Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences,
Journal Year:
2024,
Volume and Issue:
480(2299)
Published: Oct. 1, 2024
The
Lotka–Volterra
system
is
a
set
of
ordinary
differential
equations
describing
growth
interacting
ecological
species.
One
the
debated
questions
understanding
how
number
species
in
influences
stability
model.
Robert
May
studied
large
systems
may
become
unstable
when
species–species
interactions
do
not
vanish.
This
outcome
has
frequently
been
interpreted
as
universal
phenomenon
and
summarized
‘large
are
unstable’.
By
exploring
general
interaction
networks,
we
show
that
competitive
maintain
even
for
despite
non-vanishing
strength.
We
establish
sufficient
conditions
threshold
on
interspecific
strength,
formulated
terms
maximum
minimum
degrees
(or
weights)
rather
than
network’s
size.
For
values
below
this
threshold,
coexistence
all
attained,
regardless
Our
finding
generalizes
May’s
result
by
showing
it
outlier
nodes
with
degree
cause
instability
system.
Peer Community Journal,
Journal Year:
2025,
Volume and Issue:
5
Published: Jan. 2, 2025
One
of
the
more
difficult
challenges
in
community
ecology
is
inferring
species
interactions
on
basis
patterns
spatial
distribution
organisms.
At
its
core,
problem
that
distributional
reflect
'realized
niche',
net
result
a
complex
interplay
processes
involving
dispersal,
environmental,
and
interaction
effects.
Disentangling
these
effects
can
be
at
least
two
distinct
levels.
From
statistical
point
view,
splitting
population's
variation
into
contributions
from
partners,
abiotic
environment
proximity
requires
'natural
experiments'
where
all
three
factors
somehow
vary
independently
each
other.
On
conceptual
level,
it
not
even
clear
how
to
meaningfully
separate
processes:
for
instance,
could
depend
state
biotic
environment,
may
combine
highly
non-additive
ways.
Here
we
show
latter
issue
arises
almost
inescapably,
simple
theoretical
setting
designed
minimize
it.
Using
model
competitive
metacommunity
dynamics
direct
are
assumed
context-independent,
accurately
cross-species
correlations
major
challenge
under
but
most
restrictive
assumptions.
However,
also
find
possible
estimate
moments
(mean
value
variance)
much
robustly,
if
precise
values
cannot
inferred.
Consequently,
argue
study
multi-species
still
informative
approaches
build
distributions
parameters
predict
macroscopic
outcomes
assembly.
Journal of Statistical Mechanics Theory and Experiment,
Journal Year:
2025,
Volume and Issue:
2025(2), P. 023301 - 023301
Published: Feb. 3, 2025
Abstract
We
investigate
a
disordered
multi-dimensional
linear
system
in
which
the
interaction
parameters
are
colored
noises,
varying
stochastically
time
with
defined
temporal
correlations.
refer
to
this
type
of
disorder
as
‘annealed’,
contrast
quenched
couplings
fixed
over
time.
Using
generating
functional
methods,
we
extend
dynamical
mean-field
theory
accommodate
annealed
and
employ
it
find
exact
solution
model
limit
large
number
degrees
freedom.
Our
analysis
yields
analytical
results
for
non-stationary
autocorrelation,
stationary
variance,
power
spectral
density,
phase
diagram
model.
Some
unexpected
features
emerge
upon
changing
correlation
interactions.
The
variance
critical
generally
found
be
non-monotonic
functions
also
that
re-entrant
transition
can
take
place
when
is
varied.
Bacterial
communities
are
pivotal
to
maintaining
ecological
function
and
preserving
the
rich
tapestry
of
biological
diversity.
The
rapid
development
environmental
sequencing
technologies,
such
as
metagenomics,
has
revolutionized
our
capacity
probe
However,
despite
these
advances,
a
theoretical
understanding
connecting
empirical
data
with
ecosystem
modelling,
in
particular
framework
disordered
systems
akin
spin
glasses,
is
still
its
infancy.
Here,
we
present
comprehensive
using
theories
decode
microbiome
data,
which
offers
insight
into
forces
that
shape
macroecological
states.
By
employing
quenched
generalized
Lotka-Volterra
model,
analyze
species
abundance
healthy
diseased
human
gut
microbiomes.
Results
reveal
emergence
two
distinct
patterns
species-interaction
networks,
elucidating
pathways
through
dysbiosis
may
drive
instability.
Interaction
thus
provide
window
systemic
shifts
accompanying
transition
from
health
disease,
offering
new
perspective
on
dynamics
microbial
community.
Our
findings
suggest
potential
theory
characterize
microbiomes
by
capturing
essence
interactions
their
consequences
stability
functioning,
leveraging
linkages
dynamics.
Bacterial
communities
are
pivotal
to
maintaining
ecological
function
and
preserving
the
rich
tapestry
of
biological
diversity.
The
rapid
development
environmental
sequencing
technologies,
such
as
metagenomics,
has
revolutionized
our
capacity
probe
However,
despite
these
advances,
a
theoretical
understanding
connecting
empirical
data
with
ecosystem
modelling,
in
particular
framework
disordered
systems
akin
spin
glasses,
is
still
its
infancy.
Here,
we
present
comprehensive
using
theories
decode
microbiome
data,
which
offers
insight
into
forces
that
shape
macroecological
states.
By
employing
quenched
generalized
Lotka-Volterra
model,
analyze
species
abundance
healthy
diseased
human
gut
microbiomes.
Results
reveal
emergence
two
distinct
patterns
species-interaction
networks,
elucidating
pathways
through
dysbiosis
may
drive
instability.
Interaction
thus
provide
window
systemic
shifts
accompanying
transition
from
health
disease,
offering
new
perspective
on
dynamics
microbial
community.
