced view. For example, Lavoie (2013) found that small
herbaria – like other NHCs from small- to medium-size NHMs usually containing specimens
collected regionally (Fig. 1, Table S1) – are being consulted as often as very large ones for
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research purposes. As a second example, Pilotto et al. (2020) showed that regional
biodiversity trends can deviate substantially from global ones, thus stressing the need for
scale-dependent assessments (see also Wyborn & Evans, 2021). !
The digitization status of NHCs could be coarsely classified as (i) no digitization, (ii) NHC data
(partially) available as a spreadsheet file, (iii) NHC data stored in an NHM-owned database,
and (iv) like (iii), but also connected off-/online to a global database such as GBIF (Edwards
et al., 2000). NHM-based database solutions can either be ‘idiosyncratic’ or seize software
knowledge and solutions of available packages such as Specify (Specify Collections
Consortium, 2021), among others. Even from such a coarse classification a trade-off
becomes quickly evident. Sharing NHC data through a global initiative such as GBIF requires
standardization of data, including potentially time-consuming issues like taxonomic matching
and geo-referencing. Small- to medium-size NHMs on the other hand, while housing
numerous and yet untapped detailed regional data, are often delayed with the digitization
process and/or with making available already existing data, partly due to scarce funding and
dedicated manpower (e.g. Garretson, 2021). Interestingly, however, for example in
Switzerland the leading NHMs are not necessarily more advanced in the digitization process
than medium-size institutions (proportionally speaking; Fig. 1), not least due to the vast
number of objects the leading NHMs house (Swiss Academies of Arts and Sciences, 2019).
Thus, a possible trade-off involves NHC data with a broad geographical extent in part already
made available by leading NHMs (e.g. through GBIF) vs. equally important regional data or
specimens not yet available to assist regionally rooted research questions, including
biodiversity trends at appropriate spatial scales. !
A second unfortunate circumstance hampering a more frequent use of NHC data for research
purposes relates to the way already digitized collections are made available to researchers.
More often than not, for projects focusing on regional ecological or evolutionary processes
researchers have to contact all relevant small- to medium-size NHMs individually, followed by
a non-negligible time to homogenize the data to find out whether these NHCs are useful in
the first place. The alternative of tapping global databases, unfortunately, is not very helpful
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for these researchers either, because in these global databases NHC data from small NHMs
are largely absent; besides, recently Beardsley et al. (2018) found that informatics knowledge
and skills are still rudimentary in academia to allow seizing all opportunities offered by global
databases, for example by using application programming interfaces. Finally, even
researchers focusing on individual leading NHMs will face hurdles with respect to assessing
the usefulness of these NHC data. In fact, even these NHMs (e.g. Berlin1, London2, Paris3) –
not differently from global initiatives like GBIF4 – tend to display available data in a ‘simplified’
way, using lists, summary statistics and/or maps displaying collection localities. However,
such approaches do seldom match research needs, which for example focus on how species
communities changed over time.!
Eventually, the majority of NHC data will be available through global databases. For the time
being, however, all NHMs should pursue their responsibility of informing the stewardship of
life on Earth more actively – including sharing forces among NHMs – by making available all
NHC data so far digitized to help researchers efficiently generate much-needed knowledge to
address and combat the ongoing biodiversity crisis. To this end, in this study we propose
simple spatial and temporal analyses and visualizations of NHC data to allow scientists a
rapid online assessment in terms of the respective research questions. The general idea is to
‘meet halfway’ between NHMs and research institutions. Clearly, it is not feasible to anticipate
all possible research questions, and therefore NHMs offering exhaustive analyses would be a
futile endeavor; the bulk of data inspection and analyses lie within the responsibility of
researchers. Furthermore, the aim is to offer access to data in their current status, well aware
(and clearly communicated) that for example an NHC is only partly digitized or that some
aspect of it is being refined. For NHMs to simply passively wait until potentially existing
spreadsheet files are requested does not, in our opinion, comply with the NHMs’ primary
institutional duties amidst a worsening biodiversity crisis. In sum, the proposed methods and
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1 https://portal.museumfuernaturkunde.berlin/!
2 https://www.nhm.ac.uk/our-science/data.html!
3 https://science.mnhn.fr/institution/mnhn/search!
4! !https://www.gbif.org/occurrence/search!
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ideas in this article not only should attract more researchers to use NHC data, they will also
make the value of small- to medium-size NHMs more visible. Finally, the proposed methods
will also be useful to NHMs themselves to better understand their collections and guide their
future development – needs exemplified by a recent survey (SPNHC, 2018); see the
Discussion for further details. !
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Materials and methods!
After addressing the data requirements for our proposed methods, we present the latter within
the four sub-sections A collection’s diversity, Temporal data, Spatial data, and Combination of
methods. We conclude this section by introducing the data used – a butterfly collection – to
present a selection of possible results, i.e. analyses and visualizations. Note that, in what
follows we do not cover simple summary statistics (e.g. distributions with mean, range, etc.)
already presented within several web-applications (see Introduction and Discussion for some
examples). For simplicity, in the following we will often mention an NHC as the sample to be
analyzed. Clearly, in an interactive online environment the user could choose any sample of
interest, for example with respect to taxonomy or spatial extent.!
