Hello, and welcome to the Physics World Weekly
podcast.
I'm Margaret Harris, and this episode of the
podcast is sponsored by EPL,
a journal that publishes original, high quality letters
in all areas of physics.
EPL operates under the scientific policy and control
of the European Physical Society
and is published by EDP Sciences,
the Societa Italiana de Physica,
and IOP Publishing, which also publishes Physics World.
My guests in this episode are the co
authors of an invited mini review article or
perspective
in EPL on the subject of theoretical ecology.
The article was published in June, its title
is
Statistical Physics Approaches to Ecological Communities,
and its authors are Ada Altieri and Silvia
deMonte.
Ada is an associate professor at the Laboratory
for Matter and Complex Systems at the Universite
Paris Cite, France,
and Sylvia is a senior researcher at the
Institute of Biology in the Ecole Normale Superieure
in Paris and the Max Planck Institute for
Evolutionary Biology in Pleuron, Germany.
Ada Altieri and Silvia de Monte, welcome to
the podcast.
Thank you. Thank you so much. Okay. The
first thing I want to get straight for
our listeners is
what is theoretical ecology? You know, what kinds
of questions are you asking? What kinds of
problems are you trying to solve?
Perhaps, I will start.
So theoretical ecology is a pretty broad field
that has a long history.
It has,
traditionally, we think, it started
around the beginning of the 20 century with,
the proposal of using some low dimensional models,
so models of interaction between, just a few
species, typically two species,
to try and understand
some patterns that were observed
in,
ecological systems.
So the sort of the chief,
model people refer to is, the Lotka Volterra
predator prey equations
that were
independently
proposed,
by
Lotka in,
1910
and by Volterra
in 1926
to explain,
why
natural populations seem to vary
over, different years in the number of individuals
in ways that
looked a bit
disconnected,
from, the environmental
year to year variations.
And so they realized,
and this was a really an important realization
that ecological systems
might be maintained out of equilibrium
by the interactions
between species.
So if you have just, you know, a
few species and you're able to know what
is, the probability of interaction or what are
the growth rates of one and the other,
you can still rely on this kind of
models. But there is another
vast array of models that have been developed,
especially in the last thirty years or so
that deal with,
communities that are composed of a vast number
of species
where it is
much more difficult to estimate parameters.
I want to bring Ada in just because
I want to get a couple of examples
if I can of the types of species
that you're talking about in communities. You know,
what's what was a good example of a
two species interaction that's very easy to model
with these
equations that were developed in 1910, 1926?
We can think of just prey predator,
so fox and rabbit,
kind of species.
But as Heather was saying, so the most
remarkable
aspect of recent years, so the true novelty
right now is that we are trying
to characterize emergent mechanisms and collective behaviors of
large ecological communities,
for instance, gut microbial communities in terms of
odor versus disorder phase transition.
So this is one of the goal of
of our approach.
And the second one is also to to
provide
quantitative
estimators, so quantitative discriminators
for detecting
different rigids
in this kind of communities.
What kind of extra complexities does it add
trying to model, say, microbial species? I think,
Sylvia, you were talking about sometimes
you can't get accurate estimates in the way
you can get accurate estimates of, say, foxes
and rabbits.
Yeah. Indeed. So these microbial communities, they really
have a huge number of species
in
many environments, natural environments.
And you can sometimes reconstruct synthetic communities in
the lab. And then these synthetic communities allow
you to measure growth rates, to measure interaction
rates.
But this involves
estimating
a large number of parameters and a lot
of experimental work.
This can be done for relatively
simple communities
and, in control settings.
However,
when you deal with communities,
in nature or, in a gut,
you can't really go and extract one species
and or measure in situ.
So
you often
only have an idea
of what kind
of statistical
features
have the distribution
of interactions.
Or at least this is what our work
is about,
trying to infer, for instance, the statistical features
from something that can
be measured
at the level of the community
without knowing
exactly
what's in every single species is doing.
So can you use statistical physics models to
predict what will happen
in real ecosystems,
like, I don't know, tipping points or circumstances
which
one species in a community might become extinct
or the community itself becomes unstable?
