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biology
Article
Leave or Stay: Simulating Motility and Fitness of
Microorganisms in Dynamic Aquatic Ecosystems
Alexandra Klimenko 1, 2, * , Yury Matushkin 1,2,3 , Nikolay Kolchanov 1,2,3 and Sergey Lashin 1,2,3
Citation: Klimenko, A.;
Matushkin, Y.; Kolchanov, N.; Lashin,
S. Leave or Stay: Simulating Motility
and Fitness of Microorganisms in
Dynamic Aquatic Ecosystems. Biology
2021,10, 1019. https://doi.org/
10.3390/biology10101019
Academic Editor: John R. Turner
Received: 7 September 2021
Accepted: 4 October 2021
Published: 9 October 2021
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4.0/).
1
Systems Biology Department, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of
Science, Lavrentiev Avenue 10, 630090 Novosibirsk, Russia; mat@bionet.nsc.ru (Y.M.);
kol@bionet.nsc.ru (N.K.); lashin@bionet.nsc.ru (S.L.)
2
Kurchatov Genomics Center, Institute of Cytology and Genetics, Siberian Branch of the Russian Academy of
Science, Lavrentiev Avenue 10, 630090 Novosibirsk, Russia
3Natural Science Department, Novosibirsk State University, Pirogova St. 1, 630090 Novosibirsk, Russia
*Correspondence: klimenko@bionet.nsc.ru
Simple Summary:
Motile bacteria are widespread in various water ecosystems along with nonmotile
species, which posits the question: what makes motility an advantage in such habitats, and under
what conditions? This simulation study addresses these problems using a computer model of
competition of two microbial species: Nomad of a motile population and Settler of a sedentary
one. We simulated their competition under various environmental conditions such as the nutrient
availability and frequency of changes in the location of the nutrient source as well as depending on
some population parameters determining how much energy it takes for a bacterium to migrate and
what the effect of density-dependent mortality is on the outcome of Settler vs. Nomad competition.
We showed that dynamic and nutrient-scarce environments favour motile populations, whereas
nutrient-rich and stagnant environments promote sedentary microorganisms. Moreover, the energetic
costs of migration determine whether or not the motile population outcompetes the sedentary one,
though it also depends on such conditions as nutrient availability. There is also another way for
Settler to succeed even without penalties for migration—by grasping an opportunity to occupy the
nutrient source, bringing about a biotic desert around it, which cannot be overcome by Nomad
constantly searching for locally optimal conditions.
Abstract:
Motility is a key adaptation factor in scarce marine environments inhabited by bacteria. The
question of how a capacity for adaptive migrations influences the success of a microbial population
in various conditions is a challenge addressed in this study. We employed the agent-based model
of competition of motile and sedentary microbial populations in a confined aquatic environment
supplied with a periodic batch nutrient source to assess the fitness of both. Such factors as nutrient
concentration in a batch, batch period, mortality type and energetic costs of migration were considered
to determine the conditions favouring different strategies: Nomad of a motile population and
Settler of a sedentary one. The modelling results demonstrate that dynamic and nutrient-scarce
environments favour motile populations, whereas nutrient-rich and stagnant environments promote
sedentary microorganisms. Energetic costs of migration determine whether or not the Nomad
strategy of the motile population is successful, though it also depends on such conditions as nutrient
availability. Even without penalties for migration, under certain conditions, the sedentary Settler
population dominates in the ecosystem. It is achieved by decreasing the local nutrient availability
near the nutrient source, as motile populations relying on a local optimizing strategy tend to follow
benign conditions and fail, enduring stress associated with crossing the valleys of suboptimal
nutrient availability.
Keywords:
motility; migratory costs; marine bacteria; agent-based modelling; ecological modelling
Biology 2021,10, 1019. https://doi.org/10.3390/biology10101019 https://www.mdpi.com/journal/biology
Biology 2021,10, 1019 2 of 17
1. Introduction
In contrast to well-studied symbiotic gut microbiota living in abundant nutrient
conditions, marine bacteria live in the world of scarce and ephemeral nutrition sources.
Hence, motility is one of the key factors of adaptation in these conditions [
1
], providing
bacteria with an advantage in resource-limited physically structured habitats, even in the
case of undirected motility [
2
]. The capacity to sense the gradients of essential chemicals,
which is known as chemotaxis, is very important for the adaptive potential of bacterial
motility [
3
,
4
]. The biophysics and molecular and signalling machinery of chemotaxis
in model organisms such as Escherichia coli are relatively well-studied at the microscale
level
[5–11]
, namely the results of the immediate reaction of bacterial cells to their local
environment. However, there is a lack of understanding of how the ability for adaptive mi-
grations influences the evolutionary success of a population. Overall, adaptive migrations
of microorganisms act as a key factor involved in resolving the struggle for existence in
microbial ecosystems [12,13].
There are two different strategies microorganisms resort to when facing environmental
changes: either the adaptation to existing conditions, e.g., by adjusting their metabolism to
an alternative energy source; or migration following the optimal environmental conditions
and invading new biotopes, where they compete with the species of a local commu-
nity [
14
–
16
]. Both strategies are relevant for marine bacteria who can either attach to the
nutrient sources and colonize it by growing a biofilm or rapidly detect short-lived nutrient
sources and constantly move towards them as fugitive species do [
17
]. The impact of such
an adaptive behaviour at the scale of individuals on the community-level dynamics is
of a fundamental scientific interest since it is important for achieving a comprehensive
understanding of structure and functioning of respective ecosystems. Moreover, this inter-
connection is covered by the perspective on particular aspects of ecology and evolution of
search behaviour [18].
The problem of interrelation between migratory activity and population fitness has
been investigated in many species; among those are marine fish such as the Salmonidae
family, bacteria (Escherichia coli) and amoeba (Dictyostelium discoideum) [
19
–
22
]. Motility
improves foraging behaviour and raises the chances of successful mating; however, a
migratory activity of organisms incurs certain energetic costs, whereas the cell’s energy
reserve might be invested into the reproduction instead of migration [
23
,
24
]. Various
groups of organisms manage this emerging trade-off between reproductive investment and
migration differently. For instance, chinook salmon resort to developmental modification,
resulting in an increased number-to-size ratio of eggs with a greater migration distance [
25
].