Data requirements!
For the following methods, the requirements in terms of data from a specific collection are:!
! a specimen’s taxonomic attributes: species name, genus, family (and higher if sensible);!
! a collection date, where a year should suffice for most cases; nonetheless, for example for
phenology-related research questions collection day and month might be worthwhile
displaying (e.g. Belitz et al., 2021);!
! a collection locality: while we assume that most specimens have a geographic label (e.g.
country or city), either geo-referenced data provided by the collector can be used, or
alternatively some approximate coordinates in case no such data but instead a named
collection location was provided; for spatially implicit analyses, cities could be
conveniently used instead of locality coordinates (see sub-section Spatial data).!
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A collection’s diversity!
Specimens are characterized by different attributes, ranging from taxonomical ones to
collection attributes such as locality and date. The first proposed analysis summarizes the
diversity of an NHC in terms of a taxonomic attribute (e.g. species) and the respective
number of specimens, akin to analyses used in biodiversity assessments (e.g. Morris et al.,
2014, and references therein). In fact, although species richness (i.e. species counts) as a
metric is intuitive and frequently used to characterize an NHC (but also biodiversity
assessments), using relative species abundances more accurately captures (un-)evenness in
a sample (Chao et al., 2014). To this end, we suggest the use of Hill numbers because of
their intuitive interpretation, reflecting the ‘effective number of species’ in a sample, and
overcoming several shortcomings of species richness (Chao et al., 2014; Hill, 1973; Jost,
2019). Furthermore, Hill numbers can be easily derived from transforming biodiversity metrics
such as the Simpson or Shannon-Wiener index, respectively. For a given sample (e.g. an
NHC or a subset of it), a Hill number gives the ‘corresponding’ number of equally abundant
species, computed using the (potentially) uneven number of specimens in the sample. If all
species in the sample are represented with the same number of specimens, then there is no
difference between Hill number and the collection’s species number. Realistically, however, a
Hill number will be (much) lower than the latter, signaling that the specimens are (very)
unequally distributed among species in the collection. In this study, we will use the Simpson
index to derive Hill numbers; see the Supplementary methods for additional details. As a side
note, an additional and more general use of Hill numbers is to display so-called diversity
profiles, for example to compare the evenness of two families in a collection (Jost, 2019).
Finally, although we will restrict our attention to the species level, Hill numbers can be
computed for other levels of organization, for example using taxonomic families or collection
localities.!
The second proposed analysis of a collection’s diversity concerns the relative abundance
(RA) of a selected group of species, for example butterflies inhabiting a habitat of interest. As
recently shown by Gotelli et al. (2021), correctly computed RAs from NHCs in fact scale with
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RAs computed using field observations, therefore allowing researchers for example to
glimpse at how communities in a region of interest changed over time. Note, however, that
the main purpose of such analyses when lacking field data to calibrate RAs is to classify the
community’s species according to RAs or respective ranks. To derive RAs of species, a set of
specimens is analyzed by fitting a Dirichlet distribution, with the species list and the number of
specimens per species as the distribution’s arguments; see the Supplementary methods as
well as Gotelli et al. (2021) for further technical details and caveats.!
Finally, a collection’s diversity can also be described in terms of specimen similarity with
respect to some attribute. For example and similarly to phylogenetic trees, the collection’s
species could be hierarchically clustered based on their similarity in terms of collection
localities: the more localities are shared among two species, the closer they are in the tree
(dendrogram). The same approach could also be used to cluster specimens using collection
years within a broader region. Two frequently used indices are the Jaccard and Ruzicka
similarity index, respectively (Cha, 2007), both ranging from zero to one. To compute the
similarity between two sets using Jaccard’s index, for example the number of collection
localities two collections have in common is divided by the unique number of localities of the
two collections joined together. The idea of Ruzicka’s index is similar, but here the number of
localities is further weighted by the number of their occurrences in the collections; see Cha
(2007) for further details. Finally, the dissimilarity between two sets corresponds to the
complement of the similarity index, i.e. one minus the latter.!
Temporal data!
The afore-mentioned diversity metrics can be represented temporally – as a temporal profile
– either on a continuous time axis or by binning into time periods. More generally, we want to
propose three additional simple ways of organizing and displaying temporal data, namely the
use of cumulative data, sliding windows, and parametric representations of temporal data.!
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The use of cumulative data is one effective way to show and/or compare how fast (or not) a
collection or a subsets of interest (e.g. a taxonomic family) has grown over time: the
cumulative data could be displayed as absolute numbers or as proportion of the final, i.e.
current, number of attribute. A simple possibility is for example tallying up species-specific
specimens that have been populating the NHC (or subset): for a population geneticist, this
quickly reveals when and/or where enough individuals have accumulated to form a suitable
sample. Equally interesting is the accumulation of unique attributes in a collection, such as
the number of (new) species or (new) locations. Combining such data quickly reveals how
one attribute changed as a function of another one, e.g. unique species vs. unique collection
localities (see below, parametric representation).!
