\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage[ngerman,greek,polish,english]{babel}



\usepackage{float}








\begin{document}

\title{Bacterial age distribution in soil -- life cycles in hot and cold spots}



\author[1]{Benedict Borer}%
\author[1]{Dani Or}%
\affil[1]{ETH Zürich}%


\vspace{-1em}



  
  \date{May 08, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Soil bacteria live in patchy and dynamic environments where cells in
adjacent microhabitats may realize vastly different generation times
ranging from hours to years within small soil volumes. This study links
bacterial population demographics with soil conditions to better
estimate mean bacterial cell ages by tracking individual lineages over
space and time using a mechanistic model of bacterial life in soil.
Results show heavy-tailed distributions of generation times that follow
a power law across all hydration conditions, implying no simple
definition of mean soil bacterial age where soil volumes may harbor
cells with very broad range of ages living side by side. The study
highlights ubiquitous conditions that support a ``genetic reservoir'' of
physiological traits for each bacterial species that may be preserved in
soil cold spots and reintroduced during episodic reunification events
(soil wetting).%
\end{abstract}%



\sloppy


\section*{Introduction}

{\label{introduction}}

Notwithstanding the harsh and dynamic environmental conditions, soil
microbial life thrives at all scales -- with a single gram of fertile
soil containing up to 10\textsuperscript{10} prokaryotic
cells\textsuperscript{1}. Remarkably, even with such high potential
abundance, soil bacteria inhabit less than 1\% of the available soil
surface\textsuperscript{2}, being largely associated with small soil
volumes of nutrient-rich and densely populated hotspots (the
rhizosphere, detritusphere, or within soil
aggregates\textsuperscript{3}). Aqueous phase facilitated cell
dispersion, accessibility and diffusion of nutrients within soil
hotspots with high cell growth rates (similar to the growth of
copiotrophic bacteria grown in laboratory settings\textsuperscript{4}).
In contrast, the remaining 99\% of soil surfaces (and volumes) support
very little to no bacterial activity (hence the term biological ``cold
spots'') due to a lack of nutrients\textsuperscript{5} and unfavorable
hydration conditions\textsuperscript{6}. These contrasting conditions
may occur within small soil volumes and result in significant generation
time disparity, with rapid cell proliferation coexisting next to nearly
dormant bacterial cells that support their maintenance with limited
prospects for growth and cell division. Even after episodic wetting
events that reconnect bacterial habitats and permit temporary infusion
of nutrients, subsequent internal drainage fragments the aqueous phase
and growth rates drop following diminishing accessibility and
availability of nutrients. We seek to understand the consequences of
this common disparity in local bacterial growth rates in soil (in both
space and time)\textsuperscript{3} and impacts on cell lineage
propagation and average bacterial cell ages in soil under different
environmental conditions (characterized by soil type, cover, climatic
conditions and land use).

At present, there are no direct methods for inferring bacterial cell age
within a natural soil sample. We define cell age as the elapsed time
since last cell division, and generation time as the cell age at
division (also known as the interdivision time, doubling time or
cell-cycle time\textsuperscript{7}). Experimentally, cell age and
related generation time distributions are deduced indirectly from growth
rates or microbial activity data. Multiple techniques have been used for
measuring growth rates \emph{in situ} , such as direct cell
counts\textsuperscript{8}, radioactively labeled thymidine/leucine
incorporation rates\textsuperscript{9,10} or using observed and expected
mutation accumulation rates\textsuperscript{11}. More recently,
omics-based methods, such as quantitative stable isotope probing (qSIP)
using H\textsubscript{2}O\textsuperscript{18}, have emerged as a novel
technique to measure growth rates in environmental
samples\textsuperscript{12} and have even enabled the quantification of
growth rates at the taxon level\textsuperscript{13}. Using these
techniques, mean generation times of soil microbial communities have
been determined for a wide range of conditions (Fig. 1).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1: Distribution of experimentally measured bacterial
generation times in topsoil and the rhizosphere compared to
computationally obtained, generation time distributions in wet and dry
conditions.} Red data points represent literature
values\textsuperscript{4,14--21} and represent a mean value for each
sample whereas computational results show the distribution of individual
generation times within one hypothetical sample under different
hydration conditions.

A critical drawback of the above-mentioned techniques is that the
estimated growth rates in soil are sample mean values but cannot resolve
the within sample age distribution\textsuperscript{9}. Additionally,
most methods suffer from poorly resolved detection limits that favor
identification of rapid growth, thereby biasing the demographic picture
in favor of younger cells. Theoretically, we expect bacterial life in
patchy soil microenvironments to produce far broader age distributions
than could be resolved by current measurement methods. While direct
experimental evidence from soil is scarce, we can gain insights from
analogous patchy environments such as bacterial age in the
phyllosphere\textsuperscript{22}. Studies have tracked the reproductive
success (the total number of offspring produced by an individual) of
isogenic bacterial cells by linking these to leaf patchy nutrient
distribution and overall local carrying capacity\textsuperscript{22}.
These experiments have shown a broad distribution of reproductive
success (and thus generation times) for individual cell lineages despite
their isogenic characteristics, which supports the role of contrasting
growth conditions in soil. We hypothesize that microscale spatial
variations in soil hydration state or nutrient distributions would shape
the age and generation time distribution of bacterial cells. To test
this hypothesis, we employ a modeling framework that combines the
salient features of soil aqueous phase configurations with
individual-based bacterial cell growth and
dispersal\textsuperscript{23}. The model tracks the life history of each
bacterial cell within the simulation domain, and its lineage with
reference to the localized nutrient concentrations experienced (see Fig.
2 for an example). This enables attribution of the (simulated) life
history of each cell to local conditions and to its age and generation
time, thus providing estimates of community age and generation time
distributions by integrating across the bacterial population. The
soil-like landscape and the aqueous phase distribution within it vary
with hydration state giving rise to limited diffusive fluxes imposed by
thin water films that support survival of bacterial cells near their
maintenance rate whilst neighboring cells close to nutrient sources may
proliferate at near maximum growth rates (Fig. 2). In addition to
mechanistically modeling the emergence of bacterial age distribution in
a soil-like system, we capitalize on a heuristic analytical
formulation\textsuperscript{24} for linking local heterogeneity in
bacterial growth conditions (nutrients and hydration) to the resulting
bacterial age distribution.

