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Citation: Le, T.T.Y.; Becker, A.;
Kleinschmidt, J.; Mayombo, N.A.S.;
Farias, L.; Beszteri, S.; Beszteri, B.
Revealing Interactions between
Temperature and Salinity and Their
Effects on the Growth of Freshwater
Diatoms by Empirical Modelling.
Phycology 2023,3, 413–435. https://
doi.org/10.3390/phycology3040028
Academic Editor: Saúl Blanco
Received: 29 August 2023
Revised: 15 September 2023
Accepted: 20 September 2023
Published: 22 September 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Revealing Interactions between Temperature and Salinity and
Their Effects on the Growth of Freshwater Diatoms by
Empirical Modelling
T. T. Yen Le 1,*, Alina Becker 2, Jana Kleinschmidt 2, Ntambwe Albert Serge Mayombo 2, Luan Farias 1,
Sára Beszteri 3and Bánk Beszteri 2
1Department of Aquatic Ecology, Faculty of Biology, University of Duisburg-Essen, D-45141 Essen, Germany;
luan.farias@uni-due.de
2Department of Phycology, Faculty of Biology, University of Duisburg-Essen, D-45141 Essen, Germany;
alina.becker@stud.uni-due.de (A.B.); jana.kleinschmidt@stud.uni-due.de (J.K.);
ntambwe.mayombo@uni-due.de (N.A.S.M.); bank.beszteri@uni-due.de (B.B.)
3Department of Biodiversity, Faculty of Biology, University of Duisburg-Essen, D-45141 Essen, Germany;
sara.beszteri@uni-due.de
*Correspondence: yen.le@uni-due.de; Tel.: +49-2011834020
Abstract:
Salinization and warming are of increasing concern for freshwater ecosystems. Interactive
effects of stressors are often studied in bifactorial, two-level experimental setups. The shape of
environmental reaction norms and the position of the “control” conditions along them, however, can
influence the sign and magnitude of individual responses as well as interactive effects. We empirically
model binary-stressor effects in the form of three-dimensional reaction norm surfaces. We monitored
the growth of clonal cultures of six freshwater diatoms, Cymbella cf. incurvata,Nitzschia linearis,
Cyclotella meneghiniana,Melosira varians,Ulnaria acus, and Navicula gregaria at various temperature (up
to 28
◦
C) and salinity (until the growth ceased) shock treatments. Fitting a broad range of models and
comparing them using the Akaike information criterion revealed a large heterogeneity of effects. A
bell-shaped curve was often observed in the response of the diatoms to temperature changes, while
their growth tended to decrease with increasing electrical conductivity. C. meneghiniana was more
tolerant to temperature, whilst C. incurvata and C. meneghiniana were the most sensitive to salinity
changes. Empirical modelling revealed interactive effects of temperature and salinity on the slope
and the breadth of response curves. Contrasting types of interactions indicates uncertainties in the
estimation by empirical modelling.
Keywords: modelling; multiple stressors; global changes; primary producers; synergism; tolerance
1. Introduction
Given their contribution of up to 20% of the global primary production [
1
] as well as
their role in the global cycling of carbon, nitrogen, phosphorus, and silicon [
2
,
3
], diatoms
are of high importance in the functioning of aquatic ecosystems. Due to the simplicity
of sampling, preparation, and preservation of their silicate shells (frustules), freshwater
benthic diatoms are widely used as environmental indicators, both in routine water quality
assessment and paleolimnology [
4
,
5
]. Information on the ecological profiles of individual
taxa is often expressed in terms of specific biotic indices, which summarize information on
preference and tolerance ranges in a highly compressed form [
6
]. Alternatively, individual
environmental parameters can be quantitatively linked to diatom community composition
quantitatively using transfer functions or machine learning approaches [7,8].
One central topic in the assessment of the effects of multiple environmental variables
(stressors) is the presence or absence and nature of interactive effects. Such interactions refer
to situations when the combined effects of changes in multiple abiotic factors on organismal
Phycology 2023,3, 413–435. https://doi.org/10.3390/phycology3040028 https://www.mdpi.com/journal/phycology
Phycology 2023,3414
viability differ from the summed effects of the individual environmental changes [
9
,
10
].
Such interactions can take different forms. For example, at the eco-physiological level,
changes in one variable might affect the niche width, the location of the optimum, or the
position of the tolerance limits relative to another. In practice, these interactions are often
studied in two-level, two-stressor, full-factorial experiments. A classification system has
emerged for characterizing multiple stressor effects in this context, differentiating between
additive (no-interaction), synergistic, and antagonistic types (and in some cases, more
categories are included) [11,12].
One limitation of this approach is that such a stressed-baseline comparison is agnostic
of the shape of organismal tolerance profiles, which are nevertheless seen as a fundamental
determinant of biological responses [
13
,
14
]. In spite of this disadvantage, such a design
is still adopted, probably because of the increasing difficulty of statistically modelling
ecological profiles in more than one dimension. One aspect of this difficulty is the large
number of functional forms proposed to describe ecological reaction norms; for instance,
at least a dozen different functional forms have been proposed for temperature [
15
]. In
a more-than-one dimensional setting, different functional forms may apply to the indi-
vidual abiotic predictors, and possibilities to capture interactive effects contribute further
degrees of freedom, leading to an overwhelming variety of possibilities for mathematical-
statistical models.
In the present research, we approached this problem by compiling a range of functional
forms potentially describing reaction norms, in terms of growth, of freshwater diatoms
to salinity and temperature; combining them in additive and interactive forms to depict
three-dimensional reaction norm surfaces; and confronting the obtained broad range of
possible model forms with data obtained from laboratory experiments. The experiments
quantified the growth rate of clonal freshwater diatom cultures under a treatment matrix
including several temperature and salinity levels. Compromise between data fit and the
number of model parameters was quantified by the Akaike information criterion (AIC). We
hypothesized that interactive terms are usually required to capture observed responses to
temperature and salinity changes, and that the variability of such interactions would exceed
a simple synergism–antagonism dichotomy. Although the effects of temperature [
16
,
17
]
or salinity [
18
,
19
] upon growth were studied repeatedly in marine phytoplankton, such
a study has, to our knowledge, never before been published on freshwater phytobenthic
diatoms.
2. Materials and Methods
2.1. Organisms and Culture Conditions
The diatom strains were isolated from a single microphytobenthos sample obtained
from a flow-through mesocosm ExStream. The mesocosm was supplied from the small
stream Boye (without any modification of the water) at its confluence with the Haarbach
and Kischemsbach in Gladbeck (51.55
◦
N, 6.95
◦
W, North Rhine-Wesphalia, Germany) in
the spring of 2021. Using light (oil immersion optics) and scanning electron microscopy of
oxidized frustule preparations, the strains were identified as Cymbella cf. incurvata,Nitzschia
linearis,Cyclotella meneghiniana,Melosira varians,Ulnaria acus, and Navicula gregaria. The
strains were isolated and maintained in SFM + Si medium (Appendix ATable A1) in PK520
WLED climate chambers (polyKlima GmbH, Freising, Germany) with “True Daylight LED”
illumination at 15
◦
C with a light–dark cycle of 10:14 h and a light intensity of 100
µ
E/cm
2
.