However, unicellular organisms cannot enjoy such flexibility at the tissue- and organ-
level and are compelled to meet the challenge by adopting a particular life strategy on a
species level or, in some cases, at the level of the population by implementing diversified
phenotypes [
26
] and dynamic life strategies [
27
]. Motility and chemotaxis are widespread
among bacteria inhabiting marine environments [
1
,
28
,
29
], though nonmotile groups such
as SAR11 [
30
,
31
] and Prochlorococcus [
32
] do exist as well. The cost of motility varies
for different species: marine bacteria, such as Vibrio alginolyticus and Pseudoalteromonas
haloplanktis, swim ~3- to 5-fold faster than E. coli, whose typical velocity range is 15 to
30
µ
m/s, and spend a ~10- to 25-fold larger amount of energy (because the propulsive
power increases with the square of the swimming speed) [
28
]. Consider the fact that the
most expensive part of E. coli’s motility is the synthesis and operation of flagella, which
constitutes ~2% and ~0.1% of their energy expenditure, respectively [
33
]. From here, one
can obtain an estimate of the energy expenditure spent for motility among marine bacteria
ranging from 2% to 50% of their total energy budgets. In this way, the fitness cost of
motility in bacteria is associated with both direct spending energy on movement (e.g., via
rotating flagella) and with the maintenance of respective molecular machinery, especially
the biosynthesis of flagella [
34
]. Thus, migration via chemotaxis can be quite expensive
for the energy budgets of motile bacteria posing a trade-off between energy investment
into optimal foraging strategies and allocation of resources into direct reproduction. This
Biology 2021,10, 1019 3 of 17
growth–motility trade-off has been recently explored in [
23
], where the regulation of such
complex and costly bacterial behaviours as motility and chemotaxis has been investigated
as a function of the bacterial growth rate, both theoretically and experimentally. Studying
the impact of such a trade-off on a population’s fitness in aquatic ecosystems constitutes
a great challenge for modelling eco-evolutionary processes, and that is the question we
would like to address in this simulation study.
2. Materials and Methods
Despite some recent experimental progress [
23
], the problem of interconnection be-
tween a migratory capacity of organisms and their fitness remains largely obscure. More-
over, high-throughput pairwise competition experiments might be challenging because
they are costly, and it is difficult to assess species-specific migratory costs
in vivo
and to
choose appropriate model species. On the other hand, computational simulation enables a
researcher to investigate the space solution thoroughly and draw conclusions for a gen-
eral case. To a certain extent, one can consider this problem to be a special case of the
interconnection between genotype and phenotype. In this case, we deal with a complex
behavioural phenotype that is influenced by a number of factors ranging from the nutrient
concentration in the local environment of motile cells to ecological interactions with the
representatives of other species.
Therefore, to obtain the answers to the questions raised above, we have built a simpli-
fied model of competition of two microbial populations in confined aquatic environment
supplied with a periodically blinking batch nutrient source. One of the populations pos-
sesses a chemotaxis capacity being able to migrate adaptively along the nutrient gradient,
whereas another one is sedentary and distributes undirectedly by the process of passive
transport (e.g., as a result of cell shoving), which, on a large scale, is similar to diffu-
sion for substances (see Figure 1a). A comparison of final abundances of two competing
populations with different strategies in various conditions sheds light on whether mi-
gration grants an advantage in these conditions or not compared to spending energy for
immediate reproduction.
Biology 2021, 10, x FOR PEER REVIEW 3 of 18
growth–motility trade-off has been recently explored in [23], where the regulation of such
complex and costly bacterial behaviours as motility and chemotaxis has been investigated
as a function of the bacterial growth rate, both theoretically and experimentally. Studying
the impact of such a trade-off on a population’s fitness in aquatic ecosystems constitutes
a great challenge for modelling eco-evolutionary processes, and that is the question we
would like to address in this simulation study.
2. Materials and Methods
Despite some recent experimental progress [23], the problem of interconnection be-
tween a migratory capacity of organisms and their fitness remains largely obscure. More-
over, high-throughput pairwise competition experiments might be challenging because
they are costly, and it is difficult to assess species-specific migratory costs in vivo and to
choose appropriate model species. On the other hand, computational simulation enables
a researcher to investigate the space solution thoroughly and draw conclusions for a gen-
eral case. To a certain extent, one can consider this problem to be a special case of the
interconnection between genotype and phenotype. In this case, we deal with a complex
behavioural phenotype that is influenced by a number of factors ranging from the nutrient
concentration in the local environment of motile cells to ecological interactions with the
representatives of other species.
Therefore, to obtain the answers to the questions raised above, we have built a sim-
plified model of competition of two microbial populations in confined aquatic environ-
ment supplied with a periodically blinking batch nutrient source. One of the populations
possesses a chemotaxis capacity being able to migrate adaptively along the nutrient gra-
dient, whereas another one is sedentary and distributes undirectedly by the process of
passive transport (e.g., as a result of cell shoving), which, on a large scale, is similar to
diffusion for substances (see Figure 1a). A comparison of final abundances of two com-
peting populations with different strategies in various conditions sheds light on whether
migration grants an advantage in these conditions or not compared to spending energy
for immediate reproduction.
Start source
Distant source
Diffusion
Blinking
Diffusion
Rich
environments Poor and
extremely
scarce
environments
Model
Dynamic
environments
Stagnant
environments
Linear
Quadratic
No costs
High costs
“Settler” population
•Undirected slow movement
“Nomad” population
•Undirected slow
movement +
•10% of population
actively migrate along
the nutrient gradient
via chemotaxis
Nutrient concentration
a
bc
Start
position
of Settler
and
Nomad
Figure 1. Conceptual diagram of two population strategies (a), the habitat structure (b) and simulation scenarios (c).
Biology 2021,10, 1019 4 of 17
2.1. The Settler–Nomad Model
We have used the Haploid Evolutionary Constructor (HEC) [
35
–
37
] software to build
the models of competition of motile and sedentary populations of microorganisms in a
confined aquatic environment supplied with a periodic batch nutrient source. The HEC
is designed for building agent-based models of microbial communities [
38
]. It is based
on the super-individual concept [
39
] and allows creating multilayer ecological models of
microbial populations inhabiting spatially structured environments. The basic functionality
of HEC (see Supplementary Materials for a detailed description) was extended to take into
account the diversity in energetic costs of migration.
To estimate which conditions allow the motile population to make use of its advantage
and dominate over the sedentary one, we have investigated a model of a community
consisting of two microbial populations in different model scenarios (see Section 2.2 for
details). These populations inhabit a spatially structured environment supplied with a
periodic source of a nutrient (also called nonspecific substrate or NS), which distributes
throughout the environment via diffusion. A 10
×
10 2-dimensional (2D) square lattice
with non-permeable boundaries represents the spatial structure of the habitat in the model
(see Figure 1b). Such an environment can be regarded as a counterpart of a stagnant
pond. The nutrient source blinks periodically between the two opposite corners of the
lattice. That is, the nutrient comes into the system in batches periodically either through
the top-left corner or through the bottom-right corner at a time. Let us call “start source”
the NS source position that coincides with the start location occupied by both populations
of microorganisms and “distant source” the NS source position that is located in the
opposite corner of the lattice. Thus, both nutrient sources refresh asynchronously—the
“start source” goes first and after a certain time period elapses it turns out to be depleted
while the nutrient is supplied via the “distant source” for the same period until the nutrient
source blinks back to the start position and the cycle runs all over again. This blinking
periodic change of nutrient supply is one of the simplest cases of a dynamically changing
habitat with contrasting conditions, which might be associated with external factors that
result in periodic appearance of nutrient sources in different parts of the system, such
as, for example, periodic organic effluents to the aquatic environment. The time step is
synchronized with an average generation turnover, which is considered equal to 30 min to
be definite. Initially, the nutrient is distributed spatially homogeneously, but subsequently,
the heterogeneity increases due to the localized batch nutrient source and foraging activity
of cells.