\section*{Methods: Modeling bacterial age and cell lineages in
soil}

{\label{methods-modeling-bacterial-age-and-cell-lineages-in-soil}}

The spatially explicit mechanistic modeling framework (IndiMeSH) was
used to simulate bacterial life in heterogeneous soil
microhabitats\textsuperscript{23} mimicking a soil aggregate (or a
hotspot around an active root segment, Fig. 2). The domain is comprised
of an angular pore network occupying a spherical soil volume (10 mm
radius) containing individual pore channel segments with lengths of 100
microns (106,901 pores). The pore channels with triangular cross
sections are drawn from a uniform distribution of central angles between
30\selectlanguage{ngerman}° and 150° with inscribed pore radii sampled from a lognormal
distribution with mean 30 microns and variance 10 microns. These
ingredients allow for systematic variations of the domain heterogeneity
by varying pore sizes in 50 randomly located regions of the pore
network. Hydration conditions are prescribed as boundary conditions (for
the soil volume) that translate into a distribution of micro-aqueous
habitats based on the pore network (see Borer et al.
2019\textsuperscript{23}). The effective water film thickness is derived
for each individual pore channel based on its geometry and the
prescribed matric potential. A carbon source was placed at the center of
the simulation domain (constant concentration of 0.1 mM) with oxygen
sources at the periphery of the pore network, following Henry's law
(constant source of 0.27 mM). This arrangement of boundary conditions
gave rise to counter gradients of oxygen and carbon mimicking conditions
frequently found in natural soil hotspots\textsuperscript{3}. For
simplicity, we modeled bacterial cells as obligate aerobes, with Monod
kinetics including carbon and oxygen limitation terms. Under optimal
conditions (no oxygen or carbon limitation), the simulated bacterial
cells have a mean generation time of 28 minutes. We focus on aerobic
growth since this is the most common state in most near surface soils.
In some soils and under certain conditions, saturated conditions
throughout the soil profile may prevail, however, for simplicity and
considering the long time horizons of the analyses, we neglected these
cases. All model parameters concerning bacterial growth are shown in
Table S1 and are based on Borer et al. 2018\textsuperscript{25}.
Bacterial cells are inoculated homogeneously across the domain (1000
cells) with a total simulation time of 30 days at 10s time steps. The
age of each individual bacterial cell is captured as the time since last
division. For each dividing cell, its current age is stored as the
generation time while resetting the age of the daughter cells. A unique
identifier is assigned to each inoculated cell that is inherited by its
progeny, enabling tracking of reproductive success, generation time
distribution and cell age distribution of each lineage.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2: Bacterial population demographics shaped by diffusion
and dispersal limitations around soil hot spot as affected by hydration
conditions.} a) Spatial visualization of simulated bacterial cell ages
for -1 kPa and -5 kPa representing wet and dry conditions, respectively.
Diffusion and dispersal restrictions in dry conditions expose individual
lineages to harsh conditions resulting in older cells growing close to
their maintenance rate. b) The model represents bacterial cells as
individual agents inhabiting angular pore networks where aqueous
diffusion is limited by thin water films, resulting in a patchy nutrient
landscape and localized growth conditions and limited cell dispersal
ranges. c) The spatially patchy resource landscape gives rise to
bacterial ``hotspots'' (nutrient rich and accessible by a well-connected
aqueous phase) and ``cold spots'' reflecting nutrient limitations and
fragmentation. Cell lineages inhabiting hotspots proliferate and attain
high reproductive success whereas (kin) isogenic lineages in cold spots
persist with minimal prospects for growth and dispersal.