Instead of simply showing how NHC aspects of interest differ over time, say, on a yearly
basis, from a research point of view the use of a sliding window might be a better choice: the
use of a sliding window simply means computing a metric such as a diversity index for a
period of a determined length, 20 years say, and ‘sliding’ the operation stepwise over the
whole time period spanned by the NHC. There are several reasons why such a temporal
(pre-)analysis of data might be a sensible idea. For example, for population geneticists a
crucial life history attribute is generation length, and hence a generation length of 5 years,
say, does not require defining a ‘population’ (sample) for a single year. An analogous
argument is valid for ecological aspects: conservation biologists interested in community
composition and turnover expect such processes on a time scale (much) longer than per
year. For example, Blöchlinger (1985) used a period of approximately 20 years when
assembling a then valid butterfly species list for the Swiss canton of Thurgau.!
As a last idea of displaying temporal data we want to stress the usefulness of parametric data
representations. In mathematics, for example a system of two parametric functions means
that both equations have a parameter in common, for example time. Simply put, instead of or
in addition to plotting both equations as a function of time, both equations can be plotted one
against the other: for values on the x-axis – that depend on specific time points – values on
the y-axis are associated that depend on the same, corresponding time points; in such
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parametric representations the common parameter, in this example time, is implicitly given
along the (dotted) graph. The advantage of this approach is that it quickly allows showing
how, for example, two attributes of interests changed together (as a function of ‘each other’)
in the NHC; see the Supplementary material for additional details.!
Spatial data!
The cumulative display of collection localities (preceding sub-section) already allows showing
spatial characteristics of an NHC in an implicit way, that is, by neglecting the explicit
geographic location of the collection localities. In fact, this is an interesting approach for
NHCs (or subsets) that lack geo-referenced collection localities: by treating space implicitly,
the unique localities such as city names in the NHC could be considered. When specimens
are geo-referenced – either with original coordinates or with approximated ones – an NHC’s
spatial characteristics can be made more precise using a Voronoi tessellation, having the aim
of partitioning a geographic area covered by the specimens in a ‘meaningful’ and
parsimonious way.!
Computing a Voronoi tessellation for a given space, for example a geographic area, is akin to
fully filling a two-dimensional space like a wall with tilts (‘tessellation’). In contrast to identical
tilts, however, a Voronoi tessellation (potentially) leads to polygons (‘tilts’) that differ in size
and shape, because they reflect all collection localities that are the starting point of the
tessellation. Therefore, the partitioning of the whole space generates information about the
distribution and density of collection localities, potentially as a function of time, and the
respective specimens. !
It is beyond the scope of this study to introduce mathematical properties of and algorithms for
constructing Voronoi tessellations (and Delaunay triangulations; see below); recommendable
books are Aurenhammer et al. (2013) and Okabe et al. (2000). Simply put, computing a
tessellation starts with a set of producer points, for the present case collection localities. For
two neighboring localities, a perpendicular line is drawn halving the straight-line connection
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between the two localities. When this procedure is repeated for other neighbors of a focal
locality at a time, every locality will be surrounded by a polygon. Crucially, a) the locality is the
only one in its polygon, and b) every other point in space in that polygon has as its nearest
NHC collection locality the one producing the polygon in the first place. Therefore, given a set
of collection localities a geographic area is partitioned into space-filling polygons with
(potentially) different sizes and shapes. Further, every polygon – also called the dominance
area of the producer point (i.e. collection locality) – represents the space in the region only
covered by specimens collected at that specific collection locality. This could, for example,
hint at the confidence one might put on those specimens representing the diversity in the
whole area included in the polygon. The advantage of using a Voronoi tessellation is its
parsimonious nature with respect to space: the end result simply shows how an NHC is
spatially ‘organized’: instead of the many covariates shaping for example a habitat suitability
model, a species-specific tessellation shows how a region of interest is represented by
specimens in an NHC. Further, constructing Voronoi tessellations for a moderate number of
locations is computationally very efficient and fast, without involving for example typical GIS-
data. !
The so-called dual of a Voronoi tessellation is the Delaunay triangulation (Okabe et al., 2000).
While the former is based on perpendicular lines halving the straight-line connections
between two neighboring localities, a Delaunay triangulation is constructed using these
connection lines. We highlight two additional insights gained with constructing a Delaunay
triangulation. First, it offers a fast way of deriving spatial clusters, for example by only
retaining connections that are less than a predetermined distance apart; the latter could be
dictated by average dispersal distance. Second, a Delaunay triangulation offers a quick way
to quantify the spatial ‘holes’, so-called empty circles, in an NHC. On the one hand, the empty
circles could reflect habitat requirements of a species, so that a ‘hole’ is expected if that part
of the region is unsuitable for the species. On the other hand, empty circles allow quickly
spotting parts of a region that have been (unwillingly) neglected so far to populate an NHC.!