2.2. Temperature and Salinity Experiments
Experiments were performed in 24-well cell culture plates (neoLab Migge GmbH,
Heidelberg, Germany) in at least 4 replicates, with 2 mL total volume per well. Salinity
was manipulated by adding NaCl (Carl Roth GmbH + Co. KG, Roth, Germany) to the
basic SFM + Si media to obtain various concentrations up to 3000 mg/L. In addition,
pH was kept at 7.0 (
±
0.1). The conductivity of the media was measured with a PCE-
PHD 1 pH-conductivity meter (Meschede, Germany). After calibrating added salinity
Phycology 2023,3415
values against measured conductivity in the used media, conductivity could be calculated
as 0.432 + 0.00295
×
added salt concentration (the latter expressed as mg/L Cl
−
). For
consistency, throughout the rest of the paper, total salinity of media will be expressed as
electric conductivity. Initial cell densities were separately adjusted to each strain based
on a calibration of
in vivo
chlorophyll fluorescence values measured with a Tecan Infinite
200 Pro microplate reader (Tecan Group Ltd., Männedorf, Switzerland), similarly to the
method applied by Albrecht et al. [
20
] with the following specifications: bottom reading
mode with an excitation wavelength of 450 nm and detection at 680 nm. The plates were
cultured in the climate chambers as described above for one week at different temperatures
ranging from 5 to 28
◦
C.
In vivo
chlorophyll fluorescence was measured with the Tecan
Infinite 200 Pro plate reader as described above at the same time of day over the seven days
of experiments.
2.3. Calculation of Specific Growth Rate
In cultivation, the growth curve of microalgae usually includes a lag phase [
21
] at
which the growth is delayed because of physiological adjustment and the presence of
non-viable cells [
22
,
23
]. This was found to be the case in our experiments as well; therefore,
the specific growth rate (
µ
; 1/d) was calculated for the phase where the fluorescence signal
increased exponentially (mostly days 3–7) using the following equation:
dN
dt =µ×N(1)
where Nis the fluorescence on the measuring day [24].
2.4. Empirically Modelling Diatom Growth
2.4.1. Multiplicative and Decoupled Models
The growth rate of diatoms as a function of environmental variables has usually been
written as a function of growth-affecting factors representing the stressor [
25
–
28
]. In this
method, each factor ranging from 0 to 1 is a multiplier in the growth rate calculation.
Considering the influence of temperature and electrical conductivity:
µ=µmax ×fT×fS(2)
with
fS
and
fT
(/) being salinity and temperature factors, respectively; and
µmax
(1/d)
being the maximum growth rate. In other words, the effect of each factor is considered
multiplicative and decoupled.
As the stress caused by various factors is considered multiplicative and decoupled in
this model, the influence of temperature could be integrated as the effects on the maximum
growth rate, yielding the temperature-dependent growth rate (
µT
). Accordingly, the above
equation could be modified as:
µ=µT×fS(3)
A variety of equations have been applied previously to describe the temperature-
dependent growth rate (Table S1, Supplementary Material), temperature factor (Table S2,
Supplementary Material), and salinity factor (Table S3, Supplementary Material). These
equations were combined and modified to consider all possible ways that factors in
Equations (1) and (2) might be affected by temperature and/or salinity in a simple mul-
tiplicative or interactive manner. The latter can include: (1) the temperature-dependent
growth rate is influenced by salinity; (2) the temperature factor is impacted by salinity;
(3) the salinity factor is affected by temperature; and (4) the optimum, maximum, or the
lower/upper level of one environmental factor is affected by another.
2.4.2. Polynomial Regression Equations
Another common approach to modelling diatom growth in various environmental
conditions is to use polynomial regression equations [
29
,
30
]. Considering the effects of
Phycology 2023,3416
temperature and salinity, the diatom growth rate can be written as a polynomial equation
without (Equation (4)) and with (Equation (5)) interactions:
µ=a+b1×S+c1×T+b2×S2+c2×T2(4)
µ=a+b1×S+c1×T+b2×S2+c2×T2+d×S×T(5)
Equations (4) and (5) depict the relationship between the growth rate and two variables
(temperature T and salinity S expressed by the electrical conductivity). In these equations,
a
is the intercept term (i.e., the growth rate at 0
◦
C and electrical conductivity 0 mS/cm);
b1
and
c1
represent the main effect for each variable;
b2
and
c2
represent square effects; and d
stands for the interaction between temperature and electrical conductivity.
2.4.3. Data Fitting
Nonlinear least-square fitting of the growth rate as a function of temperature and
electrical conductivity was conducted using SigmaPlot 15.0, providing estimates of the
coefficients in the equations as well as statistical parameters (R
2
,p, and AIC). In the
data fitting, only the lowest salinity at which the growth did not take place (zero or
negative specific growth rate) was considered in order to reduce uncertainties in the
analysis. The scenarios with definite confidence intervals for estimated parameters are
given in
Tables S4–S9
, Supplementary Material. For selecting the best model for each
species, we used the Akaike Information Criterion [
31
] as a metric, aiming to balance model
complexity (number of parameters) against model fit. The model with the lowest AIC value
was considered to provide the best such compromise, i.e., generalizability.
3. Results and Discussion
3.1. Variations in the Response to Temperature and Salinity among Diatom Species
Among the six strains investigated, C. meneghiniana (Figure S1C) and U. acus
(Figure S1E) were least affected by temperature changes (Figure S1, Supplementary ma-
terial). At the background electrical conductivity level of the culture medium (i.e., NaCl
was not added to the culture medium), the growth rate of C. meneghiniana stabilized in the
temperature range of up to 25
◦
C (Figure S1C), indicating a high tolerance of this strain
to temperature changes in the investigated range. Given conductivity below 2 mS/cm,
U. acus grew at any temperature (Figure S1E). In contrast, C. incurvata was the most strongly
affected by temperature changes, with wide variations in its growth rate with varying
temperatures (Figure S1A). At 25
◦
C, the growth of C. incurvata ceased, regardless of salinity.
The growth of C. incurvata,M. varians,U. acus, and N. gregaria followed a typi-
cal bell-shaped curve, i.e., below the optimum temperature, the growth rate increased
with increasing temperature; above the optimum temperature, the growth rate decreased
with increasing temperature (Figure S1). A different pattern was recorded for N. linearis
(Figure S1B). At the background electrical conductivity, the growth rate of this strain de-
creased with increasing temperature up to 20
◦
C and increased with increasing temperature
above 20
◦
C (Figure S1B). These patterns were altered by the effects of electrical conductivity
changes with greater fluctuations in the temperature-growth curve (Figure 1). A bell-shaped
temperature-growth curve has been reported previously for diatoms [
29
,
32
,
33
]. Up to the
optimum temperature, the increase in the growth rate of phytoplankton with increasing
temperature is related to enhanced enzymatic activities, photosynthesis, and nutrient up-
take [
34
]. The sharp decreases in the growth at high temperatures have been ascribed to
deactivation of enzymes or modification of proteins [
35
], which disrupts metabolism and
consequently causes mortality of cells [
36
]. In addition, photosynthetic performance and
efficiency of phytoplankton might be inhibited by high temperature due to impairment in
the photosynthetic electron transport and carbon fixation [37].