\section*{Results}

{\label{results}}

Soil hydration status has been shown to be a key variable that governs
multiple functions of microbial habitats such as nutrient diffusion
(both aqueous and gaseous)\textsuperscript{6}, community
structure\textsuperscript{26}, horizontal gene transfer
rate\textsuperscript{27}, cell dispersal\textsuperscript{28--30} and
accessibility to nutrients\textsuperscript{6}. From a nutrient flux
perspective, too wet or too dry soil conditions are (generally)
unfavorable, due to either a lack of oxygen when saturated or limited
aqueous nutrient diffusion in dry soil. Optimal nutrient and gaseous
fluxes are often supported at intermediate hydration
levels\textsuperscript{31}. Although details of soil microhabitats are
experimentally inaccessible, macroscopic hydration conditions reflect
average diffusive nutrient fluxes and connectivity conditions that, in
turn, affect the landscape of bacterial growth, age and generation time
distributions. We use the soil water matric potential (marking the
energy state of soil water) to represent prevailing hydration conditions
due to its direct control over liquid organization in soil pores (via
capillary interface curvatures and thickness of adsorptive films on soil
surfaces). The simulations consider a simple scenario of an obligate
aerobic bacterial species growing on a single carbon source (see details
in the Modeling section). Fig. 3a depicts the final population size for
each hydration state. For saturated conditions (matric potential of 0
kPa and -1 kPa), bacterial community growth is restricted by low oxygen
diffusion through the water saturated pores limiting growth of the
obligate aerobic bacteria. Intermediate hydration conditions (-2 kPa and
-3 kPa) create an optimal balance of aqueous and gaseous nutrient
diffusion that enables rapid growth. As drier conditions set in, thin
water films limit aqueous nutrient diffusion thereby reducing bacterial
community size. Fig. 3b shows the empirical cumulative distribution
function of the cell generation times during the simulation. On average,
the shortest generation times were realized at -2 kPa to -3 kPa (optimal
balance between gaseous and aqueous nutrient diffusion) and diverged
towards longer mean generation times for wetter or drier conditions
(Table S2).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3: Variations in simulated bacterial population sizes and
generation time distributions with hydration conditions} . a) Final
simulated population size depending on hydration conditions where
optimal growth conditions occur at intermediate hydration conditions
that support sufficient diffusion of both gaseous and aqueous nutrients.
b)~Empirical cumulative distributions of observed generation times
during the simulated time. On average, the shortest generation times
where obtained at -2 and -3 kPa due to optimal growth conditions. The
cumulative density function curves for generation times at 0~kPa and -1
kPa are congruent. Log-log visualization of the extrapolated simulation
data and fitted power law distribution fits for the wet (-1 kPa)
scenario (c) and dry (-7 kPa) scenario (d) where the inset in the latter
shows the power law distribution equation. In drier conditions (-3 kPa
and higher), habitat fragmentation results in spatially isolated
subpopulations growing at vastly different growth rates giving rise to
the wide distribution in generation times. e) Fitted power law
coefficient \selectlanguage{greek}α \selectlanguage{english}for all hydration conditions. A lower coefficient
indicates a more pronounced tail of the power law distribution (and
suppression of the frequency of short generation times).

The study focuses on isogenic bacterial populations and their spatially
distributed responses to conditions similar to a soil microbial hotspot
and its surroundings where high nutrient concentrations support rapid
cell proliferation near the nutrient source. The majority of realized
generation times in a simulated hotspot are in the order of hours to
days for most hydration conditions (shortest generation time at optimal
conditions is 0.5 hr). However, the generation time distributions are
characterized by persistence of very long generation times (a heavy
tail), as shown in Fig. 3b. Interestingly, we find that under wet
conditions (Fig. 3c), the tail of the distribution is truncated (i.e.
fewer long generation times) due to bacterial motility through the
water-saturated pore spaces that enable them to relocate towards more
favorable conditions\textsuperscript{32}. Under dry conditions (Fig.
3d), cell motility is greatly reduced and the dispersal range is
restricted\textsuperscript{30} with reduced nutrient fluxes that result
in a wide distribution of generation times following a power law (fitted
power law and exponentially truncated power laws to the original and
extrapolated simulation data are shown in Fig. S1 and S2, respectively).
The fitted power law and exponentially truncated power law equations are
shown in Equations 1 and 2 (with x the generation time,
x\textsubscript{min} the minimum generation time of 0.5 h, \selectlanguage{greek}Γ \selectlanguage{english}the gamma
function, \selectlanguage{greek}α \selectlanguage{english}the power law coefficient and \selectlanguage{greek}λ \selectlanguage{english}the exponential
coefficient).\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\(p\left(x\right)=\left(\alpha-1\right)*x_{\min}^{\alpha-1}*x^{-\alpha}\) & (1)\tabularnewline
\midrule
\endhead
\(p\left(x\right)=\frac{\lambda^{1-\alpha}}{\Gamma(1-\alpha,\lambda x_{\min})}*x^{-\alpha}*e^{-\lambda x}\) & (2)\tabularnewline
\bottomrule
\end{longtable}

The distributions of generation times in Fig. 3c, 3d, S3 and S4 were
extrapolated by calculating the time required to complete a life cycle
(generate the necessary biomass to cell division) based on observed
growth rates. These estimated times are then added to the current cell
age for predicting the most likely cell division under present and local
conditions. We find that the main influence of hydration conditions lies
in the suppression of rapidly dividing cells whilst simultaneously
promoting the emergence of a more pronounced tail of the distribution
(following diminishing nutrient conditions in drier conditions). The
changes in the age distribution power law exponent with hydration status
are summarized in Fig. 3e. The largest value of the exponent is
associated with conditions under -3 kPa dominated by relatively short
generation times. Under drier soil conditions, thin water films limit
both bacterial motility\textsuperscript{30} and carbon
diffusion\textsuperscript{6}, resulting in slower growth and a more
pronounced tail of the generation time distribution (lower \selectlanguage{greek}α \selectlanguage{english}values in
Fig. 3e). The choice of obligate aerobe as model bacterium implies
sensitivity to saturated conditions with oxygen diffusion limitations
irrespective of location, the resulting age distribution under these
conditions must be interpreted with caution. The power law age
distribution results for the unsaturated pore network (-3 to -7 kPa)
show a persistent decrease in the slope (lower values of \selectlanguage{greek}α\selectlanguage{english}) that reflect
the disproportional suppression of the rapid growth in hotspots, with
reduced effects on the already restricted growth in the cold spots that
flatten the power law age distribution.