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We conclude this sub-section with a few refinements that may be appealing for displaying
NHC data. First, while we presented the construction of a Voronoi tessellation using collection
localities as ‘points’, a tessellation could also be constructed using areas: this is especially
interesting if the average diameter of collection localities (e.g. a particular habitat type) is not
vanishingly small compared to the center-to-center distance among them (Okabe et al., 2000,
and references therein). Furthermore, this approach could be worthwhile considering if,
instead of geo-referenced localities, cities or named localities are used to represent collection
sites. Second, an implicit assumption of a two-dimensional tessellation is that the whole
region of interest is potentially suitable for the species analyzed. At the opposite end are for
example aquatic organisms that require water bodies as habitat: in such case, it might be
more sensible to construct a one-dimensional tessellation for example along a river system or
the respective catchment areas (e.g. Dakowicz & Gold, 2002). Third, mathematically a
Voronoi tessellation can be easily computed using more than two dimensions. For three
dimensions, a habitat volume is partitioned into polyhedrons: this could be appealing for
specimens collected in a soil. As a second example, two space dimensions could be coupled
to a time dimension: this would allow constructing empty spheres in an NHC, that is, to
quickly show for which time periods and sub-regions there are no specimens in the NHC.!
Combination of different methods!
The focus of the results to be presented below is on combining different approaches
presented so far. In fact, it is such combinations that are of special interest to researchers: for
example, combining spatial and temporal data, or combining Voronoi tessellations with
diversity metrics, among many other possibilities. Further, all these analyses can be
performed with different taxonomic or ecological groupings: while a metapopulation ecologist
or population geneticist might be interested in single-species specimens, an environmentalist
might focus on sets of species tied to endangered habitat types, and an NHM collaborator
might focus on whole taxonomic families/orders up to the whole NHC.!
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An example collection!
To illustrate possible results of the proposed analyses and visualizations, we use the butterfly
collection of the Swiss NHM Thurgau as data source. Specifically, we will analyze all
specimens of the families Papilionidae, Pieridae, Nymphalidae, Satyridae, Lycaenidae,
Hesperiidae, and Zygaenidae collected in the Swiss canton of Thurgau; for simplicity,
henceforth we will refer to the specimens of these seven families as the NHC. Table S1
summarizes these data, including additional information on the whole Lepidoptera collection. !
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Results!
The aim of this section is to present a selection of possible analyses and visualizations, not
least to motivate creative thinking with respect to peculiarities of different NHCs and research
questions. Thus, the butterfly collection (Table S1) serves as an illustrative example, and we
refrain from providing a detailed analysis. Furthermore, while the following figures are
necessarily ‘flat’, visualizations will benefit from an interactive and – where appropriate –
three-dimensional online display (e.g. Plotly Technologies Inc., 2015). This online interactivity
also allows selecting and displaying data at the scale of interest, e.g. taxonomically and/or
spatially speaking; the following data selection is but one among many possibilities.!
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A collection’s diversity!
We start with the temporal profile of the whole butterfly collection over 130 years (Fig. 2)
using a sliding window of 20 years (cf. Blöchlinger 1985); we stress the term ‘profile’ and
caution against using visualizations like Fig. 2 to directly infer biodiversity dynamics ‘in the
wild’, where the samples were collected (but see Fig. 3b, relative abundances). For Fig. 2, we
highlight three results. First, over 60 years (1920-1980) on average 60 or more species are in
the collection for every time slide of 20 years, with a peak of 80 species in the second half of
the 1950s. Second, the proportional Hill numbers for the 20th century are in general high
(60% or higher), indicating a rather homogenous distribution of specimens per species. Third,
in the 1980s the collection has increased considerably in terms of specimens, which
temporarily lowered the respective Hill numbers, i.e. these new specimens temporarily
increased the inhomogeneity among species. In sum, the six decades from 1920 to 1980
would offer an interesting window into past diversity, for example to compare how certain
ecological communities or taxonomic groups changed (see next sub-section): in fact, a main
reason of insect declines in the 20th century is the agricultural intensification at an industrial
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scale after World War II (European Environment Agency, 2019). Note that the scope of a
visualization like Fig. 2 is to allow a bird’s view on a selected sample: additional analyses
would be needed to investigate the influence for example of collection effort or other variables
such as financial resources on the temporal diversity profile of a collection or subset of it.!
Figure 2 | Temporal diversity profile of a Swiss butterfly collection. Diversity of all butterfly species in the
Lepidoptera collection of the Natural history museum Thurgau (Table S1), computed with a sliding window
spanning 20 years; every year on the x-axis represents the last year of these windows. Shown are (legend):
species richness (number of species), the number of specimens (scaled), absolute Hill numbers, and proportional
Hill numbers (computed with respect to species richness). !
Figure 3 (next page) | Dendrograms and species distribution. (a) For the two families Lycanidae (blues; upper
row) and Zygaenidae (burnets; lower row), two dendrograms computed using Jaccard’s dissimilarity index are
shown, based on shared collection years (left column) or collection localities (right column). For all dendrograms,
the higher the value (max. 1) the less the respective attribute two species have in common. (b) Relative
abundance of burnet moth species (Zygaenidae) and respective ranks, computed for 3 different time periods. In
the right panel all marker sizes per time period are scaled relative to the most common species (rank #1), which
has the same marker size for all time periods.! !
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(Dis-)Similarity!
