1. Public good diffusion limits microbial mutualism
Zijnge V et al. PLoS ONE 2010:5
Rajita Menon
Korolev Lab
Kolenbrander et al. (2010)
Menon, R & Korolev, KS, Phys. Rev. Lett. (2015)

2. Complex microbial networks do amazing things
Global interaction network in human microbiome
Individual dynamics to bigger picture : focus is shifting in microbial ecology studies.
Example of public goods importance : Jim Collins paper here. Two-way interactions maintain the complexity of ecosystems. Metabolite exchange can allow coexistence of 50 species even.
Faust K, Sathirapongsasuti JF, Izard J, Segata N, Gevers D, et al. Plos Comp. Biol. (2012)

3. Diffusible molecules mediate microbial interactions
Public BADS (Antibiotics)
Antibiotic simple example, ring of inhibition (s.aureus inhibited by penicillin), same thing with cross feeding (Daniel’s paper metabolic eclipse)- leads to non trivial effects like the eclipse. Segue from here, saying that selection of diffusivities is not often studied, but it was studied last year in THIS data set
MODELING DIFFUSION IS VERY IMPORTANT
textbookofbacteriology.net
Antibiotic ring of inhibition

4. Is diffusivity of public goods under selection?
How does nutrient diffusivity affect mutualism?
Are nutrient diffusivities under selection?
Recent example – siderophores. Remove paper figure with text. Maybe interaction are driven by cheaters cooperators (Allen, Gore, Nowak). But cross feeding is not explained by all this.
In some context we know the effect of diffusion but nor for cross feeding
Add data figure from figure
Abergel et al., PNAS (2006)

5. Cross feeding : simple example of diffusive interaction
Two-way cross feeding
is the simplest
microbial community
species A
species B
Show petri dish pictures for Momeni. Picture of Shou who designed this system that has been studied extensively.
Well mixed culture they coexist, but you have to grow them in a petri dish to see the coexistence and segregation
Momeni et al., eLife (2013)
Muller et al., PNAS (2014)

6. Cross feeding : simple example of diffusive interaction
Two-way cross feeding
is the simplest
microbial community
species A
species B
Show petri dish pictures for Momeni. Picture of Shou who designed this system that has been studied extensively.
Well mixed culture they coexist, but you have to grow them in a petri dish to see the coexistence and segregation
Momeni et al., eLife (2013)
Muller et al., PNAS (2014)
W. Shou

7. Coexistence and segregation in interacting yeast cultures
Cooperative yeast partners intermix
Competitive yeast partners segregate
Show petri dish pictures for Momeni. Picture of Shou who designed this system that has been studied extensively.
Well mixed culture they coexist, but you have to grow them in a petri dish to see the coexistence and segregation
Scale bar = 100 micron
Momeni et al., eLife (2013)

8. Coexistence is fragile in space
Genetic drift causes demixing
Mutualism opposes demixing
First predicted by Korolev and Nelson. It’s well known that random effects create differences in species that persist over time and cause demixing. Mutualism counters this effect, but in space it’s fragile and lost easily. 2 aspects of space, demixing + diffusion. Demixing is well understood, but not diffusion.
Without diffusion – mutualism is same as coexistence. With diffusion, benefit even in segregated domains i.e mutualism without coexistence
Seen by Shou/ Momeni
And Muller/Murray
Muller et al., PNAS (2014)
increasing benefit of cross feeding

9. High nutrient diffusivity promotes demixing
extent of mutualism
critical diffusivity
public goods diffusivity

10. Domains grow much faster than diffusion length
domain length
length
diffusion length
Graph with diffusion distance + domain size on same plot. Here’s what is going on. Diffusion is root D (simple physics).
Domain size grows because diffusion reduces the selection for mutualism.
To see this => cartoon
No equations, no exponents
public goods diffusivity

11. Nutrient diffusion reduces selection for mutualism
One by one, 2 plots. First one just species. Next whole thing without annotations. Bottom plot for selection, write the formula for s effective in words. No need for analytic expressions
Hallatschek, Oskar, et al. PNAS (2007)

12. Nutrient diffusion reduces selection for mutualism
selection = difference in public good concentration
selection
One by one, 2 plots. First one just species. Next whole thing without annotations. Bottom plot for selection, write the formula for s effective in words. No need for analytic expressions
Hallatschek, Oskar, et al. PNAS (2007)

13. Effective selection near domain boundary is reduced
species fractions
selection
public goods conc.
One by one, 2 plots. First one just species. Next whole thing without annotations. Bottom plot for selection, write the formula for s effective in words. No need for analytic expressions
selection

14. Now we can use the results of game theory
Now use results of game theory to predict things

15. Critical diffusivity
population size has the largest effect on critical diffusivity
In words, critical diffusivity. Confirmed in simulations. Shows that mapping works. Using this we can also have a prediction for domain size which can be tested experimentally

16. Dynamics with different public good diffusivities
Are DA and DB under selection?

17. Dynamics with different public good diffusivities
Are DA and DB under selection?
Expect selection because this is all important: then we saw that there was none! But found that was because of nonlinearity! Details gave us something new (biologist/phycisist joke)

18. Dynamics with different public good diffusivities
Are DA and DB under selection?
linear fitness profile
fitness
Simplistic function = linear fitness, biology doesn’t work this way.
Add graphs for fitness function instead of nonlinearity formulae
public goods concentration

19. Dynamics with different public good diffusivities
nonlinearities are important
Are DA and DB under selection?
fitness
public goods concentration

20. Dynamics with different public good diffusivities
nonlinearities are important
Are DA and DB under selection?
fitness
public goods concentration

21. Dynamics with different public good diffusivities
nonlinearities are important
Are DA and DB under selection?
fitness
public goods concentration
Diminishing returns in fitness favor slow diffusion

22. Why nonlinearities matter?
Consider small DA and large DB

23. Why nonlinearities matter?
Consider small DA and large DB
diminishing returns
species A inside B domain
fitness
species A
species A inside A domain
public goods concentration

24. Summary
nutrient diffusion destroys mutualism

25. Summary nutrient diffusion destroys mutualism
nutrient diffusion rescales selection

26. Summary nutrient diffusion destroys mutualism
nutrient diffusion rescales selection
game theoretic model with diffusion

27. Summary nutrient diffusion destroys mutualism
nutrient diffusion rescales selection
nonlinearities select for slow or fast diffusion
game theoretic model with diffusion

28. THANK YOU!