The resulting power law distribution of generation times in soil (as
obtained from numerical simulations) can be linked more generally and
analytically to microbial habitats that exhibit a wide distribution of
cell growth rates\textsuperscript{24,33}. A recent analysis showed that
cell age distributions of an isogenic bacterial population growing in a
chemostat follow an exponential decay\textsuperscript{33}. Based on this
assumption, the age distribution of a community consisting of many
subpopulations growing at different rates is expected to follow a power
law distribution (derivation in Appendix S1). An analogous derivation
has been used for lag time distribution of cell rejuvenation leading to
power law distributions of rejuvenation
probabilities\textsuperscript{24}. This analytical derivation is related
to simulated conditions in dry soils, where immobilized cells and patchy
nutrient conditions give rise to a wide distribution of growth rates as
nutrient fluxes diminish or the aqueous phase becomes restrictive with
soil drying (Fig. S3) leading to a power law age distribution for the
respective population (Fig. S1 and S2).

Power law distributed cell ages induces a broad range of reproductive
success where only few lineages dominate the total bacterial biomass in
a community. Reproductive success is defined here as the maximum number
of generations attributed to a lineage (parent cell) during the
simulated time. Lineages with high reproductive success are those very
few inoculated cells and their progeny that contribute disproportionally
to the final population biomass, and are further defined as the dominant
fraction. In contrast, a large proportion of the inoculated cells are
incapable of proliferating and only contribute a minute fraction to the
final biomass (rare fraction). To classify lineages into dominant and
rare, we use a minimum cross-entropy algorithm originally developed for
image thresholding\textsuperscript{34}. Fig. 4a shows the fraction of
the initial inoculum classified as either dominant or rare lineage.
Interestingly, motility under wet conditions plays an important role as
it enables individual cells to relocate towards favorable conditions,
thereby equilibrating reproductive success between lineages rendering
most of lineages as dominant. Under dry conditions, the combination of
diffusion-limiting thin water films with pinning forces that limit cell
dispersal ranges\textsuperscript{6,30} result in proliferation of only a
few lineages that are close to the carbon source. More generally,
conditions that support motion and migration equalize the contribution
of lineages whereas restrictive conditions that limit dispersal and
resources patchiness favor a few rare lineages. For all hydration
conditions, the summed contribution of the rare lineages is less than
3\% of the final population biomass. This stark difference in
reproductive success between the rare and dominant lineages translates
to equally prominent differences in their mean age distribution (Fig.
4b) and the mean generation times (Fig. 4c) of these lineages. The mean
cell age of individual lineages diverges towards older cells for rare
lineages and younger cells for dominant lineages with increasing matric
potential (drier conditions) (Fig. 4b). The observed mean young cell age
for rare lineages primarily stem from lineages that divided very late in
the simulation due to growth close to the maintenance rate. Thus, these
results suggest a bimodal distribution of bacterial age distributions in
soil for bacterial cells growing close to a carbon source (hotspot) and
within the bulk soil (cold spots) especially for drier conditions (Fig.
S4). Similarly, there is a relationship between the average generation
time and the relative abundance of individual lineages (Fig. 4c).
Overall, rare lineages have a longer average generation time compared to
dominant lineages, which is expected theoretically when considering the
different reproductive success of the two groups.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4: Characteristics of dominant (highest reproductive
success) and rare lineages vary with hydration conditions.} a)
Percentage of lineages from the inoculum classified as dominant and
rare. With a decline in bacterial motility towards drier conditions,
most inoculated lineages cannot proliferate and contribute to the rare
fraction of the community. Above numbers (in red) report the
contribution (in percentage) of the dominant lineages to the final
community biomass. b) Mean lineage cell age depending on their
classification into rare and dominant shows an overall older cell
population for the rare fraction due to their lower reproductive
success. c)~Mean lineage generation time in relation to their relative
abundance (log) for three hydration conditions. The rare fraction is
typically associated with longer mean generation times and only occurs
in drier conditions where aqueous nutrient diffusion is limited to thin
water films and capillary pinning forces immobilize bacterial cells.

\section*{Discussion}

{\label{discussion}}

Access to patchy soil microenvironments is mediated by the (often
fragmented) aqueous phase that controls diffusion of nutrients, activity
of extracellular enzymes and the speed and range of bacterial cell
dispersal. Nutrient rich domains disconnect from neighboring soil
volumes shortly after episodic and short-lived wetting events thus
maintaining broad distributions of growth rates and generation times of
soil bacteria\textsuperscript{9,10}. Limitations of the current
experimental methods and inability to resolve soil bacterial age
distributions motivated the use of mechanistic modeling that represents
physical microhabitats and simulates individual bacterial cells
interacting with their environments to track life histories of cell
lineages and estimate generation time distributions. Simulation results
show a broad range of growth rates marked by extremely slow growth rates
similar to experimental observations in batch cultures where cells
entered a deep starvation mode of balancing metabolic activity and cell
maintenance (in line with the mechanism in the mechanistic simulations)
in response to diminishing nutrient conditions\textsuperscript{35}.
Analogous observations have been made in fertile soils where average
population doubling times exceeding 100 days are common and
reproducible\textsuperscript{9}, with experiments in harsher conditions
suggesting that bacterial generation times may become indefinitely long
as nutrient interception balances cell maintenance
rates\textsuperscript{36--38}.