Instead of focusing on a temporal profile as done for Fig. 2, in Fig. 3a we show how the
species of the families Lycaenidae and Zygaenidae are similarly represented in the collection
in terms of shared collection localities or collection years. As for localities in common,
members of both families show a high degree of within-family dissimilarity. For years in
common, in both families there is a cluster of five species with a moderate similarity
(highlighted in light green), but especially for the blues many species do not share any
collection year. This result is an additional reason to use time periods (derived using sliding
windows): for ecological questions, having precise collection years in common is – in general
– of secondary importance.!
We now turn the attention to the relative abundance (RA) of burnet moth species
(Zygaenidae) in the collection (Fig. 3b), computed for three different time periods. While we
selected the contiguous time periods ‘ad hoc’, using a sliding window could help select
appropriate time periods (Fig. S1). Of the nine burnet moth species, at most eight are
represented in the NHC for a given period. Further, the six-spot burnet was the most common
in all periods, while several other species were always rare and some disappeared altogether.
This can be shown more clearly by ranking the species (right panel) using the RAs from the
left panel in Fig. 3b; in addition to the time-dependent ranks, the right panel also shows the
RAs in terms of the respective marker size that, for every period, has been scaled with
respect to the RA of the six-spot burnet. As in the left panel, it becomes clear that rare
species usually remained rare over time or disappeared altogether. Interestingly, however,
the transparent burnet (Z. purpuralis) and the narrow-bordered five-spot burnet (Z. lonicerae)
ranked 2nd and 3rd in the first period (1950-1970), respectively, but then disappeared.
Finally, the species ranking for 1990-2009 broadly matches the species abundance
categories of Hafner (2018) accompanying the current species list for the Swiss canton of
Thurgau. !
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Spatio-temporal analyses!
In contrast to Fig. 2, where species richness was presented as a temporal profile using a
sliding (temporal) window, an additional informative presentation is the use of cumulative
numbers of species over the time period spanned by the NHC, specifically by recording the
appearance of new species (Fig. 4a). At the species level, the same can be done tallying up
the number of the respective specimens, in Fig. 4a shown for the common blue (P. icarus)
and the six-spot burnet (Z. filipendulae). The added value then comes from combining two
different accumulation curves, for example unique species and unique collection localities
(Fig. 4b): in parametric representation, where time points are now implicitly shown using dots,
it quickly becomes clear how the NHC (or a subset of interest) has evolved over time. For
example, focusing on the whole NHC Fig. 4b makes clear that approximately 90% of the
eventual species richness had already been reached with approximately 50% of the eventual
collection localities in the 1970s. For the two example species, we find different evolutions:
while new specimens of the six-spot burnet entered the collection in proportion to new
locations – the red line in Fig. 4b approximately follows the diagonal – for the common blue
the accumulation resembles a sigmoid curve, with a highly increased collection of specimens
starting in the 1980s, when approximately the remaining 40% of specimens started populating
the NHC with 80% of the localities already represented in the collection by 1980. Ultimately,
the ‘preferred’ curve shape depends on a researcher’s question, maybe calling for
homogeneity of a sample in time and/or space. We reiterate that such parametric
representations could be very useful to display specimens without geo-referencing, and
instead using for example the associated city.!
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Figure 4 | Spatio-temporal changes. (a) Shown are, as a function of time, the cumulative number of new species
or specimens and collection localities, respectively, for the whole NHC and for the two species Common blue
(Poliommatus icarus) and Six-spot burnet (Zygaena filipendilae, legend). (b) Same data as shown in panel (a),
but now in parametric representation (years are implicitly shown as dots) and proportional to the respective values
in 2010.!
For all geo-referenced specimens in the NHC we now present several possibilities of using
Voronoi tessellations and Delaunay triangulations, starting with a historic overview. For Fig. 5,
we constructed three different Voronoi tessellations, based on specimens collected in three
consecutive time periods (panel titles), allowing two main insights. First, the spatial collection
density increased over time, also leading to smaller polygon sizes (dominance of collection
localities). These dominances are compared for the periods 1911-1960 and 1961-2010
(histogram): despite the dominances becoming smaller over time, the distribution in the most
recent period is still rather skewed: such information might not only be interesting for
researchers in using the NHC to understand past biodiversity, it is equally useful for the NHM
staff to evaluate current, and plan future, collection efforts. Second, the spatial collection
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effort in the last 50 years has included the south, southeast, and to a lesser extent the
westernmost parts of the canton of Thurgau, regions that were barely considered in the
preceding 50 years.!
!
Figure 5 | Spatial density of collection localities over time. Shown is the evolution of the NHC’s spatial density,
here captured by Voronoi tessellation polygons for three time periods (panel title). For the end years 1960 and
2010, the distribution of the respective locality dominances (polygon sizes in km2) are compared using histograms.!
!