Phycology 2023,3417
Phycology 2023, 3, FOR PEER REVIEW 5
ascribed to deactivation of enzymes or modification of proteins [35], which disrupts me-
tabolism and consequently causes mortality of cells [36]. In addition, photosynthetic per-
formance and efficiency of phytoplankton might be inhibited by high temperature due to
impairment in the photosynthetic electron transport and carbon fixation [37].
0.2
0.1
0.1
0.0
-0.1
0.5
0.4
0.3
0.2
0.0
0.5
1.0
1.5
2.0
2.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
A
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
B
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
C
Figure 1. Simulation of the growth of Cymbella incurvata based on experimental data according to
non-interactive multiplicative Equation (ST13) ((A); R2 = 0.97; AIC = −91.06), interactive multiplica-
tive Equation (ST2) ((B); R2 = 0.88; AIC = −62.08), and polynomial Equation (4) ((C); R2 = 0.82; AIC =
−59.42).
The growth rate of the investigated freshwater diatoms commonly declined with in-
creasing electrical conductivity (Figure S1). For example, the growth rate of C. incurvata
and C. meneghiniana decreased with increasing salinity regardless of temperature (Figure
S1). For the other strains, their response to salinization was more diverse, sometimes
showing a unimodal response (maximal growth rate at intermediate salinity levels). How-
ever, an inhibition of the growth rate with increasing electrical conductivity was still dom-
inant (Figure S1). The bell-shaped conductivity-growth curve was only seen at high tem-
perature (25 °C; Figure S1). The growth of N. gregaria was least affected by salinity changes
(Figure S1F). Decreases in the growth rate of this diatom were only evident at conductivity
above 5 mS/cm (Figure S1F). At temperature below 25 °C, N. gregaria still grew at electrical
Figure 1.
Simulation of the growth of Cymbella incurvata based on experimental data according to
non-interactive multiplicative Equation (ST13) ((
A
); R
2
= 0.97; AIC =
−
91.06), interactive multiplica-
tive Equation (ST2) ((
B
); R
2
= 0.88; AIC =
−
62.08), and polynomial Equation (4) ((
C
); R
2
= 0.82;
AIC = −59.42).
The growth rate of the investigated freshwater diatoms commonly declined with in-
creasing electrical conductivity (Figure S1). For example, the growth rate of C. incurvata and
C. meneghiniana decreased with increasing salinity regardless of temperature (Figure S1).
For the other strains, their response to salinization was more diverse, sometimes showing
a unimodal response (maximal growth rate at intermediate salinity levels). However, an
inhibition of the growth rate with increasing electrical conductivity was still dominant
(Figure S1). The bell-shaped conductivity-growth curve was only seen at high tempera-
ture (25
◦
C; Figure S1). The growth of N. gregaria was least affected by salinity changes
(Figure S1F). Decreases in the growth rate of this diatom were only evident at conductivity
above 5 mS/cm (Figure S1F). At temperature below 25
◦
C, N. gregaria still grew at electrical
conductivity above 9.00 mS/cm (Figure S1F). In contrast, C. meneghiniana was among the
diatoms most affected by salinization (Figure S1C). Different results have been reported for
Phycology 2023,3418
this diatom. Roubeix and Lancelot [
38
] revealed a bell-shaped response of C. meneghiniana
to salinity changes ranging from 0 to 33‰ with a maximum growth rate at 18‰.
According to Kirst [
19
], organisms might be affected by changes in salinity for several
reasons, including: (1) osmotic stress and subsequent effects on the cellular water potential;
(2) ion stress resulting from the uptake or loss of ions; and (3) change of the cellular ionic
ratios because of the selective ion permeability of the membrane. Salinity exerts profound
effects on the growth of algae by influencing the osmotic pressure, nutrient absorption,
and suspension of algae [
39
]. The growth at low salinity levels may be controlled by the
availability of certain ions [
40
]. At high ion concentrations, the decline in water potential
can affect metabolism [
41
]. In addition, energy requirements of osmoregulation can lead to
reduced availability of energy and metabolites for cell growth [
41
]. These factors might
contribute to the decline in growth at extreme salinity levels [41].
3.2. Empirical Modelling of Diatom Growth Considering Temperature and Salinity
Based on the value of AIC, various models were considered the best to describe the
growth of various strains at different temperature–salinity conditions (Table 1).
3.2.1. Cymbella cf. incurvata
Non-interactive multiplicative Equation (ST13) was the best for describing the growth
of C. incurvata at various temperatures and conductivity levels (R
2
= 0.97; AIC =
−
91.06;
Table S4; Figure 1A):
µ= c×ed×T× 1−T−z
w/2 2!!× 1−S−Sopt
Smax −So pt 2!(ST13)
where
z
(
◦
C) is the optimum temperature of the quadratic portion; when
d
= 0, this value
is identical to the optimum temperature of the whole curve (i.e., the growth reaches the
maximum rate and the thermal response is symmetric);
w
(
◦
C) is the thermal breadth
(i.e., the range over which diatoms grow);
Sopt
(mS/cm) is the optimum conductivity;
and
Smax
(mS/cm) is the maximum conductivity above which the growth ceases. The
second and third best models, although quite distant in terms of AIC (Equation (ST12),
AIC =
−
77.93; Equation (ST8), AIC =
−
69.45), were also non-interactive ones, speaking
for a relatively robust conclusion that interactive effects are not necessary to explain the
observed pattern in salinity- and temperature-dependent growth of this strain.
Phycology 2023,3419
Table 1. Best models selected for the investigated freshwater diatoms based on AIC.
Strain Best Model Symbol (Unit) Model Parameter AIC
Cymbella cf. incurvata µ=c×ed×T×1−T−z
w/2 2×1−S−Sopt
Smax −So pt 2
z(◦C)
Optimum temperature of the quadratic portion; when d= 0,
this value is identical to the optimum temperature of the
whole curve (i.e., growth reaches the maximum rate, and the
thermal response is symmetric) −91.06
w(◦C)
the thermal breadth (i.e., the range over which diatoms grow)
Sopt (mS/cm) Optimum conductivity
Smax (mS/cm) Maximum conductivity above which growth ceases
Nitzschia linearis µ=µmax ×1−T−Top t
w×(1+aST ×S)/2 2×e−kS×(S−Sop t )2µmax (1/d) Maximum growth rate reached at the optimum temperature
Topt ;◦C) and the optimum conductivity So pt ; mS/cm) −133.49
w(◦C)
Thermal breadth that can be affected by salinity depending on
the interaction coefficien aST (cm/mS)
kS(cm2/mS2)Salinity effect factor
Cyclotella meneghiniana µ=µmax ×1−T−Top t
w×(1+aST ×S)/2 2×e−kS×(S−Sop t )2See above See above −43.90
Melosira varians µ=µ20 ×θT−20×1−S−So pt
Smax ×(1+aST ×T)−So pt 2µ20 (1/d) Growth rate at 20 ◦C
−51.79
Sopt (mS/cm) Optimum conductivity
Smax (mS/cm) Maximum conductivity above which growth ceases
Ulnaria acus µ=µmax ×e−kT×(T−Topt ×(1+aST ×S))2×1−S−So pt
Smax −So pt 2
kT(1/◦C2)
Temperature effect factor describing the change in the growth
rate with increasing temperature below or above the optimum
Topt ;◦C) −94.70
Sopt (mS/cm) Optimum conductivity for growth
Smax (mS/cm) Maximum conductivity for growth
aST (cm/mS) Represents the interactive effect
Navicula gregaria µ=µmax ×(e−kT1×(T−Top t )2f or T ≤Topt
e−kT2×(T−Topt )2f or T >Topt
×e−kS×(S−Sopt )2µmax (1/d) is Maximum growth rate obtained at the optimum temperature
Topt (◦C) and the optimum conductivity So pt (mS/cm) −229.82
kT1and kT2(1/◦C2)Temperature effect factors at temperature below and above
the optimum, respectively
kS(cm2/mS2)Salinity effect factor.
