LIMNOLOGY
and
OCEANOGRAPHY: METHODS
Limnol. Oceanogr.: Methods 9, 2011, 432–442
© 2011, by the American Society of Limnology and Oceanography, Inc.
Reconstructing the realized niche of phytoplankton species from
environmental data: fitness versus abundance approach
Nico Grüner1*, Christina Gebühr2, Maarten Boersma2, Ulrike Feudel1, Karen H. Wiltshire2,3, and Jan A. Freund1
1
Institute for Chemistry and Biology of the Marine Environment (ICBM) – University of Oldenburg, P.O. Box 2503, 26111
Oldenburg, Germany
2
Alfred Wegener Institute for Polar and Marine Research, Biologische Anstalt Helgoland, P.O. Box 180, 27483 Helgoland, Germany
3
School of Engineering and Science, Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany
Abstract
The classification of the ecological niche and the grouping of species into generalists and specialists are established ecological concepts. In this study, we compare two methods for the calculation of the realized ecological
niche from long-term species data. As the first method, we present a new approach to reconstruct the realized
niche not in terms of abundance but via a measure of fitness (optimal niche), which we call the Optimal Niche
Estimate (ONE). The second method, the outlying mean index (OMI) analysis, is performed with abundance
data for calculating the ecological niche. We demonstrate and discuss differences between methods by applying them to time series of three phytoplankton species from the Helgoland Roads long-term data set: Ceratium
fusus, Odontella regia, and Paralia sulcata.
the typically reduced n-dimensional hypervolume that is actually occupied by a species is called the realized niche, an expression also found in Hutchinson (1957).
In experimental ecology, the transition from the fundamental to the realized niche is often paralleled by the step
from laboratory experiments to field work. While in a typical
laboratory experiment, all but a few abiotic factors are kept
constant and biotic factors are preferably excluded, in the field
all factors including the biotic or interaction milieu (McGill et
al. 2006) (competitors, predators, and prey) are dynamic quantities and prone to fluctuations. Therefore, projections of the
fundamental niche reconstructed from laboratory experiments may vastly differ from corresponding projections of the
realized niche reconstructed from field data.
Several statistical methods exist for describing the ecological niche of species. These include measuring the individual
distribution of species between several environmental parameters (Colwell and Futuyma 1971), quantifying niche breadth
using the proportional similarity index (Feinsinger et al. 1981)
or determining species-environment relationships using ordination methods (ter Braak 1986; Dolédec and Chessel 1994).
A relatively recent method measures the distance between the
average habitat conditions used by a species and the average
habitat conditions of the sampling area or period (Dolédec et
al. 2000, after Hausser 1995). Because this method determines
the marginality of a given species, it is called outlying mean
index (OMI) analysis. The niche parameters are calculated by
an ordination technique, weighting the environmental factors
The concept of an ecological niche was introduced by J.
Grinnell (1917). The concept was popularized by G. E.
Hutchinson (1957) who formally identified a niche as an “ndimensional hypervolume”, where n-dimensional refers to the
number of all ecological factors relative to a species and comprising all environmental conditions “which would permit
the species S1 to exist indefinitely”. Because this definition
considers a species under defined conditions, it represents the
fundamental niche, a term Hutchinson credited R. H.
MacArthur with. As a result of biological interactions a species
hardly ever realizes the full size of its fundamental niche, and
*Corresponding author: E-mail: gruener@icbm.de
Acknowledgments
We thank the crews of RV Aade and RV Ellenbogen for their dedication to the long-term monitoring program, and we acknowledge all
those who measured the physicochemical parameters, temperature, and
nutrients and counted phytoplankton samples at Helgoland Roads. We
thank Germany`s National Meteorological Service (Deutscher
Wetterdienst) for providing the wind speed and sunshine duration data.
We thank John Smol and two anonymous reviewers for help in clarifying
this manuscript and Sabrina Brüse for fruitful discussions. This study is
partly funded by the German Research Foundation (DFG) and is part of
the priority program 1162 “The Impact of Climate Variability on Aquatic
Ecosystems: Match and Mismatch Resulting from Shifts in Seasonality
and Distribution” (AQUASHIFT), and partly by the German Federal
Ministry of Education and Research (BMBF, FK2 03F0609A and
03F0603C).