Henceforth, we will refer to the population of motile microorganisms as Nomad and
to the population of sedentary microorganisms as Settler. We will also refer to the described
above model as the Settler–Nomad model.
At the [i,j] node of the spatial lattice, the population abundances on the (n+ 1)-th
iteration of both Nomad and Settler populations obey the following balance equation:
Pn+1[i,j]=growth(Pn[i,j],r[i,j]) −mort(PSettler
n[i,j],PNom ad
n[i,j])+
+immi gr(Pn[neighbourhood]) −emigr(Pn[i,j]) (1)
where
Pn+1[i,j]
is the population abundance on the (n+ 1)-th iteration, r[i,j] is the number
of accumulated nutrient molecules by the cells of the population (population energy re-
serve),
immi gr(Pn[neighbourhood])
is the population abundance increase associated with
the cells of the same population immigrated into the [i,j] node from its 4-cross neighbour-
hood,
emigr(Pn[i,j])
is the population abundance decrease associated with the cells of the
same population emigrated from the [i,j] node (both processes are described in the Supple-
mentary Materials, Document S1) and
growth(Pn[i,j],r[i,j])
is the term that expresses the
population’s growth with the nutrient availability as a limiting factor:
growth(Pn[i,j],r[i,j]) =Pn[i,j]·1+r[i,j]/K
1+r[i,j]/(B·K+N)(2)
Biology 2021,10, 1019 5 of 17
where Nis the genetically determined nutrient utilization efficacy (in this paper, N= 1), B,K
are the adjustable parameters shaping the abundance curve (see Supplementary Materials,
in our case, K= 5, B= 0.8), and
Pn+1[i,j]
and r[i,j] are the same as in (1). In this study, we
do not model the energy reserve explicitly and use the consumed nonspecific substrate
molecules as its proxy instead. The process of the consumption of nutrients including the
nutrient consumption rate as well is described in detail in the Supplementary Materials.
Note that if the reserve is depleted (r= 0), there is no immigration and emigration—the
migration flow halts.
Furthermore,
mortPSettler
n[i,j],PNom ad
n[i,j]
is a mortality term, i.e., an equation term
that describes the way of natural population decline. We consider two types of mortality:
quadratic (density-dependent) and linear (proportional). In the first case, the mortal-
ity term is described as follows:
mortPSettler
n[i,j],PNom ad
n[i,j]=deathco e f f ·(PSettler
n[i,j]+
PNom ad
n[i,j])2
, and in the second case:
mortPSettler
n[i,j],PNom ad
n[i,j]=deathco e f f ·
(PSettler
n[i,j]+PNom ad
n[i,j])
, where
deathco e f f
is the death coefficient. As one can see, the
mortality rate of Nomad or Settler is a function of the overall density of both populations
in the local node and local overpopulation casts its adverse effects on both populations.
Thus, the interspecific competition between Nomad and Settler breaks into two parts—the
competition for the available nutrients in the environment and spatial competition for the
nodes to inhabit. Though the same node can be occupied by the cells of both populations,
this situation is quite unfortunate for them because it leads to a lesser per-cell nutrient
uptake and higher mortality toll.
As has been already mentioned, the population abundance in a particular node
depends not only on the reproduction, which is described in Equation (2), and death of
cells but also on migration fluxes (see Equation (1)) brought about by both active movement
of cells and their passive advection. We take into account the adaptive migration of cells
via chemotaxis—the detailed description of the used algorithm one can find in [
36
,
37
] and
in the Supplementary Materials—but it is worth mentioning some of its crucial points
here. A free-floating portion of actively migrating cells (we take 10% of the population
in a particular node, which is in a broad agreement with observed values for coastal
seawater samples [
29
]) is divided between favourable directions according to the attraction
values of respective lattice nodes. We estimate the attraction of environmental conditions
in the adjacent (neighbour) nodes based on the difference between attractants in the
neighbour and the current nodes. After that, neighbour nodes are separated into two
lists—unappealing nodes with lower attraction values than it is in the current node and
attractive nodes possessing higher attraction values. The difference of these two lists
defines the change of population size in the current node (see Supplementary Materials
for a detailed description). It should be noted that the portion of actively moving cells in
the current node divides between all favourable directions and the share of a direction
is proportional to its attraction value. Thus, we assume motile cells to be capable of
chemotaxis to spread through the environment due to both random swimming and by
following nutrient gradients, whereas the cells without chemotactic capacity only spread
randomly, i.e., without any specific direction.
To take into account the migration costs, we have proposed a sub-model of penalty for
migration with two parameters. The first parameter (h) controls the degree of nonlinearity
in the migratory costs function (see Equation (3)) and it is fixed in all simulation scenarios.
The second parameter (x) corresponds to a basic genetic background determining the
migration costs, and it varies throughout different simulation scenarios, bringing about
Nomad populations characterized by various energetic costs of migration. Both parame-
ters can be attributed to the costs associated with the maintenance of respective genetic
regulatory networks involved in the mechanisms that control the chemotaxis machinery in
any particular microorganism. In the case wherein the cell’s energy reserve is less than is
necessary to pay the penalty fee, no migration is performed and no energy is expended
(details of the cell’s energy balance is below, see Equation (5)).
Biology 2021,10, 1019 6 of 17
Thus, we regard C(x) as a migratory costs function (see Figure 2), and the following
equation binds migration energy costs and organism-specific parameters controlling energy
expenditure associated with its motility:
C(x)=xh
1+xh(3)
where xis the value of the parameter that controls basic migration costs; in this article we
treat xas a variable of C(x), i.e., C(x) is a function of x; and
h
is the value of the parameter
that controls the degree of nonlinearity between the migratory costs function and basic
migration costs.
Biology 2021, 10, x FOR PEER REVIEW 6 of 18
netic regulatory networks involved in the mechanisms that control the chemotaxis ma-
chinery in any particular microorganism. In the case wherein the cell’s energy reserve is
less than is necessary to pay the penalty fee, no migration is performed and no energy is
expended (details of the cell’s energy balance is below, see Equation (5)).