Yeah. So for instance, a small change in
environmental
condition or system parameters
that can be demographic
fluctuations
of birth and the processes
can cause a sudden turnover,
so irreversible
shift
from one equilibrium state to another equilibrium state.
So we can, for instance, detect a phase,
a self sustaining
phase where all species
survive
and another phase where all species get extinct.
So this kind of transition
is typically referred to as a tipping point
and in theoretical and statistical physics
is also called
a spinodal
transition
because it's associated with a vanishing
eigenvalue
of a stability matrix a stability matrix,
which provide information on the emergent criticality, the
emergent transition.
So following intuition from statistical physics, we can
try
to estimate and characterize these tipping points.
Empirically
speaking, in real ecosystem,
one could measure fluctuation
of the average abundance
with respect to environmental noise, which affect the
current capacity, so the maximum attainable value of
a species abundance,
or also individual
growth rates.
So this is perfectly
doable in in a real ecosystem
and provides
early word signal
of the proximity
to a deep endpoint.
How applicable is your work to actually colleges
out in the field? Is this one of
your goals, or is it all very far
removed several steps back from that?
So I suppose that in the field, there
are people who,
do this.
So
I personally
don't, go that far because,
my
focus
and that of my collaborators
is mostly
to try and understand
how
the mechanisms,
that are involved in ecology
shape
patterns that can be observed at the level
of a community.
And the reason we focus on this is
that it is still pretty poorly understood
how
processes
turn into patterns.
So what we can observe typically
are patterns.
Like, I don't know, we we go out
in the field
and we measure how many individuals are there
of every species.
So if it's a microbial community, there are
many, many different species, hundreds or thousands of
different species. And then there are ways to
estimate
how many
of each of these species is there.
Once you have this kind of information,
you can
write down histograms,
do some
statistics
on this data.
And these statistics, they turn out to be
sometimes,
different from one ecosystem to another, but sometimes
they are incredibly similar.
And we still
don't understand completely
why certain patterns
are so
conserved or universal if you want, to use,
a physics term.
And sometimes instead, we would like actually to
focus on differences rather than on what is
the same everywhere.
So
our,
goal is mainly to
understand
what determines
this,
regularities,
and what determines the differences.
And then, of course, the the ultimate goal
would be to be able to go out
in nature and to be able to say,
okay, this ecosystem that has these statistical features
is particularly endangered, for instance,
rather than this other one is instead,
you know, a stable ecosystem.
We observe, for instance, this kind of differences
between, ecosystems
that are,
like,
associated,
to hosts. So they have evolved for a
long time
within a host. So they are sort of
more,
stable in in their functioning
rather than ecosystems,
like, I don't know, plankton ecosystems,
that have a very, very high turnover,
and, they tend to have many species that
are rare and plausibly to an extinction threshold.
I like the distinction you made between patterns
and processes. You want to be able to
go out and see a pattern in nature
or in the gut or in the laboratory
and say, ah, because I see this pattern,
these are the processes that are going on,
and therefore,
this is what might happen next. Yep. That's
exactly what people have been trying to do
for a long time.
The fact is that, so as we review
in the article,
there had been many different approaches where people
started from hypothesis that seem to be ecologically
reasonable,
and then they'd use the pattern. And then
they went out in nature, looked at the
pattern that looked like that and said, ah,
okay. I I believe then then my model
is right.
But
one of the problems
that has emerged is that different models tend
to provide very similar patterns
that are very hard to distinguish
from empirical data.
And then
it is still,
one of the open questions that we raised,
in the more perspective part. So what is
exactly
that is peculiar
of a given model
and, how can we distinguish models that start
from very different assumptions
Mhmm. Based on data?
Okay. So as you've already alluded, you've written
the paper recently for the journal EPL in
which you discussed some basic classes of statistical
physics models that you as theoretical ecologists use
and the challenges that future models need to
address.
I wonder if we could discuss a few
of these challenges
in a bit more depth. We've already talked
about species interactions, including higher order interactions. What
does it mean?
So it basically means that the interaction between
two species
is modulated by the presence of a third
one or a fourth one.