DOI 10.4319/lom.2011.9.432
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Realized niche: fitness versus abundance
Sampling and data sets
In 1962, the Biologische Anstalt Helgoland started a periodic water sampling and measurement at Helgoland Roads,
North Sea (54°11.3¢N; 7°54.0¢E) (Wiltshire and Manly 2004).
Surface water samples were taken three times per week until
1974 and five times per week thereafter (Franke et al. 2004).
The water samples were taken from the surface as representative of the entire water column, which is generally well-mixed
as a result of strong tidal currents (Hickel 1998). Daily identification and quantification of the phytoplankton community,
the photometrical determination of inorganic nutrients (such
as nitrite, nitrate, ammonia, phosphate, and silicate) and the
measurement of temperature, Secchi depth and salinity were
carried out (Wiltshire 2004). Due to missing values of Secchi
depth and silicate concentrations in the period from 1962-67,
we used the long-term data of the phytoplankton and the
physico-chemical parameters from 1968 to 2008. This longterm abiotic dataset was reviewed and quality controlled by
Raabe and Wiltshire (2009) through a careful comparison with
other available data sets [e.g., BSH (Hamburg), ICES (Copenhagen) and MUDAB (Hamburg)] for the North Sea.
Sunshine duration (hours) and wind speed (Beaufort scale)
were provided by Germany’s National Meteorological Service
(Deutscher Wetterdienst, DWD). The environmental variables
included in the analysis are thus temperature, Secchi depth,
salinity, concentrations of total dissolved inorganic nitrogen
(sum of ammonium, nitrate and nitrite), phosphate, silicate,
sunshine duration, and wind speed.
As an additional environmental factor, we included this
interaction milieu into our analysis. This interaction milieu
was established by the sum of the abundances of 23 phytoplankton species as a measure for inter- and intraspecific competition. To include the latter, the three investigated species
(Ceratium fusus, Odontella regia, and Paralia sulcata) here are
part of this sum. No formal zooplankton was included into
this data, although some of the dinoflagellates also graze on
the diatoms. We took these 23 species as the most abundant
and representative ones in this dataset. The species were: Ceratium furca, Ceratium fusus, Ceratium horridum, Ceratium lineatum, Ceratium tripos, Eucampia zodiacus, Guinardia delicatula,
Guinardia striata, Noctiluca scintillans, Odontella aurita, Odontella regia, Odontella rhombus, Odontella sinensis, Paralia sulcata,
Phaeocystis ssp., Porosira glacialis, Prorocentrum micans, Protoperidinium depressum, Scrippsiella ssp., Skeletonema costatum,
Thalassionema nitzschioides, Thalassiosira rotula, Torodinium
robustum. These species were representative species of this
habitat (Hoppenrath 2004; Wiltshire and Dürselen 2004). Two
species were pooled to genus level due to the lower abundances (Hoppenrath 2004).
We demonstrated our niche analysis with three members of
this list: Ceratium fusus, Odontella regia and Paralia sulcata. The
OMI method was recently applied to the long-term data series
of Paralia sulcata at Helgoland Roads, and hence to connect
our analysis to previous work (Gebühr et al. 2009), we selected
by the species’ abundance. The OMI method gives a niche for
the analyzed species characterized by niche position and
niche breadth. Niche position is a measure of the distance
between the mean habitat conditions used by this species and
the mean habitat conditions of the sampling site. Therefore,
niche position describes the location (center) of the realized
niche in the n-dimensional hypervolume. Niche breadth
describes the tolerance of a species associated with the environmental parameters in the habitat, i.e., the expansion of the
niche in the hypervolume (Dolédec et al. 2000; Heino and
Soininen 2006; Tsiftsis et al. 2008).
Until now, all quantitative methods of niche description
were abundance-oriented. Here, we propose and investigate a
fitness-oriented approach, the Optimal Niche Estimate (ONE).
A species-specific optimal niche is reconstructed by extracting
those moments of a growth period in which the selected
species grows fastest. Hutchinson’s original notion defined a
niche as the n-dimensional hypervolume where a species can
exist indefinitely. In a seasonally varying environment, we can
think of no easy way to separate conditions for indefinite existence from those which lead to extinction. Fastest growth,
however, reflects optimal conditions. We estimate the volume
of a correlation ellipsoid for the moments of fastest growth
(high fitness) and assess its value in relation to that of the
ellipsoid of environmental values for the full time range,
much in the same way as is done in the OMI method.