Thus, we regard C(x) as a migratory costs function (see Figure 2), and the following
equation binds migration energy costs and organism-specific parameters controlling en-
ergy expenditure associated with its motility:
𝐶(𝑥)= 𝑥
1+ 𝑥 (3)
where x is the value of the parameter that controls basic migration costs; in this article we
treat x as a variable of C(x), i.e., C(x) is a function of x; and ℎ is the value of the parameter
that controls the degree of nonlinearity between the migratory costs function and basic
migration costs.
Figure 2. The dependence of migration penalty fee on migration costs parameter under nonlinearity
parameter h = 4.
Henceforth, we evaluate the penalty for migration as a fraction of the cell’s maximal
energy reserve value that is expended if the cell migrates (see (4–6) for a detailed descrip-
tion of the dynamics of consumed amount of nutrient in the cells of a particular popula-
tion). In this model, we regard the consumed nonspecific substrate (NS) resources as an
energy reserve of a cell (see Table S1 in the Supplementary Materials for a summary of
Settler–Nomad model state variables). Thus, the penalty for migration represents the ac-
tual spending accumulated NS for motility. The equation that reflects the dynamics of
energy reserves of a particular population in the [i,j]-node before the migration simulation
step is applied as follows: 𝑟[𝑖,
𝑗
]= 𝑟[𝑖,
𝑗
]+ 𝑁𝑆 (4)
where NS
consumed
is the number of molecules of the nutrient consumed by the cells belong-
ing to the population under consideration (see paragraph 2.1 in the Supplementary Mate-
rials for the detailed description of the nutrient consumption submodel).
Then, taking into account passive transport of cells and active motility via chemo-
taxis, we derive the following formula:
𝑟
′
[𝑖,𝑗]=⎩
⎪
⎨
⎪
⎧
𝑟
[𝑖,
𝑗
]−𝑀⋅𝐶(𝑥)+𝑟
_
−𝑟
_
+𝑟
_
−𝑟
_
,𝑟
[𝑖,
𝑗
]
𝑃
𝑀⋅𝐶(𝑥)
𝑟
[𝑖,
𝑗
]+𝑟
_
−𝑟
_
,𝑟
[𝑖,𝑗]
𝑃
≤𝑀⋅𝐶(𝑥) (5)
where r
pass_immigr
and r
pass_emigr
are the energy reserve income and outcome via passive
transport of cells of the population into and out of the current node, respectively; r
act_immigr
and r
act_emigr
are the energy reserve income and outcome via immigration and emigration
Figure 2.
The dependence of migration penalty fee on migration costs parameter under nonlinearity
parameter h= 4.
Henceforth, we evaluate the penalty for migration as a fraction of the cell’s maximal
energy reserve value that is expended if the cell migrates (see (4–6) for a detailed description
of the dynamics of consumed amount of nutrient in the cells of a particular population).
In this model, we regard the consumed nonspecific substrate (NS) resources as an energy
reserve of a cell (see Table S1 in the Supplementary Materials for a summary of Settler–
Nomad model state variables). Thus, the penalty for migration represents the actual
spending accumulated NS for motility. The equation that reflects the dynamics of energy
reserves of a particular population in the [i,j]-node before the migration simulation step is
applied as follows:
rn+10[i,j]=rn[i,j]+NSconsumed (4)
where NS
consumed
is the number of molecules of the nutrient consumed by the cells belonging
to the population under consideration (see paragraph 2.1 in the Supplementary Materials
for the detailed description of the nutrient consumption submodel).
Then, taking into account passive transport of cells and active motility via chemotaxis,
we derive the following formula:
Biology 2021,10, 1019 7 of 17
rn+100 [i,j]=
rn+10[i,j]−M·C(x)+rpass_immigr −rpass_emigr +ract_immigr −ract_emi gr,rn+10[i,j]
Pn
>M·C(x)
rn+10[i,j]+rpass_immigr −rpass_emigr ,rn+10[i,j]
Pn
≤M·C(x)
(5)
where r
pass_immigr
and r
pass_emigr
are the energy reserve income and outcome via passive
transport of cells of the population into and out of the current node, respectively; r
act_immigr
and r
act_emigr
are the energy reserve income and outcome via immigration and emigra-
tion of cells of the population into and out of the current node, respectively, mediated
by chemotaxis; P
n
is the population abundance; Mis the maximal amount of nutrient
molecules that can be consumed per cell; and C(x) is a migratory costs function. r
pass_immigr
,
r
pass_emigr
,r
act_immigr
and r
act_emigr
dynamics are described in the Supplementary Materials,
paragraph 1.4.
rn+1[i,j]= (1−R−kdegrad )·rn+100 [i,j](6)
where Ris the costs for reproduction and k
degrad
is the nutrient degradation rate.
R+kdegrad = 0.999.
Let us clarify the biological assumptions underlying the chemotaxis simulation al-
gorithm. Since we are interested in population dynamics and the time scale of HEC is
calibrated accordingly based on the mean generation time, the effects of chemotaxis appear
on the same scale and we consider its integral effect on a population level. For this reason,
we do not describe movement irregularities of distinct cells on short time intervals (such as
seconds or split seconds) in detail in the model since they appear to be averaged out on this
simulation scale. Meanwhile, other factors step forward and influence the effect of motility
on a population dispersion—namely, the adaptation to the baseline signal of attractants in
the current location and rough attractant gradient on a wider spatial scale. The former is
achieved by the one-off nature of a chemotaxis act—the cells have moved to the adjacent
node and their propulsion does not have momentum [
40
], they adapt to the baseline signal
as the literature on bacterial chemotaxis signalling pathways indicates [
11
]. The latter is
attained by the algorithm evaluating the attraction values of nodes [
36
]. A cell swimming
via chemotaxis expends energy. Those cells who run out of their energy reserves halt their
flagellar motor rotation until they gain more energy again [
41
]. Thus, a constraint for an
active movement for cells that do not have enough energy has a clear physical sense.
2.2. Simulation Scenarios
We have investigated two groups of simulation scenarios—those without migration
penalty and those with energetic costs of migration. Both groups follow the Settler–Nomad
model described in Section 2.1 and we varied such parameters as nutrient concentration
in a batch, a batch period and a mortality term (see Table 1for the details). For the model
that takes into account migration energy costs, we varied migration penalty fee value
as well. See Figure 1c for a conceptual diagram of examined simulation scenarios and
corresponding varied parameters.
