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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 *

Phycology 2023,3429

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