Through this relationship and a resampling procedure to test
for the statistical significance, we identify specialists and more
generalized species. Identifying fitness with fastest growth of
the species, our approach places emphasis on the aspect of fitness and has to be seen in contrast to all approaches based on
abundance.
Here, we demonstrate the reconstruction of different
niches of three phytoplankton species (Ceratium fusus, Odontella regia, and Paralia sulcata). Our application is based on the
Helgoland Roads long-term data (1962-2008), a high frequency (on weekdays, Monday till Friday) time series comprising species cell counts (biotic factors) and physico-chemical parameters (abiotic factors) (Wiltshire 2004; Wiltshire et al.
2010). We discuss the differences between our ONE fitness
approach and the abundance-based OMI analysis, recently
applied to a part of the Helgoland Roads data series (Gebühr et
al. 2009). Finally, we show how to extend and refine niche
analysis by including features of correlation ellipsoids beyond
the mere volume.
Material and procedures
Sampling site
Helgoland is located in the German Bight about 65 km off
the German coast in a hydrographically dynamic area, which
can be under the influence of oceanic as well as coastal waters
(Bauerfeind et al. 1990). The sampling site, Helgoland Roads
(54°11.3¢N; 7°54.0¢E) is situated between the two small islands
of Helgoland.
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Realized niche: fitness versus abundance
• After one detected inflection point, the abundance curve has
to fall below 10% of the annual maximum before accepting
the next point. Because raw data exhibit high variability on
short time scales, blooms with two closely connected peaks
can appear. These interspersed dips presumably resulted from
algal patches drifting through the narrow channel between
the two islands at Helgoland.
P. sulcata and added the two other species, O. regia as an example for a species occurring the whole year and C. fusus as a typical summer species. Therefore, these species were taken here
as an example to demonstrate the procedure. The quality of
the phytoplankton data were controlled by Wiltshire and
Dürselen (2004). The comparison of the electronic database
with the original lists recorded by the different persons and
inclusion of available metadata were an integral part of this
evaluation.
Data preprocessing
The abundance data were pretreated using a smoothing
spline algorithm (Reinsch 1967), programmed and supplied
by Mieruch and coworkers (Mieruch et al. 2010), and abiotic
data were interpolated linearly to fill the short gaps (i.e., weekends, missing values due to storm events, etc.) in these time
series. These and all other computations for the fitness-based
approach (Method 1: ONE) were executed in MATLAB (MathWorks 2009).
Method 1: Optimal niche estimate (ONE)
Detection of the inflection points
As a measure for the fastest growth of single phytoplankton
species the inflection points of the smoothed abundance
curves were computed. These points were extracted for every
bloom event and as net growth was highest at these days, we
propose that these indicated the times of highest fitness of the
species. The extraction was performed by an algorithm obeying the following criteria (Fig. 1):
• To exclude inflection points at rather low values of
smoothed cell counts, we set an acceptance threshold at 10%
of the annual maximum. The use of a percentage is due to the
normal but large interannual variation of peaks.
It is possible to detect more than one inflection point per
year, in particular for species with a spring and summer
bloom. The result of this algorithm was a list containing the
times of maximal net growth (high fitness) for each species
investigated.
Principal component analysis and visualization
It is complicated to visualize a large number of factors [in
our case a total of nine: 8 abiotic environmental factors plus
the biotic interaction milieu (sum of 23 species)]. Hence, to
reduce this high dimensionality, we performed a principal
component analysis (PCA) of the multivariate data series constituted by all considered environmental factors (McGarigal et
al. 2000; Handl 2002; Jolliffe 2004). Fig. 2 shows how the variance was distributed among the nine principal components.
This was the share of the total variance each principal component (PC) accounted for (PC1: 31%, PC2: 18%, PC3: 11%)
and showed the consequences of the dimension reduction.
The cumulative variance contains the variance explained by
the considered PCs.
According to the scree-plot criterion (Cattell 1966), the
reduction to two dimensions would be appropriate. By taking
the Kaiser-Guttmann criterion (Guttman 1954, Kaiser 1960),
only PCs with an eigenvalue larger or equal to one should be
included in the analysis. Because of the normalization before
the PCA, PCs with an eigenvalue larger than one explain
more variance than a single original variable (dotted line in
• Only inflection points on ascending parts of the abundance
curve were taken into account.