Lower batch period values correspond to the environments that are more dynamic,
whereas higher batch period values correspond to the ones that are more stagnant. Similarly,
different values of nutrient concentration in a batch, i.e., the amount of nutrients that are
added into the node located at the nutrient source, produce the environments with different
nutrient richness. We will call a habitat characterized by high nutrient concentration in
a batch (1
×
10
−1
M) a “rich” environment and that characterized by low concentration
(1
×
10
−5
M) a “poor” one. The environments bearing very low NS concentration in a
batch (1
×
10
−10
M) will be called “extremely scarce” hereafter. Comparing the quadratic
mortality with a linear one allows us to conclude whether density-dependent mortality
accounts for the effects observed in the model or is explained by a deeper underlying cause.
Both types of mortality terms are described in Section 2.1.
Biology 2021,10, 1019 8 of 17
Table 1.
Settler–Nomad model parameter values for the simulation scenarios considered in the study. For the full set of
tested combinations of parameters see the Supplementary Materials.
Values
Parameters
Nutrient
concentration in
a batch (M) 1×10−11×10−21×10−31×10−41×10−51×10−61×10−71×10−81×10−91×10−10
Migratory costs
(%) 0 2 5 10 15 20 25 33.33 50 99.99
Period
(generations) 1 25 50 100
Intermediate values were considered for some
cases 500 1000
Mortality term
(categorical) Quadratic mortality Linear mortality
All groups of simulation scenarios were run for 9000 iterations yielding simulation
results on population dynamics in the system, which covers a time period of half a year.
3. Results
In this study, we have investigated the model of competition of motile and sedentary
species and the impact of a capacity for adaptive migration on a population abundance
in various conditions. There is a number of factors—both population and environmental
ones—that shape the context of competition between motile and sedentary microorgan-
isms. The nutrient concentration in a batch and a batch period are among environmental
factors, while migration energetic costs and a mortality term, describing the way of natural
population decline, can be regarded as intrinsic traits of the populations. It should be noted
that two kinds of simulation scenarios describing mortality either as quadratic or linear
term correspond to the classic Verhulst density-dependent mortality and proportional
mortality caused by constant adverse factors, respectively, such as, e.g., average pressure of
external amensals that are not taken into account in the examined ecosystem. Comparing
the simulation results of two types of the model—one that takes into account energetic
costs of migration and one that does not—allows us to answer the following questions:
•
What are the critical migration penalty fee values that Nomad can bear while keeping
the dominance in the system?
•How does it depend on other environmental and population factors?
3.1. The Impact of Motility on Fitness
In order to draw the baseline, first of all, we have calculated the simulation results
for the model that do not take into account energetic costs of migration. That is one pole
corresponding to the situation when the mechanism underlying cells’ motility is designed
quite effectively so that the energetic costs of migration are negligible. These results are
summarized in the Table 2.
The simulations show that the mortality term, the batch period and the nutrient
concentration in a batch affect the dominance patterns in the ecosystem. It should be
mentioned that though this fact is not included in Table 2, in the “extremely scarce”
environment (1
×
10
−10
M nutrient concentration in a batch), Nomad outcompetes Settler,
making use of its motility advantage regardless of the batch period (50
≤period ≤
1000
iterations), and it does even under quadratic mortality. However, further examination of
the model shows that the Nomad’s dominance can be challenged under certain conditions.
Similarly to the “extremely scarce” case, under linear mortality in a “poor” envi-
ronment (1
×
10
−5
M nutrient concentration in a batch), Nomad outcompetes Settler,
regardless of the batch period (see Table 2). It is achieved due to Nomad moving freely
between both nutrient sources and occupying the space that is more beneficial at every time
moment (see spatial population dynamics time snapshots in the Supplementary Materials).
However, the situation changes under quadratic mortality in a “poor” environment where
the effect of density-dependent factors results in the fact that in stagnant environments
characterized by a long batch period (period 1000); though Settler dominates in the system,
Biology 2021,10, 1019 9 of 17
the populations polarize according to the nutrient sources—Nomad occupies the “distant”
source, while Settler controls the “start” nutrient source. One can see it clearly looking at
the spatial dispersion of cells (see Figure 3), which allow to disentangle how exactly Settler
and Nomad share the common habitat.
Biology 2021, 10, x FOR PEER REVIEW 10 of 18
effect of density-dependent factors results in the fact that in stagnant environments char-
acterized by a long batch period (period 1000); though Settler dominates in the system,
the populations polarize according to the nutrient sources—Nomad occupies the “dis-
tant” source, while Settler controls the “start” nutrient source. One can see it clearly look-
ing at the spatial dispersion of cells (see Figure 3), which allow to disentangle how exactly
Settler and Nomad share the common habitat.
Figure 3. Heatmaps of spatial dispersion snapshots of Settler and Nomad cells in the habitat taken
at the end of the simulation run under various simulation scenarios. The heatmap scale represents
the abundance measured in the number of cells. The “start” nutrient source is located in the upper-
left corner while the “distant” source is located in the opposite bottom-right corner.
In “rich” (1 × 10
−1
M nutrient concentration in a batch) environments under linear
mortality, Settler controls the “start” nutrient source regardless of the batch period (see
Table 2). However, the batch period influences the situation around the “distant” nutrient
source; in more dynamic environments, Nomad manages to occupy it, while in more stag-
nant ones, as the batch period steadily increases, Settler pushes Nomad to the outskirts of
Figure 3.
Heatmaps of spatial dispersion snapshots of Settler and Nomad cells in the habitat taken at
the end of the simulation run under various simulation scenarios. The heatmap scale represents the
abundance measured in the number of cells. The “start” nutrient source is located in the upper-left
corner while the “distant” source is located in the opposite bottom-right corner.
Biology 2021,10, 1019 10 of 17
Table 2.
Pivot table of the outcomes (who is dominant in the system) for various groups of parameter
values. The batch period is measured in generations.
Mortality term
Linear
Period 50 Period 1000 Period 1 Period 1000
Nomad Nomad
Settler (almost parity
with Nomad) Settler
Quadratic
period ≤127 period ≥128 period 1 period 1000
Nomad Settler Settler (Nomad
extincts)
Settler (Nomad
extincts)
“Poor” environment
(1 ×10−5M nutrient concentration in a
batch)
“Rich” environment
(1 ×10−1M nutrient concentration in a
batch)
Nutrient abundance
In “rich” (1
×
10
−1
M nutrient concentration in a batch) environments under linear
mortality, Settler controls the “start” nutrient source regardless of the batch period (see
Table 2). However, the batch period influences the situation around the “distant” nutrient
source; in more dynamic environments, Nomad manages to occupy it, while in more
stagnant ones, as the batch period steadily increases, Settler pushes Nomad to the outskirts
of the habitat. In the case of quadratic mortality in “rich” environments, the Nomad
population is disproportionately affected by density-dependent factors while pursuing the
most favourable conditions and it goes extinct while Settler thrives regardless of the batch
period value.