So suppose that species
a competes
with species b for nutrients,
then suppose now that the strength of this
competitive
effect is reduced
if species c is present because
c improves soil condition via
nitrogen fixation
or other effect.
So overall, a, b, and c work
out altogether
and affect both the stability and the dynamics
of the community.
So on one hand, I higher interaction
have the potential to add another layer of
complexity,
to add more biological
complexity and realism to the community. But on
the other hand, they further complicate the analysis.
So rigorously understanding how relevant they are in
maintaining diversity in the community is still an
open question.
I would just perhaps
step back a second
and just say that,
many
simplified models of ecosystems
usually only consider pairwise interactions.
It is certainly more realistic to take into
account higher order interactions
even though most results have been obtained so
far for this simple setting where basically
interactions among
a very complex community
just boil down to interaction between pairs of
species.
Another simplification
is this idea that obviously any real ecosystem,
even a bacterial ecosystem with millions of individuals
will have a finite number of species.
Why is this hard to model mathematically?
Indeed, ecological communities have a varying number of
species.
So macroorganisms
like,
animals and plants
have communities that are composed of, you know,
at maximum a few 100 of different species.
And this is the number is much higher
for
microbial communities.
But, indeed it is not infinite.
So the problem is to find
the right spot between,
very low dimensional systems. So that can be
analyzed
with methods,
from, I don't know, bifurcation analysis,
dynamic system theory,
and these other models that come from statistical
physics, where you have in principle,
an infinite number of species.
What turns out is that in many cases,
even though, results are obtained in the thermodynamic
limit,
a lot of conclusions still hold for
a reasonable number of species.
So, at a certain point, of course, this
breaks down,
but there are even some features that are
actually
strictly
low dimensional
or, low co dimensional, and therefore
they can be,
described
even, with, tools from,
dynamical system theory
despite, being emergent from
a system with a very, very high number
of degrees of freedom.
I will also like to say that the
kind of techniques that we are describing in
our review are typically referred to as mean
field approach. So one of these is dynamical
mean field theory. And so it's very helpful.
It's very useful to characterize
emergent mechanisms, collective behaviors,
but it has been also shown that it
can fail in the presence of sparse networks.
So when the network is not completely connect
and each node, each species
is just connected, is just related to a
few
of them.
And so in this case, we should improve
and refine
our techniques to take into account also finite
size fluctuations.
And so combine it at the same time
numerical simulation
with rigorous analytical method.
What does failure look like when you're modeling
a system like this? How do you know
when your model has failed? Do you have
to compare it with experimental data or you're
just like, oh gosh. That's pretty something really
unphysical?
Yeah. So experimental
data that are available or rather,
let's say, empirical data
for,
natural communities
are typically this,
measures of species abundances.
So this can be either like a snapshot
measures.
Like, I go out in the ocean,
I sample,
I come back, and then I sequence,
whatever I find in the water.
Or in some cases and actually more and
more luckily,
there are time series. So there are, you
know, one can access the variation over time
of the abundance of different species.
And so this time series are particularly valuable
because,
they provide a different perspective
abandoned again.
So if we don't access this temporal variation,
we will never know exactly
which species
are abundant,
and whether
there is something that is interesting
also in the dynamics and not only
on, you know, our snapshot
vision of the ecosystem.
So this goes back to the idea by
Lotka and Volterra that, you know, ecosystems need
not be at equilibrium.
They can also live, in states,
that are variable.
And we know now, especially thanks to the
latest developments,
where statistical physics has contributed a lot, that
there are many different,
out of equilibrium regimes,
that can be partially
described by statistical physics methods.
Do you have an example
of something that statistical physics has been very
successful in describing and out of the equilibrium
system?
So something we have been studying
are the distribution of abundances of planktonic
protest communities.
So protests are,
unicellular eukaryotes.
And, there have been surveys,
in the last years,
where,
basically the whole
the total biodiversity
of the sunlit ocean has been revealed
by sampling
in many different locations in the world ocean.
And one striking feature there was,
that
most species
appear to be rare,
and one could assess
what was the law of decay of abundances.
So if you rank species from the most
abundant to the least abundant.