Fig. 1. Detection of one inflection point (filled black circle) shown for an
Fig. 2. Fractions of the total variance (left ordinate) and cumulative variance (right ordinate) distributed among the 9 principal components.
algal bloom of C. fusus, normalized to the annual maximum (smoothed
data, line: 10% of the annual maximum).
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Realized niche: fitness versus abundance
Fig. 2). This was the case for the first three principal components of our PCA (third PC 0.99). We chose these criteria
because of the simple and practical application. Another reason for the selection of three PCs was that we had to find an
appropriate solution for the stretch of taking enough PCs and
not losing too much information on the one hand and getting a high estimation error by increasing the dimension on
the other hand (see “Assessment” for a test of the sensitivity
to axes number). We applied this classical test, but one can
argue if this is the best method. Therefore, we give the advice
to check for the results of the PCA. The environmental factors
included in this PCA should also be selected with care. One
can see in this approach that we included some climate data
from the DWD to the analysis, which we considered as
important environmental factors for phytoplankton growth.
Light, included through sunshine duration, was doubtlessly
an important factor here. By including irrelevant factors, the
reduction to lower the dimension might cause misinterpretations through unimportant information in the principal
components.
Geometrically speaking, a PCA translates the origin of the
coordinate system into the data cloud’s center of gravity
(defined by the vector of mean values) and aligns the basis
vectors with the principal axes of the correlation ellipsoid
(Brandt 1999) via rotations. The result of the PCA has same
dimension than the original data set, but normally a projection on a lower dimensional space is aspired. A result of this
projection is shown in Fig. 3 for the three species. The light
gray points correspond to the bulk of the whole dataset and
are species-unspecific whereas the bigger black circles indicate
the environmental conditions at the inflection points, i.e., the
instants of fastest growth and were highly species specific.
This enabled a comparison of the environmental and the
species-specific cluster.
The varying lengths of the principal axes reflect different
size of the hypervolume in different directions of projection
space. To obtain one quantity for the niche width, we computed the product of the axes lengths. This quantity was the
volume (up to a dimension specific proportionality factor,
e.g., p for 2 d and 4/3p for 3 d) of the correlation ellipsoid that
was estimated from the inflection point (ONE-) cluster. Since
the length of the i-th principal axis was given by the square
root of the i-th eigenvalue li of the covariance matrix (Brandt
1999) the product of the first n principal axis
n
lengths was given by the expression Π li . This volume of
i =1
the correlation ellipsoid is an unbiased measure. With the
lengths of the longest and shortest ellipsoid’s semiaxis, we further characterized the shape.
We repeated the estimation of a covariance matrix but now
using the whole dataset and computed the volume of the
related ellipsoid in projection space. An illustration of these
ellipsoids for the chosen three species is displayed in Fig. 4.
Fig. 3. Species-unspecific principal component cluster (light gray points)
and the species-specific inflection points (filled black circles). For a better
visualization, here we display only the first two principal components.
The light gray AP-cluster ellipsoid in Fig. 4 (here and in the
following AP is used as an acronym for “all points”) is species435
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Realized niche: fitness versus abundance
unspecific and is identical in all three panels. By contrast, the
black ONE-ellipsoids, related to species-specific inflection
points (filled black circles), exhibits significant variation thus
demonstrating their species-specific character. A normalization of the ONE-ellipsoid to the AP-ellipsoid was executed and
thereby the results were on a scale between 0 and the order of
1. The other advantage of this standardization was that the
dimension specific geometrical factor dropped out when computing the ratio.
Statistics
To decide whether a species should be regarded as specialist
or nonspecialist, we had to assess the normalized volume of
the ONE-ellipsoid. Even so, this still left us with the uncertainty resulting from the fact that the estimation of correlation ellipsoids from a possibly small number of points introduces considerable estimation errors. To estimate the range of
these statistical fluctuations, we adopted a resampling procedure: The same number of points used to estimate the ONEellipsoid was picked randomly from the AP-cluster and the
corresponding volume was computed. This step was repeated
10000 times to test the null hypothesis, which assumes that
the inflection points are scattered randomly across the APcluster, with the consequence that the volume of the ONEellipsoid was identical to the volume of the AP ellipsoid
within statistical fluctuations. Binning the volumes resulting
from the 10000 random pickings generates histograms like
those shown in Fig. 5. The gray lines indicate the volume of
the ONE-ellipsoids and the black bars show the resample’s volumes. The p-value was directly calculated as the fraction of
ellipsoids that had a volume identical to or smaller than the
ONE-ellipsoid.