Simulation results have consistently produced broad age distributions
that follow a power law with varying slopes as a function of hydration
conditions (Fig. 3, S1 and S2). A power law age distribution is also
derived analytically based on heuristic assumptions (see derivation in
Appendix S1). For both, the numerical and analytical models, the key
ingredient for emergence of a power law bacterial age distribution is a
wide range of growth rates within the system under consideration. This
assumption is difficult to validate \emph{in situ,} since current
methods to determine growth rates in soil measure a sample average
growth rate (which would bias the observed growth rate towards rapid
growing cells) and cannot resolve the growth rate distribution of
individual cells. The resulting wide distribution of growth rates in the
mechanistic model is a consequence of the patchy nutrient landscape
dictated by thin water films especially in dry conditions (Fig. S3) for
which the simulation data show a generation time distribution following
a power law more closely (Fig. 3d). Interestingly, the mechanistic model
(that makes no assumptions regarding growth rate or population age
distributions), and the simple analytical approach independently predict
a power law distribution of soil bacterial generation time and cell age.
A consequence of such distribution is that no simple mean bacterial
generation time or cell age can be defined due to the heavy tail cell
age distribution implying that a soil sample may harbor a nearly
unbounded range of bacterial ages. We may define the average cell age of
certain fractions of the population (Table S2), such estimates would
however be highly biased towards the younger and more abundant cells. A
deviation between the analytically derived power law coefficient \selectlanguage{greek}α\selectlanguage{english}=2 and
fitted coefficients for numerical results in the range of 1.2 to 1.35
(Fig. 3e), suggesting that the mechanistic simulations predict a heavier
tail of the distribution compared to analytical derivation. Given the
higher level of complexity in the assumption-free mechanistic model, and
inability to extract the real spectrum of cell growth rates and resource
distribution, we defer resolution of the power law slope to future
studies.

In addition to shaping cell growth rate distribution, hydration
conditions affect population dynamics and induce a division of the
bacterial community into dominant and rare lineages. By virtue of their
position relative to nutrient sources, dominant lineages that contribute
most to the overall biomass (but constitute the minority of the original
inoculated cell lineages) proliferate and achieve high reproductive
success, which translates to shorter generation times and younger cells
on average. In contrast, the rare lineages grow very slowly, thereby
exhibiting overall longer generation times and aged cells. Thus,
considering a soil volume that contains at least a single hotspot, we
expect the emergence of a bimodal distribution of cell ages with younger
cells in the bacterial hotspots and old cells sparsely distributed in
the bulk soil (cold spots) mediated by diffusional and dispersal
constraints (Fig. S4). Although the present study focuses on an isogenic
and copiotrophic bacterial species, our results show how the interplay
of bacterial hot and cold spots and diffusion limitations provide
mechanisms that support the emergence of within species
diversity\textsuperscript{39}. The mechanistic simulations suggest that
even for isogenic cells, a large generational gap between different
lineages emerges due to favorable spatial positioning, especially in dry
conditions where motility is suppressed. In population genetic terms,
the standing genetic variation in nascent soil bacterial hotspots, which
is initially generated by mutations or gene flow, is primarily shaped by
genetic drift as opposed to natural selection, facilitating the
generation of within species diversity even at the smallest scale. In
addition to promoting within species diversity, an interesting analogy
exists between the rare and dominant lineages in our simulations and the
rare and common species found in natural soil\textsuperscript{40}. The
key mechanism fostering a power law age distribution is a wide range of
bacterial growth rates. Recent experimental results have provided
glimpses into a wide distribution of taxon-specific growth rates for the
same soil sample\textsuperscript{41}, raising the question of whether
bacterial cold spots (representing the rare lineages) also harbor the
tail of the bacterial species distribution (rare species).