Phycology 2023,3420
This equation could explain the growth rate of C. incurvata better than interactive
multiplicative equations (the best one is Equation (ST2); R
2
= 0.88; AIC =
−
62.08; Figure 1B)
and the polynomial equation (R
2
= 0.82; AIC =
−
59.42; Figure 1C). Noticeably, estimates of
all the parameters in Equation (S13) for C. incurvata were statistically significant (Table S4).
According to Equation (ST13), the growth of C. incurvata followed an asymmetric bell-
shaped response. The growth rate of this strain increased with increasing temperature,
reaching the highest level at the optimum temperature higher than the optimum level
of the quadratic portion (
d
> 0) of 15.5
◦
C (14.6–16.3
◦
C). The thermal breadth of this
diatom was estimated as 14.8
◦
C (12.7–16.9
◦
C; Table S4; Figure 1A). The temperature
response contributes to the difference between Equations (ST13), i.e., asymmetric, and
(ST12), i.e., symmetric. Between them, the asymmetric response (ST13) explained the
variation in the growth of C. incurvata better than the symmetric one (ST12; Table S4). Also,
according to Equation (ST13), the conductivity-growth rate followed a bell-shaped response
curve. These responses to temperature and conductivity changes produce an evident peak
of the growth rate, as displayed in Figure 1A. However, with an optimum conductivity of
0.63 mS/cm, just slightly above the background conductivity (0.43 mS/cm), the growth of
C. incurvata was mainly inhibited by salinization at the investigated conditions (Table S4).
This explains the relatively good fit of Equations (ST8), (ST9), and (ST10), in which the
growth is inhibited by the addition of NaCl at any concentration (Table S4). In addition,
based on Equation (ST13), the growth of this diatom strain ceased at conductivity of
4.88 mS/cm (0.88–8.87 mS/cm; Table S4). According to Equation (ST7), which also yields
all significant coefficients, the growth rate of this diatom strain was inhibited by 50% at
conductivity of 1.81 mS/cm (1.75–1.88 mS/cm; Table S4). However, the analysis using
polynomial equations yielded a different trend (Table S4). In particular, according to these
equations, the growth of C. incurvata was significantly affected by temperature, but not by
salinity (Table S4; Figure 1C); however, the fit of these models was relatively poor when
compared to the above-mentioned top candidates (Table S4).
3.2.2. Nitzschia linearis
The bell-shaped response of N. linearis as observed from the experiment could be
described by various equations (Table S5) with a number of them giving statistically sig-
nificant estimates, i.e., Equations (ST5), (ST2), (ST14), (ST15), and (S19). Among them, the
interactive-multiplicative Equation (ST15) gave the lowest AIC value (Table S5;
R2= 0.59; AIC = −133.49; Figure 2B):
µ=µmax × 1−T−Topt
w×(1+aST ×S)/2 2!×e−kS×(S−So pt)2(ST15)
with
µmax
(1/d) being the maximum growth rate reached at the optimum temperature (
Topt
;
◦
C) and the optimum conductivity (
Sopt
; mS/cm);
w
(
◦
C) being the thermal breadth that
can be affected by salinity depending on the interaction coefficient
aST
(cm/mS); and
kS
(cm2/mS2) being the salinity effect factor.
Phycology 2023,3421
Phycology 2023, 3, FOR PEER REVIEW 9
𝜇=𝜇×1− 𝑇−𝑇
𝑤×1+𝑎 ×𝑆2
⁄×𝑒× (ST15)
with 𝜇𝑚𝑎𝑥 (1/d) being the maximum growth rate reached at the optimum temperature
(𝑇𝑜𝑝𝑡; °C) and the optimum conductivity (𝑆𝑜𝑝𝑡; mS/cm); 𝑤 (°C) being the thermal breadth
that can be affected by salinity depending on the interaction coefficient 𝑎𝑆𝑇 (cm/mS); and
𝑘𝑆 (cm2/mS2) being the salinity effect factor.
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0
1
2
3
4
5
6
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
A
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0
1
2
3
4
5
6
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
B
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0
1
2
3
4
5
6
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
C
Figure 2. Simulation of the growth of Nischia linearis based on experimental data according to non-
interactive multiplicative Equation (ST14) ((A); R2 = 0.53; AIC = −130.43), interactive multiplicative
Equation (ST15) ((B); R2 = 0.59; AIC = −133.49), and polynomial Equation (4) ((C); R2 = 0.51; AIC =
−128.74).
Equation (ST15) could describe the variations in the growth of N. linearis with varying
temperature and conductivity beer than non-interactive multiplicative equations (the
best of which was Equation (ST14); R2 = 0.53; AIC = −130.43; Figure 2A; Table S5) and pol-
ynomial equations (Table S5; Figure 2C). Both Equations (ST14) and (ST15) depict a bell-
shaped response of growth rate to both temperature and salinity. According to the best
Figure 2.
Simulation of the growth of Nitzschia linearis based on experimental data according to
non-interactive multiplicative Equation (ST14) ((
A
); R
2
= 0.53; AIC =
−
130.43), interactive multiplica-
tive Equation (ST15) ((
B
); R
2
= 0.59; AIC =
−
133.49), and polynomial Equation (4) ((
C
); R
2
= 0.51;
AIC = −128.74).
Equation (ST15) could describe the variations in the growth of N. linearis with varying
temperature and conductivity better than non-interactive multiplicative equations (the
best of which was Equation (ST14); R
2
= 0.53; AIC =
−
130.43; Figure 2A; Table S5) and
polynomial equations (Table S5; Figure 2C). Both Equations (ST14) and (ST15) depict a
bell-shaped response of growth rate to both temperature and salinity. According to the
best Equation (ST15), the thermal breadth for N. linearis becomes narrower with increasing
salinity (Table S5). Similar interactions were predicted with the second ranking model
(Equation (ST17); AIC =
−
131.76). The inclusion of this interactive effect improved the
predictive potential. This is shown by the lower AIC of Equation (ST15) compared to
Equation (ST5), which uses the same functional forms apart from the interaction (Table S5).