The significance of this computation depended on the
number of inflection points. A small number of inflection
points caused a high estimation error. In Fig. 6 (upper panel),
we show results of a simulation with various choices for the
number of points. Each vertical column corresponds to a specific choice of the number of points and related histograms
(cf. Fig. 5) are coded by color. As before, the resamples were
calculated 10000 times for each chosen number of points. As
expected, with increasing number of points the observed contraction of the null statistics raised the chance of finding statistically significant normalized volumes. To delimit the range
of the null statistics, we plotted the standard quantiles in addition to mean and median. Specialists (smaller normalized volumes) were relatively easy to identify, but generalists were
harder to detect since the resampling histogram exhibits comparatively long tails. This pushed the upper quantiles to relatively large values and one had to reconsider a practical
choice. To solve this problem, we added a measure for the
range of specialization. This measure was constructed corresponding to Fig. 6; we extracted the species’ result and normalized it to the quantiles. In this perspective the 5% quantile
corresponded to –1, the median to 0 and the 95% to 1. According to this procedure, we obtained a range of specialization,
Fig. 4. Illustration of the correlation ellipsoids: inflection points in dark
gray, whole data set in light gray. For a better visualization, here we display only the first two PCs.
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Realized niche: fitness versus abundance
Fig. 6. Upper panel: Simulation of the resampling procedure with the
original AP-cluster (gray area, upright histograms from Fig. 5 for different
numbers of inflection points [4-180]). The lines show the different significance quantiles, the median and the mean of the normalized volumes.
10000 resamples are executed with the numbers of points in the theoretical ONE-ellipsoid noted on the x-axis. The volume on the y-axis is
again normalized to the volume of the AP-cluster (CFS: C. fusus, ORG: O.
regia, PSL: P. sulcata). Lower left panel: Simulation of the resampling procedure with different number of points taken out of an AP-cluster subset
with normalized volume 0.32 (artificial specialist). Blue lines correspond
to the upper panel, green lines to the subsamples, and the black squares
identify the type II error of 5% and 1%, respectively. Lower right panel:
Type II error as a function of the number of points, the two curves correspond to the different acceptance thresholds.
species with –1 and below were classified as specialists and
species with 1 and above were classified as generalists. The
results for the species showed the range of (non-) specialization and C. fusus was classified as a specialist with –1.11, the
other species were found in the intermediate range. O. regia
was found close to the median with –0.11 and P. sulcata on the
upper end with 0.74.
Some studies of specialists and generalists have suffered
from type II errors (false negative, was here a rejection of a true
specialist\generalist). Telford et al. (2006) quantified the type
II error through a simulation technique. We performed a similar simulation and quantified the type II error for an artificial
specialist. To explain the method, we picked 8312 points out
of our AP-cluster (14968 points) thus forming a subset with a
normalized volume of 0.32 (i.e., the volume of the smallest
ONE-ellipsoid for C. fusus). Again, we resampled this subset by
randomly picking a given number of points. The null statistic
was generated by 10000 repetitions of this procedure. The type
II error was quantified as the fraction of resamples being
rejected as a specialist, i.e., those resamples that fall above the
acceptance threshold for a specialist (1% or 5% quantiles,
Fig. 5. Histogram of the normalized volumes of 10000 randomly resampled ellipsoids and marked volume of the ONE-ellipsoid (indicated by
black lines). The histogram shape depends on the species-specific number of points defining the ONE-ellipsoid.