An additional example of using a Voronoi tessellation is combining it with information on the
NHC’s diversity (Fig. 6a). For the whole period, we show the polygons for the northwestern
part of the Swiss canton of Thurgau, colored according to the species richness of the
respective geo-referenced collection locality (white dots). A ‘desirable’ regional pattern to look
for could be a cluster of adjacent small polygons with bright colors, like in the region northeast
from the city of Frauenfeld (red dot): for these collection localities, not only a moderate-to-high
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species richness is present in the NHC, but given the comparatively small polygon sizes the
region is also ‘densely’ sampled and presumably representative of the diversity in the field. A
further way of visualizing such data could be scaling species richness per locality by the
respective polygon size (a locality’s dominance; not shown): this would make the balance
between regional species richness and spatial density of the NHC’s specimens visually more
explicit.
One way of seizing the advantages of a Delaunay triangulation (the dual of a Voronoi
tessellation) is to spot empty regions in the NHC by computing empty circles (Fig. 6b). As
already mentioned in the section Materials and methods, empty circles could reflect habitat
requirements of a species or they highlight parts of a region that have been (unwillingly)
neglected so far to populate an NHC. The four selected circles shown in Fig. 6b – of which
the underlying geographical area could be easily computed – are situated in the southern and
eastern part of the canton of Thurgau, mirroring the results from Fig. 5, there based on
Voronoi tessellations. If a temporal dimension is added to the two spatial ones (Fig. S4), the
displayed empty sphere neatly summarizes the findings from Fig. 5, namely that the NHC
‘suffers’ from a considerable lack of specimens from the southern part of the canton, for the
early period of the collection.
At the species level, an advantageous and efficient way of using a Delaunay triangulation is
to construct spatial clusters (Fig. 7). For example, a population geneticist might be interest in
studying the consequences of isolation-by-distance. For a selected period and given an
average dispersal distance of the species, the clustering quickly shows which specimens
could be considered to form a ‘sub-population’, to be contrasted with other ones. For the
common blue (P. icarus) and the six-spot burnet (Z. filipendulae), where for visual purposes
we arbitrarily selected 6 km as a cut-off, the clusters of the six-spot burnet (including single-
locality ones) are more numerous and cover a larger part of the canton; for the common blue,
the visualization quickly reveals a big cluster in the middle parts of the canton, covering
approximately 50% of the north-south axis. At the community level, the described clustering
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(a)
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(b)
Figure 6 | Spatial analyses. (a) Partitioning of space using all collection localities as producer points for a Voronoi
tessellation; shown is the northwestern part of the Swiss canton of Thurgau, with the city of Frauenfeld marked in
red. Brighter polygon colors indicate higher biodiversity (Hill numbers; color bar). (b) Based on a Delaunay
triangulation using all collection localities, the map shows the 4 largest empty circles located within the canton’s
boundary (on land).
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approach could also be used to highlight (i.e. visually connect) communities from collection
localities with a similar species composition, for example based on Jaccard’s index (Fig. S2).
Note, however, that clustering based on a Delaunay triangulation is focused on ‘nearest
neighbors’: different algorithms (see e.g. Dale, 2017) will have to be used to highlight globally
connected communities (Fig. S3).!
Comparison of several NHCs!
We conclude with the possibility of comparing NHCs from different museums, in case such
data are digitally available. From a researcher’s and computation point of view, it might be
interesting to select a ‘minimum’ number of NHCs while maximizing the presence of some
attribute(s) of interest. To illustrate this approach, we randomly split the butterfly collection
into 4 virtual separate collections (Fig. 8): the marker sizes in the 4 corners in each panel
scale with the number of specimens in the (virtual) collections. Using Ruzicka’s index, we
computed all pairwise similarities (colored lines), and this analysis for example quickly offers
two insights. First, the small collection in the upper left corner is very similar to the big
collection in the lower left corner in terms of species, collection localities, and collection years
(connection lines almost yellow): the smaller collection is basically ‘fully’ represented in the
bigger collection. Second, a different small collection (lower right corner) shows a pronounced
dissimilarity to the big collection in the lower left corner in terms of all three attributes
(connection lines tending to dark green): depending on the question at hand, for the
researcher it may therefore be sensible to include this small collection into the final analyses
because of the complementarity to the big one.!
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Figure 7 | Spatial clusters. Collection localities and clusters (based on a Delaunay triangulation) are shown for
the common blue (Poliommatus icarus; blue) and six-spot burnet (Zygaena filipendulae; red). Localities (dots) that
are less then 6 km apart form a cluster and are connected by lines (Delaunay edges).
!
Figure 8 | Comparing different NHCs. To illustrate the approach, the butterfly collection of the NHM Thurgau has
been randomly split into 4 virtual separate collections; the marker sizes in the 4 corners in each panel scale with
the number of specimens in that (virtual) collection. In each panel, all pairwise NHC comparisons are represented
by a colored line, where the color reflects Ruzicka’s similarity index (color bar) and a brighter color indicates higher
similarity. The specimens in the 4 collections are compared with respect to three attributes (panel title).! !
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Discussion!