And methods
derived by statistical physics and
using this, lot of models,
this time a generalized lot of models. So
with
many, many different species
allowed to
reproduce, the observation,
that this decay,
of the so called species abundance distribution
is actually a power law. And that this
power law has an exponent that is different
from one that is, the typical exponent of
the Ziff's
law. Models also
sort of,
retrieve exponents that are in the same order
of magnitude. So,
that is between, let's say, one and two
as those that are observed empirically.
And this, and this kind of observation is
actually
linked in, with
different models. So some of them,
so
this lots of Volterra, some others, neutral models.
But lots of Volterra models are particularly
useful because they also provide a dynamical
picture of, what is the underpinning of this
distribution.
That is, the idea that there are at
a given time,
a few species that are highly dominant and
successful,
but this highly successful species do not stay
there forever, and there is a permanent turnover
of successful and rare species.
So all the diversity that is,
observed is actually necessary to maintain
overall
this very high diversity
of controlling communities.
Which presumably has some implications for conservation. You
can't just go out and save one species
because you have to save them all if
you want to preserve the Absolutely. Absolutely. Exactly.
Because if you throw away the rare species,
actually, your system stops oscillating
and
stops this dynamics
of turnover.
I want to get into this idea of
the importance of time in in the modeling
because one of the things you say in
your paper is is actually quite hard to
model is evolution. Now all organisms evolve, and
some organisms evolve fairly slowly because they only
have
descendants every few years. But bacteria, of course,
which you're talking about modeling a lot, they
evolve quite quickly. Why is this hard to
model, and why is it so important that
future models should capture it?
Yeah. Evolution is is really the central feature
of,
of life.
And, indeed, in biology,
we we are faced
all over the place, with the fact that
when we give a name to an entity
like a species, actually, this species is changing
over time.
And it is changing in terms of, the
the composition of the gene pool, in the
species,
and then species can branch
and produce new species.
So this is particularly
it's hard to model, but at the same
time,
it can, there are lots of models that
take this into account.
What is, difficult to model is that we
cannot really predict,
what will be the effect
of mutations.
So this is again is our stochastic processes
that allow us,
or nature to explore
a number of different phenotypes
and a number potentially of different communities
or species,
but we cannot really say which will be
the new species that will appear.
And this is somehow
problematic
if you want to be sure that the
novelty
obeys
some given,
law.
At the same time,
if one
considers,
that, mutations
happen
gradually
so that, you hardly ever have
immense,
jumps, in the phenotypic space,
then you can still
try and describe an evolutionary process in terms
of what is the expected distribution
of the phenotypic effects
of mutations.
And then in this way, you can
introduce,
new species.
Then you you need the tools that are
a bit different. So, they they are available,
like, I don't know, adaptive dynamics, for instance.
It is a method that takes into account,
whether a new species that appears will invade
a system or will not.
There are methods from population genetics,
quantitative genetics.
So
the the I I would say that these
methods
have not as yet been
systematically applied to communities.
So they are more often
applied to organisms,
which have,
if you want to also within an organism,
there is a sort of an ecosystem of
genes.
So there is a hope that they can
be actually, they are starting to be
now generalized,
to account also for the evolution of communities.
Recently, there have been studies in which,
people try to,
model couplings and interaction not as sequential
variables, but also as annealed variables, so varying
in time.
And so this can be of interest in
many different systems, so in aquatic systems, plantonic
community.
Sylvia has already discussed this kind of subject.
But, since I have a background in spin
glass theory and this other system,
I would like also to
add that this kind of techniques turn out
to be particularly
powerful
for modeling
gut,
microbial communities. And so very recently, we have
tried to to better understand
the the emergent patterns
in healthy versus
disease
individuals, disease communities. So for instance, community characterized
by,
affected by Crohn disease or ulcerative colitis.
And so the gut microbiota
is a typical instance, a typical example of
system in which you can distinguish
two different time scales.
One, a fast time scale which is driven
by,
daily feeding with and circadian plots
that set the scale over
twenty four hours
and slower time scales that are modulated by
seasonal changes,
diet variation,
and overall
long term stability.
So, again, this is
an open question in theoretical ecology. It's a
very challenging topic,
which we are trying to address from
a theoretical perspective.