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Realized niche: fitness versus abundance
in the analysis and the dimension reduction will underestimate the environmental parameters. In Table 1, we compiled
the results for two, three, and four dimensions. We continued
with three dimensions, and we had a representation of 60%
from the total variance and the possibility to show the results
graphically. The main point here was to show that the results
for the specialist were convincing for three axes. Table 1 shows
that the p-value is lowest and this as the optimal solution. At
four axes the estimation error was higher and the significance
test failed more often, shown by the higher p-value. The
decreasing trend of a smaller normalized volume for the specialist with the dimension is expected, because of adding axis
with lower explained variance. This shows the advantage of
the dimension reduction to lowering the risk of a high estimation error. It is not possible to give a general number of
axes one should extract, and we give the advice to conduct a
comparable test. We found the PCA to be a transparent
method supported by the applied resampling technique,
which provided levels of significance for empirical distributions and was assumption free.
The calculated volumes are different between the three analyzed species. The length of the semiaxis explained the expansion in the subspace. An extreme value for one of these
lengths indicated an extremely (small or large) axis and could
be a useful in the interpretation of volumes (here we do not
have such an extreme value for one of the axes). The normalized volume for C. fusus was bigger for only two dimensions,
for three and four it stayed more or less constant on a lower
value. The expansion of the cluster for O. regia was smallest for
three dimensions, two dimensions and four dimensions
showed a trend toward bigger volumes. By a comparison with
the OMI method, the result for three dimensions seemed to be
most appropriate. P. sulcata showed the biggest volume for
three dimensions, because Paralia sulcata changed the timing
of presence over the whole data set and the average niche
should show a broad expansion.
OMI
Niche position describes the location in the hypervolume,
i.e., low numbers describe a position close to the average environmental conditions (center) and vice versa. The niche
breadth describes the tolerance of a species, i.e., the expansion
of the niche in the hypervolume. The niche positions for all
shown as blue lines in the lower left panel in Fig. 6). The values resulting for various numbers of points are plotted in the
lower right panel in Fig. 6. Already for 30 points, we find a
type II error less than 5%.
Method 2: Outlying mean index (OMI)
The niche position and niche breadth of the three phytoplankton species were determined with the OMI analysis
using R v.2.12.1 (R Core Development Team 2010) and the
software package ADE-4 (Thioulouse et al. 1997). This multivariate technique quantifies niche parameters along several
environmental gradients (Dolédec et al. 2000; Lappalainen
and Soininen 2006) by measuring the distance between the
average habitat conditions used by a species and the average
habitat conditions of the sampling area or period (Dolédec et
al. 2000, after Hausser 1995). The parameters are computed by
an ordination technique and weighted by the abundance. The
results are two measures, niche position and niche breadth.
The position describes the location of the niche in the hypervolume and the breadth describes the corresponding expansion (Dolédec et al. 2000; Heino and Soininen 2006; Tsiftsis et
al. 2008). With an analyses of only one species (or habitat), it
is hardly possible to tell if this is a specialist or a generalist, the
classification is therefore done in a comparative way. Niche
position and niche breadth were calculated on a yearly basis
for the abundance data and with biotic interaction milieu. The
ONE gave a niche for the complete timeframe and can be
interpreted as an envelope over yearly niches. In contrast, the
yearly niche of the OMI analysis may be interpreted as the
realized niche for the species for each single year.
Assessment
ONE
The extent of the ONE-ellipsoid (Fig. 4) of C. fusus is visibly
smaller than that of the AP ellipsoid but the spread of the
ONE-ellipsoid of P. sulcata is nearly the same as the AP ellipsoid. O. regia is found to be in an intermediate position. This
visual impression is confirmed by the obtained numerical values. Table 1 shows the different amounts of total variance by
the PCA after extracting different numbers of PC.
Extracting the appropriate number of PCs after applying
the PCA has to be taken seriously. By taking fewer axes than
optimal, an amount of information is lost and not represented
Table 1. Results for the extraction of a different number of PCs calculated for the three species [d: dimension (number of extracted
PCs)]; n: number of inflection points, l max (min): length of the longest (shortest) semiaxis, percentage of total variance: 49.08 for 2
d, 60.1 for 3 d and 70.84 for 4 d.
d
norm. volume
l max
l min
p-value
2
Ceratium fusus (n=61)
3
4
0.598
1.191
1.0204
0.002
0.319
1.2613
0.5055
< 10–6
0.222
1.2083
0.465
0.016
2
Odontella regia (n=94)
3
4
1.148
1.7985
1.5538
0.903
438
0.765
1.7405
0.6601
0.456
1.072
1.8169
0.7542
0.802
2
Paralia sulcata (n=133)
3
4
0.833
1.6439
1.295
0.058
1.245
1.8062
1.1015
0.836
0.816
1.6903
0.6859
0.689
Grüner et al.