Specimens housed in natural history museums (NHMs) worldwide offer a unique opportunity
to understand the past and produce knowledge to alleviate the current biodiversity crisis. As
sketched in the Introduction, data availability for researchers interested in or already working
with natural history collection (NHC) data continues being ‘sub-optimal’: many NHCs are still
awaiting digitization, and not few already digitized NHCs are only available by direct request
to the respective NHM. Clearly, NHMs can do better, by providing their data online in a
research-oriented way. Besides, analyses and visualizations of NHCs are also useful to
NHMs themselves (e.g. SPNHC, 2018), for example to characterize the status quo of an
NHC, to guide future collection efforts, and to evidence the value of NHMs and their efforts
«to inform the stewardship of life on Earth» (Krishtalka & Humphrey, 2000:611). As an
incentive, in this study we have proposed several analyses and visualizations to allow
researchers a quick online assessment of an NHC’s suitability for the question(s) at hand. As
a side note, despite our focus on NHC data and how these could assist research in the
natural sciences, the methods are general enough to be used for example in the humanities
with collections of cultural objects. In the following, we broaden the view beyond
methodological aspects to discuss some issues and questions surrounding a rapid transition
to a more pronounced effort by NHMs to display their already available data online.!
One issue often heard with respect to making NHC data available online concerns data
quality. While it is laudable that NHM curators strive for ‘perfect data’ (Krishtalka & Humphrey,
2000), it is also true that – if clearly communicated and appropriately flagged – even
‘imperfect’ or partially available data can be very useful to tackle a scientific question, with
appropriate (statistical) methods. In fact, several studies have tried to understand how reliable
or biased NHC data are and have proposed solutions/corrections to such ‘imperfections’ (e.g.
Daru et al., 2018; Meineke & Daru, 2021; Ward, 2012). On the other hand, some global
initiatives stress the need for geo-referenced data when receiving new NHC data from NHMs.
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While such data can indeed be useful (e.g. Fig. 5-7), the process of retrospectively geo-
referencing is time- and, more generally, resource-consuming. Moreover, such retrospectively
generated data are always prone to uncertainty to a certain extent, all the more for specimens
collected, say, a century ago with sparse metadata available (if at all). We suggest the focus
to shift from the needs of NHMs and platforms displaying currently available data to the needs
and challenges researchers face: they know best what kind of data suits the envisioned
analyses, existing and newly developed ones. Nonetheless, because many NHMs employ
highly trained scientists, implementing the here proposed methods would certainly benefit
from a tight collaboration between academic researchers and NHM professionals.!
Who should implement all of this? Given the pressing need to make NHC data available as
fast as possible, there probably is no unique solution spanning the needs over the whole
range from small-sized NHMs to global data initiatives. With regard to digitization, it is true
that many NHMs are under-funded and thus have difficulty in allocating enough resources to
this process (e.g. Garretson, 2021; Shultz et al., 2021). It is also true, however, that many
national and international agencies and institutions are increasing funding opportunities to aid
digitization (e.g. Bøkman, 2021; SwissCollNet, 2021; van Hoose, 2021). It would be probably
helpful for small- to medium-size NHMs to share forces when applying for funding, but also
tackle the digitization process together, seizing synergies, discussing uncertainties (data-
related and otherwise), and efficiently finding solutions to obstacles. Furthermore, sharing
forces in many situations probably means acting regionally: while this may appear to
counteract global efforts envisioned by many initiatives, as mentioned in the Introduction
regional-scale initiatives can help generate knowledge that is equally relevant to
understanding variation in global biodiversity processes.!
With regard to analyzing and visualizing digitized NHC data, nowadays fortunately many tools
are available to quickly set up web applications for interactive data visualizations (e.g. Google
LLC, 2021; Mailhot, 2021; Plotly Technologies Inc., 2015; Sievert, 2020). For example, the
COVID-19 pandemic has spurred the set-up of many reliable websites summarizing and
computing epidemic-related information and metrics based on several data streams;
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successful sites have even be created by private persons and researchers in no time (e.g.
Probst, 2020; Systrom & Vladeck, 2020). Nonetheless, here too sharing forces among NHMs
will certainly facilitate setting up useful, research-oriented web applications. Furthermore,
regionally focused projects will have the advantage of connecting neighboring NHCs that,
together, offer an extended regional window into past diversity. In sum, the urgency of the
task can nowadays easily be met in terms of programming a web application, even as a
‘temporary’ solution until all available data will eventually be accessible through global
initiatives.!
Krishtalka and Humphrey (2000:611) started their article with an (un)willingly witty wake-up
call:!
« As natural history museums prepare to enter the twenty-first century, much of their
core still sits in the 1800s. Despite enormous expansion in collections and exhibits
during the past 100 years, many museums still resemble Victorian cabinets of
natural history. Many still behave as isolated island endemics undergoing genetic
drift, eschewing the hybrid vigor and collaborative power of a community. »!
Fortunately, the situation today is (a bit) different, but natural history museums can do better:
they have to embrace the urgency and trade-offs surrounding current applications of NHC
data to aid researchers worldwide in producing timely and much-needed knowledge on the
dangerously continued biodiversity crisis. Especially small- to medium-size institutions should
more actively embark in this community-wide endeavor: the precious regional data these
institutions harbor are of particular relevance for understanding global changes.!
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Supplementary material!
Supplementary methods ...……….………………….………………….…………………….
36
Supplementary Table S1 ……....………………………..….…………….…………………..