And one of the most exciting areas in
medicine as well. Sylvia, do you have some
of that? Yeah. I agree.
Yes. Just thinking,
so
that I would like to point out that
there is
one particularly interesting
topic in a community evolution. That is what
happens when you apply
selection at multiple levels,
at the same time. So you can consider
for instance, in the gut, of course, bacteria
compete against one another.
And, there is a short timescale,
that is associated
with ecological and also evolutionary changes that are
driven
by competition.
But then at the same time, they get
selected because they are in our gut, so
they provide
a function to the host.
So this can be reproduced
also in the lab if you have,
microcosps
that contain,
different species,
and then you can
score these microcosps
according to a given
collective feature. I don't know, total biomass.
And this is something,
that is,
now that there are people who are developing
these methods,
in the hope of, being able
to select communities that have this,
some particular property
like, they are useful for bioremediation
or they produce a particular product.
So what is challenging in this case is
that, you are selecting also at the level
of the communities.
So there is,
competition between communities
for a feature that is a collective feature.
So this,
kind of multilevel selection
is, really,
very actively researched upon, in this moment, and
mathematical models,
including models from statistical physics
are being used to try and understand
under what conditions
can
this evolution
be most efficient?
When does it fail
and,
how to actually
obtain communities,
that provide,
a specific function.
And this would presumably
potentially in the future help someone say, okay.
So this person has symptoms
of irritable bowel syndrome, IBS, Crohn's disease, or
something like that.
And we've seen
these conditions in their guts, and we think
that changing the system in some way would
help the system the ecosystem in their gut
evolve into something that was not the disease
state. Yeah. Yes. Or you might be able
at a certain point to swallow a pill
that has been that contains a community that
was evolved
in order to,
help,
the gut reestablish
its original state.
Yeah. For instance, you can think of performing
a fecal microbiota transplant from a healthy donor
to an healthy recipient
and to study the evolution
of the community
over several months.
In that new environment that has been placed
in as opposed to where it came from.
Yeah. And I will also add that our
gut is a very
structured ecosystem.
So it's it's important
to take
structure
into account in this kind of model. For
instance, by using a meta community scenario in
which different patches are connected
with with the others.
So was it strange for you, Ada, to
go from thinking about spin glasses and the
physics of that to thinking about the statistical
physics of gut microbiomes?
Yeah. It might appear
a quite exotic topic. I have a background
in statistical physics of disorders system, field theory,
and so on. So very recently, in collaboration
with the team of gastroenterologists
in Padua in Italy,
we try to connect disorder systems
akin to spin glasses
that are still in their infancy
with metagenomic
data from healthy versus unhealthy dataset
where for unhealthy immune patients that are affected
by Crohn disease and ulcerative colitis.
So the the kind of strategies that we
perform, that we apply, is basically
based on the following approach.
So we propose some order parameters,
mean abundance and high order correlations
between species abundance that are typically
referred to as overlap, self overlap, and intrastate
overlap in spin glass theory.
We measure this quantity from data for the
two cohorts,
for the two data set, healthy versus unhealthy.
And then in a high dimensional setting, so
based on
the disorder generalized loca paltura model,
we infer a limited set of parameters.
So mean and variance of the interaction matrix,
demographic noise amplitude, and an immigration parameter,
which is crucial
to prevent one species from getting extinct in
in this kind of setting. And so by
inferring this kind of quantity, we could actually
decode
microbiome data,
which offer insight into the ecological
forces that shapes
macroecological
states. And indeed, we managed to classify,
the two data set, the two cohorts for
healthy versus unhealthy, and we could actually have
visible clusterization
of the two.
One characterized
by higher
heterogeneity
and higher demographic fluctuations
in such a way to to interpret this
kind of fundings as,
being more stable with respect to external
perturbation,
antibiotic
treatment,
changes
in the diet,
and another characterized
by smaller
heterogeneity
and smaller demographic noise. And so this could
open the room
for targeted strategies
in microbial dynamics,
also for for better investigating
the appearance of multiple alternative stable states in
this kind of community. Because indeed, an healthy
dataset seems to be more
captured
and seems to get closer and closer to
the stability line of the single equilibrium regime.