Realized niche: fitness versus abundance
Fig. 8. Mean niche positions (filled dots) and mean niche breadths (error
bars) of Ceratium fusus, Odontella regia, and Paralia sulcata from 1968 to
2008.
species fluctuated for the time period from 1968 to 2008. The
niche breadth for Ceratium fusus was generally very small indicating a narrow niche (Fig. 7). In general, the lower values in
niche breadth and the higher values in niche position indicated
that C. fusus grows under more specialized conditions (Fig. 7).
No typical pattern could be found for the niche position for
Odontella regia but some extreme deviations of niche position
in the abundance-based analyses were found. Also, there was
no permanent shift of the niche position within the investigated time period and the average niche position was not significantly higher than that of C. fusus (Figs. 7, 8). From the
high values of niche position occupied by O. regia, one would
expect a more specialized species, but the niche breadth was
variable within the investigated time period and showed
higher values thus suggesting that O. regia was more of a generalist. Because of these diametrical descriptors, O. regia could
not be safely classified.
In contrast to both other algae, Paralia sulcata showed significantly lower values in niche position, explaining an occurrence at the average conditions (Figs. 7, 8) of the environment.
More importantly, the niche breadth was significantly higher
than the one of C. fusus (Figs. 7, 8). Both observations indicated that P. sulcata is a generalist. The niche of P. sulcata was
rather narrow in the period from 1980 to 1996 and then
widens abruptly, which suggested a transition from a more specialized to a more generalized strain (see Gebühr et al. 2009).
Discussion
Comparison of ONE and OMI
The ONE as well as the OMI analyses detected different
classifications for the three phytoplankton species (C. fusus,
O. regia, and P. sulcata), which can be explained by all three
algae living in different habitat conditions. P. sulcata and O.
Fig. 7. Annual niche positions (filled dots) and niche breadths (error
bars) of Ceratium fusus, Odontella regia, and Paralia sulcata (cf. Gebühr et
al. 2009) from 1968 to 2008.
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Realized niche: fitness versus abundance
cific effects, we performed a cross comparison employing
both methods, the single point ONE analysis and the abundance weighted OMI analysis, with both approaches, abundance, and fitness. This comparison shows that a reconstruction of the ecological niche can be accomplished via both
approaches and are not method specific (see Web Appendix A
for detailed description).
The main objective of our study was to investigate the consequences for niche reconstruction when changing from
abundance- to a fitness-based approach. This fitness-based
approach explains the ecology of phytoplankton species in a
new way. The fitness-based niche is ecologically more meaningful than the abundance-based niche, because indefinite
existence (Hutchinson 1957) is rather a question of fitness
than abundance. Identifying fitness with sheer abundance can
be misleading since highest abundance specifies a moment
when net growth ceases. Several other reasons may explain
the stagnation and subsequent decline of population size, for
instance, increased grazing pressure or viral infection, and we
admit that reduced net growth expressing poor fitness is only
one of them—but a not so unlikely one. By contrast, most
rapid net growth can only be explained by high fitness—sufficiently high to overcompensate for all losses.
For bloom-forming species fitness is linked with instantaneous growth rates, in other cases other fitness indicators
might be more relevant, e.g., a high metabolic rate or a high
cell division rate. Both methods (ONE and OMI) of ecological
niche classification are based on multivariate data analysis
techniques. Since the OMI was already discussed at length in
other publications (Dolédec et al. 2000; Lappalainen and
Soininen 2006) we will here devote remaining space to the
novel ONE method. The ONE employed in this study is applicable to other bloom-forming species, i.e., to species which
exhibit rapid growth within a short period as, for instance,
zooplankton or bacteria. The ONE method allows a classification of these planktonic species, and the results can be interpreted in ecological terms. The standard way in phytoplankton ecology is a classification of groups or functional groups
and not single species. With our detailed data set, we have the
opportunity to do this on a species-specific level. The optimal
niche can be discussed and interpreted for every species with
respect to its fitness, here the fastest growth. In this work, a
classification of three exemplary species is reached. C. fusus is
found to be a specialist and P. sulcata a more general species.