Our
findings
suggest
potential
theory
characterize
microbiomes
by
capturing
essence
interactions
their
consequences
stability
functioning,
leveraging
linkages
dynamics.
PLoS Computational Biology,
Journal Year:
2025,
Volume and Issue:
21(5), P. e1013044 - e1013044
Published: May 8, 2025
Ecology
has
historically
benefited
from
the
characterization
of
statistical
patterns
biodiversity
within
and
across
communities,
an
approach
known
as
macroecology.
Within
microbial
ecology,
macroecological
approaches
have
identified
universal
diversity
abundance
that
can
be
captured
by
effective
models.
Experimentation
simultaneously
played
a
crucial
role,
advent
high-replication
community
time-series
allowed
researchers
to
investigate
underlying
ecological
forces.
However,
there
remains
gap
between
experiments
performed
in
laboratory
documented
natural
systems,
we
do
not
know
whether
these
recapitulated
lab
experimental
manipulations
produce
effects.
This
work
aims
at
bridging
ecology
Using
time-series,
demonstrate
observed
nature
exist
setting,
despite
controlled
conditions,
unified
under
Stochastic
Logistic
Model
growth
(SLM).
We
found
demographic
(e.g.,
migration)
impact
patterns.
By
modifying
SLM
incorporate
said
alongside
details
sampling),
obtain
predictions
are
consistent
with
outcomes.
combining
models,
macroecology
viewed
predictive
discipline.
PLoS ONE,
Journal Year:
2023,
Volume and Issue:
18(7), P. e0288926 - e0288926
Published: July 21, 2023
While
the
human
gut
microbiome
has
been
intensely
studied,
we
have
yet
to
obtain
a
sufficient
understanding
of
genetic
diversity
that
it
harbors.
Research
efforts
demonstrated
considerable
fraction
within-host
variation
in
is
driven
by
ecological
dynamics
co-occurring
strains
belonging
same
species,
suggesting
an
lens
may
provide
insight
into
empirical
patterns
diversity.
Indeed,
model
self-limiting
growth
and
environmental
noise
known
as
Stochastic
Logistic
Model
(SLM)
was
recently
shown
successfully
predict
temporal
within
single
host.
However,
its
ability
across
hosts
be
tested.
In
this
manuscript
I
determine
whether
predictions
SLM
explain
unrelated
for
22
common
microbial
species.
Specifically,
stationary
distribution
explains
allele
frequencies
predicts
harboring
given
(i.e.,
prevalence)
sites.
The
accuracy
correlated
with
independent
estimates
strain
structure,
follow
statistically
similar
forms
due
existence
strain-level
ecology.
Physical Review Research,
Journal Year:
2024,
Volume and Issue:
6(2)
Published: April 19, 2024
The
ecological
and
evolutionary
dynamics
of
large
populations
can
be
addressed
theoretically
using
concepts
methodologies
from
statistical
mechanics.
This
approach
has
been
extensively
discussed
in
the
literature,
both
within
realm
population
genetics,
which
focuses
on
genes
or
“genotypes,”
adaptive
dynamics,
emphasizes
traits
“phenotypes.”
Following
this
tradition,
here
we
construct
a
theoretical
framework
allowing
us
to
derive
“macroscopic”
equations
general
“microscopic”
stochastic
representing
fundamental
processes
reproduction,
mutation,
selection
community
individuals,
each
one
characterized
by
its
phenotypic
features.
Importantly,
our
setup,
timescales
are
intertwined,
makes
it
particularly
suitable
describe
microbial
communities,
timely
topic
utmost
relevance.
leads
probabilistic
description—even
case
arbitrarily
populations—of
distribution
individuals
space
as
encoded
what
call
“generalized
Crow-Kimura
equation”
replicator-mutator
equation.”
We
discuss
limits
such
an
equation
reduces
(deterministic)
theory
“adaptive
dynamics,”
i.e.,
standard
space.
Moreover,
emphasize
aspects
that
beyond
reach
dynamics.
In
particular,
developing
simple
model
growing
competing
illustrative
example,
demonstrate
resulting
probability
undergo
“dynamical
phase
transitions.”
These
transitions
may
involve
shifts
unimodal
bimodal
distribution,
generated
branching
event,
multimodal
through
cascade
events.
Furthermore,
formalism
allows
rationalize
these
cascades
parsimonious
Landau's
transitions.
Finally,
extend
account
for
finite
illustrate
possible
consequences
“demographic”
effects.
Altogether,
present
extends
and/or
complements
existing
approaches
paves
way
more
systematic
studies
communities
well
future
developments
including
analyses
process
perspective
nonequilibrium
Published
American
Physical
Society
2024
Physical review. E,
Journal Year:
2024,
Volume and Issue:
110(1)
Published: July 8, 2024
This
study
investigates
the
role
of
spatial
segregation,
prompted
by
competition
avoidance,
as
a
key
mechanism
for
emergent
coexistence
within
microbial
communities.
Recognizing
these
communities
complex
adaptive
systems,
we
challenge
sufficiency
mean-field
pairwise
interaction
models,
and
consider
impact
dynamics.
We
developed
an
individual-based
simulation
depicting
bacterial
movement
through
pattern
random
walks
influenced
leading
to
formation
spatially
segregated
clusters.
model
was
integrated
with
Lotka-Volterra
metapopulation
framework
focused
on
competitive
interactions.
Our
findings
reveal
that
segregation
combined
low
diffusion
rates
high
compositional
heterogeneity
among
patches
can
lead
in
reveals
novel
underpinning
stable,
coexisting
microbe
clusters,
which
is
nonetheless
incapable
promoting
case
isolated
pairs
species.
underscores
importance
considering
factors
understanding
dynamics
ecosystems.