So there is still room for discussion, and
we would like to work on this kind
of topics in the next few months and
and few years.
At the end of your EPL paper, you
expressed some hope that statistical physics can bring
ideas not only for officially describing currently available
observations,
but also for planning future ones.
How might your ecologist or biologist or even
medical colleagues
use the finding of statistical physics
to plan future observations?
Yeah. Our hope is that statistical physics approach
and intuition from
disorder system cannot prioritize
observation that are most informative about underlying
ecological mechanisms.
We mentioned Crohn disease and ulcerative colitis. So
can
statistical physics can definitely help in
providing
quantitative fingerprints, quantitative order parameters for distinguished different
regimes. So I will say, first of all,
can be very efficient
in detecting phase transition and criticality,
and ecologists
could plan experiments along environmental
gradients
or under control perturbations,
like increasing variability in species abundance,
tuning, pH
level,
or nutrient amount in a well controlled
chemical condition, for instance, in a chemostat reactor.
Second, probing multistability
with replicated
samples.
So we mentioned several times single temporal snapshot
versus
longitudinal
data, long time series,
and also
trying to reduce the dimensionality
of the model
and to have information
on the community
just based on
a few parameters.
So
I will say that these are three main
directions.
So this can open the road to have
controlled strategies in many different
ecological and biological
systems.
I think that, yeah, the main
goal
of our work is to be able to
propose to ecologists
some
order parameters or some statistical,
means,
of distinguishing,
different processes.
So I wouldn't say that so far,
ecologists
would come to us and ask, okay. What
is
the other parameter I should look at?
But I think that there have been, so
many progresses in the last few years,
that the news are now starting to percolate
also
in the ecological
community.
Though it is challenging,
to communicate across disciplines
and to be able to reach out to
the people who actually plan
the observational campaigns,
which are often planned on considerations
that are different, from, those,
theorists
for good reasons. I am not saying they
shouldn't, but we we will, anyway,
get more and more data because this is
the trend. There's more and more observational data
that will be available and that are
more and more,
available in public repositories.
So this,
will make our work easier.
What are some of the challenges
of connecting with the data that's gathered by
observational scientists for you as a theoretical ecologist?
Yeah. So there are several
challenges.
First of all, there are differences,
in perspective,
even over the same data,
from people coming from physics
and people coming more from,
experimental ecology.
So there is
a trend,
in
the recent decades that has been spurred by
the availability
of methods
of sequencing that are more and more sophisticated
and increasingly cheaper
to actually collect
a lot a lot of data and then
proceed
with statistical approaches,
mining this data and trying to find out
what are
the signals
of, I don't know, variation,
from
one place to another
of ecosystems.
Our point of view is typically to start
from a hypothesis,
and this is also true for a lot
of theoretical biology.
You start from hypothesis and then you would
like data to be gathered to support or
not this hypothesis.
And, the two things are complimentary,
but, sometimes there is like a language barrier
and the the perspective barrier that makes it
not completely
easy for us,
to
speak to an ecological
audience.
And this part of this, is that
ecology
has a long history,
and there are, schools of thought that are
rooted in this history.
And we do not necessarily
know
all of this, coming from physics,
even though I personally have been, in a
college and evolution of almost forever now.
But still, I feel like I am a
physicist,
and
the perspective I bring on the data is
more that of a physicist
than, of an ecologist.
I suppose it takes all perspective to see
the entire problem and to solve it. Hopefully
so. That's the effort that we are trying
to do with, ADA also engaging,
with medical doctors.
Doctors. Yeah. That's the hope.
Well, Sylvia and Ada, thank you very much
for coming on the podcast. It's been wonderful
speaking with you.
Thank you very much for having us, and,
all the best.
That was Ada Altieri and Silvia de Monte
talking about statistical physics approaches to ecological communities.
If you'd like to know more about this
work, check out their paper in EPL, which
is open access and freely available via the
IOPscience
website.
My thanks to Ade and Sylvia, to our
producer Fred Iles, and to the journal EPL,
which sponsored this episode of the Physics World
weekly podcast.
Join us again next week for more fascinating
stories from the world of physics.