This discrepancy in dynamics between lineages (or strains/species)
culminates in the creation of a ``genetic reservoir'' (also termed
microbial genetic seed banks\textsuperscript{42}) where rapid
proliferation generates genetic variation that persists through time
owing to the slow growing and rare lineages acting as keepers of traits.
Often such genetic reservoirs have been associated with the fraction of
the bacterial population at a state of reduced metabolic activity
(dormancy) within larger soil volumes\textsuperscript{43}. Our results
suggest that even under ubiquitous hydrological conditions and within
small soil-volumes (mm\textsuperscript{3}) occupied by a single
bacterial hotspot, the persistence of rare lineages existing close to
the maintenance rate provides a simple and intuitive mechanism for the
emergence of heavy tailed generation time distributions that contribute
to the soil bacterial genetic reservoir. Admittedly, the mechanistic
model is a highly abstracted and simplified reality representing a small
domain with limited heterogeneity where a single, aerobic species
growing on a sole carbon source in absence of environmental variables
(e.g. pH or temperature) with the exception of hydration conditions.
Natural soil consists of numerous additional constraints such as highly
complex pore spaces, restricted nutrient accessibility, a plethora of
potential carbon sources and additional biotic factors (intraspecific
variability, trophic interactions and non-growth associated
maintenance). Since our simulations represent the optimal case of rapid
bacterial growth, the above-mentioned processes are likely to extend the
generation time distribution and contribute further to bacterial seed
banks in soil\textsuperscript{43}. In analogy, we also expect a range of
biotic and abiotic processes to act in the opposite direction. These
would truncate the range of applicability of power law bacterial age
distribution. The lowest limit for the age range is defined by
physiological constraints affecting rapid bacterial growth (i.e. the
shortest biologically possible generation time), whereas mechanisms that
truncate the upper range of the power law are more complicated to
determine. Unlike animal age, the lifetime of a bacterial cell is not
limited\textsuperscript{36--38}. However, there are other mechanisms of
bacterial death which shape the cell age distribution, such as grazing
of bacteria\textsuperscript{44}, large-scale bacterial death associated
with episodic wetting events\textsuperscript{45} or phage
infections\textsuperscript{46} supporting a ``forever young''
hypothesis\textsuperscript{47}. If the mechanisms above act uniformly on
the total population, they would affect primarily the dominant lineages
(due to their high relative abundance), yet, over extended periods we
expect gradual erosion of older cells and rejuvenation of the overall
community. Since many of the above-mentioned mechanisms are related to
the microscale liquid organization in soil pores, the resulting
bacterial cell age and generation time distribution represents a
delicate balance between processes that promote and suppress survival of
old bacterial cells as a function of soil hydration conditions.

Both the extrapolated generation time calculation of the mechanistic
model and the analytical derivation assume steady state conditions
concerning bacterial growth rates. Steady state rarely exists in natural
soil habitats, which are often subjected to diurnal and seasonal effects
including episodic wetting events that reconnect the patchy environment
and thus could homogenize conditions for a brief window of time. As a
soil gradually dries, the brief homogenization of the conditions may
result in reshuffling of lineages where previously proliferating
lineages may experience harsh conditions and vice versa. Such resetting
events have not been included in the mechanistic model nor in the
analytical age model. In addition to shaping the bacterial age and
generation time distributions, these stochastic events may facilitate
horizontal gene transfer (especially in the subsequently drier
conditions\textsuperscript{27}) between genetically distant bacterial
cells through reconnecting previously segregated patches and providing a
mechanism to access the genetic reservoir directly.

The natural emergence of a soil genetic reservoir for each species (old
bacterial cells inhabiting soil cold spots) may be specifically
important for ecosystem stability and function. The dynamic nature of
soil as a microbial habitat creates scenarios where adapted gene
variants are outcompeted due to changing environmental conditions. If
environmental conditions revert to a previous state, a genetic memory
may promote rapid adaption of the soil microbial
communities\textsuperscript{48}. Evidence for the importance of the
microbial seed bank in soil has been found in the disproportionate
response of rare taxa during following rapid changes in environmental
cues\textsuperscript{49} or during a controlled 45-week experiment
including a thermal disturbance\textsuperscript{50}. In both cases,
resuscitation of dormant taxa from the vast soil genetic reservoir was
key for ecosystem stability and function. Additionally, the presence of
old bacterial cells enhances the potential for horizontal gene transfer
of ancient traits that may provide additional benefits. This is
particularly true for soil where close proximity in dry soil (after an
episodic wetting event that reconnected proximal soil volumes) increases
the rate of horizontal gene transfer due to spatial
confinement\textsuperscript{27}.

The original aim of estimating bacterial cell age and generation time
distributions in soils in relation to heterogeneity and hydration
conditions began with a very simple question: ``What is the average age
of a soil bacterial cell?'', and ended with an equally simple answer:
``practically any age''. In contrast to macrobiota with a finite life
span where an average age in an ecosystem is well defined, providing a
similar answer for prokaryotes living within heterogeneous soil is far
more complicated. The proximity of vastly different ages and generations
of the same bacterial species that may coexist a few hundred microns
apart raise several intriguing possibilities. Considering reconnection
of subpopulations with large generational gaps by episodic soil wetting
events, could offer opportunities for regaining physiological traits
lost during prolonged segregation and potentially provide a ubiquitous
mechanism for sustaining genetic reservoir of traits and
ecotypes\textsuperscript{39}.

\textbf{Acknowledgments}

We thank Noah Fierer (University of Colorado, Boulder) for motivating
this work with the question ``\emph{what is the average age of soil
bacteria?} '' We also thank Robin Tecon and Samuel Bickel (ETH, Zurich)
for discussing the presented material on numerous occasions.

\section*{References}

{\label{references}}

1. Bardgett, R. D. \& Van Der Putten, W. H. Belowground biodiversity and
ecosystem functioning. \emph{Nature} \textbf{505} , 505--511 (2014).

2. Young, I. M. \& Crawford, J. W. Interactions and self-organization in
the soil-microbe complex. \emph{Science} \textbf{304} , 1634--1637
(2004).

3. Kuzyakov, Y. \& Blagodatskaya, E. Microbial hotspots and hot moments
in soil: Concept \& review. \emph{Soil Biol. Biochem.} \textbf{83} ,
184--199 (2015).

4. B\selectlanguage{ngerman}ååth, E. \& Johansson, T. Measurement of bacterial growth rates on
the rhizoplane using 3H-thymidine incorporation into DNA. \emph{Plant
Soil} \textbf{126} , 133--139 (1990).