With Equation (ST15), the maximum growth rate of 0.59 (1/d) was reached at 15.9
◦
C
(14.7–17.1
◦
C; Table S5) and 2.44 mS/cm (2.02–2.86 mS/cm; Table S5). The significant
influence of temperature and salinity was also found with the non-interactive polynomial
equation (Equation (4)) as given in Table S5.
3.2.3. Cyclotella meneghiniana
With the limited data from the experiment on the growth of C. meneghiniana, high uncer-
tainty is inherent in our empirical modelling (Table S6). No equations with all significant co-
efficients were found (Table S6). According to polynomial equations (
Equations (4) and (5))
,
the growth rate of C. meneghiniana was not significantly affected by temperature or salinity
Phycology 2023,3422
(Figure 3C; Table S6). This is consistent with the limited variations in the growth rate of
this freshwater diatom with temperature and salinity changes described above. However,
the optimum temperature and conductivity could be estimated by various multiplicative
equations (Table S6). Similar to N. linearis, the growth rate of C. meneghiniana could be
best simulated with interactive multiplicative Equation (ST15) (R
2
= 0.80;
AIC = −43.90
;
Figure 3B; Table S6). According to this equation, the maximum growth rate of C. meneghini-
ana (0.89; 1/d) was reached at 17.3
◦
C (13.9–20.8
◦
C) and 0.69 mS/cm (0.58–0.81 mS/cm).
Compared to the estimations for these coefficients, high uncertainty is included in the
estimate for the salinity effect factor (
kS
) and the thermal breadth (
w
; Table S6). Different
estimates were obtained by combining the Arrhenius equation for temperature responses
with various salinity functions (Table S6). According to the best non-interactive equa-
tion (Equation (ST25)) (R
2
= 0.52; AIC =
−
34.29; Figure 3A; Table S6), the growth rate of
C. meneghiniana increased with increasing temperature. An opposite pattern was found
with Equation (ST24), which describes the salinity–growth rate with a Michaelis–Menten
function (Table S6). Equation (ST24) yielded a maximum conductivity of 1.38 mS/cm
(1.06–1.71 mS/cm; Table S6).
Phycology 2023, 3, FOR PEER REVIEW 11
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
A
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
B
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
C
Figure 3. Simulation of the growth of Cyclotella meneghiniana based on experimental data according
to non-interactive multiplicative Equation (ST25) ((A); R2 = 0.52; AIC = −34.29), interactive multipli-
cative Equation (ST15) ((B); R2 = 0.80; AIC = −43.90), and polynomial Equation (4) ((C); R2 = 0.58; AIC
= −34.25).
3.2.4. Melosira varians
The growth of M. varians at various temperature and conductivity levels was best
simulated with the interactive Equation (ST11) (R2 = 0.57; AIC = −51.79; Figure 4B; Table
S7):
𝜇=𝜇×𝜃×1− 𝑆−𝑆
𝑆×1+𝑎 ×𝑇−𝑆 (ST11)
where 𝜇20 (1/d) is the growth rate at 20 °C; 𝑆𝑜𝑝𝑡 (mS/cm) is the optimum conductivity;
and 𝑆𝑚𝑎𝑥 (mS/cm) is the maximum conductivity above which the growth ceases.
Equation (ST11) stood out as it had the lowest AIC and included all significant coef-
ficients (Table S7). According to this equation, the growth rate of M. varians exponentially
Figure 3.
Simulation of the growth of Cyclotella meneghiniana based on experimental data according
to non-interactive multiplicative Equation (ST25) ((
A
); R
2
= 0.52; AIC =
−
34.29), interactive multi-
plicative Equation (ST15) ((
B
); R
2
= 0.80; AIC =
−
43.90), and polynomial Equation (4) ((
C
); R
2
= 0.58;
AIC = −34.25).
Phycology 2023,3423
3.2.4. Melosira varians
The growth of M. varians at various temperature and conductivity levels was best sim-
ulated with the interactive Equation (ST11) (R2= 0.57; AIC = −51.79; Figure 4B; Table S7):
µ=µ20 ×θT−20× 1−S−So pt
Smax ×(1+aST ×T)−Sopt 2!(ST11)
where
µ20
(1/d) is the growth rate at 20
◦
C;
Sopt
(mS/cm) is the optimum conductivity; and
Smax (mS/cm) is the maximum conductivity above which the growth ceases.
Phycology 2023, 3, FOR PEER REVIEW 12
increased with increasing temperature at the investigated range (𝜃 = 1.11; Table S7; Figure
4B). At low salinity levels, the growth rate of M. varians increased with increasing conduc-
tivity and reached the maximum growth rate at 1.20 mS/cm (1.06–1.34 mS/cm; Table S7).
Above this optimum conductivity, the growth rate decreased with increasing conductiv-
ity and ceased at the maximum conductivity of 6.41 mS/cm (3.81–8.90 mS/cm; Table S7).
Moreover, the maximum conductivity might be lowered by temperature increases. This
interaction explains the lower growth rate at 25 °C compared to the rate at lower temper-
atures at low conductivity (Figure S1D). In other words, the effect of temperature was
hidden in the interaction term. Different temperature and salinity responses could be in-
terpreted by the best non-interactive multiplicative equation, which also has all significant
coefficients (Equation (ST9); R2 = 0.21; AIC = −42.61; Figure 4A; Table S7). With this equa-
tion, the maximum growth rate of M. varians (0.44; 1/d) was obtained in the medium with-
out addition of NaCl and at 15.5 °C (9.5–21.5 °C) (Figure 4A). The growth of this diatom
was linearly inhibited by NaCl at any concentration. In addition, the growth of M. varians
ceased at the temperature outside the range of 15.5 ± 9.4 °C (thermal breadth: 18.8 °C;
Table S7). In contrast to the influence of temperature and salinity estimated by multiplica-
tive equations, non-significant effects were predicted by polynomial equations (Table S7).
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
A
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
B
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
C
Figure 4. Simulation of the growth of Melosira varians based on experimental data according to non-
interactive multiplicative Equation (ST9) ((A); R2 = 0.21; AIC = −42.61), interactive multiplicative
Figure 4.
Simulation of the growth of Melosira varians based on experimental data according to
non-interactive multiplicative Equation (ST9) ((
A
); R
2
= 0.21; AIC =
−
42.61), interactive multiplica-
tive Equation (ST11) ((
B
); R
2
= 0.57; AIC =
−
51.79), and polynomial Equation (5) ((
C
); R
2
= 0.45;
AIC = −45.37).