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Supplementary Figures S1-S4 ………..........……..….………………….…………………..
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Supplementary methods!
Hill numbers!
To derive the Hill number 2D (see below) used in the main text, we start with the Simpson
index !=!!
!!
!!!, where S is the number of species in the NHC (or a subset of interest), and
!!=!!! is the relative (i.e. proportional) presence of species i in this set, with !!
specimens among the total number N of specimens (of all species); for an NHC, !!
! can be
interpreted as the probability of randomly picking two specimens from the collection pertaining
to the same species i. Often, the Gini-Simpson index (1 – !) is used to quantify the diversity
of a sample, where values approaching 1 indicate a high diversity, and values approaching 0
a low one.!
The Hill number 2D, here with q = 2 (see Hill, 1973), used in the main text is computed as 2D
= 1/!. If q is set to 0, we recover species richness, and with q = 1 the Hill number gives the
evenness based on the Shannon-Weaver index.!
Relative abundance (Dirichlet distribution)!
To correctly estimate the relative abundance (i.e. proportion) of species in the NHC (or a sub-
set of interest), the Dirichlet distribution should be used (Gotelli et al., 2021). Hereto, the
distribution’s ‘parameters’ are a species list and a second list with the number of specimens
per species in the set of interest. Unfortunately, there is no simple expression for the
distribution’s mean or variance (e.g. to compute a 95% confidence interval). As suggested by
Gotelli et al. (2021), given the two lists a bootstrap of a high enough number of iterations of
random sampling from the Dirichlet distribution can be performed to estimate the mean
relative abundance of species and (if needed) a 95% confidence interval; see Table S2 in
Gotelli et al. (2021) for an illustrative example set.! !
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Parametric representation of data!
To motivate the use of parametric representations of data as proposed in the main text, we
here show a very simple example of a system of two parametric equations. For this example,
we assume that both the number of specimens and collection localities in an NHC,
respectively !! and !!, growth linearly with time ! according to
!!=!!+!!!,!
!!=!!+!!!.!
If we are interested in expressing the number of specimens as a function of collection
localities, i.e. !!, we first solve the locality equation for time, leading to !=!!−!!!!.
Next, we substitute this expression into the specimen equation, leading to
!
!!=!!+!!
!!−!!
!!
,!
which, for this simple example again is a linear equation. Thus, we have achieved a
dependency of the number of specimens on the number of collection localities. However, time
is not explicitly present anymore but only considered implicitly through the time points at
which !!, and consequently !!, are measured. When working with data, for example
using two arrays for !! and !!, all elements in these arrays are simply ordered according
to the time points when both quantities were measured.! !
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Supplementary tables and figures!
Table S1 | Summary of the Lepidoptera collection of the Natural history museum Thurgau. For the whole
collection and the seven families included in this study, the table shows (from left to right): the number of
specimens; the proportion of specimens collected in Switzerland and the canton of Thurgau, respectively (in
percent, rounded); the proportion of geo-referenced specimens collected in Switzerland (in percent, rounded).!
Number of
specimens
Percent (rounded) of specimens from …
Percent (rounded)
of geo-referenced
Swiss specimens
… Switzerland
… canton of Thurgau
Lepidoptera
22’130
94
51
57
Butterflies
4’221
88
31
33
Papilionidae
206
84
19
20
Pieridae
566
89
43
39
Nymphalidae
1’138
83
36
33
Satyridae
911
91
22
31
Lycaenidae
1’017
92
27
33
Hesperiidae
383
90
37
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Figure S1 | Presence of two butterfly families (Lycaenidae, Zygaenidae) over time in the NHC. Note that, in
contrast to Fig. 2, each point in the current figure states whether the respective species is present in the collection
over a time window of five years (vs. 20 years in Fig. 2). ! !
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!
Figure S2 | Spatial biodiversity similarity (local). The map shows all collection localities (white dots) from the
butterfly collection in the Swiss canton of Thurgau (cf. Table S1). After computing a Delaunay triangulation based
on these localities, every edge was colored using the respective pairwise Jaccard similarity index, where brighter
colors indicate a higher similarity in species composition (color bar). Edges with a value less than 0.1 are not
shown for better readability.!
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Figure S3 | Spatial biodiversity similarity (global). The six panels show six different collection locality clusters
(connected components) at the ‘global’ scale (as opposed to a local level as shown in Fig. S2, there based on a
Delaunay triangulation), with the number of localities reported in the respective title. Based on the Jaccard
similarity matrix for all localities (species composition similarity), for illustrative purposes only pairwise similarities
ranging from 0.45 to 0.6 are shown. Note that all six connected components are independent of each other. For
further methodological details see e.g. Dale (2017). !
! !
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!
!
Figure S4 | Largest empty spheres (time-space). In addition to two spatial axes (x and y, in kilometers; cf. Fig.
6b), the figure is increased by a third, temporal axis (z, in years), with the aim of computing and displaying empty
spheres. Every empty sphere – for illustrative purposes only one is shown – does not contain any collection event,
i.e. in a given year at a given place. The dots show all collection events in the analyzed butterfly collection (cf.
Table S1). !