5. Kieft, T. L. Size matters: Dwarf cells in soil and subsurface
terrestrial environments. in \emph{Nonculturable Microorganisms in the
Environment} 19--46 (2000).

6. Tecon, R. \& Or, D. Biophysical processes supporting the diversity of
microbial life in soil. \emph{FEMS Microbiol. Rev.} \textbf{41} ,
599--623 (2017).

7. Van Heerden, J. H. \emph{et al.} Statistics and simulation of growth
of single bacterial cells: Illustrations with B. subtilis and E.
coli.\emph{Sci. Rep.} \textbf{7} , 1--11 (2017).

8. Clarholm, M. \& Rosswall, T. Biomass and turnover of bacteria in a
forest soil and a peat. \emph{Soil Biol. Biochem.} \textbf{12} , 49--57
(1980).

9. Harris, D. \& Paul, E. A. Measurement of bacterial growth rates in
soil. \emph{Appl. Soil Ecol.} \textbf{1} , 277--290 (1994).

10. Rousk, J. \& Bååth, E. Growth of saprotrophic fungi and bacteria in
soil. \emph{FEMS Microbiol. Ecol.} \textbf{78} , 17--30 (2011).

11. Gibson, B., Wilson, D. J., Feil, E. \& Eyre-Walker, A. The
distribution of bacterial doubling times in the wild. \emph{Proc. R.
Soc. B Biol. Sci.} \textbf{285} , 20180789 (2018).

12. Schwartz, E. \emph{et al.} Stable isotope probing with 18O-water to
investigate microbial growth and death in environmental
samples.\emph{Curr. Opin. Biotechnol.} \textbf{41} , 14--18 (2016).

13. Purcell, A. M. \emph{et al.} Quantitative stable isotope probing
with H218O to measure taxon-specific microbial growth. \emph{Methods
Soil Anal.} \textbf{4} , (2019).

14. Barber, D. A. \& Lynch, J. M. Microbial growth in the
rhizosphere.\emph{Soil Biol. Biochem.} \textbf{9} , 305--308 (1977).

15. Söderberg, K. H. \& Bååth, E. Bacterial activity along a young
barley root measured by the thymidine and leucine incorporation
techniques. \emph{Soil Biol. Biochem.} \textbf{30} , 1259--1268 (1998).

16. Olsson, S., Bååth, E. \& Söderström, B. Growth of Verticillium
dahliae Kleb. hyphae and of bacteria along the roots of rape ( Brassica
napus L.) seedlings. \emph{Can. J. Microbiol.} \textbf{33} , 916--919
(1987).

17. Bowen, G. D. \& Rovira, A. D. Microbial colonization of plant
roots.\emph{Annu. Rev. Phytopathol.} \textbf{14} , 121--144 (1976).

18. Zelenev, V. V., Van Bruggen, A. H. C. \& Semenov, A. M. `BACWAVE,' a
spatial-temporal model for traveling waves of bacterial populations in
response to a moving carbon source in soil. \emph{Microb.
Ecol.}\textbf{40} , 260--272 (2000).

19. Bennett, R. A. \& Lynch, J. M. Bacterial growth and development in
the rhizosphere ofgnotobiotic cereal plants.
\emph{Microbiology}\textbf{125} , 95--102 (1981).

20. Christensen, H., Funck-Jensen, D. \& Kjøller, A. Growth rate of
rhizosphere bacteria measured directly by the tritiated thymidine
incorporation technique. \emph{Soil Biol. Biochem.} \textbf{21} ,
113--117 (1989).

21. Bloem, J., de Ruiter, P. C., Koopman, G. J., Lebbink, G. \&
Brussaard, L. Microbial numbers and activity in dried and rewetted
arable soil under integrated and conventional management. \emph{Soil
Biol. Biochem.} \textbf{27} , 655--665 (1992).

22. Remus-Emsermann, M. N. P., Tecon, R., Kowalchuk, G. A. \& Leveau, J.
H. J. Variation in local carrying capacity and the individual fate of
bacterial colonizers in the phyllosphere. \emph{ISME J.} \textbf{6} ,
756--765 (2012).

23. Borer, B., Ataman, M., Hatzimanikatis, V. \& Or, D. Modeling
metabolic networks of individual bacterial agents in heterogeneous and
dynamic soil habitats (IndiMeSH). \emph{PLOS Comput. Biol.} \textbf{15}
, e1007127 (2019).

24. \selectlanguage{polish}Ş\selectlanguage{english}im\selectlanguage{polish}ş\selectlanguage{english}ek, E. \& Kim, M. Power-law tail in lag time distribution
underlies bacterial persistence. \emph{Proc. Natl. Acad. Sci. U. S.
A.}\textbf{116} , 17635--17640 (2019).

25. Borer, B., Tecon, R. \& Or, D. Spatial organization of bacterial
populations in response to oxygen and carbon counter-gradients in pore
networks. \emph{Nat. Commun.} \textbf{9} , 1--11 (2018).

26. Kleyer, H., Tecon, R. \& Or, D. Rapid shifts in bacterial community
assembly under static and dynamic hydration conditions in porous
media.\emph{Appl. Environ. Microbiol.} \textbf{86} , (2019).