Equation (ST11) stood out as it had the lowest AIC and included all significant co-
efficients (Table S7). According to this equation, the growth rate of M. varians exponen-
tially increased with increasing temperature at the investigated range (
θ
= 1.11; Table S7;
Figure 4B). At low salinity levels, the growth rate of M. varians increased with increasing
conductivity and reached the maximum growth rate at 1.20 mS/cm (1.06–1.34 mS/cm;
Table S7). Above this optimum conductivity, the growth rate decreased with increasing
conductivity and ceased at the maximum conductivity of 6.41 mS/cm (3.81–8.90 mS/cm;
Table S7). Moreover, the maximum conductivity might be lowered by temperature in-
creases. This interaction explains the lower growth rate at 25
◦
C compared to the rate at
lower temperatures at low conductivity (Figure S1D). In other words, the effect of tem-
perature was hidden in the interaction term. Different temperature and salinity responses
could be interpreted by the best non-interactive multiplicative equation, which also has
all significant coefficients (Equation (ST9); R
2
= 0.21; AIC =
−
42.61; Figure 4A; Table S7).
Phycology 2023,3424
With this equation, the maximum growth rate of M. varians (0.44; 1/d) was obtained in the
medium without addition of NaCl and at 15.5
◦
C (9.5–21.5
◦
C) (Figure 4A). The growth of
this diatom was linearly inhibited by NaCl at any concentration. In addition, the growth of
M. varians ceased at the temperature outside the range of 15.5
±
9.4
◦
C (thermal breadth:
18.8
◦
C; Table S7). In contrast to the influence of temperature and salinity estimated by
multiplicative equations, non-significant effects were predicted by polynomial equations
(Table S7).
3.2.5. Ulnaria acus
With more data on the growth of U. acus, more equations could be applied (Ta-
ble S8). A number of equations yielded statistically significant estimates of all coefficients
(Table S8). Among them, Equation (ST35) could describe the growth of this diatom strain
best (R2= 0.74; AIC = −94.70; Figure 5B) with all significant coefficients (Table S8):
µ=µmax ×e−kT×(T−To pt×(1+aST ×S))2× 1−S−Sopt
Smax −So pt 2!(ST35)
where
kT
(1/
◦
C
2
) is the temperature effect factor describing the change in the growth rate,
with increasing temperature below or above the optimum (
Topt
;
◦
C);
Sopt
and
Smax
(mS/cm)
are the optimum and maximum conductivity for the growth, respectively; and a
ST
(cm/mS)
represents the interactive effect. Also, the second (Equation (ST17), AIC =
−
90.30) and
third (Equation (ST33), AIC =
−
89.33) ranking model had interactive effects, whilst the best
non-interactive model (Equation (ST18)) yielded poor performance (AIC =
−
88.67; Table S8).
Phycology 2023, 3, FOR PEER REVIEW 13
Equation (ST11) ((B); R2 = 0.57; AIC = −51.79), and polynomial Equation (5) ((C); R2 = 0.45; AIC =
−45.37).
3.2.5. Ulnaria acus
With more data on the growth of U. acus, more equations could be applied (Table S8).
A number of equations yielded statistically significant estimates of all coefficients (Table
S8). Among them, Equation (ST35) could describe the growth of this diatom strain best (R2
= 0.74; AIC = −94.70; Figure 5B) with all significant coefficients (Table S8):
𝜇=𝜇×𝑒××××1− 𝑆−𝑆
𝑆−𝑆 (ST35)
where 𝑘𝑇 (1/°C2) is the temperature effect factor describing the change in the growth rate,
with increasing temperature below or above the optimum (𝑇𝑜𝑝𝑡 ; °C); 𝑆𝑜𝑝𝑡 and 𝑆𝑚𝑎𝑥
(mS/cm) are the optimum and maximum conductivity for the growth, respectively; and
aST (cm/mS) represents the interactive effect. Also, the second (Equation (ST17), AIC =
−90.30) and third (Equation (ST33), AIC = −89.33) ranking model had interactive effects,
whilst the best non-interactive model (Equation (ST18)) yielded poor performance (AIC =
−88.67; Table S8).
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
15
20
25
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
A
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
15
20
25
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
B
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
10
15
20
25
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
C
Figure 5.
Simulation of the growth of Ulnaria acus based on experimental data according to non-
interactive multiplicative Equation ST18 ((
A
); R
2
= 0.67; AIC =
−
88.67), interactive multiplicative
Equation ST35 ((
B
); R
2
= 0.74; AIC =
−
94.70), and polynomial Equation (4) ((
C
); R
2
= 0.51; AIC =
−
80.87).
Phycology 2023,3425
According to Equation (ST35), the growth of U. acus reached the maximum rate of 0.52
(1/d) at 17.1
◦
C (12.2–22.0
◦
C) and 1.08 mS/cm (0.79–1.37 mS/cm) (Figure 6B; Table S8).
Remarkably, the optimum of the symmetric temperature–growth curve was swept left by
salinization (Table S8). Including such interactive effects improved the predictive potential
as shown by better statistical parameters in the estimation with Equation (ST35) (with
interactions) compared to Equation (ST34) (without interactions; Table S8). The growth
of U. acus ceased at conductivity above 2.29 mS/cm (2.02–2.56 mS/cm; Table S8). The
response to temperature and salinity in Equation (ST35) could be similarly expressed by
Equation (ST33), which yielded a thermal breadth of 28.1 ◦C (11.7–44.4 ◦C; Table S8).
Phycology 2023, 3, FOR PEER REVIEW 15
multiplicative Equation (ST52) (R2 = 0.86; AIC = −219.61; Figure 6B; Table S9) or the non-
interactive polynomial Equation (4) (R2 = 0.84; AIC = −222.78; Figure 6C; Table S9). More-
over, all the best formulation forms display a non-interactive norm that is consistent with
the data fiing with polynomial equations (Table S9).
-0.4
-0.2
0.0
0.2
0.4
0.6
0
5
10
15
20
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
A
-0.4
-0.2
0.0
0.2
0.4
0.6
0
5
10
15
20
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
B
-0.4
-0.2
0.0
0.2
0.4
0.6
0
5
10
15
20
10
12
14
16
18
20
22
24
Specific growth rate (1/d)
Conductivity (mS/cm)
Temperature (
o
C)
C
Figure 6. Simulation of the growth of Navicula gregaria based on experimental data according to non-
interactive multiplicative Equation (ST26) ((A); R2 = 0.86; AIC = −229.82), interactive multiplicative
Equation (ST52) ((B); R2 = 0.83; AIC = −219.61), and polynomial Equation (4) ((C); R2 = 0.84; AIC =
−222.78).
3.3. Temperature and Salinity Tolerance of Freshwater Diatoms
In the present study, we aempted to estimate the salinity and temperature sensitiv-
ity of selected freshwater diatom strains by shock treatments, meaning that the cultures
were not acclimated to the treatment conditions before their growth rates were measured.
This means that our data might underestimate the niche breadth as well as the severity of
non-optimal growth conditions upon growth rates. The lack of a uniform acclimation
phase might also contribute to a relatively high noise-to-signal ratio in our growth rate
measurements. With these reservations, we summarize the general conclusions from the
above observations as relating to possible shapes of the temperature–salinity response
Figure 6.
Simulation of the growth of Navicula gregaria based on experimental data according to
non-interactive multiplicative Equation (ST26) ((
A
); R
2
= 0.86; AIC =
−
229.82), interactive multiplica-
tive Equation (ST52) ((
B
); R
2
= 0.83; AIC =
−
219.61), and polynomial Equation (4) ((
C
); R
2
= 0.84;
AIC = −222.78).