Settler’s domination around the “start” source can be explained by the initial location
of the sedentary population; while Nomad leaves, Settler stays around the start source,
establishing its dominance. Moreover, as has been discussed above, it holds not only for
the “rich” environments but also for the “poor” ones, though in the latter case, Nomad has
more opportunities, especially if the batch period is low. However, further investigation
taking into account various initial distributions of cells is needed to conclude whether this
effect is robust or not.
Thus, even without any migration penalty fees only under certain conditions Nomad
is able to take an advantage from its adaptive behaviour—namely in nutrient poor and
dynamic environments where spatial localization of the nutrient source changes quickly
bringing about dynamic inequality in the nutrient availability.
3.2. The Impact of Diversity in Energetic Costs of Migration
Introducing the migration penalty fee, it is important to find out what the thresholds
of its value are that determine whether Nomad dominates in the habitat or Settler does.
We have scrutinized the impact of the migration penalty fee value on the outcome of
the competition in the Settler–Nomad model under different mortality types and in the
environments characterized by different nutrient concentration in a batch but the same
fixed batch period that equals to 50 generations. The summary of the results is presented
in Tables 3and 4.
The observed patterns do not fit into plain linear correlations. However, as the penalty
fee value increases, Nomad’s abundance fraction decreases until it faces a certain limit,
which varies for the environments characterized by different nutrient concentrations in
a batch. This fact can be explained by either Nomad’s lacking energy reserves to move
anywhere as the migration penalty fee increases and nutrient availability decreases or by
spending those limited resources to establish in already occupied nodes rather than to
reclaim new water areas.
Biology 2021,10, 1019 11 of 17
Table 3.
Nomad’s abundance fraction against migration penalty fee in the environments varying by
nutrient concentration in a batch from “extremely scarce” to the “rich” ones. The batch period equals
50 generations. The quadratic mortality term is used.
Migration Penalty Fee (%)
Nutrient concentration in a batch (M)
0% 2% 5% 10% 15% 20% 25% 33.33% 50% 99.99%
1×
10−10% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−20% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−366% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−499% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−583% 56% 1% 1% 1% 1% 1% 1% 1% 1%
1×
10−641% 67% 65% 11% 11% 11% 11% 11% 11% 11%
1×
10−714% 50% 50% 50% 50% 50% 50% 50% 50% 50%
1×
10−861% 50% 50% 50% 50% 50% 50% 50% 50% 50%
1×
10−977% 50% 50% 50% 50% 50% 50% 50% 50% 50%
1×
10−10 78% 50% 50% 50% 50% 50% 50% 50% 50% 50%
Table 4.
Nomad’s abundance fraction against migration penalty fee in the environments varying by
nutrient concentration in a batch from “extremely scarce” to the “rich” ones. The batch period equals
to 50 generations. The linear mortality term is used.
Migration Penalty Fee (%)
0% 2% 5% 10% 15% 20% 25% 33.33% 50% 99.99%
Nutrient concentration in a batch (M)
1×
10−149% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−249% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−350% 0% 0% 0% 0% 0% 0% 0% 0% 0%
1×
10−452% 51% 1% 1% 1% 1% 1% 1% 1% 1%
1×
10−599% 65% 65% 64% 6% 6% 6% 6% 6% 6%
1×
10−696% 81% 80% 20% 20% 20% 20% 20% 20% 20%
1×
10−761% 50% 50% 50% 50% 50% 50% 50% 50% 50%
1×
10−871% 50% 50% 50% 50% 50% 50% 50% 50% 50%
1×
10−972% 50% 50% 50% 50% 50% 50% 50% 50% 50%
1×
10−10 72% 50% 50% 50% 50% 50% 50% 50% 50% 50%
In the relatively abundant conditions characterizing intermediate environments be-
tween the “rich” (1
×
10
−1
M nutrient concentration in a batch) and the “poor” (
1×10−5M
nutrient concentration in a batch) ones, introducing a migration penalty fee results in
Nomad’s fraction becoming negligible up to the complete extinction of Nomad (see
Biology 2021,10, 1019 12 of 17
Table 3).
Notably, the mortality type does not affect this tendency significantly, though tak-
ing into account density-dependent factors worsens the implications for Nomad, whereas
linear mortality mitigates them.
It is worth noting that there is a certain turning point in migration penalty fee value
that determines quite narrow area of parameter space where Nomad strategy turns out to
be successful and the value of that point depends on environmental conditions, in particular
on the nutrient concentration in a batch. In this respect, the picture of spatial dispersion
of cells belonging to different populations might answer what the causes underlying this
dominance switch are (see Figure 4).
Biology 2021, 10, x FOR PEER REVIEW 13 of 18
Figure 4. The effect of the migration penalty fee value on the spatial dispersion of Settler and Nomad cells in the habitat
(the snapshots are taken at the end of the simulation run under quadratic mortality, the results under linear mortality does
not differ significantly). Heatmap scale represents the abundance measured in the number of cells. The “start” nutrient
source is located in the upper-left corner while the “distant” source is located in the opposite bottom-right corner. One can
see that as the energetic costs of migration increases, the dominance switch occurs in the following cases—turning from
scenario with nutrient concentration in a batch equal to 1 × 10
−5
M and penalty fee value equal to 2% (a) to the scenario
with the same nutrient concentration in a batch but higher penalty fee value equal to 5% (b), and turning from scenario
with nutrient concentration in a batch equal to 1 × 10
−6
M and penalty fee value equal to 5% (c) to the scenario with the
same nutrient concentration in a batch but higher penalty fee value equal to 10% (d).
It is evident from Figure 4 that if there is no clear dominance of either Settler or No-
mad (see Figure 4a,c), both populations separate spatially and divide control over differ-
ent nutrient sources—Nomad takes over the “distant” source while Settler firmly occupies
the “start” source. This is in good correspondence with the previous studies [17] showing
that such competition-dispersal trade-offs do occur in microorganisms and bring about
ecologically differentiating populations who either specialize to colonize particles by at-
taching and growing biofilms, or hone rapid detection and swimming to reach short-lived
particle patches. If the dominance switch occurs abruptly after increasing the penalty fee
value (see Table 3 and Figure 4 switches from a to b and from c to d scenarios), it is usually
caused by the capture of both nutrient source by Settler who manages to push Nomad
back while the latter sustains losses (Figure 4b,d).
A detailed investigation into the impact of the nutrient batch period is an arduous
task that could be a matter of a distinct study. However, a rough estimate for the boundary
cases of “rich” and “extremely scarce” (1 × 10
−10
M nutrient concentration in a batch) envi-
ronments inferred for short and long batch periods (see Table 5) demonstrates that the
nutrient concentration in a batch and energetic costs of migration might play a more sig-
nificant role in determining the outcome of Settler–Nomad competition than the nutrient
batch period does. However, there is no conclusive analysis of the impact of the nutrient
batch period at the moment, and this point is open for the further discussion.