27. Tecon, R., Ebrahimi, A., Kleyer, H., Levi, S. E. \& Or, D.
Cell-to-cell bacterial interactions promoted by drier conditions on soil
surfaces. \emph{Proc. Natl. Acad. Sci. U. S. A.} \textbf{115} ,
9791--9796 (2018).

28. Dechesne, A., Wang, G., Gulez, G., Or, D. \& Smets, B. F.
Hydration-controlled bacterial motility and dispersal on
surfaces.\emph{Proc. Natl. Acad. Sci.} \textbf{107} , 14369--14372
(2010).

29. Ebrahimi, A. N. \& Or, D. Microbial dispersal in unsaturated porous
media: Characteristics of motile bacterial cell motions in unsaturated
angular pore networks. \emph{Water Resour. Res.} \textbf{50} ,
7406--7429 (2014).

30. Tecon, R. \& Or, D. Bacterial flagellar motility on hydrated rough
surfaces controlled by aqueous film thickness and
connectedness.\emph{Sci. Rep.} \textbf{6} , 19409 (2016).

31. Ebrahimi, A. \& Or, D. Hydration and diffusion processes shape
microbial community organization and function in model soil
aggregates.\emph{Water Resour. Res.} \textbf{51} , 9804--9827 (2015).

32. Lunn, M. \emph{et al.} Quantifying the roles of immigration and
chance in shaping prokaryote community structure. \emph{Environ.
Microbiol.} \textbf{8} , 732--740 (2005).

33. Painter, P. R. \& Marr, A. G. Mathematics of
microbialpopulations.\emph{Annu. Rev. Microbiol.} \textbf{22} , 519--548
(1968).

34. Li, C. H. \& Lee, C. K. Minimum cross entropy
thresholding.\emph{Pattern Recognit.} \textbf{26} , 617--625 (1993).

35. Gray, D. A. \emph{et al.} Extreme slow growth as alternative
strategy to survive deep starvation in bacteria. \emph{Nat.
Commun.}\textbf{10} , 1--12 (2019).

36. Greenblatt, C. L. \emph{et al.} Micrococcus luteus - Survival in
amber. \emph{Microb. Ecol.} \textbf{48} , 120--128 (2004).

37. Johnson, S. S. \emph{et al.} Ancient bacteria show evidence of DNA
repair. \emph{Proc. Natl. Acad. Sci. U. S. A.} \textbf{104} ,
14401--14405 (2007).

38. Jaakkola, S. T. \emph{et al.} The complete genome of a viable
archaeum isolated from 123-million-year-old rock salt. \emph{Environ.
Microbiol.} \textbf{18} , 565--579 (2016).

39. Van Rossum, T., Ferretti, P., Maistrenko, O. M. \& Bork, P.
Diversity within species: interpreting strains in microbiomes.\emph{Nat.
Rev. Microbiol.} 1--16 (2020).

40. Bickel, S. \& Or, D. Soil bacterial diversity mediated by microscale
aqueous-phase processes across biomes. \emph{Nat. Commun.} \textbf{11} ,
1--9 (2020).

41. Koch, B. J. \emph{et al.} Estimating taxon-specific population
dynamics in diverse microbial communities. \emph{Ecosphere} \textbf{9} ,
e02090 (2018).

42. Lennon, J. T. \& Jones, S. E. Microbial seed banks: The ecological
and evolutionary implications of dormancy. \emph{Nat. Rev.
Microbiol.}\textbf{9} , 119--130 (2011).

43. Locey, K. J., Fisk, M. C. \& Lennon, J. T. Microscale insight into
microbial seed banks. \emph{Front. Microbiol.} \textbf{7} , 2040 (2017).

44. Clarholm, M. Protozoan grazing of bacteria in soil-impact and
importance. \emph{Microb. Ecol.} \textbf{7} , 343--350 (1981).

45. Blazewicz, S. J., Schwartz, E. \& Firestone, M. K. Growth and death
of bacteria and fungi underlie rainfall-induced carbon dioxide pulses
from seasonally dried soil. \emph{Ecology} \textbf{95} , 1162--1172
(2014).

46. Shapiro, O. H., Kushmaro, A. \& Brenner, A. Bacteriophage predation
regulates microbial abundance and diversity in a full-scale bioreactor
treating industrial wastewater. \emph{ISME J.} \textbf{4} , 327--336
(2010).

47. Kuzyakov, Y. \& Mason-Jones, K. Viruses in soil: Nano-scale undead
drivers of microbial life, biogeochemical turnover and ecosystem
functions. \emph{Soil Biol. Biochem.} \textbf{127} , 305--317 (2018).

48. Overballe-Petersen, S. \& Willerslev, E. Horizontal transfer of
short and degraded DNA has evolutionary implications for microbes and
eukaryotic sexual reproduction. \emph{BioEssays} \textbf{36} ,
1005--1010 (2014).

49. Aanderud, Z. T., Jones, S. E., Fierer, N. \& Lennon, J. T.
Resuscitation of the rare biosphere contributes to pulses of ecosystem
activity. \emph{Front. Microbiol.} \textbf{6} , 24 (2015).

50. Sorensen, J. W. \& Shade, A. Dormancy dynamics and dispersal
contribute to soil microbiome resilience. \emph{Philos. Trans. R. Soc. B
Biol. Sci.} \textbf{375} , 20190255 (2020).

\selectlanguage{english}
\FloatBarrier
\end{document}