O. regia is a representative of species, which can hardly be classified by ONE and is found in the intermediate range of specialization. One advantage of the method is that the normalized volume gives a well interpretable degree of specialization
for every species and does not lead to a simplistic binary classification into specialists and generalists.
Reconstruction methods for yearly niches (like the OMI)
should always be complemented with those across several
years (like the ONE) since both have their advantages and
drawbacks. The risk of yearly niche analyses is to over-inter-
regia occurred throughout the whole year and thereby experience a wide range of environmental parameters whereas C.
fusus typically occurs in the summer months and is therefore
more specialized.
With the OMI analysis, it is possible (but not restricted to)
to analyze the species on a yearly basis, and this is a very interesting and fascinating aspect. The advantage of the detection
of changes in the ecology and the influence of shifts in the
environment on the species can be noteworthy information.
According to both methods, C. fusus is a clear specialist
whereas, according to the niche breadth, P. sulcata is a generalist. C. fusus is typically found in summer, where the water
temperature is elevated, and the day length longer. Typical for
this alga is the independence of silicate because dinoflagellates
do not need silicate for their valve formation like diatoms do.
This matches the typical summer conditions found at Helgoland Roads in agreement with the occurrence of C. fusus in
late spring and summer times. P. sulcata is an alga which
recently has begun to be present throughout the whole year,
reflecting the fact that the species complex can now tolerate a
wider range of environmental conditions (cf. Gebühr et al.
2009). P. sulcata seems to be well adapted to the seasonally
changing environmental parameters in this habitat.
In the OMI analyses, O. regia takes on an intermediate position. The ONE method reaches no significant result for O.
regia. In the OMI analysis, the intermediate position is
reflected by the combination of a higher niche position, suggesting a specialist, and a larger niche breadt, which indicates
the generalist. O. regia is a large centric diatom species that
also occurs throughout the whole year in the water column at
Helgoland Roads but the abundance is not as high as for P. sulcata and the species is not detected so frequently over the
investigated time period. This might be the reason that the
yearly ecological niche of O. regia cannot be described by the
OMI consistently, but this should not be the case for the ONE
method. Here it is based on the expansion of the ONE-ellipsoid and so an average or envelope niche.
The OMI method gives a yearly niche and the classification is based on these changes over the years. The problem
with this conception is the drastic change from one year to
another, and it has to be discussed, if this is biologically
meaningful - is it conceivable, that one species has a completely different niche in two consecutive years? The reasons
for these changes can be found in the changing environment,
but a species cannot adapt in such a short time span. This situation could only be explained by the presence of different
adapted strains in the system. The classical concept of the
ecological niche explains the cloud of factors a species can
persist; this is reached by the ONE method in a new, but comparable way. An analysis of changes or trends is not yet integrated and a sliding analysis across few years is, because of the
loss of a statistical significance, not feasible. An evaluation of
the Helgoland Roads dataset in this direction is left to future
studies. To disentangle method-specific from approach-spe440
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Comments and recommendations
Here we propose a new approach to detect the ecological
niche based on a fitness parameter. Our ONE analysis is a new
approach to classify the ecological niche. An application to
other data are conceivable given an appropriate definition of
the moments of highest fitness.
We applied a PCA in this analysis, but it is not essential. We
could calculate the niche volume in an n-dimensional space as
well, but this could lead to higher estimation errors. If the
original data set is low dimensional, this would give an appropriate and satisfying result.
By an inclusion of existing zooplankton abundance data
(Greve et al. 2004), the grazing pressure on phytoplankton
species at Helgoland can be accounted for. Grazers can be
included, whereby the effect of grazers on the maximal
growth rate is not expected to be large.
In line with Hutchinson’s niche definition we have, so far,
only evaluated ellipsoid volumes plus maximal and minimal
semiaxis. More ecologically relevant information may be contained in further geometrical features of the ONE-ellipsoid,
e.g., the location of its center, i.e., the equivalent to the niche
position, or the specific orientation of its principal axes.
Moreover, the by-now 45 years range of the Helgoland
Roads data seems sufficient for a sliding or split window analysis aiming to detect statistically significant changes (trends,
break points) of niche parameters and interpret them in an
ecological context. Extensions of our analysis in these directions will be left to future research.
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Submitted 5 April 2011
Revised 23 August 2011
Accepted 30 August 2011
442