Figure 4.
The effect of the migration penalty fee value on the spatial dispersion of Settler and
Nomad cells in the habitat (the snapshots are taken at the end of the simulation run under quadratic
mortality, the results under linear mortality does not differ significantly). Heatmap scale represents
the abundance measured in the number of cells. The “start” nutrient source is located in the upper-
left corner while the “distant” source is located in the opposite bottom-right corner. One can see
that as the energetic costs of migration increases, the dominance switch occurs in the following
cases—turning from scenario with nutrient concentration in a batch equal to 1
×
10
−5
M and penalty
fee value equal to 2% (
a
) to the scenario with the same nutrient concentration in a batch but higher
penalty fee value equal to 5% (
b
), and turning from scenario with nutrient concentration in a batch
equal to 1
×
10
−6
M and penalty fee value equal to 5% (
c
) to the scenario with the same nutrient
concentration in a batch but higher penalty fee value equal to 10% (d).
It is evident from Figure 4that if there is no clear dominance of either Settler or
Nomad (see Figure 4a,c), both populations separate spatially and divide control over
different nutrient sources—Nomad takes over the “distant” source while Settler firmly
occupies the “start” source. This is in good correspondence with the previous studies [
17
]
showing that such competition-dispersal trade-offs do occur in microorganisms and bring
about ecologically differentiating populations who either specialize to colonize particles by
attaching and growing biofilms, or hone rapid detection and swimming to reach short-lived
particle patches. If the dominance switch occurs abruptly after increasing the penalty fee
value (see Table 3and Figure 4switches from a to b and from c to d scenarios), it is usually
caused by the capture of both nutrient source by Settler who manages to push Nomad back
while the latter sustains losses (Figure 4b,d).
Biology 2021,10, 1019 13 of 17
A detailed investigation into the impact of the nutrient batch period is an arduous
task that could be a matter of a distinct study. However, a rough estimate for the boundary
cases of “rich” and “extremely scarce” (1
×
10
−10
M nutrient concentration in a batch)
environments inferred for short and long batch periods (see Table 5) demonstrates that
the nutrient concentration in a batch and energetic costs of migration might play a more
significant role in determining the outcome of Settler–Nomad competition than the nutrient
batch period does. However, there is no conclusive analysis of the impact of the nutrient
batch period at the moment, and this point is open for the further discussion.
Table 5.
Pivot table of outcomes (who is dominant in the system) for various groups of parameter
values. The results do not differ for either quadratic and linear mortality except for the cases marked
with an asterisk (*) where under linear mortality the following outcome is observed: Settler/Nomad
(full parity). Batch period is measured in generations.
Migration
Penalty Fee
Fee Value ≤0.3% Period 50 Period 1000 Period 1 Period 1000
Nomad Nomad Settler * Settler
Fee Value ≥0.4%
Period 50 Period 1000 Period 1 Period 1000
Settler/Nomad
(Full Parity).
Settler/Nomad
(Full Parity). Settler Settler
“Extremely Scarce” Environment “Rich” Environment
Nutrient Abundance
Furthermore, since the critical value of the migration penalty fee is too close to zero, it
means that actually in the “extremely scarce” environment, the Nomad strategy cannot
confer real benefit if energetic costs of migration are significant (
≥
0.4% of maximal cell’s
energy reserve). However, as was demonstrated above, there is a certain parameter interval
between the “extremely scarce” and “rich” environments where it is possible and the
Nomad population does gain an advantage of its motility to take the dominant position in
the ecosystem.
4. Discussion
A capacity for adaptive migrations plays an important role in the eco-evolutionary
dynamics of microbial populations determining their success in the ecosystem. However,
the trade-off between migratory energy costs and investment into reproduction imposes
specific constraints on employing migration-based foraging strategies. The results of our
simulation study show that the success in the interspecific competition brought by a po-
tential advantage conferred by the capacity for active migrations is limited by ecological
and population factors. Moreover, under certain conditions, the Settler strategy appears
to be more successful than the Nomad one, even without introducing any penalties that
account for energetic costs of migration. However, the fact that in the nutrient-rich envi-
ronments, even under linear mortality, Nomad concedes the leadership to Settler needs
to be explained. We attribute that effect to the emergence of “biotic desert” around the
Settler occupying the “start” nutrient source (see Figure S1). Though from the viewpoint of
Nomad’s dispersion it is reminiscent of a “volcano effect” [
42
], which is the situation when
steady-state bacterial aggregation forms a ring of higher density some distance away from
an optimal environment, it has a different underlying cause. While the biological cause of
the “volcano effect” is that the bacterium cannot sense rapid changes in its environment
quickly enough, in our model, we instead have a situation stemming from the competition
of two different populations. Since the Settler cells decrease the local nutrient availability
in the source’s vicinity, Nomad cannot break through this self-organized “exclusion zone”
to the nutrient source because the nutrient concentration around the source is low and it
signals that the environmental conditions are unfavourable. Thus, fugitive motile popula-
tions relying on a locally optimal foraging strategy tend to follow benign conditions and
Biology 2021,10, 1019 14 of 17
fail enduring stress associated with crossing the valleys of suboptimal nutrient availability.
However, these conclusions hold under the set of assumptions that describe a particular
situation when both populations invade a vacant habitat through the same spot, while the
model of blinking nutrient source is quite reductive. Though such a simplistic approach is
a good way to start, to assess different cell dispersion scenarios and to reflect the transient
nature of resource hotspots in the ocean, it is reasonable to take into account various initial
distributions of cells as well as more a complex model of a resource landscape that changes
over time and is characterized by the continuous appearance of new spots. Thus, further
investigation is needed to determine whether such an effect is robust in relation to the initial
location of the sedentary population and to various dynamic modes of nutrient supply.
The results of our simulation study indicate that there is a turning point in the mi-
gration penalty fee value determining whether the Nomad strategy of being a motile
population is successful or not. However, this value heavily depends on the nutrient
availability, and the overall spectrum of conditions favouring the Nomad strategy is esti-
mated to be quite narrow, imposing constraints on Nomad’s trade-off between spending
energy on migration and reproduction investment. It turned out that more dynamic and
scarce environments favour the dominance of fugitive motile populations, whereas the
cost of motility exceeds the benefit in nutrient-rich and stagnant environments, which
tend to promote the dominance of sedentary microorganisms. Therefore, these constraints
shape eco-evolutionary dynamics in such aquatic microbial systems affecting the processes
of assembly and the evolution of microbial communities. Moreover, density-dependent
quadratic mortality is more detrimental for a motile population than a linear one since
chemotaxis drives its cells to organize into densely populated areas. Furthermore, though
providing more adequate description, taking into account the energetic costs of migration
does not change these major trends, yet it allows us to portray a more detailed picture of
the competition between two types of microorganisms, relying on different strategies in
terms of motility.