According to the best non-interactive multiplicative equation (Equation (ST18); R
2
=
0.67; AIC =
−
88.67; Table S8; Figure 5A), the conductivity–growth curve exhibits asymmet-
ric responses, i.e., at conductivity above the optimum, the growth rate decreases with a
higher slope compared to the change at conductivity below the optimum. Higher uncer-
tainty is included in the estimation with this equation as two effect factors are required to
simulate the asymmetric response (Table S8). Statistically significant estimates of all coeffi-
cients could be obtained when the number of coefficients was reduced (Equations (ST5),
(ST9), (ST10), (ST19), and (ST25); Table S8). However, these equations display different
temperature- and conductivity-growth responses. Contrasting with a common bell-shaped
response curve (Equations (ST5), (ST10), (ST9), and (ST25)), Equation (ST9) exhibits a
Phycology 2023,3426
linear inhibition of the growth rate by salinization. Equations (ST10) and (ST25) display an
exponential increase in the growth rate with increasing temperature (monotonic response),
while the other equations show the opposite trend at temperatures above the optimum
(bell-shaped response). In contrast to such influences of temperature and salinity predicted
with these equations, the growth rate of U. acus was estimated to be not significantly
affected based on polynomial equations (Table S8; Figure 5C).
3.2.6. Navicula gregaria
Data fitting for the growth of N. gregaria with a number of equations yielded statisti-
cally significant coefficients, albeit with different interpretations (Table S9). According to
Equations (ST5), (ST15), (ST6), (ST9), (ST19), (ST20), and (ST48), this diatom exhibited a
symmetric response to temperature changes, contrasting with Equations (ST26) and (ST47).
Most of the equations indicate a decrease in the growth rate with decreasing electrical
conductivity, while Equations (ST15) and (ST19) represented a bell-shaped response curve.
Based on AIC, the growth rate of N. gregaria could be best explained by non-interactive
Equation (ST26) (R2= 0.86; AIC = −229.82; Figure 6A; Table S9):
µ=µmax ×(e−kT1×(T−To pt)2f or T ≤Topt
e−kT2×(T−Topt )2f or T >Topt
×e−kS×(S−Sopt )2(ST36)
where
µmax
(1/d) is the maximum growth rate obtained at the optimum temperature
Topt
(
◦
C) and the optimum conductivity
Sopt
(mS/cm);
kT1
and
kT2
(1/
◦
C
2
) are the temperature
effect factors at temperature below and above the optimum, respectively; and
kS
(cm
2
/mS
2
)
is the salinity effect factor.
According to Equation (ST26), N. gregaria responded to temperature changes in an
asymmetric norm. In particular, the growth rate decreased more strongly with temperature
increases at high temperatures than at low temperatures. This contrasted with the sym-
metric response to salinity changes. The maximum growth rate (0.6; 1/d) was reached at
18.4
◦
C (17.3–19.4
◦
C) and 2.13 mS/cm (0.29–3.96 mS/cm; Table S9). Equation (ST26) could
explain the variation in the growth rate of N. gregaria better than the interactive multiplica-
tive Equation (ST52) (R
2
= 0.86; AIC =
−
219.61; Figure 6B; Table S9) or the non-interactive
polynomial Equation (4) (R
2
= 0.84; AIC =
−
222.78; Figure 6C; Table S9). Moreover, all
the best formulation forms display a non-interactive norm that is consistent with the data
fitting with polynomial equations (Table S9).
3.3. Temperature and Salinity Tolerance of Freshwater Diatoms
In the present study, we attempted to estimate the salinity and temperature sensitivity
of selected freshwater diatom strains by shock treatments, meaning that the cultures were
not acclimated to the treatment conditions before their growth rates were measured. This
means that our data might underestimate the niche breadth as well as the severity of
non-optimal growth conditions upon growth rates. The lack of a uniform acclimation phase
might also contribute to a relatively high noise-to-signal ratio in our growth rate measure-
ments. With these reservations, we summarize the general conclusions from the above
observations as relating to possible shapes of the temperature–salinity response surfaces.
For further refinement of the modelling approach, pre-acclimated culture experiments will
be beneficial.
The temperature tolerance range could be well estimated by empirical modelling
described in the previous section for investigated diatom strains, except for M. varians
and C. meneghiniana (Table 2). The growth rate of M. varians was expected to increase
exponentially with increasing temperature with the best equation, as mentioned above.
Our analysis indicates small variations in the optimum temperature among investigated
freshwater diatoms (Table 2). In contrast, larger variations were revealed in the thermal
breadth (Table 2). Among the diatoms, C. meneghiniana had the widest thermal tolerance,
followed by N. linearis and U. acus (Table 2). The variations in the optimum temperature
Phycology 2023,3427
among the investigated freshwater diatoms (except for M. varians) were smaller than those
reported in previous studies, probably related to the difference in the isolation approaches.
For example, from other previous studies, the optimum temperature range differs among
estuarine epipelic diatoms isolated from cohesive sediments sampled from three different
sites along the Colne Estuary, UK: 10–20
◦
C for Navicula phyllepta, 10–30
◦
C for Navicula
perminuta, and 20–35
◦
C for Navicula salinarum [
42
]. The diatom N. gregaria isolated from
the epipelon reached the maximal growth at the lowest temperature (15
◦
C), compared to
Nitzschia gracilis and Nitzschia palea isolated from the epiphyton, Navicula minima v. atomides
(20
◦
C) from the episammon, or Navicula seminulum (30
◦
C) from the epipelon [
22
]. The
growth of an estuarine clone of Nitzschia americana increased with increasing temperature
up to 25 ◦C, above which the growth rate declined [29].
Table 2.
Temperature and salinity tolerance of the freshwater diatoms estimated with the best equation.
Strain
Temperature Response Salinity Response
Optimum
Temperature
(◦C)
Thermal
Breadth (◦C)
Temperature
Tolerance
Range (◦C)
Optimum
Conductivity
(mS/cm)
Maximum
Conductivity
(mS/cm)
Half-
Saturation
Conductivity
(mS/cm)
Cymbella cf.
incurvate 15.8 (15.3–16.3) 14.8 (12. 7–16.9) 15.5 ±7.4 0.63 (0.35–0.90) 1.81 (1.75–1.88) 0.81 (0.01–1.61)
Nitzschia linearis
15.9 (14.7–17.1) 31.8 (24.1–39.4) 15.9 ±15.9 2.44 (2.02–2.87) 5.29 (4.84–5.74) 4.60 (1.17–8.04)
Cyclotella
meneghiniana 17.3 (13.9–20.8) 59.6 (0–121.0) 17.3 ±29.8 0.69 (0.58–0.81) 1.38 (1.06–1.71)
Melosira varians 1.20 (1.06–1.34) 6.41 (3.81–8.90)
Ulnaria acus 17.1 (12.2–22.0) 28.1 (11.7–44.4) 17.1 ±14.1 1.08 (0.79–1.37) 2.29 (2.02–2.56)
Navicular
gregaria 18.4 (17.3–19.4) 19.3 (17.9–20.6) 18.4 ±9.7 2.12 (0.29–3.96) 9.01
(6.65–11.37)
The optimum and the maximum conductivity could be estimated for all investigated
strains, demonstrating N. linearis,M. varians, and N. gregaria as the most tolerant (Table 2).