Notably, the results of our theoretical investigation are in accordance with some previ-
ous findings in the field. For instance, ref. [
23
] have shown with experiment and theory
that in poor nutritional conditions, Escherichia coli increases its investment in motility in
proportion to the reproductive fitness advantage provided by the ability to follow nutrient
gradients. Though the difference of studies is quite remarkable, specifically in the used
phenomenological laws of cell growth, taking into account autoinducers and the fact that
they consider the nutritional value of carbon source rather than nutrient concentration in a
batch, we believe that our results qualitatively relate to a comparable setting. Furthermore,
the scenarios observed in our simulation study under nutrient poor conditions and bear-
able costs for migration exhibit spatial separation of two different populations: Nomad
establishes around the “distant” source while Settler controls the “start” source. It echoes
the results of [
17
], who showed on two recently diverged populations of Vibrio cyclitrophi-
cus that while cells of one of the populations increase their uptake rate via attachment to
the nutrient patches, another population exploits the temporal variability of the resource
landscape employing chemotaxis. Thus, both studies stress the phenomenon of ecological
differentiation between a strategy that maximizes the access to resources at the patch level
and one that favours access to resources at the landscape level. However, the novelty of
our results is of a systematic study of variation in migratory costs and its impact on the
corresponding eco-evolutionary patterns. It should be also noted that we cannot consider
the Settler population as completely nonmotile since the passive transport coefficient may
be interpreted as undirected movement similar to diffusion for the substrate. From this
point of view, Settler–Nomad competition portrays itself as a rivalry between blindly
motile unhasty cells and swift fugitive cells possessing sensory and signalling apparatus
associated with chemotaxis.
Motile forms have an advantage in nutrient-poor conditions corresponding to envi-
ronments inhabited by marine bacteria. However, since we observe the prosperity of both
strategies in nature and neither of the two completely supplants another, the issue of how
Biology 2021,10, 1019 15 of 17
such diversity is sustained is an intriguing question for further investigations to answer.
As some studies indicate [
17
], the dynamic and micro-heterogeneous nature of aquatic
environments might be one of the possible factors that results in a constantly changing
direction of selection hindering the occurrence of selective sweeps. Another compelling
problem is how both genetic and non-genetic population diversity in motility traits influ-
ences a population’s fitness. There is a number of studies addressing this question [
43
,
44
],
though a comprehensive view is yet to be integrated.
5. Conclusions
The results presented in this paper elucidate principal aspects of competition between
bacteria with different foraging strategies—Nomad of motile population actively pursuing
the spots of high concentration of the nutrient and Settler of sedentary one, which trades
chemotaxis ability for increased reproduction rate. While motility grants tangible advan-
tage for the nutrient searching behavior and, therefore, has an impact on fitness, there
are also energetic costs of migration, energy expenditure associated with active motility
that could be invested into reproduction instead. Moreover, depending on availability
of nutrients and the rate of change of their localization in the environment, the benefit
of chemotaxis varies by its contribution into species fitness—variable and nutrient poor
environments actualize this advantage, nutrient rich and stagnant habitats tend to diminish
its adaptive potential. Altogether, it shapes the parameter space of ecological factors, which
influence the success of a particular strategy.
It is important to note a number of limitations stemming from the assumptions taken
in our model concerning time scale, structure of the environment and genetic variation.
First, since the focus of our work is centered around the assessment of the impact of motil-
ity on the evolutionary success of a population, we stick to the time scale of generational
turnover. On the other hand, fine micro-scale simulation approaches acting on a single cell
level are computationally demanding for modelling of microbial populations, which limit
the number of simulation scenarios that can be investigated. Whereas, we focused on the
population level effects where the differences in local nutrient histories mostly average out
to the aggregate dynamics. Evidently, such an approach has its own limitations, especially
for the cases when small cell numbers matter but since we investigate the population
processes, we believe that we stay within its constraints. Second, as we mentioned we
consider simplified environment, yet spatially structured and dynamic, in order to draw
the baseline and to understand the mechanics of Settler-Nomad competition in such a
simple setting. This is a foundation to move towards future development of present model,
taking into account various natural environments characterized by more complex nutrient
distribution factors, which correspond to widely present in natural aquatic environments
organic sources originating from the activity of zoo- and phyto-plankton and other biologi-
cal macro-objects. Third, we do not cover the aspects associated with genetic variation in
the current paper. However, natural selection is able to act upon populations of microor-
ganisms affecting function of genetic machineries that control cell motility and efficient
utilization of substrates. Taking into account these factors in more sophisticated models
come across as being a prospective direction of further investigations.
That being said, we have shown in this simulation study that even under the above-
mentioned assumptions there is the growth-motility trade-off in the system and a potential
advantage conferred by a microbial motility is constrained by different factors—both
population and environmental ones, especially under the competition with other species.
Therefore, one should take into account these factors to conclude whether this poten-
tial advantage becomes actually adaptive or not. We also show that there is a certain
parameter space where two populations coexist and divide the control under the environ-
ment. Though current study elucidates some of the aspects, mechanisms and constraints
of competition between different strategies in terms of bacterial motility, the interrela-
tion between adaptive migrations of microorganisms and their fitness, in general case,
Biology 2021,10, 1019 16 of 17
remains to be a fundamental problem yet to be investigated using both computational and
experimental approaches.
Supplementary Materials:
The following are available online at https://www.mdpi.com/article/10
.3390/biology10101019/s1: Figure S1: An example of “abiotic desert” emerging around the “start”
nutrient source occupied by Settler population, Table S1: Settler–Nomad model state variables,
Table S2: All the parameters of the Settler–Nomad model, Document S1: “Haploid evolutionary
constructor” modelling approach, and additional materials.
Author Contributions:
Conceptualization, A.K. and S.L.; investigation, A.K.; methodology, A.K.,
Y.M. and S.L.; supervision, Y.M., N.K. and S.L.; visualization, A.K.; writing—original draft, A.K. and
S.L.; writing—review and editing, A.K., Y.M., N.K. and S.L. All authors have read and agreed to the
published version of the manuscript.
Funding:
This research was funded by the Russian State Budget (project No. 0259-2019-0008) and
the Kurchatov Genomic Centre of the Institute of Cytology and Genetics, SB RAS (075-15-2019-1662).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement:
The data presented in this study are available in the Supplementary
Materials. The HEC software used for generating the simulation results is available at https://evol-
constructor.bionet.nsc.ru/?page_id=34&lang=enpage (accessed on 8 October 2021).
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or
in the decision to publish the results.
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