By contrast, C. incurvata and C. meneghiniana were the most sensitive to salinization with the
lowest optimum and maximum conductivity (Table 2). Except for N. gregaria, the growth of
the investigated freshwater diatoms ceased at electrical conductivity above 8.90 mS/cm
(Table 2). Our results reveal the difference in the tolerance to temperature and salinity
changes among the investigated freshwater diatoms. As a result of species-specific tolerance
to salinity, the species composition and distribution of diatoms has been considered to be
indicative of salinity gradients [
43
–
51
]. Therefore, an understanding of the tolerance of
diatoms to salinity might provide a better understanding on their distribution in nature
and facilitate predicting the species succession. Consequently, diatom-based models have
been developed to quantitatively reconstruct salinity changes [47,48,52].
Different mathematical formulations of single-stressor reaction norms can be classi-
fied into two groups: (1) formulations that describe a monotonic response to increasing
stressor intensity; and (2) formulations that exhibit a bell-shaped (unimodal or hormetic)
relationship. The bell-shaped curve can be symmetric around the optimum or asymmetric,
i.e., the response decreases to the right more steeply than to the left. In other words, at high
stressor intensity, small changes in this environmental variable could significantly inhibit
the growth of diatoms. The more profound inhibition of diatom growth by changes at high
levels compared to low ranges reported previously [
32
,
53
] is clear evidence of the asym-
metric response of diatoms. In this regard, our data set generated from four to five different
temperature treatments is not sufficiently informative to differentiate between the latter
two possibilities for temperature reaction norms. Furthermore, interactive effects between
temperature and salinity might lead to or change the asymmetric response to one of these
two environmental variables, as discussed below. The asymmetric temperature–growth
curve for diatoms is also supported by their different responses between the stressor regime
and the recovery phase [
54
]. In terms of responses to salinity changes, we found both
Phycology 2023,3428
monotonically decreasing as well as bell-shaped curves, indicating that some freshwater
diatoms from the sampled habitat perform better under elevated salt concentrations than
at very low salt levels. This is not surprising insofar as the locality sampled being affected
by elevated salinity levels (conductivity often reaching, sometimes exceeding, 2 mS/cm).
3.4. Ambiguity in Empirically Modelling Interactive Effects under Various
Environmental Conditions
3.4.1. Diversity of Interaction Types
Our assessment above indicates ambiguity in evaluating the effects of temperature
and salinity on diatom growth by empirical modelling. Further ambiguity is inherent in
the assessment of interactions between these two factors. Interactions between temperature
and salinity could be interpreted in different ways (Tables S4–S9, Supplementary material).
Of the two polynomial equations used, the one without interaction (Equation (4)) better
described the growth of C. incurvata,N. linearis,C. meneghiniana,M. varians,U. acus, and N.
gregaria than the one with interaction (Equation (5)), based on AIC (Tables S4–S9). Several
further possibilities could be conceived to capture possible interactive effects in polynomial
models. However, for the forms applied here, we generally conclude that polynomial
formulations were never among the best fitting models tested. Beyond polynomials, a
number of multiplicative equations indicated significant interactive effects of temperature
and salinity (Tables S4–S9). For four of the six tested strains, interactive models were found
to be the best based on AIC values (Tables S4–S9). With respect to ecological reaction norms,
interactive effects of two stressors are conceivable in several different types, as illustrated
in Tables 3and 4. The two main basic types of interactive effects can be summarized in
several ways: one stressor shifting the location of the optimum to another; one stressor
changing the slope of the (monotonic or bell-shaped) response curve, on one or both sides
of the optimum; and one stressor affecting through a combination of the above mechanisms.
Previous studies have also indicated that temperature and salinity might interact with
each other, affecting the growth of diatoms [
29
,
55
,
56
]. The interactions revealed in the
present study have been reported previously, mostly for marine diatoms. For example,
the optimum temperature for the growth of the diatom N. americana depended on the
salinity level [29]. The tolerance of Thalassiosira rotula to low salinity levels increased with
temperatures ranging from 0 to 15 ◦C [57].
Table 3.
Illustration of various types of interactive effects visualized by a comparison of changes in
the shape of a reaction norm.
Interaction ID Type of Interaction Interactive Effects Simulation
AStressor 1—modulated slope
of the response to stressor 2
Salinization increased or
decreased the slope of the
temperature–growth curve,
which is accompanied by the
narrowed or broadened thermal
breadth, respectively. Similar
effects can be exerted by
temperature increases on the
conductivity–growth curve.
Phycology 2023, 3, FOR PEER REVIEW 18
Table 3. Illustration of various types of interactive effects visualized by a comparison of changes in
the shape of a reaction norm.
Interaction
ID Type of Interaction Interactive Effects Simulation
A
Stressor 1—modu-
lated slope of the re-
sponse to stressor 2
Salinization increased or decreased the
slope of the temperature–growth curve,
which is accompanied by the narrowed
or broadened thermal breadth, respec-
tively. Similar effects can be exerted by
temperature increases on the conductiv-
ity–growth curve.
B
Stressor 1—shifted
optimum level of
stressor 2
Salinization increases the optimum
temperature of the bell-shaped temper-
ature–growth curve
C Combination of A and
B
The temperature–growth curve is mod-
ulated both vertically and horizontally
b
y salinization. Salinization narrows
the thermal breadth. Both the optimum
temperature and the maximum growth
rate are lowered.
Table 4. Various types of interactions revealed for freshwater diatoms. The best model for each strain
with respect to AIC value marked with double asterisk; models within 6 AIC units from the laer
(relative likelihood compared to best model < 5%) with a single asterisk.
Equation Interaction ID
AIC
Cymbella rrrr
incurvata
Nitzschia rrrr
linearis
Cyclotella rrrr
meneghiniana
M
elosia rrrr
varians Ulnaria acus Navicula rrrr
g
regaria
ST7 A −52.53 −33.02
ST15 A −133.49 ** −43.90 ** −173.43
ST17 A −131.76 * −90.30 *
ST34 A −88.75 *
ST11 A −56.91 −51.79 **
ST21 A −120.46 −32.72 −42.93
ST31 A −43.25
ST22 A −117.83 −78.93
ST23 A −118.88 −87.97 *
ST37 A −88.43 *
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Table 3. Cont.
Interaction ID Type of Interaction Interactive Effects Simulation
BStressor 1—shifted optimum
level of stressor 2
Salinization increases the
optimum temperature of the
bell-shaped temperature
–growth curve
Phycology 2023, 3, FOR PEER REVIEW 18
Table 3. Illustration of various types of interactive effects visualized by a comparison of changes in
the shape of a reaction norm.
Interaction
ID Type of Interaction Interactive Effects Simulation
A
Stressor 1—modu-
lated slope of the re-
sponse to stressor 2
Salinization in